ring_theory.finite_presentation ⟷ Mathlib.RingTheory.FinitePresentation

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

@@ -272,20 +272,20 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       all_goals dsimp [g]; rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom]
       · rw [MvPolynomial.aeval_map_algebraMap, ← aeval_unique]
         have := Ideal.subset_span hx
-        rwa [hs] at this 
+        rwa [hs] at this
       ·
         rw [map_sub, MvPolynomial.aeval_map_algebraMap, ← aeval_unique, aeval_C, ht',
           Subtype.coe_mk, sub_self]
     apply leI.antisymm
     intro x hx
-    rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx 
+    rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx
     let s₀ := _; change x ∈ Ideal.span s₀
     have :
       x ∈
         (map (algebraMap R A) : _ →+* AX).srange.toAddSubmonoid ⊔ (Ideal.span s₀).toAddSubmonoid :=
       by
       have : x ∈ (⊤ : Subalgebra R AX) := trivial
-      rw [← ht''] at this 
+      rw [← ht''] at this
       apply adjoin_induction this
       · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
         · rw [algebra_map_eq, ← sub_add_cancel (C x) (map (algebraMap R A) (t' ⟨x, hx⟩)), add_comm]
@@ -307,9 +307,9 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
         · refine' add_mem (Ideal.mul_mem_left _ _ hq₂) (Ideal.mul_mem_right _ _ hq₁)
     obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
     rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
-      add_zero] at hx 
+      add_zero] at hx
     suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
-      refine' add_mem _ hq; rw [hs] at this ; exact this hx
+      refine' add_mem _ hq; rw [hs] at this; exact this hx
     rw [Ideal.span_le]
     intro x hx
     apply Ideal.subset_span
@@ -374,7 +374,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
   obtain ⟨_, ⟨x, rfl⟩, y, hy, rfl⟩ := add_submonoid.mem_sup.mp this
   refine' add_mem _ hy
   simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
-    show f y = 0 from leI hy, add_zero, hh'] at hx 
+    show f y = 0 from leI hy, add_zero, hh'] at hx
   suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
   rw [Ideal.span_le]
   intro x hx

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

@@ -207,6 +207,18 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι :
   by
   rw [iff_quotient_mv_polynomial'] at hfp ⊢
   classical
+  obtain ⟨ι', _, f, hf_surj, hf_ker⟩ := hfp
+  skip
+  let g := (MvPolynomial.mapAlgHom f).comp (MvPolynomial.sumAlgEquiv R ι ι').toAlgHom
+  cases nonempty_fintype (Sum ι ι')
+  refine'
+    ⟨Sum ι ι', by infer_instance, g,
+      (MvPolynomial.map_surjective f.to_ring_hom hf_surj).comp (AlgEquiv.surjective _),
+      Ideal.fg_ker_comp _ _ _ _ (AlgEquiv.surjective _)⟩
+  · convert Submodule.fg_bot
+    exact RingHom.ker_coe_equiv (MvPolynomial.sumAlgEquiv R ι ι').toRingEquiv
+  · rw [AlgHom.toRingHom_eq_coe, MvPolynomial.mapAlgHom_coe_ringHom, MvPolynomial.ker_map]
+    exact hf_ker.map MvPolynomial.C
 #align algebra.finite_presentation.mv_polynomial_of_finite_presentation Algebra.FinitePresentation.mvPolynomial_of_finitePresentation
 -/
 
