group_theory.noncomm_pi_coprod ⟷ Mathlib.GroupTheory.NoncommPiCoprod

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

@@ -153,7 +153,7 @@ def noncommPiCoprodEquiv :
     where
   toFun ϕ := noncommPiCoprod ϕ.1 ϕ.2
   invFun f :=
-    ⟨fun i => f.comp (MonoidHom.single N i), fun i j hij x y =>
+    ⟨fun i => f.comp (MonoidHom.mulSingle N i), fun i j hij x y =>
       Commute.map (Pi.mulSingle_commute hij x y) f⟩
   left_inv ϕ := by ext; simp
   right_inv f := pi_ext fun i x => by simp

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

@@ -6,7 +6,7 @@ Authors: Joachim Breitner
 import GroupTheory.OrderOfElement
 import Data.Finset.NoncommProd
 import Data.Fintype.BigOperators
-import Data.Nat.Gcd.BigOperators
+import Data.Nat.GCD.BigOperators
 import Order.SupIndep
 
 #align_import group_theory.noncomm_pi_coprod from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"

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

@@ -66,7 +66,7 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
   induction' s using Finset.induction_on with i s hnmem ih
   · simp
   · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
-    simp only [Finset.forall_mem_insert] at hmem 
+    simp only [Finset.forall_mem_insert] at hmem
     have hmem_bsupr : s.noncomm_prod f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
       by
       refine' Subgroup.noncommProd_mem _ _ _
@@ -74,12 +74,12 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
       have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
       exact this (hmem.2 x hx)
     intro heq1
-    rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1 
+    rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1
     have hnmem' : i ∉ (s : Set ι) := by simpa
     obtain ⟨heq1i : f i = 1, heq1S : s.noncomm_prod f _ = 1⟩ :=
       subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupr hnmem') hmem.1 hmem_bsupr heq1
     intro i h
-    simp only [Finset.mem_insert] at h 
+    simp only [Finset.mem_insert] at h
     rcases h with ⟨rfl | _⟩
     · exact heq1i
     · exact ih hcomm hmem.2 heq1S _ h
@@ -140,7 +140,7 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
   rw [Pi.mulSingle_eq_same]
   rw [Finset.noncommProd_eq_pow_card]
   · rw [one_pow]; exact mul_one _
-  · intro j hj; simp only [Finset.mem_erase] at hj ; simp [hj]
+  · intro j hj; simp only [Finset.mem_erase] at hj; simp [hj]
 #align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingle
 #align add_monoid_hom.noncomm_pi_coprod_single AddMonoidHom.noncommPiCoprod_single
 -/
@@ -226,7 +226,7 @@ theorem injective_noncommPiCoprod_of_independent
   apply (MonoidHom.ker_eq_bot_iff _).mp
   apply eq_bot_iff.mpr
   intro f heq1
-  change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1 
+  change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1
   change f = 1
   have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
     Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ _ _ hind (by simp) heq1
@@ -250,8 +250,8 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   rintro i
   rw [disjoint_iff_inf_le]
   rintro f ⟨hxi, hxp⟩
-  dsimp at hxi hxp 
-  rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp 
+  dsimp at hxi hxp
+  rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp
   rotate_left
   · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
   cases' hxp with g hgf

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

@@ -60,7 +60,29 @@ generalizes (one direction of) `subgroup.disjoint_iff_mul_eq_one`. -/
       "`finset.noncomm_sum` is “injective” in `f` if `f` maps into independent subgroups.\nThis generalizes (one direction of) `add_subgroup.disjoint_iff_add_eq_zero`. "]
 theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι) (f : ι → G) (comm)
     (K : ι → Subgroup G) (hind : CompleteLattice.Independent K) (hmem : ∀ x ∈ s, f x ∈ K x)
-    (heq1 : s.noncommProd f comm = 1) : ∀ i ∈ s, f i = 1 := by classical
+    (heq1 : s.noncommProd f comm = 1) : ∀ i ∈ s, f i = 1 := by
+  classical
+  revert heq1
+  induction' s using Finset.induction_on with i s hnmem ih
+  · simp
+  · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
+    simp only [Finset.forall_mem_insert] at hmem 
+    have hmem_bsupr : s.noncomm_prod f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
+      by
+      refine' Subgroup.noncommProd_mem _ _ _
+      intro x hx
+      have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
+      exact this (hmem.2 x hx)
+    intro heq1
+    rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1 
+    have hnmem' : i ∉ (s : Set ι) := by simpa
+    obtain ⟨heq1i : f i = 1, heq1S : s.noncomm_prod f _ = 1⟩ :=
+      subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupr hnmem') hmem.1 hmem_bsupr heq1
+    intro i h
+    simp only [Finset.mem_insert] at h 
+    rcases h with ⟨rfl | _⟩
+    · exact heq1i
+    · exact ih hcomm hmem.2 heq1S _ h
 #align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independent
 #align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_independent
 -/
@@ -96,7 +118,11 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
     where
   toFun f := Finset.univ.noncommProd (fun i => ϕ i (f i)) fun i _ j _ h => hcomm h _ _
   map_one' := by apply (Finset.noncommProd_eq_pow_card _ _ _ _ _).trans (one_pow _); simp
-  map_mul' f g := by classical
+  map_mul' f g := by
+    classical
+    convert @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
+    · ext i; exact map_mul (ϕ i) (f i) (g i)
+    · rintro i - j - h; exact hcomm h _ _
 #align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprod
 #align add_monoid_hom.noncomm_pi_coprod AddMonoidHom.noncommPiCoprod
 -/
@@ -139,6 +165,15 @@ def noncommPiCoprodEquiv :
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
   classical
+  apply le_antisymm
+  · rintro x ⟨f, rfl⟩
+    refine' Submonoid.noncommProd_mem _ _ _ _ _
+    intro i hi
+    apply Submonoid.mem_sSup_of_mem; · use i
+    simp
+  · refine' iSup_le _
+    rintro i x ⟨y, rfl⟩
+    refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
 #align add_monoid_hom.noncomm_pi_coprod_mrange AddMonoidHom.noncommPiCoprod_mrange
 -/
@@ -169,6 +204,15 @@ namespace MonoidHom
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
   classical
+  apply le_antisymm
+  · rintro x ⟨f, rfl⟩
+    refine' Subgroup.noncommProd_mem _ _ _
+    intro i hi
+    apply Subgroup.mem_sSup_of_mem; · use i
+    simp
+  · refine' iSup_le _
+    rintro i x ⟨y, rfl⟩
+    refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 -/
@@ -179,6 +223,16 @@ theorem injective_noncommPiCoprod_of_independent
     (hind : CompleteLattice.Independent fun i => (ϕ i).range)
     (hinj : ∀ i, Function.Injective (ϕ i)) : Function.Injective (noncommPiCoprod ϕ hcomm) := by
   classical
+  apply (MonoidHom.ker_eq_bot_iff _).mp
+  apply eq_bot_iff.mpr
+  intro f heq1
+  change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1 
+  change f = 1
+  have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
+    Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ _ _ hind (by simp) heq1
+  ext i
+  apply hinj
+  simp [this i (Finset.mem_univ i)]
 #align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independent
 #align add_monoid_hom.injective_noncomm_pi_coprod_of_independent AddMonoidHom.injective_noncommPiCoprod_of_independent
 -/
@@ -193,6 +247,27 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   by
   cases nonempty_fintype ι
   classical
+  rintro i
+  rw [disjoint_iff_inf_le]
+  rintro f ⟨hxi, hxp⟩
+  dsimp at hxi hxp 
+  rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp 
+  rotate_left
+  · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
+  cases' hxp with g hgf
+  cases' hxi with g' hg'f
+  have hxi : orderOf f ∣ Fintype.card (H i) := by rw [← hg'f];
+    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
+  have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
+    rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
+  change f = 1
+  rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
+  convert ← Nat.dvd_gcd hxp hxi
+  rw [← Nat.coprime_iff_gcd_eq_one]
+  apply Nat.Coprime.prod_left
+  intro j _
+  apply hcoprime
+  exact j.2
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
 -/

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

@@ -60,29 +60,7 @@ generalizes (one direction of) `subgroup.disjoint_iff_mul_eq_one`. -/
       "`finset.noncomm_sum` is “injective” in `f` if `f` maps into independent subgroups.\nThis generalizes (one direction of) `add_subgroup.disjoint_iff_add_eq_zero`. "]
 theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι) (f : ι → G) (comm)
     (K : ι → Subgroup G) (hind : CompleteLattice.Independent K) (hmem : ∀ x ∈ s, f x ∈ K x)
-    (heq1 : s.noncommProd f comm = 1) : ∀ i ∈ s, f i = 1 := by
-  classical
-  revert heq1
-  induction' s using Finset.induction_on with i s hnmem ih
-  · simp
-  · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
-    simp only [Finset.forall_mem_insert] at hmem 
-    have hmem_bsupr : s.noncomm_prod f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
-      by
-      refine' Subgroup.noncommProd_mem _ _ _
-      intro x hx
-      have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
-      exact this (hmem.2 x hx)
-    intro heq1
-    rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1 
-    have hnmem' : i ∉ (s : Set ι) := by simpa
-    obtain ⟨heq1i : f i = 1, heq1S : s.noncomm_prod f _ = 1⟩ :=
-      subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupr hnmem') hmem.1 hmem_bsupr heq1
-    intro i h
-    simp only [Finset.mem_insert] at h 
-    rcases h with ⟨rfl | _⟩
-    · exact heq1i
-    · exact ih hcomm hmem.2 heq1S _ h
+    (heq1 : s.noncommProd f comm = 1) : ∀ i ∈ s, f i = 1 := by classical
 #align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independent
 #align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_independent
 -/
@@ -118,11 +96,7 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
     where
   toFun f := Finset.univ.noncommProd (fun i => ϕ i (f i)) fun i _ j _ h => hcomm h _ _
   map_one' := by apply (Finset.noncommProd_eq_pow_card _ _ _ _ _).trans (one_pow _); simp
-  map_mul' f g := by
-    classical
-    convert @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
-    · ext i; exact map_mul (ϕ i) (f i) (g i)
-    · rintro i - j - h; exact hcomm h _ _
+  map_mul' f g := by classical
 #align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprod
 #align add_monoid_hom.noncomm_pi_coprod AddMonoidHom.noncommPiCoprod
 -/
@@ -165,15 +139,6 @@ def noncommPiCoprodEquiv :
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
   classical
-  apply le_antisymm
-  · rintro x ⟨f, rfl⟩
-    refine' Submonoid.noncommProd_mem _ _ _ _ _
-    intro i hi
-    apply Submonoid.mem_sSup_of_mem; · use i
-    simp
-  · refine' iSup_le _
-    rintro i x ⟨y, rfl⟩
-    refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
 #align add_monoid_hom.noncomm_pi_coprod_mrange AddMonoidHom.noncommPiCoprod_mrange
 -/
@@ -204,15 +169,6 @@ namespace MonoidHom
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
   classical
-  apply le_antisymm
-  · rintro x ⟨f, rfl⟩
-    refine' Subgroup.noncommProd_mem _ _ _
-    intro i hi
-    apply Subgroup.mem_sSup_of_mem; · use i
-    simp
-  · refine' iSup_le _
-    rintro i x ⟨y, rfl⟩
-    refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 -/
@@ -223,16 +179,6 @@ theorem injective_noncommPiCoprod_of_independent
     (hind : CompleteLattice.Independent fun i => (ϕ i).range)
     (hinj : ∀ i, Function.Injective (ϕ i)) : Function.Injective (noncommPiCoprod ϕ hcomm) := by
   classical
-  apply (MonoidHom.ker_eq_bot_iff _).mp
-  apply eq_bot_iff.mpr
-  intro f heq1
-  change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1 
-  change f = 1
-  have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
-    Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ _ _ hind (by simp) heq1
-  ext i
-  apply hinj
-  simp [this i (Finset.mem_univ i)]
 #align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independent
 #align add_monoid_hom.injective_noncomm_pi_coprod_of_independent AddMonoidHom.injective_noncommPiCoprod_of_independent
 -/
@@ -247,27 +193,6 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   by
   cases nonempty_fintype ι
   classical
-  rintro i
-  rw [disjoint_iff_inf_le]
-  rintro f ⟨hxi, hxp⟩
-  dsimp at hxi hxp 
-  rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp 
-  rotate_left
-  · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
-  cases' hxp with g hgf
-  cases' hxi with g' hg'f
-  have hxi : orderOf f ∣ Fintype.card (H i) := by rw [← hg'f];
-    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
-  have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
-    rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
-  change f = 1
-  rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
-  convert ← Nat.dvd_gcd hxp hxi
-  rw [← Nat.coprime_iff_gcd_eq_one]
-  apply Nat.Coprime.prod_left
-  intro j _
-  apply hcoprime
-  exact j.2
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
 -/

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

@@ -264,7 +264,7 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
   convert ← Nat.dvd_gcd hxp hxi
   rw [← Nat.coprime_iff_gcd_eq_one]
-  apply Nat.coprime_prod_left
+  apply Nat.Coprime.prod_left
   intro j _
   apply hcoprime
   exact j.2

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

@@ -297,7 +297,7 @@ theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
     ∀ (x : H i) (y : H j), Commute ((H i).Subtype x) ((H j).Subtype y) := by rintro ⟨x, hx⟩ ⟨y, hy⟩;
   exact hcomm i j hne x y hx hy
 #align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commute
-#align add_subgroup.commute_subtype_of_commute AddSubgroup.commute_subtype_of_commute
+#align add_subgroup.commute_subtype_of_commute AddSubgroup.addCommute_subtype_of_addCommute
 -/
 
 #print Subgroup.noncommPiCoprod /-

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

@@ -257,9 +257,9 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   cases' hxp with g hgf
   cases' hxi with g' hg'f
   have hxi : orderOf f ∣ Fintype.card (H i) := by rw [← hg'f];
-    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
   have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
-    rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+    rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
   change f = 1
   rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
   convert ← Nat.dvd_gcd hxp hxi

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

@@ -3,11 +3,11 @@ Copyright (c) 2022 Joachim Breitner. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joachim Breitner
 -/
-import Mathbin.GroupTheory.OrderOfElement
-import Mathbin.Data.Finset.NoncommProd
-import Mathbin.Data.Fintype.BigOperators
-import Mathbin.Data.Nat.Gcd.BigOperators
-import Mathbin.Order.SupIndep
+import GroupTheory.OrderOfElement
+import Data.Finset.NoncommProd
+import Data.Fintype.BigOperators
+import Data.Nat.Gcd.BigOperators
+import Order.SupIndep
 
 #align_import group_theory.noncomm_pi_coprod from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"
 

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

@@ -242,7 +242,7 @@ variable (hcomm)
 #print MonoidHom.independent_range_of_coprime_order /-
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent fun i => (ϕ i).range :=
   by
   cases nonempty_fintype ι
@@ -346,7 +346,7 @@ variable (hcomm)
 #print Subgroup.independent_of_coprime_order /-
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent H := by
   simpa using
     MonoidHom.independent_range_of_coprime_order (fun i => (H i).Subtype)

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Joachim Breitner. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joachim Breitner
-
-! This file was ported from Lean 3 source module group_theory.noncomm_pi_coprod
-! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.GroupTheory.OrderOfElement
 import Mathbin.Data.Finset.NoncommProd
@@ -14,6 +9,8 @@ import Mathbin.Data.Fintype.BigOperators
 import Mathbin.Data.Nat.Gcd.BigOperators
 import Mathbin.Order.SupIndep
 