@@ -227,7 +239,82 @@ open MvPolynomial
 -- We follow the proof of https://stacks.math.columbia.edu/tag/0561
 -- TODO: extract out helper lemmas and tidy proof.
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
-    (hRB : FinitePresentation R B) [hRA : FiniteType R A] : FinitePresentation A B := by classical
+    (hRB : FinitePresentation R B) [hRA : FiniteType R A] : FinitePresentation A B := by
+  classical
+  obtain ⟨n, f, hf, s, hs⟩ := hRB
+  let RX := MvPolynomial (Fin n) R
+  let AX := MvPolynomial (Fin n) A
+  refine' ⟨n, MvPolynomial.aeval (f ∘ X), _, _⟩
+  · rw [← Algebra.range_top_iff_surjective, ← Algebra.adjoin_range_eq_range_aeval, Set.range_comp,
+      _root_.eq_top_iff, ← @adjoin_adjoin_of_tower R A B, adjoin_image, adjoin_range_X,
+      Algebra.map_top, (Algebra.range_top_iff_surjective _).mpr hf]
+    exact subset_adjoin
+  · obtain ⟨t, ht⟩ := hRA.out
+    have := fun i : t => hf (algebraMap A B i)
+    choose t' ht'
+    have ht'' : Algebra.adjoin R (algebraMap A AX '' t ∪ Set.range (X : _ → AX)) = ⊤ :=
+      by
+      rw [adjoin_union_eq_adjoin_adjoin, ← Subalgebra.restrictScalars_top R]
+      congr 1
+      swap; · exact Subalgebra.isScalarTower_mid _
+      rw [adjoin_algebra_map, ht]
+      apply Subalgebra.restrictScalars_injective R
+      rw [← adjoin_restrict_scalars, adjoin_range_X, Subalgebra.restrictScalars_top,
+        Subalgebra.restrictScalars_top]
+    let g : t → AX := fun x => C (x : A) - map (algebraMap R A) (t' x)
+    refine' ⟨s.image (map (algebraMap R A)) ∪ t.attach.image g, _⟩
+    rw [Finset.coe_union, Finset.coe_image, Finset.coe_image, Finset.attach_eq_univ,
+      Finset.coe_univ, Set.image_univ]
+    let s₀ := _; let I := _; change Ideal.span s₀ = I
+    have leI : Ideal.span s₀ ≤ I := by
+      rw [Ideal.span_le]
+      rintro _ (⟨x, hx, rfl⟩ | ⟨⟨x, hx⟩, rfl⟩)
+      all_goals dsimp [g]; rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom]
+      · rw [MvPolynomial.aeval_map_algebraMap, ← aeval_unique]
+        have := Ideal.subset_span hx
+        rwa [hs] at this 
+      ·
+        rw [map_sub, MvPolynomial.aeval_map_algebraMap, ← aeval_unique, aeval_C, ht',
+          Subtype.coe_mk, sub_self]
+    apply leI.antisymm
+    intro x hx
+    rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx 
+    let s₀ := _; change x ∈ Ideal.span s₀
+    have :
+      x ∈
+        (map (algebraMap R A) : _ →+* AX).srange.toAddSubmonoid ⊔ (Ideal.span s₀).toAddSubmonoid :=
+      by
+      have : x ∈ (⊤ : Subalgebra R AX) := trivial
+      rw [← ht''] at this 
+      apply adjoin_induction this
+      · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
+        · rw [algebra_map_eq, ← sub_add_cancel (C x) (map (algebraMap R A) (t' ⟨x, hx⟩)), add_comm]
+          apply AddSubmonoid.add_mem_sup
+          · exact Set.mem_range_self _
+          · apply Ideal.subset_span
+            apply Set.mem_union_right
+            exact Set.mem_range_self ⟨x, hx⟩
+        · apply AddSubmonoid.mem_sup_left
+          exact ⟨X i, map_X _ _⟩
+      · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, map_C _ _⟩
+      · intro _ _ h₁ h₂; exact add_mem h₁ h₂
+      · intro x₁ x₂ h₁ h₂
+        obtain ⟨_, ⟨p₁, rfl⟩, q₁, hq₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
+        obtain ⟨_, ⟨p₂, rfl⟩, q₂, hq₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
+        rw [add_mul, mul_add, add_assoc, ← map_mul]
+        apply AddSubmonoid.add_mem_sup
+        · exact Set.mem_range_self _
+        · refine' add_mem (Ideal.mul_mem_left _ _ hq₂) (Ideal.mul_mem_right _ _ hq₁)
+    obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
+    rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
+      add_zero] at hx 
+    suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
+      refine' add_mem _ hq; rw [hs] at this ; exact this hx
+    rw [Ideal.span_le]
+    intro x hx
+    apply Ideal.subset_span
+    apply Set.mem_union_left
+    exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
 -/
 
@@ -235,7 +322,65 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
 theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
-    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by classical
+    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
+  classical
+  obtain ⟨m, f', hf', s, hs⟩ := hfp
+  let RXn := MvPolynomial (Fin n) R
+  let RXm := MvPolynomial (Fin m) R
+  have := fun i : Fin n => hf' (f <| X i)
+  choose g hg
+  have := fun i : Fin m => hf (f' <| X i)
+  choose h hh
+  let aeval_h : RXm →ₐ[R] RXn := aeval h
+  let g' : Fin n → RXn := fun i => X i - aeval_h (g i)
+  refine' ⟨finset.univ.image g' ∪ s.image aeval_h, _⟩
+  simp only [Finset.coe_image, Finset.coe_union, Finset.coe_univ, Set.image_univ]
+  have hh' : ∀ x, f (aeval_h x) = f' x := by
+    intro x; rw [← f.coe_to_ring_hom, map_aeval]; simp_rw [AlgHom.coe_toRingHom, hh]
+    rw [AlgHom.comp_algebraMap, ← aeval_eq_eval₂_hom, ← aeval_unique]
+  let s' := Set.range g' ∪ aeval_h '' s
+  have leI : Ideal.span s' ≤ f.to_ring_hom.ker :=
+    by
+    rw [Ideal.span_le]
+    rintro _ (⟨i, rfl⟩ | ⟨x, hx, rfl⟩)
+    · change f (g' i) = 0; rw [map_sub, ← hg, hh', sub_self]
+    · change f (aeval_h x) = 0
+      rw [hh']
+      change x ∈ f'.to_ring_hom.ker
+      rw [← hs]
+      exact Ideal.subset_span hx
+  apply leI.antisymm
+  intro x hx
+  have : x ∈ aeval_h.range.to_add_submonoid ⊔ (Ideal.span s').toAddSubmonoid :=
+    by
+    have : x ∈ adjoin R (Set.range X : Set RXn) := by rw [adjoin_range_X]; trivial
+    apply adjoin_induction this
+    · rintro _ ⟨i, rfl⟩
+      rw [← sub_add_cancel (X i) (aeval h (g i)), add_comm]
+      apply AddSubmonoid.add_mem_sup
+      · exact Set.mem_range_self _
+      · apply Submodule.subset_span
+        apply Set.mem_union_left
+        exact Set.mem_range_self _
+    · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, aeval_C _ _⟩
+    · intro _ _ h₁ h₂; exact add_mem h₁ h₂
+    · intro p₁ p₂ h₁ h₂
+      obtain ⟨_, ⟨x₁, rfl⟩, y₁, hy₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
+      obtain ⟨_, ⟨x₂, rfl⟩, y₂, hy₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
+      rw [mul_add, add_mul, add_assoc, ← map_mul]
+      apply AddSubmonoid.add_mem_sup
+      · exact Set.mem_range_self _
+      · exact add_mem (Ideal.mul_mem_right _ _ hy₁) (Ideal.mul_mem_left _ _ hy₂)
+  obtain ⟨_, ⟨x, rfl⟩, y, hy, rfl⟩ := add_submonoid.mem_sup.mp this
+  refine' add_mem _ hy
+  simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
+    show f y = 0 from leI hy, add_zero, hh'] at hx 
+  suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
+  rw [Ideal.span_le]
+  intro x hx
+  apply Submodule.subset_span
+  apply Set.mem_union_right
+  exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
 -/
 