+#align_import group_theory.noncomm_pi_coprod from "leanprover-community/mathlib"@"ef7acf407d265ad4081c8998687e994fa80ba70c"
+
 /-!
 # Canonical homomorphism from a finite family of monoids
 

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

@@ -56,6 +56,7 @@ namespace Subgroup
 
 variable {G : Type _} [Group G]
 
+#print Subgroup.eq_one_of_noncommProd_eq_one_of_independent /-
 /-- `finset.noncomm_prod` is “injective” in `f` if `f` maps into independent subgroups.  This
 generalizes (one direction of) `subgroup.disjoint_iff_mul_eq_one`. -/
 @[to_additive
@@ -87,6 +88,7 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
     · exact ih hcomm hmem.2 heq1S _ h
 #align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independent
 #align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_independent
+-/
 
 end Subgroup
 
@@ -106,13 +108,12 @@ variable (ϕ : ∀ i : ι, N i →* M)
 -- We assume that the elements of different morphism commute
 variable (hcomm : Pairwise fun i j => ∀ x y, Commute (ϕ i x) (ϕ j y))
 
-include hcomm
-
 -- We use `f` and `g` to denote elements of `Π (i : ι), N i`
 variable (f g : ∀ i : ι, N i)
 
 namespace MonoidHom
 
+#print MonoidHom.noncommPiCoprod /-
 /-- The canonical homomorphism from a family of monoids. -/
 @[to_additive
       "The canonical homomorphism from a family of additive monoids.\n\nSee also `linear_map.lsum` for a linear version without the commutativity assumption."]
@@ -127,11 +128,11 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
     · rintro i - j - h; exact hcomm h _ _
 #align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprod
 #align add_monoid_hom.noncomm_pi_coprod AddMonoidHom.noncommPiCoprod
+-/
 
 variable {hcomm}
 
-include hdec
-
+#print MonoidHom.noncommPiCoprod_mulSingle /-
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
     noncommPiCoprod ϕ hcomm (Pi.mulSingle i y) = ϕ i y :=
@@ -145,9 +146,9 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
   · intro j hj; simp only [Finset.mem_erase] at hj ; simp [hj]
 #align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingle
 #align add_monoid_hom.noncomm_pi_coprod_single AddMonoidHom.noncommPiCoprod_single
+-/
 
-omit hcomm
-
+#print MonoidHom.noncommPiCoprodEquiv /-
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
 def noncommPiCoprodEquiv :
@@ -161,11 +162,9 @@ def noncommPiCoprodEquiv :
   right_inv f := pi_ext fun i x => by simp
 #align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquiv
 #align add_monoid_hom.noncomm_pi_coprod_equiv AddMonoidHom.noncommPiCoprodEquiv
+-/
 
-omit hdec
-
-include hcomm
-
+#print MonoidHom.noncommPiCoprod_mrange /-
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
   classical
@@ -180,6 +179,7 @@ theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι,
     refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
 #align add_monoid_hom.noncomm_pi_coprod_mrange AddMonoidHom.noncommPiCoprod_mrange
+-/
 
 end MonoidHom
 
@@ -197,15 +197,12 @@ variable (ϕ : ∀ i : ι, H i →* G)
 
 variable {hcomm : ∀ i j : ι, i ≠ j → ∀ (x : H i) (y : H j), Commute (ϕ i x) (ϕ j y)}
 
-include hcomm
-
 -- We use `f` and `g` to denote elements of `Π (i : ι), H i`
 variable (f g : ∀ i : ι, H i)
 
-include hfin
-
 namespace MonoidHom
 
+#print MonoidHom.noncommPiCoprod_range /-
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
@@ -221,7 +218,9 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
     refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
+-/
 
+#print MonoidHom.injective_noncommPiCoprod_of_independent /-
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
     (hind : CompleteLattice.Independent fun i => (ϕ i).range)
@@ -239,11 +238,11 @@ theorem injective_noncommPiCoprod_of_independent
   simp [this i (Finset.mem_univ i)]
 #align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independent
 #align add_monoid_hom.injective_noncomm_pi_coprod_of_independent AddMonoidHom.injective_noncommPiCoprod_of_independent
+-/
 
 variable (hcomm)
 
-omit hfin
-
+#print MonoidHom.independent_range_of_coprime_order /-
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
@@ -274,6 +273,7 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   exact j.2
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
+-/
 
 end MonoidHom
 
@@ -294,17 +294,16 @@ section CommutingSubgroups
 -- We assume that the elements of different subgroups commute
 variable (hcomm : ∀ i j : ι, i ≠ j → ∀ x y : G, x ∈ H i → y ∈ H j → Commute x y)
 
-include hcomm
-
+#print Subgroup.commute_subtype_of_commute /-
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
     ∀ (x : H i) (y : H j), Commute ((H i).Subtype x) ((H j).Subtype y) := by rintro ⟨x, hx⟩ ⟨y, hy⟩;
   exact hcomm i j hne x y hx hy
 #align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commute
 #align add_subgroup.commute_subtype_of_commute AddSubgroup.commute_subtype_of_commute
+-/
 
-include hfin
-
+#print Subgroup.noncommPiCoprod /-
 /-- The canonical homomorphism from a family of subgroups where elements from different subgroups
 commute -/
 @[to_additive
@@ -313,25 +312,27 @@ def noncommPiCoprod : (∀ i : ι, H i) →* G :=
   MonoidHom.noncommPiCoprod (fun i => (H i).Subtype) (commute_subtype_of_commute hcomm)
 #align subgroup.noncomm_pi_coprod Subgroup.noncommPiCoprod
 #align add_subgroup.noncomm_pi_coprod AddSubgroup.noncommPiCoprod
+-/
 
 variable {hcomm}
 
-include hdec
-
+#print Subgroup.noncommPiCoprod_mulSingle /-
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
     noncommPiCoprod hcomm (Pi.mulSingle i y) = y := by apply MonoidHom.noncommPiCoprod_mulSingle
 #align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingle
 #align add_subgroup.noncomm_pi_coprod_single AddSubgroup.noncommPiCoprod_single
+-/
 
-omit hdec
-
+#print Subgroup.noncommPiCoprod_range /-
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i := by
   simp [noncomm_pi_coprod, MonoidHom.noncommPiCoprod_range]
 #align subgroup.noncomm_pi_coprod_range Subgroup.noncommPiCoprod_range
 #align add_subgroup.noncomm_pi_coprod_range AddSubgroup.noncommPiCoprod_range
+-/
 
+#print Subgroup.injective_noncommPiCoprod_of_independent /-
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :
     Function.Injective (noncommPiCoprod hcomm) :=
@@ -341,11 +342,11 @@ theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Indepen
   · intro i; exact Subtype.coe_injective
 #align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independent
 #align add_subgroup.injective_noncomm_pi_coprod_of_independent AddSubgroup.injective_noncommPiCoprod_of_independent
+-/
 
 variable (hcomm)
 
-omit hfin
-
+#print Subgroup.independent_of_coprime_order /-
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
@@ -355,6 +356,7 @@ theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
       (commute_subtype_of_commute hcomm) hcoprime
 #align subgroup.independent_of_coprime_order Subgroup.independent_of_coprime_order
 #align add_subgroup.independent_of_coprime_order AddSubgroup.independent_of_coprime_order
+-/
 
 end CommutingSubgroups
 

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

@@ -64,27 +64,27 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
     (K : ι → Subgroup G) (hind : CompleteLattice.Independent K) (hmem : ∀ x ∈ s, f x ∈ K x)
     (heq1 : s.noncommProd f comm = 1) : ∀ i ∈ s, f i = 1 := by
   classical
-    revert heq1
-    induction' s using Finset.induction_on with i s hnmem ih
-    · simp
-    · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
-      simp only [Finset.forall_mem_insert] at hmem 
-      have hmem_bsupr : s.noncomm_prod f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
-        by
-        refine' Subgroup.noncommProd_mem _ _ _
-        intro x hx
-        have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
-        exact this (hmem.2 x hx)
-      intro heq1
-      rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1 
-      have hnmem' : i ∉ (s : Set ι) := by simpa
-      obtain ⟨heq1i : f i = 1, heq1S : s.noncomm_prod f _ = 1⟩ :=
-        subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupr hnmem') hmem.1 hmem_bsupr heq1
-      intro i h
-      simp only [Finset.mem_insert] at h 
-      rcases h with ⟨rfl | _⟩
-      · exact heq1i
-      · exact ih hcomm hmem.2 heq1S _ h
+  revert heq1
+  induction' s using Finset.induction_on with i s hnmem ih
+  · simp
+  · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
+    simp only [Finset.forall_mem_insert] at hmem 
+    have hmem_bsupr : s.noncomm_prod f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
+      by
+      refine' Subgroup.noncommProd_mem _ _ _
+      intro x hx
+      have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
+      exact this (hmem.2 x hx)
+    intro heq1
+    rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1 
+    have hnmem' : i ∉ (s : Set ι) := by simpa
+    obtain ⟨heq1i : f i = 1, heq1S : s.noncomm_prod f _ = 1⟩ :=
+      subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupr hnmem') hmem.1 hmem_bsupr heq1
+    intro i h
+    simp only [Finset.mem_insert] at h 
+    rcases h with ⟨rfl | _⟩
+    · exact heq1i
+    · exact ih hcomm hmem.2 heq1S _ h
 #align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independent
 #align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_independent
 
@@ -122,9 +122,9 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
   map_one' := by apply (Finset.noncommProd_eq_pow_card _ _ _ _ _).trans (one_pow _); simp
   map_mul' f g := by
     classical
-      convert@Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
-      · ext i; exact map_mul (ϕ i) (f i) (g i)
-      · rintro i - j - h; exact hcomm h _ _
+    convert @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
+    · ext i; exact map_mul (ϕ i) (f i) (g i)
+    · rintro i - j - h; exact hcomm h _ _
 #align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprod
 #align add_monoid_hom.noncomm_pi_coprod AddMonoidHom.noncommPiCoprod
 
@@ -169,15 +169,15 @@ include hcomm
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
   classical
-    apply le_antisymm
-    · rintro x ⟨f, rfl⟩
-      refine' Submonoid.noncommProd_mem _ _ _ _ _
-      intro i hi
-      apply Submonoid.mem_sSup_of_mem; · use i
-      simp
-    · refine' iSup_le _
-      rintro i x ⟨y, rfl⟩
-      refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
+  apply le_antisymm
+  · rintro x ⟨f, rfl⟩
+    refine' Submonoid.noncommProd_mem _ _ _ _ _
+    intro i hi
+    apply Submonoid.mem_sSup_of_mem; · use i
+    simp
+  · refine' iSup_le _
+    rintro i x ⟨y, rfl⟩
+    refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
 #align add_monoid_hom.noncomm_pi_coprod_mrange AddMonoidHom.noncommPiCoprod_mrange
 
@@ -210,15 +210,15 @@ namespace MonoidHom
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
   classical
-    apply le_antisymm
-    · rintro x ⟨f, rfl⟩
-      refine' Subgroup.noncommProd_mem _ _ _
-      intro i hi
-      apply Subgroup.mem_sSup_of_mem; · use i
-      simp
-    · refine' iSup_le _
-      rintro i x ⟨y, rfl⟩
-      refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
+  apply le_antisymm
+  · rintro x ⟨f, rfl⟩
+    refine' Subgroup.noncommProd_mem _ _ _
+    intro i hi
+    apply Subgroup.mem_sSup_of_mem; · use i
+    simp
+  · refine' iSup_le _
+    rintro i x ⟨y, rfl⟩
+    refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 
@@ -227,16 +227,16 @@ theorem injective_noncommPiCoprod_of_independent
     (hind : CompleteLattice.Independent fun i => (ϕ i).range)
     (hinj : ∀ i, Function.Injective (ϕ i)) : Function.Injective (noncommPiCoprod ϕ hcomm) := by
   classical
-    apply (MonoidHom.ker_eq_bot_iff _).mp
-    apply eq_bot_iff.mpr
-    intro f heq1
-    change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1 
-    change f = 1
-    have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
-      Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ _ _ hind (by simp) heq1
-    ext i
-    apply hinj
-    simp [this i (Finset.mem_univ i)]
+  apply (MonoidHom.ker_eq_bot_iff _).mp
+  apply eq_bot_iff.mpr
+  intro f heq1
+  change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1 
+  change f = 1
+  have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
+    Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ _ _ hind (by simp) heq1
+  ext i
+  apply hinj
+  simp [this i (Finset.mem_univ i)]
 #align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independent
 #align add_monoid_hom.injective_noncomm_pi_coprod_of_independent AddMonoidHom.injective_noncommPiCoprod_of_independent
 
@@ -251,27 +251,27 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
   by
   cases nonempty_fintype ι
   classical
-    rintro i
-    rw [disjoint_iff_inf_le]
-    rintro f ⟨hxi, hxp⟩
-    dsimp at hxi hxp 
-    rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp 
-    rotate_left
-    · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
-    cases' hxp with g hgf
-    cases' hxi with g' hg'f
-    have hxi : orderOf f ∣ Fintype.card (H i) := by rw [← hg'f];
-      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
-    have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
-      rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
-    change f = 1
-    rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
-    convert← Nat.dvd_gcd hxp hxi
-    rw [← Nat.coprime_iff_gcd_eq_one]
-    apply Nat.coprime_prod_left
-    intro j _
-    apply hcoprime
-    exact j.2
+  rintro i
+  rw [disjoint_iff_inf_le]
+  rintro f ⟨hxi, hxp⟩
+  dsimp at hxi hxp 
+  rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp 
+  rotate_left
+  · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
+  cases' hxp with g hgf
+  cases' hxi with g' hg'f
+  have hxi : orderOf f ∣ Fintype.card (H i) := by rw [← hg'f];
+    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+  have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
+    rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+  change f = 1
+  rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
+  convert ← Nat.dvd_gcd hxp hxi
+  rw [← Nat.coprime_iff_gcd_eq_one]
+  apply Nat.coprime_prod_left
+  intro j _
+  apply hcoprime
+  exact j.2
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
 

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

@@ -68,7 +68,7 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
     induction' s using Finset.induction_on with i s hnmem ih
     · simp
     · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
-      simp only [Finset.forall_mem_insert] at hmem
+      simp only [Finset.forall_mem_insert] at hmem 
       have hmem_bsupr : s.noncomm_prod f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
         by
         refine' Subgroup.noncommProd_mem _ _ _
@@ -76,12 +76,12 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
         have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
         exact this (hmem.2 x hx)
       intro heq1
-      rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1
+      rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1 
       have hnmem' : i ∉ (s : Set ι) := by simpa
       obtain ⟨heq1i : f i = 1, heq1S : s.noncomm_prod f _ = 1⟩ :=
         subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupr hnmem') hmem.1 hmem_bsupr heq1
       intro i h
-      simp only [Finset.mem_insert] at h
+      simp only [Finset.mem_insert] at h 
       rcases h with ⟨rfl | _⟩
       · exact heq1i
       · exact ih hcomm hmem.2 heq1S _ h
@@ -142,7 +142,7 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
   rw [Pi.mulSingle_eq_same]
   rw [Finset.noncommProd_eq_pow_card]
   · rw [one_pow]; exact mul_one _
-  · intro j hj; simp only [Finset.mem_erase] at hj; simp [hj]
+  · intro j hj; simp only [Finset.mem_erase] at hj ; simp [hj]
 #align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingle
 #align add_monoid_hom.noncomm_pi_coprod_single AddMonoidHom.noncommPiCoprod_single
 