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

@@ -207,18 +207,6 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι :
   by
   rw [iff_quotient_mv_polynomial'] at hfp ⊢
   classical
-  obtain ⟨ι', _, f, hf_surj, hf_ker⟩ := hfp
-  skip
-  let g := (MvPolynomial.mapAlgHom f).comp (MvPolynomial.sumAlgEquiv R ι ι').toAlgHom
-  cases nonempty_fintype (Sum ι ι')
-  refine'
-    ⟨Sum ι ι', by infer_instance, g,
-      (MvPolynomial.map_surjective f.to_ring_hom hf_surj).comp (AlgEquiv.surjective _),
-      Ideal.fg_ker_comp _ _ _ _ (AlgEquiv.surjective _)⟩
-  · convert Submodule.fg_bot
-    exact RingHom.ker_coe_equiv (MvPolynomial.sumAlgEquiv R ι ι').toRingEquiv
-  · rw [AlgHom.toRingHom_eq_coe, MvPolynomial.mapAlgHom_coe_ringHom, MvPolynomial.ker_map]
-    exact hf_ker.map MvPolynomial.C
 #align algebra.finite_presentation.mv_polynomial_of_finite_presentation Algebra.FinitePresentation.mvPolynomial_of_finitePresentation
 -/
 
@@ -239,82 +227,7 @@ open MvPolynomial
 -- We follow the proof of https://stacks.math.columbia.edu/tag/0561
 -- TODO: extract out helper lemmas and tidy proof.
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
-    (hRB : FinitePresentation R B) [hRA : FiniteType R A] : FinitePresentation A B := by
-  classical
-  obtain ⟨n, f, hf, s, hs⟩ := hRB
-  let RX := MvPolynomial (Fin n) R
-  let AX := MvPolynomial (Fin n) A
-  refine' ⟨n, MvPolynomial.aeval (f ∘ X), _, _⟩
-  · rw [← Algebra.range_top_iff_surjective, ← Algebra.adjoin_range_eq_range_aeval, Set.range_comp,
-      _root_.eq_top_iff, ← @adjoin_adjoin_of_tower R A B, adjoin_image, adjoin_range_X,
-      Algebra.map_top, (Algebra.range_top_iff_surjective _).mpr hf]
-    exact subset_adjoin
-  · obtain ⟨t, ht⟩ := hRA.out
-    have := fun i : t => hf (algebraMap A B i)
-    choose t' ht'
-    have ht'' : Algebra.adjoin R (algebraMap A AX '' t ∪ Set.range (X : _ → AX)) = ⊤ :=
-      by
-      rw [adjoin_union_eq_adjoin_adjoin, ← Subalgebra.restrictScalars_top R]
-      congr 1
-      swap; · exact Subalgebra.isScalarTower_mid _
-      rw [adjoin_algebra_map, ht]
-      apply Subalgebra.restrictScalars_injective R
-      rw [← adjoin_restrict_scalars, adjoin_range_X, Subalgebra.restrictScalars_top,
-        Subalgebra.restrictScalars_top]
-    let g : t → AX := fun x => C (x : A) - map (algebraMap R A) (t' x)
-    refine' ⟨s.image (map (algebraMap R A)) ∪ t.attach.image g, _⟩
-    rw [Finset.coe_union, Finset.coe_image, Finset.coe_image, Finset.attach_eq_univ,
-      Finset.coe_univ, Set.image_univ]
-    let s₀ := _; let I := _; change Ideal.span s₀ = I
-    have leI : Ideal.span s₀ ≤ I := by
-      rw [Ideal.span_le]
-      rintro _ (⟨x, hx, rfl⟩ | ⟨⟨x, hx⟩, rfl⟩)
-      all_goals dsimp [g]; rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom]
-      · rw [MvPolynomial.aeval_map_algebraMap, ← aeval_unique]
-        have := Ideal.subset_span hx
-        rwa [hs] at this 
-      ·
-        rw [map_sub, MvPolynomial.aeval_map_algebraMap, ← aeval_unique, aeval_C, ht',
-          Subtype.coe_mk, sub_self]
-    apply leI.antisymm
-    intro x hx
-    rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx 
-    let s₀ := _; change x ∈ Ideal.span s₀
-    have :
-      x ∈
-        (map (algebraMap R A) : _ →+* AX).srange.toAddSubmonoid ⊔ (Ideal.span s₀).toAddSubmonoid :=
-      by
-      have : x ∈ (⊤ : Subalgebra R AX) := trivial
-      rw [← ht''] at this 
-      apply adjoin_induction this
-      · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
-        · rw [algebra_map_eq, ← sub_add_cancel (C x) (map (algebraMap R A) (t' ⟨x, hx⟩)), add_comm]
-          apply AddSubmonoid.add_mem_sup
-          · exact Set.mem_range_self _
-          · apply Ideal.subset_span
-            apply Set.mem_union_right
-            exact Set.mem_range_self ⟨x, hx⟩
-        · apply AddSubmonoid.mem_sup_left
-          exact ⟨X i, map_X _ _⟩
-      · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, map_C _ _⟩
-      · intro _ _ h₁ h₂; exact add_mem h₁ h₂
-      · intro x₁ x₂ h₁ h₂
-        obtain ⟨_, ⟨p₁, rfl⟩, q₁, hq₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
-        obtain ⟨_, ⟨p₂, rfl⟩, q₂, hq₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
-        rw [add_mul, mul_add, add_assoc, ← map_mul]
-        apply AddSubmonoid.add_mem_sup
-        · exact Set.mem_range_self _
-        · refine' add_mem (Ideal.mul_mem_left _ _ hq₂) (Ideal.mul_mem_right _ _ hq₁)
-    obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
-    rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
-      add_zero] at hx 
-    suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
-      refine' add_mem _ hq; rw [hs] at this ; exact this hx
-    rw [Ideal.span_le]
-    intro x hx
-    apply Ideal.subset_span
-    apply Set.mem_union_left
-    exact Set.mem_image_of_mem _ hx
+    (hRB : FinitePresentation R B) [hRA : FiniteType R A] : FinitePresentation A B := by classical
 #align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
 -/
 