@@ -230,7 +230,7 @@ theorem injective_noncommPiCoprod_of_independent
     apply (MonoidHom.ker_eq_bot_iff _).mp
     apply eq_bot_iff.mpr
     intro f heq1
-    change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1
+    change finset.univ.noncomm_prod (fun i => ϕ i (f i)) _ = 1 at heq1 
     change f = 1
     have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
       Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ _ _ hind (by simp) heq1
@@ -254,8 +254,8 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     rintro i
     rw [disjoint_iff_inf_le]
     rintro f ⟨hxi, hxp⟩
-    dsimp at hxi hxp
-    rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp
+    dsimp at hxi hxp 
+    rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp 
     rotate_left
     · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
     cases' hxp with g hgf

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

@@ -50,7 +50,7 @@ images of different morphisms commute, we obtain a canonical morphism
 -/
 
 
-open BigOperators
+open scoped BigOperators
 
 namespace Subgroup
 

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

@@ -56,12 +56,6 @@ namespace Subgroup
 
 variable {G : Type _} [Group G]
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independentₓ'. -/
 /-- `finset.noncomm_prod` is “injective” in `f` if `f` maps into independent subgroups.  This
 generalizes (one direction of) `subgroup.disjoint_iff_mul_eq_one`. -/
 @[to_additive
@@ -119,12 +113,6 @@ variable (f g : ∀ i : ι, N i)
 
 namespace MonoidHom
 
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-Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of monoids. -/
 @[to_additive
       "The canonical homomorphism from a family of additive monoids.\n\nSee also `linear_map.lsum` for a linear version without the commutativity assumption."]
@@ -144,9 +132,6 @@ variable {hcomm}
 
 include hdec
 
-/- warning: monoid_hom.noncomm_pi_coprod_mul_single -> MonoidHom.noncommPiCoprod_mulSingle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
     noncommPiCoprod ϕ hcomm (Pi.mulSingle i y) = ϕ i y :=
@@ -163,9 +148,6 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
 
 omit hcomm
 
-/- warning: monoid_hom.noncomm_pi_coprod_equiv -> MonoidHom.noncommPiCoprodEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquivₓ'. -/
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
 def noncommPiCoprodEquiv :
@@ -184,9 +166,6 @@ omit hdec
 
 include hcomm
 
-/- warning: monoid_hom.noncomm_pi_coprod_mrange -> MonoidHom.noncommPiCoprod_mrange is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
   classical
@@ -227,9 +206,6 @@ include hfin
 
 namespace MonoidHom
 
-/- warning: monoid_hom.noncomm_pi_coprod_range -> MonoidHom.noncommPiCoprod_range is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
@@ -246,9 +222,6 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 
-/- warning: monoid_hom.injective_noncomm_pi_coprod_of_independent -> MonoidHom.injective_noncommPiCoprod_of_independent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
     (hind : CompleteLattice.Independent fun i => (ϕ i).range)
@@ -271,9 +244,6 @@ variable (hcomm)
 
 omit hfin
 
-/- warning: monoid_hom.independent_range_of_coprime_order -> MonoidHom.independent_range_of_coprime_order is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
@@ -326,9 +296,6 @@ variable (hcomm : ∀ i j : ι, i ≠ j → ∀ x y : G, x ∈ H i → y ∈ H j
 
 include hcomm
 
-/- warning: subgroup.commute_subtype_of_commute -> Subgroup.commute_subtype_of_commute is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
     ∀ (x : H i) (y : H j), Commute ((H i).Subtype x) ((H j).Subtype y) := by rintro ⟨x, hx⟩ ⟨y, hy⟩;
@@ -338,12 +305,6 @@ theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
 
 include hfin
 
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-Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod Subgroup.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of subgroups where elements from different subgroups
 commute -/
 @[to_additive
@@ -357,9 +318,6 @@ variable {hcomm}
 
 include hdec
 
-/- warning: subgroup.noncomm_pi_coprod_mul_single -> Subgroup.noncommPiCoprod_mulSingle is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
     noncommPiCoprod hcomm (Pi.mulSingle i y) = y := by apply MonoidHom.noncommPiCoprod_mulSingle
@@ -368,21 +326,12 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
 
 omit hdec
 
-/- warning: subgroup.noncomm_pi_coprod_range -> Subgroup.noncommPiCoprod_range is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_range Subgroup.noncommPiCoprod_rangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i := by
   simp [noncomm_pi_coprod, MonoidHom.noncommPiCoprod_range]
 #align subgroup.noncomm_pi_coprod_range Subgroup.noncommPiCoprod_range
 #align add_subgroup.noncomm_pi_coprod_range AddSubgroup.noncommPiCoprod_range
 
-/- warning: subgroup.injective_noncomm_pi_coprod_of_independent -> Subgroup.injective_noncommPiCoprod_of_independent is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :
     Function.Injective (noncommPiCoprod hcomm) :=
@@ -397,12 +346,6 @@ variable (hcomm)
 
 omit hfin
 
-/- warning: subgroup.independent_of_coprime_order -> Subgroup.independent_of_coprime_order is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align subgroup.independent_of_coprime_order Subgroup.independent_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :

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

@@ -131,16 +131,12 @@ Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_
 def noncommPiCoprod : (∀ i : ι, N i) →* M
     where
   toFun f := Finset.univ.noncommProd (fun i => ϕ i (f i)) fun i _ j _ h => hcomm h _ _
-  map_one' := by
-    apply (Finset.noncommProd_eq_pow_card _ _ _ _ _).trans (one_pow _)
-    simp
+  map_one' := by apply (Finset.noncommProd_eq_pow_card _ _ _ _ _).trans (one_pow _); simp
   map_mul' f g := by
     classical
       convert@Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
-      · ext i
-        exact map_mul (ϕ i) (f i) (g i)
-      · rintro i - j - h
-        exact hcomm h _ _
+      · ext i; exact map_mul (ϕ i) (f i) (g i)
+      · rintro i - j - h; exact hcomm h _ _
 #align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprod
 #align add_monoid_hom.noncomm_pi_coprod AddMonoidHom.noncommPiCoprod
 
@@ -160,11 +156,8 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
   rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ (Finset.not_mem_erase i _)]
   rw [Pi.mulSingle_eq_same]
   rw [Finset.noncommProd_eq_pow_card]
-  · rw [one_pow]
-    exact mul_one _
-  · intro j hj
-    simp only [Finset.mem_erase] at hj
-    simp [hj]
+  · rw [one_pow]; exact mul_one _
+  · intro j hj; simp only [Finset.mem_erase] at hj; simp [hj]
 #align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingle
 #align add_monoid_hom.noncomm_pi_coprod_single AddMonoidHom.noncommPiCoprod_single
 
@@ -182,9 +175,7 @@ def noncommPiCoprodEquiv :
   invFun f :=
     ⟨fun i => f.comp (MonoidHom.single N i), fun i j hij x y =>
       Commute.map (Pi.mulSingle_commute hij x y) f⟩
-  left_inv ϕ := by
-    ext
-    simp
+  left_inv ϕ := by ext; simp
   right_inv f := pi_ext fun i x => by simp
 #align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquiv
 #align add_monoid_hom.noncomm_pi_coprod_equiv AddMonoidHom.noncommPiCoprodEquiv
@@ -203,8 +194,7 @@ theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι,
     · rintro x ⟨f, rfl⟩
       refine' Submonoid.noncommProd_mem _ _ _ _ _
       intro i hi
-      apply Submonoid.mem_sSup_of_mem
-      · use i
+      apply Submonoid.mem_sSup_of_mem; · use i
       simp
     · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
@@ -248,8 +238,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
     · rintro x ⟨f, rfl⟩
       refine' Subgroup.noncommProd_mem _ _ _
       intro i hi
-      apply Subgroup.mem_sSup_of_mem
-      · use i
+      apply Subgroup.mem_sSup_of_mem; · use i
       simp
     · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
@@ -298,19 +287,13 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     dsimp at hxi hxp
     rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp
     rotate_left
-    · intro _ _ hj
-      apply hcomm
-      exact hj ∘ Subtype.ext
+    · intro _ _ hj; apply hcomm; exact hj ∘ Subtype.ext
     cases' hxp with g hgf
     cases' hxi with g' hg'f
-    have hxi : orderOf f ∣ Fintype.card (H i) :=
-      by
-      rw [← hg'f]
-      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
-    have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) :=
-      by
-      rw [← hgf, ← Fintype.card_pi]
+    have hxi : orderOf f ∣ Fintype.card (H i) := by rw [← hg'f];
       exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+    have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
+      rw [← hgf, ← Fintype.card_pi]; exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
     change f = 1
     rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
     convert← Nat.dvd_gcd hxp hxi
@@ -348,9 +331,7 @@ include hcomm
 Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
-    ∀ (x : H i) (y : H j), Commute ((H i).Subtype x) ((H j).Subtype y) :=
-  by
-  rintro ⟨x, hx⟩ ⟨y, hy⟩
+    ∀ (x : H i) (y : H j), Commute ((H i).Subtype x) ((H j).Subtype y) := by rintro ⟨x, hx⟩ ⟨y, hy⟩;
   exact hcomm i j hne x y hx hy
 #align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commute
 #align add_subgroup.commute_subtype_of_commute AddSubgroup.commute_subtype_of_commute
@@ -408,8 +389,7 @@ theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Indepen
   by
   apply MonoidHom.injective_noncommPiCoprod_of_independent
   · simpa using hind
-  · intro i
-    exact Subtype.coe_injective
+  · intro i; exact Subtype.coe_injective
 #align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independent
 #align add_subgroup.injective_noncomm_pi_coprod_of_independent AddSubgroup.injective_noncommPiCoprod_of_independent
 

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

@@ -149,10 +149,7 @@ variable {hcomm}
 include hdec
 
 /- warning: monoid_hom.noncomm_pi_coprod_mul_single -> MonoidHom.noncommPiCoprod_mulSingle is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
@@ -174,10 +171,7 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
 omit hcomm
 
 /- warning: monoid_hom.noncomm_pi_coprod_equiv -> MonoidHom.noncommPiCoprodEquiv is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquivₓ'. -/
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
@@ -200,10 +194,7 @@ omit hdec
 include hcomm
 
 /- warning: monoid_hom.noncomm_pi_coprod_mrange -> MonoidHom.noncommPiCoprod_mrange is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
@@ -247,10 +238,7 @@ include hfin
 namespace MonoidHom
 
 /- warning: monoid_hom.noncomm_pi_coprod_range -> MonoidHom.noncommPiCoprod_range is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
@@ -270,10 +258,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 
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(DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
@@ -298,10 +283,7 @@ variable (hcomm)
 omit hfin
 
 /- warning: monoid_hom.independent_range_of_coprime_order -> MonoidHom.independent_range_of_coprime_order is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
@@ -362,10 +344,7 @@ variable (hcomm : ∀ i j : ι, i ≠ j → ∀ x y : G, x ∈ H i → y ∈ H j
 include hcomm
 
 /- warning: subgroup.commute_subtype_of_commute -> Subgroup.commute_subtype_of_commute is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
@@ -398,10 +377,7 @@ variable {hcomm}
 include hdec
 
 /- warning: subgroup.noncomm_pi_coprod_mul_single -> Subgroup.noncommPiCoprod_mulSingle is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
@@ -424,10 +400,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i
 #align add_subgroup.noncomm_pi_coprod_range AddSubgroup.noncommPiCoprod_range
 
 /- warning: subgroup.injective_noncomm_pi_coprod_of_independent -> Subgroup.injective_noncommPiCoprod_of_independent is a dubious translation:
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Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :

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

@@ -123,7 +123,7 @@ namespace MonoidHom
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of monoids. -/
 @[to_additive
@@ -152,7 +152,7 @@ include hdec
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u1} M (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) => (forall (i : ι), (fun (i : ι) => N i) i) -> M) (MonoidHom.hasCoeToFun.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => MulOneClass.toHasOne.{u3} ((fun (i : ι) => N i) i) (Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) (_inst_3 i))) i y)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) y)
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u1}} [_inst_3 : forall (i : ι), Monoid.{u1} (N i)] (ϕ : forall (i : ι), MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N j) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (MulOneClass.toMul.{u1} (N j) (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), N i) => M) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) (fun (_x : forall (i : ι), N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), N i) => M) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (MulOneClass.toMul.{max u2 u1} (forall (i : ι), N i) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)))) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) y)
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u1}} [_inst_3 : forall (i : ι), Monoid.{u1} (N i)] (ϕ : forall (i : ι), MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N j) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (MulOneClass.toMul.{u1} (N j) (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : forall (i : ι), N i) => M) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) (fun (_x : forall (i : ι), N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : forall (i : ι), N i) => M) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (MulOneClass.toMul.{max u2 u1} (forall (i : ι), N i) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)))) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) y)
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
@@ -177,7 +177,7 @@ omit hcomm
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (succ u2) (succ u1) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (succ u2) (succ u1) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (max (succ u1) (succ u2)) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (max (succ u1) (succ u2)) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquivₓ'. -/
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
@@ -203,7 +203,7 @@ include hcomm
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))}, Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.mrange.{max u2 u3, u1, max u1 u2 u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm)) (iSup.{u1, succ u2} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.completeLattice.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u3, u1, max u1 u3} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i)))
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (iSup.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (iSup.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
@@ -250,7 +250,7 @@ namespace MonoidHom
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u3, u1} (forall (i : ι), H i) (Pi.group.{u2, u3} ι (fun (i : ι) => H i) (fun (i : ι) => _inst_2 i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)) (iSup.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i)))
 but is expected to have type
-  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (iSup.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
+  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (iSup.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
@@ -273,7 +273,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u3, succ u1} (H i) G (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i))) -> (Function.Injective.{max (succ u2) (succ u3), succ u1} (forall (i : ι), (fun (i : ι) => H i) i) G (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (forall (i : ι), (fun (i : ι) => H i) i) -> G) (MonoidHom.hasCoeToFun.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)))
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u3}} [hfin : Fintype.{u3} ι] {H : ι -> Type.{u1}} [_inst_2 : forall (i : ι), Group.{u1} (H i)] (ϕ : forall (i : ι), MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : H i) (y : H j), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) (fun (_x : H j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H j) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (MulOneClass.toMul.{u1} (H j) (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u3, u2} ι (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1) (fun (i : ι) => MonoidHom.range.{u1, u2} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u1, succ u2} (H i) G (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i))) -> (Function.Injective.{max (succ u3) (succ u1), succ u2} (forall (i : ι), H i) G (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHom.noncommPiCoprod.{u2, u3, u1} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u3}} [hfin : Fintype.{u3} ι] {H : ι -> Type.{u1}} [_inst_2 : forall (i : ι), Group.{u1} (H i)] (ϕ : forall (i : ι), MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : H i) (y : H j), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) x) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) x) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) x) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) x) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) (fun (_x : H j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H j) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (MulOneClass.toMul.{u1} (H j) (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u3, u2} ι (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1) (fun (i : ι) => MonoidHom.range.{u1, u2} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u1, succ u2} (H i) G (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i))) -> (Function.Injective.{max (succ u3) (succ u1), succ u2} (forall (i : ι), H i) G (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHom.noncommPiCoprod.{u2, u3, u1} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
@@ -301,7 +301,7 @@ omit hfin
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))) -> (forall [_inst_3 : Finite.{succ u2} ι] [_inst_4 : forall (i : ι), Fintype.{u3} (H i)], (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (Nat.coprime (Fintype.card.{u3} (H i) (_inst_4 i)) (Fintype.card.{u3} (H j) (_inst_4 j)))) -> (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u2} (_inst_2 i) (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u2} (_inst_2 j) (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm j) y))) -> (forall [_inst_4 : Finite.{succ u3} ι] [hcoprime : forall (i : ι), Fintype.{u2} (_inst_2 i)], (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (Nat.coprime (Fintype.card.{u2} (_inst_2 i) (hcoprime i)) (Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u2} (_inst_2 i) (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u2} (_inst_2 j) (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm j) y))) -> (forall [_inst_4 : Finite.{succ u3} ι] [hcoprime : forall (i : ι), Fintype.{u2} (_inst_2 i)], (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (Nat.coprime (Fintype.card.{u2} (_inst_2 i) (hcoprime i)) (Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
@@ -365,7 +365,7 @@ include hcomm
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (y : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) -> G) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.subtype.{u1} G _inst_1 (H i)) x) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) -> G) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.subtype.{u1} G _inst_1 (H j)) y)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (y : Subtype.{succ u1} G (fun (x : G) => 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(Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.subtype.{u1} G _inst_1 (H i)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) (fun (_x : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) => G) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.subtype.{u1} G _inst_1 (H j)) y)))
 Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
@@ -401,7 +401,7 @@ include hdec
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))} (i : ι) (y : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)), Eq.{succ u1} G (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ (max u2 u1)) (succ u1)} (MonoidHom.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) -> G) (MonoidHom.hasCoeToFun.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u1} G _inst_1 ((fun (i : ι) => H i) i)) i y)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)))))) y)
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hdec : DecidableEq.{succ u1} ι] [hfin : Fintype.{u1} ι] {H : ι -> (Subgroup.{u2} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (H j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))} (i : ι) (y : Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u2 u1} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (Subtype.val.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) x (SetLike.coe.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1) (H i))) y)
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hdec : DecidableEq.{succ u1} ι] [hfin : Fintype.{u1} ι] {H : ι -> (Subgroup.{u2} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (H j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))} (i : ι) (y : Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u2 u1} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (Subtype.val.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) x (SetLike.coe.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1) (H i))) y)
 Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
@@ -427,7 +427,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u2) (succ u1), succ u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G 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u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u1) (succ u2), succ u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) 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Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
 Case conversion may be inaccurate. Consider using '#align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :

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

@@ -79,7 +79,7 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
         by
         refine' Subgroup.noncommProd_mem _ _ _
         intro x hx
-        have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_supᵢ₂ x hx
+        have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ x hx
         exact this (hmem.2 x hx)
       intro heq1
       rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1
@@ -201,9 +201,9 @@ include hcomm
 
 /- warning: monoid_hom.noncomm_pi_coprod_mrange -> MonoidHom.noncommPiCoprod_mrange is a dubious translation:
 lean 3 declaration is
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+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))}, Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.mrange.{max u2 u3, u1, max u1 u2 u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm)) (iSup.{u1, succ u2} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.completeLattice.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u3, u1, max u1 u3} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i)))
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (iSup.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
@@ -212,10 +212,10 @@ theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι,
     · rintro x ⟨f, rfl⟩
       refine' Submonoid.noncommProd_mem _ _ _ _ _
       intro i hi
-      apply Submonoid.mem_supₛ_of_mem
+      apply Submonoid.mem_sSup_of_mem
       · use i
       simp
-    · refine' supᵢ_le _
+    · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
       refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
@@ -248,9 +248,9 @@ namespace MonoidHom
 
 /- warning: monoid_hom.noncomm_pi_coprod_range -> MonoidHom.noncommPiCoprod_range is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u3, u1} (forall (i : ι), H i) (Pi.group.{u2, u3} ι (fun (i : ι) => H i) (fun (i : ι) => _inst_2 i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)) (supᵢ.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i)))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u3, u1} (forall (i : ι), H i) (Pi.group.{u2, u3} ι (fun (i : ι) => H i) (fun (i : ι) => _inst_2 i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)) (iSup.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i)))
 but is expected to have type
-  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) 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_inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
+  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (iSup.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
@@ -260,10 +260,10 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
     · rintro x ⟨f, rfl⟩
       refine' Subgroup.noncommProd_mem _ _ _
       intro i hi
-      apply Subgroup.mem_supₛ_of_mem
+      apply Subgroup.mem_sSup_of_mem
       · use i
       simp
-    · refine' supᵢ_le _
+    · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
       refine' ⟨Pi.mulSingle i y, noncomm_pi_coprod_mul_single _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
@@ -314,7 +314,7 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     rw [disjoint_iff_inf_le]
     rintro f ⟨hxi, hxp⟩
     dsimp at hxi hxp
-    rw [supᵢ_subtype', ← noncomm_pi_coprod_range] at hxp
+    rw [iSup_subtype', ← noncomm_pi_coprod_range] at hxp
     rotate_left
     · intro _ _ hj
       apply hcomm
@@ -413,9 +413,9 @@ omit hdec
 
 /- warning: subgroup.noncomm_pi_coprod_range -> Subgroup.noncommPiCoprod_range is a dubious translation:
 lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Pi.group.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (fun (i : ι) => Subgroup.toGroup.{u1} G _inst_1 (H i))) G _inst_1 (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)) (supᵢ.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => H i))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Pi.group.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (fun (i : ι) => Subgroup.toGroup.{u1} G _inst_1 (H i))) G _inst_1 (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)) (iSup.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => H i))
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hfin : DecidableEq.{succ u1} ι] [H : Fintype.{u1} ι] {hcomm : ι -> (Subgroup.{u2} G _inst_1)} {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (hcomm i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (hcomm j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))}, Eq.{succ u2} (Subgroup.{u2} G _inst_1) (MonoidHom.range.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (hcomm i))) (Pi.group.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (hcomm i))) (fun (i : ι) => Subgroup.toGroup.{u2} G _inst_1 (hcomm i))) G _inst_1 (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι H (fun (i : ι) => hcomm i) hcomm_1)) (supᵢ.{u2, succ u1} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))) ι (fun (i : ι) => hcomm i))
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hfin : DecidableEq.{succ u1} ι] [H : Fintype.{u1} ι] {hcomm : ι -> (Subgroup.{u2} G _inst_1)} {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (hcomm i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (hcomm j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))}, Eq.{succ u2} (Subgroup.{u2} G _inst_1) (MonoidHom.range.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (hcomm i))) (Pi.group.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (hcomm i))) (fun (i : ι) => Subgroup.toGroup.{u2} G _inst_1 (hcomm i))) G _inst_1 (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι H (fun (i : ι) => hcomm i) hcomm_1)) (iSup.{u2, succ u1} (Subgroup.{u2} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u2} (Subgroup.{u2} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u2} (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1))) ι (fun (i : ι) => hcomm i))
 Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_range Subgroup.noncommPiCoprod_rangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i := by

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

@@ -136,8 +136,7 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
     simp
   map_mul' f g := by
     classical
-      convert
-        @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
+      convert@Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
       · ext i
         exact map_mul (ϕ i) (f i) (g i)
       · rintro i - j - h
@@ -332,7 +331,7 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
       exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
     change f = 1
     rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
-    convert ← Nat.dvd_gcd hxp hxi
+    convert← Nat.dvd_gcd hxp hxi
     rw [← Nat.coprime_iff_gcd_eq_one]
     apply Nat.coprime_prod_left
     intro j _

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

@@ -123,7 +123,7 @@ namespace MonoidHom
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of monoids. -/
 @[to_additive
@@ -153,7 +153,7 @@ include hdec
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u1} M (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) => (forall (i : ι), (fun (i : ι) => N i) i) -> M) (MonoidHom.hasCoeToFun.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => MulOneClass.toHasOne.{u3} ((fun (i : ι) => N i) i) (Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) (_inst_3 i))) i y)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) y)
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u1}} [_inst_3 : forall (i : ι), Monoid.{u1} (N i)] (ϕ : forall (i : ι), MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N j) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (MulOneClass.toMul.{u1} (N j) (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), N i) => M) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) (fun (_x : forall (i : ι), N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), N i) => M) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (MulOneClass.toMul.{max u2 u1} (forall (i : ι), N i) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)))) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) y)
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u1}} [_inst_3 : forall (i : ι), Monoid.{u1} (N i)] (ϕ : forall (i : ι), MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N j) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (MulOneClass.toMul.{u1} (N j) (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), N i) => M) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) (fun (_x : forall (i : ι), N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), N i) => M) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (MulOneClass.toMul.{max u2 u1} (forall (i : ι), N i) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)))) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) y)
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
@@ -178,7 +178,7 @@ omit hcomm
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (succ u2) (succ u1) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (succ u2) (succ u1) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (max (succ u1) (succ u2)) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (max (succ u1) (succ u2)) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquivₓ'. -/
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
@@ -204,7 +204,7 @@ include hcomm
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))}, Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.mrange.{max u2 u3, u1, max u1 u2 u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm)) (supᵢ.{u1, succ u2} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.completeLattice.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u3, u1, max u1 u3} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i)))
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
@@ -251,7 +251,7 @@ namespace MonoidHom
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u3, u1} (forall (i : ι), H i) (Pi.group.{u2, u3} ι (fun (i : ι) => H i) (fun (i : ι) => _inst_2 i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)) (supᵢ.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i)))
 but is expected to have type
-  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
+  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
@@ -274,7 +274,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u3, succ u1} (H i) G (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i))) -> (Function.Injective.{max (succ u2) (succ u3), succ u1} (forall (i : ι), (fun (i : ι) => H i) i) G (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (forall (i : ι), (fun (i : ι) => H i) i) -> G) (MonoidHom.hasCoeToFun.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)))
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u3}} [hfin : Fintype.{u3} ι] {H : ι -> Type.{u1}} [_inst_2 : forall (i : ι), Group.{u1} (H i)] (ϕ : forall (i : ι), MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : H i) (y : H j), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) (fun (_x : H j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H j) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (MulOneClass.toMul.{u1} (H j) (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u3, u2} ι (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1) (fun (i : ι) => MonoidHom.range.{u1, u2} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u1, succ u2} (H i) G (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i))) -> (Function.Injective.{max (succ u3) (succ u1), succ u2} (forall (i : ι), H i) G (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHom.noncommPiCoprod.{u2, u3, u1} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u3}} [hfin : Fintype.{u3} ι] {H : ι -> Type.{u1}} [_inst_2 : forall (i : ι), Group.{u1} (H i)] (ϕ : forall (i : ι), MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : H i) (y : H j), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) (fun (_x : H j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H j) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (MulOneClass.toMul.{u1} (H j) (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u3, u2} ι (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1) (fun (i : ι) => MonoidHom.range.{u1, u2} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u1, succ u2} (H i) G (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i))) -> (Function.Injective.{max (succ u3) (succ u1), succ u2} (forall (i : ι), H i) G (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHom.noncommPiCoprod.{u2, u3, u1} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
@@ -302,7 +302,7 @@ omit hfin
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))) -> (forall [_inst_3 : Finite.{succ u2} ι] [_inst_4 : forall (i : ι), Fintype.{u3} (H i)], (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (Nat.coprime (Fintype.card.{u3} (H i) (_inst_4 i)) (Fintype.card.{u3} (H j) (_inst_4 j)))) -> (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u2} (_inst_2 i) (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u2} (_inst_2 j) (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm j) y))) -> (forall [_inst_4 : Finite.{succ u3} ι] [hcoprime : forall (i : ι), Fintype.{u2} (_inst_2 i)], (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (Nat.coprime (Fintype.card.{u2} (_inst_2 i) (hcoprime i)) (Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u2} (_inst_2 i) (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u2} (_inst_2 j) (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm j) y))) -> (forall [_inst_4 : Finite.{succ u3} ι] [hcoprime : forall (i : ι), Fintype.{u2} (_inst_2 i)], (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (Nat.coprime (Fintype.card.{u2} (_inst_2 i) (hcoprime i)) (Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
@@ -366,7 +366,7 @@ include hcomm
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (y : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) -> G) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.subtype.{u1} G _inst_1 (H i)) x) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) -> G) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.subtype.{u1} G _inst_1 (H j)) y)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (y : Subtype.{succ u1} G (fun (x : G) => 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(Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.subtype.{u1} G _inst_1 (H i)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) (fun (_x : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) => G) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.subtype.{u1} G _inst_1 (H j)) y)))
 Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
@@ -402,7 +402,7 @@ include hdec
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))} (i : ι) (y : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)), Eq.{succ u1} G (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ (max u2 u1)) (succ u1)} (MonoidHom.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) -> G) (MonoidHom.hasCoeToFun.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u1} G _inst_1 ((fun (i : ι) => H i) i)) i y)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)))))) y)
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hdec : DecidableEq.{succ u1} ι] [hfin : Fintype.{u1} ι] {H : ι -> (Subgroup.{u2} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (H j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))} (i : ι) (y : Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u2 u1} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (Subtype.val.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) x (SetLike.coe.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1) (H i))) y)
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hdec : DecidableEq.{succ u1} ι] [hfin : Fintype.{u1} ι] {H : ι -> (Subgroup.{u2} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (H j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))} (i : ι) (y : Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u2 u1} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (Subtype.val.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) x (SetLike.coe.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1) (H i))) y)
 Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
@@ -428,7 +428,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u2) (succ u1), succ u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G 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u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u1) (succ u2), succ u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) 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+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u1) (succ u2), succ u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), succ u1} (MonoidHom.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u1 u2} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, max u1 u2, u1} (MonoidHom.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
 Case conversion may be inaccurate. Consider using '#align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :

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

@@ -123,7 +123,7 @@ namespace MonoidHom
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of monoids. -/
 @[to_additive
@@ -153,7 +153,7 @@ include hdec
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u1} M (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) => (forall (i : ι), (fun (i : ι) => N i) i) -> M) (MonoidHom.hasCoeToFun.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => N i) i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) ((fun (i : ι) => _inst_3 i) i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => N i) i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => MulOneClass.toHasOne.{u3} ((fun (i : ι) => N i) i) (Monoid.toMulOneClass.{u3} ((fun (i : ι) => N i) i) (_inst_3 i))) i y)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) y)
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u1}} [_inst_3 : forall (i : ι), Monoid.{u1} (N i)] (ϕ : forall (i : ι), MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N j) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (MulOneClass.toMul.{u1} (N j) (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : forall (i : ι), N i) => M) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) (fun (_x : forall (i : ι), N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : forall (i : ι), N i) => M) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (MulOneClass.toMul.{max u2 u1} (forall (i : ι), N i) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)))) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) y)
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u1}} [_inst_3 : forall (i : ι), Monoid.{u1} (N i)] (ϕ : forall (i : ι), MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N j) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (MulOneClass.toMul.{u1} (N j) (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N j) M (Monoid.toMulOneClass.{u1} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ j) y))} (i : ι) (y : N i), Eq.{succ u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), N i) => M) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (max (succ u3) (succ u2)) (succ u1), max (succ u2) (succ u1), succ u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) (fun (_x : forall (i : ι), N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), N i) => M) _x) (MulHomClass.toFunLike.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (MulOneClass.toMul.{max u2 u1} (forall (i : ι), N i) (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max (max u3 u2) u1, max u2 u1, u3} (MonoidHom.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u3} M _inst_1)))) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => N i) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Monoid.toOne.{u1} (N i) (_inst_3 i)) i y)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (MulOneClass.toMul.{u1} (N i) (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (N i) M (Monoid.toMulOneClass.{u1} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (ϕ i) y)
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
@@ -178,7 +178,7 @@ omit hcomm
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (succ u2) (succ u1) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (succ u2) (succ u1) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (max (succ u1) (succ u2)) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)], Equiv.{max 1 (max (succ u1) (succ u2)) (succ u3), max (succ u1) (succ (max u2 u3))} (Subtype.{max (max (succ u1) (succ u2)) (succ u3)} (forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y)))) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquivₓ'. -/
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
@@ -204,7 +204,7 @@ include hcomm
 lean 3 declaration is
   forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) {hcomm : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))}, Eq.{succ u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.mrange.{max u2 u3, u1, max u1 u2 u3} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.noncommPiCoprod.{u1, u2, u3} M _inst_1 ι _inst_2 (fun (i : ι) => N i) (fun (i : ι) => _inst_3 i) ϕ hcomm)) (supᵢ.{u1, succ u2} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (ConditionallyCompleteLattice.toHasSup.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Submonoid.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (Submonoid.completeLattice.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u3, u1, max u1 u3} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i)))
 but is expected to have type
-  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
+  forall {M : Type.{u3}} [_inst_1 : Monoid.{u3} M] {ι : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} ι] [N : Fintype.{u2} ι] {_inst_3 : ι -> Type.{u1}} [ϕ : forall (i : ι), Monoid.{u1} (_inst_3 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) {hcomm_1 : Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : _inst_3 i) (y : _inst_3 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) x) _inst_1)) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) (fun (a : _inst_3 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 i) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (MulOneClass.toMul.{u1} (_inst_3 i) (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) (fun (a : _inst_3 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_3 j) => M) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (MulOneClass.toMul.{u1} (_inst_3 j) (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j))) (MulOneClass.toMul.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)) (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 j) M (Monoid.toMulOneClass.{u1} (_inst_3 j) (ϕ j)) (Monoid.toMulOneClass.{u3} M _inst_1)))) (hcomm j) y))}, Eq.{succ u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.mrange.{max u2 u1, u3, max (max u1 u2) u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{max u2 u1, u3} (forall (i : ι), _inst_3 i) M (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => _inst_3 i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i))) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.noncommPiCoprod.{u3, u2, u1} M _inst_1 ι N (fun (i : ι) => _inst_3 i) (fun (i : ι) => ϕ i) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (ConditionallyCompleteLattice.toSupSet.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Submonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)) (Submonoid.instCompleteLatticeSubmonoid.{u3} M (Monoid.toMulOneClass.{u3} M _inst_1)))) ι (fun (i : ι) => MonoidHom.mrange.{u1, u3, max u3 u1} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1) (MonoidHom.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (MonoidHom.monoidHomClass.{u1, u3} (_inst_3 i) M (Monoid.toMulOneClass.{u1} (_inst_3 i) (ϕ i)) (Monoid.toMulOneClass.{u3} M _inst_1)) (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
@@ -251,7 +251,7 @@ namespace MonoidHom
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, Eq.{succ u1} (Subgroup.{u1} G _inst_1) (MonoidHom.range.{max u2 u3, u1} (forall (i : ι), H i) (Pi.group.{u2, u3} ι (fun (i : ι) => H i) (fun (i : ι) => _inst_2 i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)) (supᵢ.{u1, succ u2} (Subgroup.{u1} G _inst_1) (ConditionallyCompleteLattice.toHasSup.{u1} (Subgroup.{u1} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i)))
 but is expected to have type
-  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
+  forall {G : Type.{u3}} [_inst_1 : Group.{u3} G] {ι : Type.{u2}} [hfin : DecidableEq.{succ u2} ι] [H : Fintype.{u2} ι] {_inst_2 : ι -> Type.{u1}} [ϕ : forall (i : ι), Group.{u1} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) {hcomm_1 : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (MulOneClass.toMul.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u3} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u1} (_inst_2 i) (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 i) G (Monoid.toMulOneClass.{u1} (_inst_2 i) (DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u3) (succ u1), succ u1, succ u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u1} (_inst_2 j) (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u3} G (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u3 u1, u1, u3} (MonoidHom.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u3} (_inst_2 j) G (Monoid.toMulOneClass.{u1} (_inst_2 j) (DivInvMonoid.toMonoid.{u1} (_inst_2 j) (Group.toDivInvMonoid.{u1} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u3} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)))))) (hcomm j) y))}, Eq.{succ u3} (Subgroup.{u3} G _inst_1) (MonoidHom.range.{max u2 u1, u3} (forall (i : ι), _inst_2 i) (Pi.group.{u2, u1} ι (fun (i : ι) => _inst_2 i) (fun (i : ι) => ϕ i)) G _inst_1 (MonoidHom.noncommPiCoprod.{u3, u2, u1} G (DivInvMonoid.toMonoid.{u3} G (Group.toDivInvMonoid.{u3} G _inst_1)) ι H (fun (i : ι) => _inst_2 i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (_inst_2 i) (Group.toDivInvMonoid.{u1} (_inst_2 i) (ϕ i))) hcomm hcomm_1)) (supᵢ.{u3, succ u2} (Subgroup.{u3} G _inst_1) (ConditionallyCompleteLattice.toSupSet.{u3} (Subgroup.{u3} G _inst_1) (CompleteLattice.toConditionallyCompleteLattice.{u3} (Subgroup.{u3} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u3} G _inst_1))) ι (fun (i : ι) => MonoidHom.range.{u1, u3} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
@@ -274,7 +274,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u3, succ u1} (H i) G (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i))) -> (Function.Injective.{max (succ u2) (succ u3), succ u1} (forall (i : ι), (fun (i : ι) => H i) i) G (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (forall (i : ι), (fun (i : ι) => H i) i) -> G) (MonoidHom.hasCoeToFun.{max u2 u3, u1} (forall (i : ι), (fun (i : ι) => H i) i) G (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => (fun (i : ι) => H i) i) (fun (i : ι) => Monoid.toMulOneClass.{u3} ((fun (i : ι) => H i) i) ((fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHom.noncommPiCoprod.{u1, u2, u3} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i))) ϕ hcomm)))
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u3}} [hfin : Fintype.{u3} ι] {H : ι -> Type.{u1}} [_inst_2 : forall (i : ι), Group.{u1} (H i)] (ϕ : forall (i : ι), MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : H i) (y : H j), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) x) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) x) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) x) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) x) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) (fun (_x : H j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H j) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (MulOneClass.toMul.{u1} (H j) (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u3, u2} ι (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1) (fun (i : ι) => MonoidHom.range.{u1, u2} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u1, succ u2} (H i) G (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i))) -> (Function.Injective.{max (succ u3) (succ u1), succ u2} (forall (i : ι), H i) G (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHom.noncommPiCoprod.{u2, u3, u1} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u3}} [hfin : Fintype.{u3} ι] {H : ι -> Type.{u1}} [_inst_2 : forall (i : ι), Group.{u1} (H i)] (ϕ : forall (i : ι), MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) {hcomm : forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : H i) (y : H j), Commute.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (MulOneClass.toMul.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (Monoid.toMulOneClass.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (DivInvMonoid.toMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) (Group.toDivInvMonoid.{u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i) x) (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) (fun (_x : H j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H j) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (MulOneClass.toMul.{u1} (H j) (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H j) G (Monoid.toMulOneClass.{u1} (H j) (DivInvMonoid.toMonoid.{u1} (H j) (Group.toDivInvMonoid.{u1} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ j) y))}, (CompleteLattice.Independent.{succ u3, u2} ι (Subgroup.{u2} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u2} G _inst_1) (fun (i : ι) => MonoidHom.range.{u1, u2} (H i) (_inst_2 i) G _inst_1 (ϕ i))) -> (forall (i : ι), Function.Injective.{succ u1, succ u2} (H i) G (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) (fun (_x : H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : H i) => G) _x) (MulHomClass.toFunLike.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (MulOneClass.toMul.{u1} (H i) (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, u1, u2} (MonoidHom.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u2} (H i) G (Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (ϕ i))) -> (Function.Injective.{max (succ u3) (succ u1), succ u2} (forall (i : ι), H i) G (FunLike.coe.{max (max (succ u2) (succ u3)) (succ u1), max (succ u3) (succ u1), succ u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (MonoidHom.noncommPiCoprod.{u2, u3, u1} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
@@ -302,7 +302,7 @@ omit hfin
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))) -> (forall [_inst_3 : Finite.{succ u2} ι] [_inst_4 : forall (i : ι), Fintype.{u3} (H i)], (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (Nat.coprime (Fintype.card.{u3} (H i) (_inst_4 i)) (Fintype.card.{u3} (H j) (_inst_4 j)))) -> (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u2} (_inst_2 i) (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u2} (_inst_2 j) (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm j) y))) -> (forall [_inst_4 : Finite.{succ u3} ι] [hcoprime : forall (i : ι), Fintype.{u2} (_inst_2 i)], (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (Nat.coprime (Fintype.card.{u2} (_inst_2 i) (hcoprime i)) (Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) x) _inst_1)))) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) (fun (a : _inst_2 i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 i) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (MulOneClass.toMul.{u2} (_inst_2 i) (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm i) x) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) (fun (a : _inst_2 j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : _inst_2 j) => G) a) (MulHomClass.toFunLike.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (MulOneClass.toMul.{u2} (_inst_2 j) (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j))))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u1 u2, u2, u1} (MonoidHom.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u2, u1} (_inst_2 j) G (Monoid.toMulOneClass.{u2} (_inst_2 j) (DivInvMonoid.toMonoid.{u2} (_inst_2 j) (Group.toDivInvMonoid.{u2} (_inst_2 j) (ϕ j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (hcomm j) y))) -> (forall [_inst_4 : Finite.{succ u3} ι] [hcoprime : forall (i : ι), Fintype.{u2} (_inst_2 i)], (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (Nat.coprime (Fintype.card.{u2} (_inst_2 i) (hcoprime i)) (Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
 Case conversion may be inaccurate. Consider using '#align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
@@ -366,7 +366,7 @@ include hcomm
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (y : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) -> G) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (Subgroup.toGroup.{u1} G _inst_1 (H i))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.subtype.{u1} G _inst_1 (H i)) x) (coeFn.{succ u1, succ u1} (MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) -> G) (MonoidHom.hasCoeToFun.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) G (Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (Subgroup.toGroup.{u1} G _inst_1 (H j))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.subtype.{u1} G _inst_1 (H j)) y)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (y : Subtype.{succ u1} G (fun (x : G) => 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(Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.subtype.{u1} G _inst_1 (H i)) x) (FunLike.coe.{succ u1, succ u1, succ u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) (fun (_x : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) => G) _x) (MulHomClass.toFunLike.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (MulOneClass.toMul.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MonoidHomClass.toMulHomClass.{u1, u1, u1} (MonoidHom.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{u1, u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H j))) G (Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H j))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.subtype.{u1} G _inst_1 (H j)) y)))
 Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
@@ -402,7 +402,7 @@ include hdec
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hdec : DecidableEq.{succ u2} ι] [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))} (i : ι) (y : coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)), Eq.{succ u1} G (coeFn.{max (succ u1) (succ (max u2 u1)), max (succ (max u2 u1)) (succ u1)} (MonoidHom.{max u2 u1, 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(SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) -> G) (MonoidHom.hasCoeToFun.{max u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u1} G _inst_1 ((fun (i : ι) => H i) i)) i y)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) G (coeSubtype.{succ u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)))))) y)
 but is expected to have type
-  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hdec : DecidableEq.{succ u1} ι] [hfin : Fintype.{u1} ι] {H : ι -> (Subgroup.{u2} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (H j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))} (i : ι) (y : Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u2 u1} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (Subtype.val.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) x (SetLike.coe.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1) (H i))) y)
+  forall {G : Type.{u2}} [_inst_1 : Group.{u2} G] {ι : Type.{u1}} [hdec : DecidableEq.{succ u1} ι] [hfin : Fintype.{u1} ι] {H : ι -> (Subgroup.{u2} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u1} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i)) -> (Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) y (H j)) -> (Commute.{u2} G (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) x y))} (i : ι) (y : Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))), Eq.{succ u2} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (FunLike.coe.{max (succ u2) (succ u1), max (succ u2) (succ u1), succ u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (_x : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2372 : forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) => G) _x) (MulHomClass.toFunLike.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (MulOneClass.toMul.{max u2 u1} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max u2 u1, max u2 u1, u2} (MonoidHom.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (MonoidHom.monoidHomClass.{max u2 u1, u2} (forall (i : ι), Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1))) (Subgroup.toSubmonoid.{u2} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u2, u1} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm) (Pi.mulSingle.{u1, u2} ι (fun (i : ι) => Subtype.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Subgroup.{u2} G _inst_1) (SetLike.instMembership.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1)) x (H i))) (fun (a : ι) (b : ι) => hdec a b) (fun (i : ι) => Subgroup.one.{u2} G _inst_1 (H i)) i y)) (Subtype.val.{succ u2} G (fun (x : G) => Membership.mem.{u2, u2} G (Set.{u2} G) (Set.instMembershipSet.{u2} G) x (SetLike.coe.{u2, u2} (Subgroup.{u2} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u2} G _inst_1) (H i))) y)
 Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
@@ -428,7 +428,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i
 lean 3 declaration is
   forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u2) (succ u1), succ u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G 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u2 u1, u1} (forall (i : ι), coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (fun (i : ι) => Monoid.toMulOneClass.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (DivInvMonoid.toMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Group.toDivInvMonoid.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) ((fun (i : ι) => H i) i)) (Subgroup.toGroup.{u1} G _inst_1 ((fun (i : ι) => H i) i)))))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
 but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u1) (succ u2), succ u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) 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+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u1) (succ u2), succ u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) 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Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
 Case conversion may be inaccurate. Consider using '#align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joachim Breitner
 
 ! This file was ported from Lean 3 source module group_theory.noncomm_pi_coprod
-! leanprover-community/mathlib commit 6f9f36364eae3f42368b04858fd66d6d9ae730d8
+! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Order.SupIndep
 /-!
 # Canonical homomorphism from a finite family of monoids
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines the construction of the canonical homomorphism from a family of monoids.
 