@@ -322,65 +235,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
 theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
-    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
-  classical
-  obtain ⟨m, f', hf', s, hs⟩ := hfp
-  let RXn := MvPolynomial (Fin n) R
-  let RXm := MvPolynomial (Fin m) R
-  have := fun i : Fin n => hf' (f <| X i)
-  choose g hg
-  have := fun i : Fin m => hf (f' <| X i)
-  choose h hh
-  let aeval_h : RXm →ₐ[R] RXn := aeval h
-  let g' : Fin n → RXn := fun i => X i - aeval_h (g i)
-  refine' ⟨finset.univ.image g' ∪ s.image aeval_h, _⟩
-  simp only [Finset.coe_image, Finset.coe_union, Finset.coe_univ, Set.image_univ]
-  have hh' : ∀ x, f (aeval_h x) = f' x := by
-    intro x; rw [← f.coe_to_ring_hom, map_aeval]; simp_rw [AlgHom.coe_toRingHom, hh]
-    rw [AlgHom.comp_algebraMap, ← aeval_eq_eval₂_hom, ← aeval_unique]
-  let s' := Set.range g' ∪ aeval_h '' s
-  have leI : Ideal.span s' ≤ f.to_ring_hom.ker :=
-    by
-    rw [Ideal.span_le]
-    rintro _ (⟨i, rfl⟩ | ⟨x, hx, rfl⟩)
-    · change f (g' i) = 0; rw [map_sub, ← hg, hh', sub_self]
-    · change f (aeval_h x) = 0
-      rw [hh']
-      change x ∈ f'.to_ring_hom.ker
-      rw [← hs]
-      exact Ideal.subset_span hx
-  apply leI.antisymm
-  intro x hx
-  have : x ∈ aeval_h.range.to_add_submonoid ⊔ (Ideal.span s').toAddSubmonoid :=
-    by
-    have : x ∈ adjoin R (Set.range X : Set RXn) := by rw [adjoin_range_X]; trivial
-    apply adjoin_induction this
-    · rintro _ ⟨i, rfl⟩
-      rw [← sub_add_cancel (X i) (aeval h (g i)), add_comm]
-      apply AddSubmonoid.add_mem_sup
-      · exact Set.mem_range_self _
-      · apply Submodule.subset_span
-        apply Set.mem_union_left
-        exact Set.mem_range_self _
-    · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, aeval_C _ _⟩
-    · intro _ _ h₁ h₂; exact add_mem h₁ h₂
-    · intro p₁ p₂ h₁ h₂
-      obtain ⟨_, ⟨x₁, rfl⟩, y₁, hy₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
-      obtain ⟨_, ⟨x₂, rfl⟩, y₂, hy₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
-      rw [mul_add, add_mul, add_assoc, ← map_mul]
-      apply AddSubmonoid.add_mem_sup
-      · exact Set.mem_range_self _
-      · exact add_mem (Ideal.mul_mem_right _ _ hy₁) (Ideal.mul_mem_left _ _ hy₂)
-  obtain ⟨_, ⟨x, rfl⟩, y, hy, rfl⟩ := add_submonoid.mem_sup.mp this
-  refine' add_mem _ hy
-  simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
-    show f y = 0 from leI hy, add_zero, hh'] at hx 
-  suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
-  rw [Ideal.span_le]
-  intro x hx
-  apply Submodule.subset_span
-  apply Set.mem_union_right
-  exact Set.mem_image_of_mem _ hx
+    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by classical
 #align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
 -/
 