 Given a family of morphisms `ϕ i : N i →* M` for each `i : ι` where elements in the

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

@@ -53,6 +53,12 @@ namespace Subgroup
 
 variable {G : Type _} [Group G]
 
+/- warning: subgroup.eq_one_of_noncomm_prod_eq_one_of_independent -> Subgroup.eq_one_of_noncommProd_eq_one_of_independent is a dubious translation:
+lean 3 declaration is
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> G) (comm : Set.Pairwise.{u2} ι ((fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} ι) (Set.{u2} ι) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} ι) (Set.{u2} ι) (Finset.Set.hasCoeT.{u2} ι))) s) (fun (a : ι) (b : ι) => Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (f a) (f b))) (K : ι -> (Subgroup.{u1} G _inst_1)), (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) K) -> (forall (x : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) x s) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (f x) (K x))) -> (Eq.{succ u1} G (Finset.noncommProd.{u2, u1} ι G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) s f comm) (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))) -> (forall (i : ι), (Membership.Mem.{u2, u2} ι (Finset.{u2} ι) (Finset.hasMem.{u2} ι) i s) -> (Eq.{succ u1} G (f i) (OfNat.ofNat.{u1} G 1 (OfNat.mk.{u1} G 1 (One.one.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))))))
+but is expected to have type
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} (s : Finset.{u2} ι) (f : ι -> G) (comm : Set.Pairwise.{u2} ι (Finset.toSet.{u2} ι s) (fun (a : ι) (b : ι) => Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (f a) (f b))) (K : ι -> (Subgroup.{u1} G _inst_1)), (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) K) -> (forall (x : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) x s) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) (f x) (K x))) -> (Eq.{succ u1} G (Finset.noncommProd.{u2, u1} ι G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)) s f comm) (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))) -> (forall (i : ι), (Membership.mem.{u2, u2} ι (Finset.{u2} ι) (Finset.instMembershipFinset.{u2} ι) i s) -> (Eq.{succ u1} G (f i) (OfNat.ofNat.{u1} G 1 (One.toOfNat1.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independentₓ'. -/
 /-- `finset.noncomm_prod` is “injective” in `f` if `f` maps into independent subgroups.  This
 generalizes (one direction of) `subgroup.disjoint_iff_mul_eq_one`. -/
 @[to_additive
@@ -83,7 +89,7 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
       · exact heq1i
       · exact ih hcomm hmem.2 heq1S _ h
 #align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independent
-#align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent
+#align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_independent
 
 end Subgroup
 
@@ -110,6 +116,12 @@ variable (f g : ∀ i : ι, N i)
 
 namespace MonoidHom
 
+/- warning: monoid_hom.noncomm_pi_coprod -> MonoidHom.noncommPiCoprod is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} M (MulOneClass.toHasMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N i) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (fun (_x : MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) => (N j) -> M) (MonoidHom.hasCoeToFun.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : Monoid.{u1} M] {ι : Type.{u2}} [_inst_2 : Fintype.{u2} ι] {N : ι -> Type.{u3}} [_inst_3 : forall (i : ι), Monoid.{u3} (N i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)), (Pairwise.{u2} ι (fun (i : ι) (j : ι) => forall (x : N i) (y : N j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) x) _inst_1)) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) (fun (_x : N i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N i) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (MulOneClass.toMul.{u3} (N i) (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N i) M (Monoid.toMulOneClass.{u3} (N i) (_inst_3 i)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ i) x) (FunLike.coe.{max (succ u1) (succ u3), succ u3, succ u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) (fun (_x : N j) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : N j) => M) _x) (MulHomClass.toFunLike.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (MulOneClass.toMul.{u3} (N j) (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j))) (MulOneClass.toMul.{u1} M (Monoid.toMulOneClass.{u1} M _inst_1)) (MonoidHomClass.toMulHomClass.{max u1 u3, u3, u1} (MonoidHom.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)) (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1) (MonoidHom.monoidHomClass.{u3, u1} (N j) M (Monoid.toMulOneClass.{u3} (N j) (_inst_3 j)) (Monoid.toMulOneClass.{u1} M _inst_1)))) (ϕ j) y))) -> (MonoidHom.{max u2 u3, u1} (forall (i : ι), N i) M (Pi.mulOneClass.{u2, u3} ι (fun (i : ι) => N i) (fun (i : ι) => Monoid.toMulOneClass.{u3} (N i) (_inst_3 i))) (Monoid.toMulOneClass.{u1} M _inst_1))
+Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of monoids. -/
 @[to_additive
       "The canonical homomorphism from a family of additive monoids.\n\nSee also `linear_map.lsum` for a linear version without the commutativity assumption."]
@@ -134,6 +146,12 @@ variable {hcomm}
 
 include hdec
 
+/- warning: monoid_hom.noncomm_pi_coprod_mul_single -> MonoidHom.noncommPiCoprod_mulSingle is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mul_single MonoidHom.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
     noncommPiCoprod ϕ hcomm (Pi.mulSingle i y) = ϕ i y :=
@@ -153,6 +171,12 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
 
 omit hcomm
 
+/- warning: monoid_hom.noncomm_pi_coprod_equiv -> MonoidHom.noncommPiCoprodEquiv is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquivₓ'. -/
 /-- The universal property of `noncomm_pi_coprod` -/
 @[to_additive "The universal property of `noncomm_pi_coprod`"]
 def noncommPiCoprodEquiv :
@@ -173,6 +197,12 @@ omit hdec
 
 include hcomm
 
+/- warning: monoid_hom.noncomm_pi_coprod_mrange -> MonoidHom.noncommPiCoprod_mrange is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_mrange : (noncommPiCoprod ϕ hcomm).mrange = ⨆ i : ι, (ϕ i).mrange := by
   classical
@@ -214,6 +244,12 @@ include hfin
 
 namespace MonoidHom
 
+/- warning: monoid_hom.noncomm_pi_coprod_range -> MonoidHom.noncommPiCoprod_range is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_rangeₓ'. -/
 -- The subgroup version of `noncomm_pi_coprod_mrange`
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
@@ -231,6 +267,12 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 
+/- warning: monoid_hom.injective_noncomm_pi_coprod_of_independent -> MonoidHom.injective_noncommPiCoprod_of_independent is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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H i) (fun (_x : forall (i : ι), H i) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : forall (i : ι), H i) => G) _x) (MulHomClass.toFunLike.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : ι), H i) G (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))))) (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (forall (i : ι), H i) G (MulOneClass.toMul.{max u3 u1} (forall (i : ι), H i) (Pi.mulOneClass.{u3, u1} ι (fun (i : ι) => H i) (fun (i : ι) => Monoid.toMulOneClass.{u1} (H i) (DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i)))))) (MulOneClass.toMul.{u2} G (Monoid.toMulOneClass.{u2} G (DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)))) (MonoidHomClass.toMulHomClass.{max (max u2 u3) u1, max u3 u1, u2} (MonoidHom.{max u3 u1, u2} (forall (i : 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(DivInvMonoid.toMonoid.{u2} G (Group.toDivInvMonoid.{u2} G _inst_1)) ι hfin (fun (i : ι) => H i) (fun (i : ι) => DivInvMonoid.toMonoid.{u1} (H i) (Group.toDivInvMonoid.{u1} (H i) (_inst_2 i))) ϕ hcomm)))
+Case conversion may be inaccurate. Consider using '#align monoid_hom.injective_noncomm_pi_coprod_of_independent MonoidHom.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent
     (hind : CompleteLattice.Independent fun i => (ϕ i).range)
@@ -253,6 +295,12 @@ variable (hcomm)
 
 omit hfin
 
+/- warning: monoid_hom.independent_range_of_coprime_order -> MonoidHom.independent_range_of_coprime_order is a dubious translation:
+lean 3 declaration is
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> Type.{u3}} [_inst_2 : forall (i : ι), Group.{u3} (H i)] (ϕ : forall (i : ι), MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : H i) (y : H j), Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H i) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H i) G (Monoid.toMulOneClass.{u3} (H i) (DivInvMonoid.toMonoid.{u3} (H i) (Group.toDivInvMonoid.{u3} (H i) (_inst_2 i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ i) x) (coeFn.{max (succ u1) (succ u3), max (succ u3) (succ u1)} (MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (fun (_x : MonoidHom.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) => (H j) -> G) (MonoidHom.hasCoeToFun.{u3, u1} (H j) G (Monoid.toMulOneClass.{u3} (H j) (DivInvMonoid.toMonoid.{u3} (H j) (Group.toDivInvMonoid.{u3} (H j) (_inst_2 j)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (ϕ j) y))) -> (forall [_inst_3 : Finite.{succ u2} ι] [_inst_4 : forall (i : ι), Fintype.{u3} (H i)], (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (Nat.coprime (Fintype.card.{u3} (H i) (_inst_4 i)) (Fintype.card.{u3} (H j) (_inst_4 j)))) -> (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u3, u1} (H i) (_inst_2 i) G _inst_1 (ϕ i))))
+but is expected to have type
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u3}} [H : DecidableEq.{succ u3} ι] {_inst_2 : ι -> Type.{u2}} [ϕ : forall (i : ι), Group.{u2} (_inst_2 i)] (hcomm : forall (i : ι), MonoidHom.{u2, u1} (_inst_2 i) G (Monoid.toMulOneClass.{u2} (_inst_2 i) (DivInvMonoid.toMonoid.{u2} (_inst_2 i) (Group.toDivInvMonoid.{u2} (_inst_2 i) (ϕ i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))), (forall (i : ι) (j : ι), (Ne.{succ u3} ι i j) -> (forall (x : _inst_2 i) (y : _inst_2 j), Commute.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (MulOneClass.toMul.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (Monoid.toMulOneClass.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (DivInvMonoid.toMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : _inst_2 i) => G) x) (Group.toDivInvMonoid.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2398 : 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(Fintype.card.{u2} (_inst_2 j) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u3, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) (fun (i : ι) => MonoidHom.range.{u2, u1} (_inst_2 i) (ϕ i) G _inst_1 (hcomm i))))
+Case conversion may be inaccurate. Consider using '#align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
@@ -311,6 +359,12 @@ variable (hcomm : ∀ i j : ι, i ≠ j → ∀ x y : G, x ∈ H i → y ∈ H j
 
 include hcomm
 
+/- warning: subgroup.commute_subtype_of_commute -> Subgroup.commute_subtype_of_commute is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commuteₓ'. -/
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
     ∀ (x : H i) (y : H j), Commute ((H i).Subtype x) ((H j).Subtype y) :=
@@ -322,6 +376,12 @@ theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
 
 include hfin
 
+/- warning: subgroup.noncomm_pi_coprod -> Subgroup.noncommPiCoprod is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod Subgroup.noncommPiCoprodₓ'. -/
 /-- The canonical homomorphism from a family of subgroups where elements from different subgroups
 commute -/
 @[to_additive
@@ -335,20 +395,38 @@ variable {hcomm}
 
 include hdec
 
+/- warning: subgroup.noncomm_pi_coprod_mul_single -> Subgroup.noncommPiCoprod_mulSingle is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingleₓ'. -/
 @[simp, to_additive]
 theorem noncommPiCoprod_mulSingle (i : ι) (y : H i) :
     noncommPiCoprod hcomm (Pi.mulSingle i y) = y := by apply MonoidHom.noncommPiCoprod_mulSingle
 #align subgroup.noncomm_pi_coprod_mul_single Subgroup.noncommPiCoprod_mulSingle
-#align add_subgroup.noncomm_pi_coprod_single AddSubgroup.noncomm_pi_coprod_single
+#align add_subgroup.noncomm_pi_coprod_single AddSubgroup.noncommPiCoprod_single
 
 omit hdec
 
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+Case conversion may be inaccurate. Consider using '#align subgroup.noncomm_pi_coprod_range Subgroup.noncommPiCoprod_rangeₓ'. -/
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod hcomm).range = ⨆ i : ι, H i := by
   simp [noncomm_pi_coprod, MonoidHom.noncommPiCoprod_range]
 #align subgroup.noncomm_pi_coprod_range Subgroup.noncommPiCoprod_range
-#align add_subgroup.noncomm_pi_coprod_range AddSubgroup.noncomm_pi_coprod_range
-
+#align add_subgroup.noncomm_pi_coprod_range AddSubgroup.noncommPiCoprod_range
+
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+but is expected to have type
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [hfin : Fintype.{u2} ι] {H : ι -> (Subgroup.{u1} G _inst_1)} {hcomm : forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))}, (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) H) -> (Function.Injective.{max (succ u1) (succ u2), succ u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) 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ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (MonoidHom.monoidHomClass.{max u1 u2, u1} (forall (i : ι), Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) G (Pi.mulOneClass.{u2, u1} ι (fun (i : ι) => Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (H i))) (fun (i : ι) => Submonoid.toMulOneClass.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1))) (Subgroup.toSubmonoid.{u1} G _inst_1 (H i)))) (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) (Subgroup.noncommPiCoprod.{u1, u2} G _inst_1 ι hfin (fun (i : ι) => H i) hcomm)))
+Case conversion may be inaccurate. Consider using '#align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independentₓ'. -/
 @[to_additive]
 theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Independent H) :
     Function.Injective (noncommPiCoprod hcomm) :=
@@ -358,12 +436,18 @@ theorem injective_noncommPiCoprod_of_independent (hind : CompleteLattice.Indepen
   · intro i
     exact Subtype.coe_injective
 #align subgroup.injective_noncomm_pi_coprod_of_independent Subgroup.injective_noncommPiCoprod_of_independent
-#align add_subgroup.injective_noncomm_pi_coprod_of_independent AddSubgroup.injective_noncomm_pi_coprod_of_independent
+#align add_subgroup.injective_noncomm_pi_coprod_of_independent AddSubgroup.injective_noncommPiCoprod_of_independent
 
 variable (hcomm)
 
 omit hfin
 
+/- warning: subgroup.independent_of_coprime_order -> Subgroup.independent_of_coprime_order is a dubious translation:
+lean 3 declaration is
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} {H : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) x (H i)) -> (Membership.Mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.hasMem.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) y (H j)) -> (Commute.{u1} G (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall [_inst_2 : Finite.{succ u2} ι] [_inst_3 : forall (i : ι), Fintype.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i))], (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (Nat.coprime (Fintype.card.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H i)) (_inst_3 i)) (Fintype.card.{u1} (coeSort.{succ u1, succ (succ u1)} (Subgroup.{u1} G _inst_1) Type.{u1} (SetLike.hasCoeToSort.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.setLike.{u1} G _inst_1)) (H j)) (_inst_3 j)))) -> (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.completeLattice.{u1} G _inst_1) H))
+but is expected to have type
+  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] {ι : Type.{u2}} [H : DecidableEq.{succ u2} ι] {hcomm : ι -> (Subgroup.{u1} G _inst_1)}, (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (forall (x : G) (y : G), (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (hcomm i)) -> (Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) y (hcomm j)) -> (Commute.{u1} G (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) x y))) -> (forall [_inst_3 : Finite.{succ u2} ι] [hcoprime : forall (i : ι), Fintype.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (hcomm i)))], (forall (i : ι) (j : ι), (Ne.{succ u2} ι i j) -> (Nat.coprime (Fintype.card.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (hcomm i))) (hcoprime i)) (Fintype.card.{u1} (Subtype.{succ u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Subgroup.{u1} G _inst_1) (SetLike.instMembership.{u1, u1} (Subgroup.{u1} G _inst_1) G (Subgroup.instSetLikeSubgroup.{u1} G _inst_1)) x (hcomm j))) (hcoprime j)))) -> (CompleteLattice.Independent.{succ u2, u1} ι (Subgroup.{u1} G _inst_1) (Subgroup.instCompleteLatticeSubgroup.{u1} G _inst_1) hcomm))
+Case conversion may be inaccurate. Consider using '#align subgroup.independent_of_coprime_order Subgroup.independent_of_coprime_orderₓ'. -/
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :

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

Before this PR, the MonoidHom version of Pi.mulSingle was called MonoidHom.single for brevity; but this is confusing when contrasted with MulHom.single which is about Pi.single.

After this PR, the name is MonoidHom.mulSingle.

Also fix the name of Pi.single_div since it is about Pi.mulSingle (and we don't have the lemma that would be called Pi.single_div).