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

@@ -3,9 +3,9 @@ Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.RingTheory.FiniteType
-import Mathbin.RingTheory.MvPolynomial.Tower
-import Mathbin.RingTheory.Ideal.QuotientOperations
+import RingTheory.FiniteType
+import RingTheory.MvPolynomial.Tower
+import RingTheory.Ideal.QuotientOperations
 
 #align_import ring_theory.finite_presentation from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.finite_presentation
-! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.FiniteType
 import Mathbin.RingTheory.MvPolynomial.Tower
 import Mathbin.RingTheory.Ideal.QuotientOperations
 
+#align_import ring_theory.finite_presentation from "leanprover-community/mathlib"@"33c67ae661dd8988516ff7f247b0be3018cdd952"
+
 /-!
 # Finiteness conditions in commutative algebra
 

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

@@ -60,6 +60,7 @@ namespace FiniteType
 
 variable {R A B}
 
+#print Algebra.FiniteType.of_finitePresentation /-
 /-- A finitely presented algebra is of finite type. -/
 theorem of_finitePresentation : FinitePresentation R A → FiniteType R A :=
   by
@@ -67,6 +68,7 @@ theorem of_finitePresentation : FinitePresentation R A → FiniteType R A :=
   apply finite_type.iff_quotient_mv_polynomial''.2
   exact ⟨n, f, hf.1⟩
 #align algebra.finite_type.of_finite_presentation Algebra.FiniteType.of_finitePresentation
+-/
 
 end FiniteType
 
@@ -74,6 +76,7 @@ namespace FinitePresentation
 
 variable {R A B}
 
+#print Algebra.FinitePresentation.of_finiteType /-
 /-- An algebra over a Noetherian ring is finitely generated if and only if it is finitely
 presented. -/
 theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentation R A :=
@@ -85,6 +88,7 @@ theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentati
   replace hnoet := (isNoetherianRing_iff.1 hnoet).noetherian
   exact hnoet f.to_ring_hom.ker
 #align algebra.finite_presentation.of_finite_type Algebra.FinitePresentation.of_finiteType
+-/
 