@@ -148,13 +148,13 @@ def noncommPiCoprodEquiv :
     where
   toFun ϕ := noncommPiCoprod ϕ.1 ϕ.2
   invFun f :=
-    ⟨fun i => f.comp (MonoidHom.single N i), fun i j hij x y =>
+    ⟨fun i => f.comp (MonoidHom.mulSingle N i), fun i j hij x y =>
       Commute.map (Pi.mulSingle_commute hij x y) f⟩
   left_inv ϕ := by
     ext
-    simp only [coe_comp, Function.comp_apply, single_apply, noncommPiCoprod_mulSingle]
+    simp only [coe_comp, Function.comp_apply, mulSingle_apply, noncommPiCoprod_mulSingle]
   right_inv f := pi_ext fun i x => by
-    simp only [noncommPiCoprod_mulSingle, coe_comp, Function.comp_apply, single_apply]
+    simp only [noncommPiCoprod_mulSingle, coe_comp, Function.comp_apply, mulSingle_apply]
 #align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquiv
 #align add_monoid_hom.noncomm_pi_coprod_equiv AddMonoidHom.noncommPiCoprodEquiv
 

Generalize MulActionHom so that it allows two different monoids acting, related by a morphism. This is inspired by the treatment of (semi)linear maps in mathlib, and allows to refactor them.

Let M, N, X, Y be types, with SMul M X and SMul N Y, and let φ : M → N be a map.

• MulActionHom φ X Y, the type of equivariant functions from X to Y, consists of functions f : X → Y such that f (m • x) = (φ m) • (f x) for all m : M and x : X.

Assume that we have Monoid M, Monoid N and that φ : M →* N. For A, B by types with AddMonoid A and AddMonoid B, endowed with DistribMulAction M A and DistribMulAction M B:

• DistribMulActionHom φ A B is the type of equivariant additive monoid homomorphisms from A to B.

Similarly, when R and S are types with Semiring R, Semiring S, MulSemiringAction M R and MulSemiringAction N S

• SMulSemiringHom φ R S is the type of equivariant ring homomorphisms from R to S.

The above types have corresponding classes:

• MulActionHomClass F φ X Y states that F is a type of bundled X → Y homs which are φ-equivariant
• DistribMulActionHomClass F φ A B states that F is a type of bundled A → B homs preserving the additive monoid structure and φ-equivariant
• SMulSemiringHomClass F φ R S states that F is a type of bundled R → S homs preserving the ring structure and φ-equivariant

Notation

We introduce the following notation to code equivariant maps (the subscript index ₑ is for equivariant) :

• X →ₑ[φ] Y is MulActionHom φ X Y.
• A →ₑ+[φ] B is DistribMulActionHom φ A B.
• R →ₑ+*[φ] S is MulSemiringActionHom φ R S.

When M = N and φ = MonoidHom.id M, we provide the backward compatible notation :

• X →[M] Y is MulActionHom ([@id](https://github.com/id) M) X Y
• A →+[M] B is DistribMulActionHom (MonoidHom.id M) A B
• R →+*[M] S is MulSemiringActionHom (MonoidHom.id M) R S

This more general definition is propagated all over mathlib, in particular to LinearMap.

The treatment of composition of equivariant maps is inspired by that of semilinear maps. We provide classes CompTriple and MonoidHom.CompTriple of “composable triples`, and various instances for them.

@@ -152,8 +152,9 @@ def noncommPiCoprodEquiv :
       Commute.map (Pi.mulSingle_commute hij x y) f⟩
   left_inv ϕ := by
     ext
-    simp
-  right_inv f := pi_ext fun i x => by simp
+    simp only [coe_comp, Function.comp_apply, single_apply, noncommPiCoprod_mulSingle]
+  right_inv f := pi_ext fun i x => by
+    simp only [noncommPiCoprod_mulSingle, coe_comp, Function.comp_apply, single_apply]
 #align monoid_hom.noncomm_pi_coprod_equiv MonoidHom.noncommPiCoprodEquiv
 #align add_monoid_hom.noncomm_pi_coprod_equiv AddMonoidHom.noncommPiCoprodEquiv
 

Sometimes, that line can be golfed into the next line. Inspired by a comment of @loefflerd; any decisions are my own.

@@ -213,7 +213,7 @@ theorem injective_noncommPiCoprod_of_independent
     (hinj : ∀ i, Function.Injective (ϕ i)) : Function.Injective (noncommPiCoprod ϕ hcomm) := by
   classical
     apply (MonoidHom.ker_eq_bot_iff _).mp
-    apply eq_bot_iff.mpr
+    rw [eq_bot_iff]
     intro f heq1
     have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
       Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ (fun _ _ _ _ h => hcomm h _ _)

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -90,7 +90,6 @@ variable {M : Type*} [Monoid M]
 -- We have a family of monoids
 -- The fintype assumption is not always used, but declared here, to keep things in order
 variable {ι : Type*} [DecidableEq ι] [Fintype ι]
-
 variable {N : ι → Type*} [∀ i, Monoid (N i)]
 
 -- And morphisms ϕ into G
@@ -181,13 +180,9 @@ end FamilyOfMonoids
 section FamilyOfGroups
 
 variable {G : Type*} [Group G]
-
 variable {ι : Type*} [hdec : DecidableEq ι] [hfin : Fintype ι]
-
 variable {H : ι → Type*} [∀ i, Group (H i)]
-
 variable (ϕ : ∀ i : ι, H i →* G)
-
 variable {hcomm : Pairwise fun i j : ι => ∀ (x : H i) (y : H j), Commute (ϕ i x) (ϕ j y)}
 
 -- We use `f` and `g` to denote elements of `Π (i : ι), H i`
@@ -275,7 +270,6 @@ namespace Subgroup
 
 -- We have a family of subgroups
 variable {G : Type*} [Group G]
-
 variable {ι : Type*} [hdec : DecidableEq ι] [hfin : Fintype ι] {H : ι → Subgroup G}
 
 -- Elements of `Π (i : ι), H i` are called `f` and `g` here

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -256,7 +256,7 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
   change f = 1
   rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
-  -- porting note: ouch, had to replace an ugly `convert`
+  -- Porting note: ouch, had to replace an ugly `convert`
   obtain ⟨c, hc⟩ := Nat.dvd_gcd hxp hxi
   use c
   rw [← hc]

Use letI := Classical.decEq ι to make Lean use the classical instance instead of the one in the variables.

@@ -89,7 +89,7 @@ variable {M : Type*} [Monoid M]
 
 -- We have a family of monoids
 -- The fintype assumption is not always used, but declared here, to keep things in order
-variable {ι : Type*} [hdec : DecidableEq ι] [Fintype ι]
+variable {ι : Type*} [DecidableEq ι] [Fintype ι]
 
 variable {N : ι → Type*} [∀ i, Monoid (N i)]
 
@@ -161,16 +161,16 @@ def noncommPiCoprodEquiv :
 @[to_additive]
 theorem noncommPiCoprod_mrange :
     MonoidHom.mrange (noncommPiCoprod ϕ hcomm) = ⨆ i : ι, MonoidHom.mrange (ϕ i) := by
-  classical
-    apply le_antisymm
-    · rintro x ⟨f, rfl⟩
-      refine Submonoid.noncommProd_mem _ _ _ (fun _ _ _ _ h => hcomm h _ _) (fun i _ => ?_)
-      apply Submonoid.mem_sSup_of_mem
-      · use i
-      simp
-    · refine' iSup_le _
-      rintro i x ⟨y, rfl⟩
-      exact ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
+  letI := Classical.decEq ι
+  apply le_antisymm
+  · rintro x ⟨f, rfl⟩
+    refine Submonoid.noncommProd_mem _ _ _ (fun _ _ _ _ h => hcomm h _ _) (fun i _ => ?_)
+    apply Submonoid.mem_sSup_of_mem
+    · use i
+    simp
+  · refine' iSup_le _
+    rintro i x ⟨y, rfl⟩
+    exact ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
 #align add_monoid_hom.noncomm_pi_coprod_mrange AddMonoidHom.noncommPiCoprod_mrange
 
@@ -198,17 +198,17 @@ namespace MonoidHom
 -- The subgroup version of `MonoidHom.noncommPiCoprod_mrange`
 @[to_additive]
 theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (ϕ i).range := by
-  classical
-    apply le_antisymm
-    · rintro x ⟨f, rfl⟩
-      refine Subgroup.noncommProd_mem _ (fun _ _ _ _ h => hcomm h _ _) ?_
-      intro i _hi
-      apply Subgroup.mem_sSup_of_mem
-      · use i
-      simp
-    · refine' iSup_le _
-      rintro i x ⟨y, rfl⟩
-      exact ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
+  letI := Classical.decEq ι
+  apply le_antisymm
+  · rintro x ⟨f, rfl⟩
+    refine Subgroup.noncommProd_mem _ (fun _ _ _ _ h => hcomm h _ _) ?_
+    intro i _hi
+    apply Subgroup.mem_sSup_of_mem
+    · use i
+    simp
+  · refine' iSup_le _
+    rintro i x ⟨y, rfl⟩
+    exact ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 
@@ -236,34 +236,34 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     (hcoprime : Pairwise fun i j => Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent fun i => (ϕ i).range := by
   cases nonempty_fintype ι
-  classical
-    rintro i
-    rw [disjoint_iff_inf_le]
-    rintro f ⟨hxi, hxp⟩
-    dsimp at hxi hxp
-    rw [iSup_subtype', ← noncommPiCoprod_range] at hxp
-    rotate_left
-    · intro _ _ hj
-      apply hcomm
-      exact hj ∘ Subtype.ext
-    cases' hxp with g hgf
-    cases' hxi with g' hg'f
-    have hxi : orderOf f ∣ Fintype.card (H i) := by
-      rw [← hg'f]
-      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
-    have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
-      rw [← hgf, ← Fintype.card_pi]
-      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
-    change f = 1
-    rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
-    -- porting note: ouch, had to replace an ugly `convert`
-    obtain ⟨c, hc⟩ := Nat.dvd_gcd hxp hxi
-    use c
-    rw [← hc]
-    symm
-    rw [← Nat.coprime_iff_gcd_eq_one, Nat.coprime_fintype_prod_left_iff, Subtype.forall]
-    intro j h
-    exact hcoprime h
+  letI := Classical.decEq ι
+  rintro i
+  rw [disjoint_iff_inf_le]
+  rintro f ⟨hxi, hxp⟩
+  dsimp at hxi hxp
+  rw [iSup_subtype', ← noncommPiCoprod_range] at hxp
+  rotate_left
+  · intro _ _ hj
+    apply hcomm
+    exact hj ∘ Subtype.ext
+  cases' hxp with g hgf
+  cases' hxi with g' hg'f
+  have hxi : orderOf f ∣ Fintype.card (H i) := by
+    rw [← hg'f]
+    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
+  have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
+    rw [← hgf, ← Fintype.card_pi]
+    exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
+  change f = 1
+  rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
+  -- porting note: ouch, had to replace an ugly `convert`
+  obtain ⟨c, hc⟩ := Nat.dvd_gcd hxp hxi
+  use c
+  rw [← hc]
+  symm
+  rw [← Nat.coprime_iff_gcd_eq_one, Nat.coprime_fintype_prod_left_iff, Subtype.forall]
+  intro j h
+  exact hcoprime h
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
 

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -170,7 +170,7 @@ theorem noncommPiCoprod_mrange :
       simp
     · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
-      refine' ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
+      exact ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
 #align add_monoid_hom.noncomm_pi_coprod_mrange AddMonoidHom.noncommPiCoprod_mrange
 
@@ -208,7 +208,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
       simp
     · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
-      refine' ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
+      exact ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
 #align add_monoid_hom.noncomm_pi_coprod_range AddMonoidHom.noncommPiCoprod_range
 

Of the 18 uses of singlePass, in 3 cases we can just use rw, in 4 cases it isn't needed at all.

In the other 11 cases we are always use it as simp (config := {singlePass := true}) only [X] (i.e. with just a single simp lemma), and that simp call would loop forever (usually failing with a maxRecDepth error, sometimes with heartbeats). I've left these as is.

There's also one case where there was a missing only.

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

@@ -130,7 +130,7 @@ theorem noncommPiCoprod_mulSingle (i : ι) (y : N i) :
     noncommPiCoprod ϕ hcomm (Pi.mulSingle i y) = ϕ i y := by
   change Finset.univ.noncommProd (fun j => ϕ j (Pi.mulSingle i y j)) (fun _ _ _ _ h => hcomm h _ _)
     = ϕ i y
-  simp (config := { singlePass := true }) only [← Finset.insert_erase (Finset.mem_univ i)]
+  rw [← Finset.insert_erase (Finset.mem_univ i)]
   rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ (Finset.not_mem_erase i _)]
   rw [Pi.mulSingle_eq_same]
   rw [Finset.noncommProd_eq_pow_card]

Performed with a regex search for ∀ (.) (.), \1 ≠ \2 →, and a few variants to catch implicit binders and explicit types.

I have deliberately avoided trying to make the analogous Set.Pairwise transformation (or any Pairwise (foo on bar) transformations) in this PR, to keep the diff small.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -188,7 +188,7 @@ variable {H : ι → Type*} [∀ i, Group (H i)]
 
 variable (ϕ : ∀ i : ι, H i →* G)
 
-variable {hcomm : ∀ i j : ι, i ≠ j → ∀ (x : H i) (y : H j), Commute (ϕ i x) (ϕ j y)}
+variable {hcomm : Pairwise fun i j : ι => ∀ (x : H i) (y : H j), Commute (ϕ i x) (ϕ j y)}
 
 -- We use `f` and `g` to denote elements of `Π (i : ι), H i`
 variable (f g : ∀ i : ι, H i)
@@ -201,7 +201,7 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
   classical
     apply le_antisymm
     · rintro x ⟨f, rfl⟩
-      refine Subgroup.noncommProd_mem _ (fun _ _ _ _ h => hcomm _ _ h _ _) ?_
+      refine Subgroup.noncommProd_mem _ (fun _ _ _ _ h => hcomm h _ _) ?_
       intro i _hi
       apply Subgroup.mem_sSup_of_mem
       · use i
@@ -221,7 +221,7 @@ theorem injective_noncommPiCoprod_of_independent
     apply eq_bot_iff.mpr
     intro f heq1
     have : ∀ i, i ∈ Finset.univ → ϕ i (f i) = 1 :=
-      Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ (fun _ _ _ _ h => hcomm _ _ h _ _)
+      Subgroup.eq_one_of_noncommProd_eq_one_of_independent _ _ (fun _ _ _ _ h => hcomm h _ _)
         _ hind (by simp) heq1
     ext i
     apply hinj
@@ -233,7 +233,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : Pairwise fun i j => Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent fun i => (ϕ i).range := by
   cases nonempty_fintype ι
   classical
@@ -262,8 +262,8 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     rw [← hc]
     symm
     rw [← Nat.coprime_iff_gcd_eq_one, Nat.coprime_fintype_prod_left_iff, Subtype.forall]
-    intro j
-    exact hcoprime _ _
+    intro j h
+    exact hcoprime h
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
 
@@ -284,13 +284,13 @@ variable (f g : ∀ i : ι, H i)
 section CommutingSubgroups
 
 -- We assume that the elements of different subgroups commute
-variable (hcomm : ∀ i j : ι, i ≠ j → ∀ x y : G, x ∈ H i → y ∈ H j → Commute x y)
+variable (hcomm : Pairwise fun i j : ι => ∀ x y : G, x ∈ H i → y ∈ H j → Commute x y)
 
 @[to_additive]
 theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
     ∀ (x : H i) (y : H j), Commute ((H i).subtype x) ((H j).subtype y) := by
   rintro ⟨x, hx⟩ ⟨y, hy⟩
-  exact hcomm i j hne x y hx hy
+  exact hcomm hne x y hx hy
 #align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commute
 #align add_subgroup.commute_subtype_of_commute AddSubgroup.addCommute_subtype_of_addCommute
 
@@ -331,7 +331,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : Pairwise fun i j => Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent H := by
   simpa using
     MonoidHom.independent_range_of_coprime_order (fun i => (H i).subtype)

Add coprime_xxx_prod_left_iff, coprime_xxx_prod_right_iff lemma for List, Multiset, Finset and Fintype. This is a PR separated from #8887.