 #print Algebra.FinitePresentation.equiv /-
 /-- If `e : A ≃ₐ[R] B` and `A` is finitely presented, then so is `B`. -/
@@ -149,12 +153,14 @@ protected theorem quotient {I : Ideal A} (h : I.FG) (hfp : FinitePresentation R
 #align algebra.finite_presentation.quotient Algebra.FinitePresentation.quotient
 -/
 
+#print Algebra.FinitePresentation.of_surjective /-
 /-- If `f : A →ₐ[R] B` is surjective with finitely generated kernel and `A` is finitely presented,
 then so is `B`. -/
 theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f.toRingHom.ker.FG)
     (hfp : FinitePresentation R A) : FinitePresentation R B :=
   equiv (hfp.Quotient hker) (Ideal.quotientKerAlgEquivOfSurjective hf)
 #align algebra.finite_presentation.of_surjective Algebra.FinitePresentation.of_surjective
+-/
 
 #print Algebra.FinitePresentation.iff /-
 theorem iff :
@@ -169,6 +175,7 @@ theorem iff :
 #align algebra.finite_presentation.iff Algebra.FinitePresentation.iff
 -/
 
+#print Algebra.FinitePresentation.iff_quotient_mvPolynomial' /-
 /-- An algebra is finitely presented if and only if it is a quotient of a polynomial ring whose
 variables are indexed by a fintype by a finitely generated ideal. -/
 theorem iff_quotient_mvPolynomial' :
@@ -193,6 +200,7 @@ theorem iff_quotient_mvPolynomial' :
     convert Submodule.fg_bot
     exact RingHom.ker_coe_equiv equiv.symm.to_ring_equiv
 #align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'
+-/
 
 #print Algebra.FinitePresentation.mvPolynomial_of_finitePresentation /-
 /-- If `A` is a finitely presented `R`-algebra, then `mv_polynomial (fin n) A` is finitely presented
@@ -230,6 +238,7 @@ theorem trans [Algebra A B] [IsScalarTower R A B] (hfpA : FinitePresentation R A
 
 open MvPolynomial
 
+#print Algebra.FinitePresentation.of_restrict_scalars_finitePresentation /-
 -- We follow the proof of https://stacks.math.columbia.edu/tag/0561
 -- TODO: extract out helper lemmas and tidy proof.
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
@@ -310,7 +319,9 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
     apply Set.mem_union_left
     exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
+-/
 
+#print Algebra.FinitePresentation.ker_fg_of_mvPolynomial /-
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
 theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
@@ -374,7 +385,9 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
   apply Set.mem_union_right
   exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
+-/
 
+#print Algebra.FinitePresentation.ker_fG_of_surjective /-
 /-- If `f : A →ₐ[R] B` is a sujection between finitely-presented `R`-algebras, then the kernel of
 `f` is finitely generated. -/
 theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
@@ -385,6 +398,7 @@ theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 #align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fG_of_surjective
+-/
 
 end FinitePresentation
 
@@ -406,9 +420,11 @@ def FinitePresentation (f : A →+* B) : Prop :=
 
 namespace FiniteType
 
+#print RingHom.FiniteType.of_finitePresentation /-
 theorem of_finitePresentation {f : A →+* B} (hf : f.FinitePresentation) : f.FiniteType :=
   @Algebra.FiniteType.of_finitePresentation A B _ _ f.toAlgebra hf
 #align ring_hom.finite_type.of_finite_presentation RingHom.FiniteType.of_finitePresentation
+-/
 
 end FiniteType
 
@@ -424,6 +440,7 @@ theorem id : FinitePresentation (RingHom.id A) :=
 
 variable {A}
 
+#print RingHom.FinitePresentation.comp_surjective /-
 theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentation) (hg : Surjective g)
     (hker : g.ker.FG) : (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.of_surjective A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra
@@ -432,15 +449,21 @@ theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentati
       commutes' := fun a => rfl }
     hg hker hf
 #align ring_hom.finite_presentation.comp_surjective RingHom.FinitePresentation.comp_surjective
+-/
 