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

@@ -261,11 +261,9 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     use c
     rw [← hc]
     symm
-    rw [← Nat.coprime_iff_gcd_eq_one]
-    apply Nat.coprime_prod_left
-    intro j _
-    apply hcoprime
-    exact j.2
+    rw [← Nat.coprime_iff_gcd_eq_one, Nat.coprime_fintype_prod_left_iff, Subtype.forall]
+    intro j
+    exact hcoprime _ _
 #align monoid_hom.independent_range_of_coprime_order MonoidHom.independent_range_of_coprime_order
 #align add_monoid_hom.independent_range_of_coprime_order AddMonoidHom.independent_range_of_coprime_order
 

This removes the need for many manual overrides, and corrects some bad names.

We have to make sure to leave function_commute and function_semiconjBy untouched.

@@ -294,7 +294,7 @@ theorem commute_subtype_of_commute (i j : ι) (hne : i ≠ j) :
   rintro ⟨x, hx⟩ ⟨y, hy⟩
   exact hcomm i j hne x y hx hy
 #align subgroup.commute_subtype_of_commute Subgroup.commute_subtype_of_commute
-#align add_subgroup.commute_subtype_of_commute AddSubgroup.commute_subtype_of_commute
+#align add_subgroup.commute_subtype_of_commute AddSubgroup.addCommute_subtype_of_addCommute
 
 /-- The canonical homomorphism from a family of subgroups where elements from different subgroups
 commute -/

The cardinality of a subgroup is greater than the order of any of its elements.

Rename

• order_eq_card_zpowers → Fintype.card_zpowers
• order_eq_card_zpowers' → Nat.card_zpowers (and turn it around to match Nat.card_subgroupPowers)
• Submonoid.powers_subset → Submonoid.powers_le
• orderOf_dvd_card_univ → orderOf_dvd_card
• orderOf_subgroup → Subgroup.orderOf
• Subgroup.nonempty → Subgroup.coe_nonempty

@@ -250,10 +250,10 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     cases' hxi with g' hg'f
     have hxi : orderOf f ∣ Fintype.card (H i) := by
       rw [← hg'f]
-      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
     have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
       rw [← hgf, ← Fintype.card_pi]
-      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
+      exact (orderOf_map_dvd _ _).trans orderOf_dvd_card
     change f = 1
     rw [← pow_one f, ← orderOf_dvd_iff_pow_eq_one]
     -- porting note: ouch, had to replace an ugly `convert`

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

@@ -233,7 +233,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent fun i => (ϕ i).range := by
   cases nonempty_fintype ι
   classical
@@ -333,7 +333,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent H := by
   simpa using
     MonoidHom.independent_range_of_coprime_order (fun i => (H i).subtype)

This reverts commit 6f8e8104. Unfortunately this bump was not linted correctly, as CI did not run runLinter Mathlib.

We can unrevert once that's fixed.

@@ -233,7 +233,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent fun i => (ϕ i).range := by
   cases nonempty_fintype ι
   classical
@@ -333,7 +333,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent H := by
   simpa using
     MonoidHom.independent_range_of_coprime_order (fun i => (H i).subtype)

Some changes have already been review and delegated in #6910 and #7148.

The diff that needs looking at is https://github.com/leanprover-community/mathlib4/pull/7174/commits/64d6d07ee18163627c8f517eb31455411921c5ac

The std bump PR was insta-merged already!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -233,7 +233,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent fun i => (ϕ i).range := by
   cases nonempty_fintype ι
   classical
@@ -333,7 +333,7 @@ variable (hcomm)
 
 @[to_additive]
 theorem independent_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
-    (hcoprime : ∀ i j, i ≠ j → Nat.coprime (Fintype.card (H i)) (Fintype.card (H j))) :
+    (hcoprime : ∀ i j, i ≠ j → Nat.Coprime (Fintype.card (H i)) (Fintype.card (H j))) :
     CompleteLattice.Independent H := by
   simpa using
     MonoidHom.independent_range_of_coprime_order (fun i => (H i).subtype)

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

This has nice performance benefits.

@@ -48,13 +48,13 @@ open BigOperators
 
 namespace Subgroup
 
-variable {G : Type _} [Group G]
+variable {G : Type*} [Group G]
 
 /-- `Finset.noncommProd` is “injective” in `f` if `f` maps into independent subgroups.  This
 generalizes (one direction of) `Subgroup.disjoint_iff_mul_eq_one`. -/
 @[to_additive "`Finset.noncommSum` is “injective” in `f` if `f` maps into independent subgroups.
 This generalizes (one direction of) `AddSubgroup.disjoint_iff_add_eq_zero`. "]
-theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι) (f : ι → G) (comm)
+theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type*} (s : Finset ι) (f : ι → G) (comm)
     (K : ι → Subgroup G) (hind : CompleteLattice.Independent K) (hmem : ∀ x ∈ s, f x ∈ K x)
     (heq1 : s.noncommProd f comm = 1) : ∀ i ∈ s, f i = 1 := by
   classical
@@ -85,13 +85,13 @@ end Subgroup
 
 section FamilyOfMonoids
 
-variable {M : Type _} [Monoid M]
+variable {M : Type*} [Monoid M]
 
 -- We have a family of monoids
 -- The fintype assumption is not always used, but declared here, to keep things in order
-variable {ι : Type _} [hdec : DecidableEq ι] [Fintype ι]
+variable {ι : Type*} [hdec : DecidableEq ι] [Fintype ι]
 
-variable {N : ι → Type _} [∀ i, Monoid (N i)]
+variable {N : ι → Type*} [∀ i, Monoid (N i)]
 
 -- And morphisms ϕ into G
 variable (ϕ : ∀ i : ι, N i →* M)
@@ -180,11 +180,11 @@ end FamilyOfMonoids
 
 section FamilyOfGroups
 
-variable {G : Type _} [Group G]
+variable {G : Type*} [Group G]
 
-variable {ι : Type _} [hdec : DecidableEq ι] [hfin : Fintype ι]
+variable {ι : Type*} [hdec : DecidableEq ι] [hfin : Fintype ι]
 
-variable {H : ι → Type _} [∀ i, Group (H i)]
+variable {H : ι → Type*} [∀ i, Group (H i)]
 
 variable (ϕ : ∀ i : ι, H i →* G)
 
@@ -276,9 +276,9 @@ end FamilyOfGroups
 namespace Subgroup
 
 -- We have a family of subgroups
-variable {G : Type _} [Group G]
+variable {G : Type*} [Group G]
 
-variable {ι : Type _} [hdec : DecidableEq ι] [hfin : Fintype ι] {H : ι → Subgroup G}
+variable {ι : Type*} [hdec : DecidableEq ι] [hfin : Fintype ι] {H : ι → Subgroup G}
 
 -- Elements of `Π (i : ι), H i` are called `f` and `g` here
 variable (f g : ∀ i : ι, H i)

Changes the way the term is elaborated so that typeclass inference is tolerated and so that instances are allowed to come from the goal without re-inferring them.

@@ -115,14 +115,11 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
     simp
   map_mul' f g := by
     classical
-      simp only
-      have := @Finset.noncommProd_mul_distrib _ _ _ Finset.univ (fun i => ϕ i (f i))
-        (fun i => ϕ i (g i)) ?_ ?_ ?_
-      · convert this
-        exact map_mul _ _ _
-      · exact fun i _ j _ hij => hcomm hij _ _
-      · exact fun i _ j _ hij => hcomm hij _ _
-      · exact fun i _ j _ hij => hcomm hij _ _
+    simp only
+    convert @Finset.noncommProd_mul_distrib _ _ _ _ (fun i => ϕ i (f i)) (fun i => ϕ i (g i)) _ _ _
+    · exact map_mul _ _ _
+    · rintro i - j - h
+      exact hcomm h _ _
 #align monoid_hom.noncomm_pi_coprod MonoidHom.noncommPiCoprod
 #align add_monoid_hom.noncomm_pi_coprod AddMonoidHom.noncommPiCoprod
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Joachim Breitner. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joachim Breitner
-
-! This file was ported from Lean 3 source module group_theory.noncomm_pi_coprod
-! leanprover-community/mathlib commit 6f9f36364eae3f42368b04858fd66d6d9ae730d8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.GroupTheory.OrderOfElement
 import Mathlib.Data.Finset.NoncommProd
@@ -14,6 +9,8 @@ import Mathlib.Data.Fintype.BigOperators
 import Mathlib.Data.Nat.GCD.BigOperators
 import Mathlib.Order.SupIndep
 
+#align_import group_theory.noncomm_pi_coprod from "leanprover-community/mathlib"@"6f9f36364eae3f42368b04858fd66d6d9ae730d8"
+
 /-!
 # Canonical homomorphism from a finite family of monoids
 

Part 2 of #5001

@@ -281,7 +281,7 @@ end FamilyOfGroups
 
 namespace Subgroup
 
--- We have an family of subgroups
+-- We have a family of subgroups
 variable {G : Type _} [Group G]
 
 variable {ι : Type _} [hdec : DecidableEq ι] [hfin : Fintype ι] {H : ι → Subgroup G}

As discussed on Zulip

Renames

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

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

@@ -69,13 +69,13 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
       have hmem_bsupr : s.noncommProd f hcomm ∈ ⨆ i ∈ (s : Set ι), K i := by
         refine' Subgroup.noncommProd_mem _ _ _
         intro x hx
-        have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_supᵢ₂ (f := fun i _ => K i) x hx
+        have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_iSup₂ (f := fun i _ => K i) x hx
         exact this (hmem.2 x hx)
       intro heq1
       rw [Finset.noncommProd_insert_of_not_mem _ _ _ _ hnmem] at heq1
       have hnmem' : i ∉ (s : Set ι) := by simpa
       obtain ⟨heq1i : f i = 1, heq1S : s.noncommProd f _ = 1⟩ :=
-        Subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_bsupᵢ hnmem') hmem.1 hmem_bsupr heq1
+        Subgroup.disjoint_iff_mul_eq_one.mp (hind.disjoint_biSup hnmem') hmem.1 hmem_bsupr heq1
       intro i h
       simp only [Finset.mem_insert] at h
       rcases h with (rfl | h)
@@ -171,10 +171,10 @@ theorem noncommPiCoprod_mrange :
     apply le_antisymm
     · rintro x ⟨f, rfl⟩
       refine Submonoid.noncommProd_mem _ _ _ (fun _ _ _ _ h => hcomm h _ _) (fun i _ => ?_)
-      apply Submonoid.mem_supₛ_of_mem
+      apply Submonoid.mem_sSup_of_mem
       · use i
       simp
-    · refine' supᵢ_le _
+    · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
       refine' ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_mrange MonoidHom.noncommPiCoprod_mrange
@@ -209,10 +209,10 @@ theorem noncommPiCoprod_range : (noncommPiCoprod ϕ hcomm).range = ⨆ i : ι, (
     · rintro x ⟨f, rfl⟩
       refine Subgroup.noncommProd_mem _ (fun _ _ _ _ h => hcomm _ _ h _ _) ?_
       intro i _hi
-      apply Subgroup.mem_supₛ_of_mem
+      apply Subgroup.mem_sSup_of_mem
       · use i
       simp
-    · refine' supᵢ_le _
+    · refine' iSup_le _
       rintro i x ⟨y, rfl⟩
       refine' ⟨Pi.mulSingle i y, noncommPiCoprod_mulSingle _ _ _⟩
 #align monoid_hom.noncomm_pi_coprod_range MonoidHom.noncommPiCoprod_range
@@ -247,7 +247,7 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
     rw [disjoint_iff_inf_le]
     rintro f ⟨hxi, hxp⟩
     dsimp at hxi hxp
-    rw [supᵢ_subtype', ← noncommPiCoprod_range] at hxp
+    rw [iSup_subtype', ← noncommPiCoprod_range] at hxp
     rotate_left
     · intro _ _ hj
       apply hcomm

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

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

@@ -66,8 +66,7 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
     · simp
     · have hcomm := comm.mono (Finset.coe_subset.2 <| Finset.subset_insert _ _)
       simp only [Finset.forall_mem_insert] at hmem
-      have hmem_bsupr : s.noncommProd f hcomm ∈ ⨆ i ∈ (s : Set ι), K i :=
-        by
+      have hmem_bsupr : s.noncommProd f hcomm ∈ ⨆ i ∈ (s : Set ι), K i := by
         refine' Subgroup.noncommProd_mem _ _ _
         intro x hx
         have : K x ≤ ⨆ i ∈ (s : Set ι), K i := le_supᵢ₂ (f := fun i _ => K i) x hx
@@ -255,12 +254,10 @@ theorem independent_range_of_coprime_order [Finite ι] [∀ i, Fintype (H i)]
       exact hj ∘ Subtype.ext
     cases' hxp with g hgf
     cases' hxi with g' hg'f
-    have hxi : orderOf f ∣ Fintype.card (H i) :=
-      by
+    have hxi : orderOf f ∣ Fintype.card (H i) := by
       rw [← hg'f]
       exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
-    have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) :=
-      by
+    have hxp : orderOf f ∣ ∏ j : { j // j ≠ i }, Fintype.card (H j) := by
       rw [← hgf, ← Fintype.card_pi]
       exact (orderOf_map_dvd _ _).trans orderOf_dvd_card_univ
     change f = 1

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -82,7 +82,6 @@ theorem eq_one_of_noncommProd_eq_one_of_independent {ι : Type _} (s : Finset ι
       rcases h with (rfl | h)
       · exact heq1i
       · refine' ih hcomm hmem.2 heq1S _ h
-
 #align subgroup.eq_one_of_noncomm_prod_eq_one_of_independent Subgroup.eq_one_of_noncommProd_eq_one_of_independent
 #align add_subgroup.eq_zero_of_noncomm_sum_eq_zero_of_independent AddSubgroup.eq_zero_of_noncommSum_eq_zero_of_independent
 

This introduces a tactic congr! that is an analogue to mathlib 3's congr'. It is a more insistent version of congr that makes use of more congruence lemmas (including user congruence lemmas), propext, funext, and Subsingleton instances. It also has a feature to lift reflexive relations to equalities. Along with funext, the tactic does intros, allowing congr! to get access to function bodies; the introduced variables can be named using rename_i if needed.

This also modifies convert to use congr! rather than congr, which makes it work more like the mathlib3 version of the tactic.

@@ -124,7 +124,6 @@ def noncommPiCoprod : (∀ i : ι, N i) →* M
       have := @Finset.noncommProd_mul_distrib _ _ _ Finset.univ (fun i => ϕ i (f i))
         (fun i => ϕ i (g i)) ?_ ?_ ?_
       · convert this
-        ext
         exact map_mul _ _ _
       · exact fun i _ j _ hij => hcomm hij _ _
       · exact fun i _ j _ hij => hcomm hij _ _