+#print RingHom.FinitePresentation.of_surjective /-
 theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.FG) : f.FinitePresentation :=
   by rw [← f.comp_id]; exact (id A).comp_surjective hf hker
 #align ring_hom.finite_presentation.of_surjective RingHom.FinitePresentation.of_surjective
+-/
 
+#print RingHom.FinitePresentation.of_finiteType /-
 theorem of_finiteType [IsNoetherianRing A] {f : A →+* B} : f.FiniteType ↔ f.FinitePresentation :=
   @Algebra.FinitePresentation.of_finiteType A B _ _ f.toAlgebra _
 #align ring_hom.finite_presentation.of_finite_type RingHom.FinitePresentation.of_finiteType
+-/
 
+#print RingHom.FinitePresentation.comp /-
 theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f.FinitePresentation) :
     (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.trans A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra g.toAlgebra
@@ -451,13 +474,16 @@ theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f
         rfl }
     hf hg
 #align ring_hom.finite_presentation.comp RingHom.FinitePresentation.comp
+-/
 
+#print RingHom.FinitePresentation.of_comp_finiteType /-
 theorem of_comp_finiteType (f : A →+* B) {g : B →+* C} (hg : (g.comp f).FinitePresentation)
     (hf : f.FiniteType) : g.FinitePresentation :=
   @Algebra.FinitePresentation.of_restrict_scalars_finitePresentation _ _ f.toAlgebra _
     (g.comp f).toAlgebra g.toAlgebra
     (@IsScalarTower.of_algebraMap_eq' _ _ _ f.toAlgebra g.toAlgebra (g.comp f).toAlgebra rfl) hg hf
 #align ring_hom.finite_presentation.of_comp_finite_type RingHom.FinitePresentation.of_comp_finiteType
+-/
 
 end FinitePresentation
 
@@ -483,9 +509,11 @@ namespace FiniteType
 
 variable {R A}
 
+#print AlgHom.FiniteType.of_finitePresentation /-
 theorem of_finitePresentation {f : A →ₐ[R] B} (hf : f.FinitePresentation) : f.FiniteType :=
   RingHom.FiniteType.of_finitePresentation hf
 #align alg_hom.finite_type.of_finite_presentation AlgHom.FiniteType.of_finitePresentation
+-/
 
 end FiniteType
 
@@ -493,35 +521,47 @@ namespace FinitePresentation
 
 variable (R A)
 
+#print AlgHom.FinitePresentation.id /-
 theorem id : FinitePresentation (AlgHom.id R A) :=
   RingHom.FinitePresentation.id A
 #align alg_hom.finite_presentation.id AlgHom.FinitePresentation.id
+-/
 
 variable {R A}
 
+#print AlgHom.FinitePresentation.comp /-
 theorem comp {g : B →ₐ[R] C} {f : A →ₐ[R] B} (hg : g.FinitePresentation)
     (hf : f.FinitePresentation) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp hg hf
 #align alg_hom.finite_presentation.comp AlgHom.FinitePresentation.comp
+-/
 
+#print AlgHom.FinitePresentation.comp_surjective /-
 theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePresentation)
     (hg : Surjective g) (hker : g.toRingHom.ker.FG) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp_surjective hf hg hker
 #align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjective
+-/
 
+#print AlgHom.FinitePresentation.of_surjective /-
 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation :=
   RingHom.FinitePresentation.of_surjective f hf hker
 #align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjective
+-/
 
+#print AlgHom.FinitePresentation.of_finiteType /-
 theorem of_finiteType [IsNoetherianRing A] {f : A →ₐ[R] B} : f.FiniteType ↔ f.FinitePresentation :=
   RingHom.FinitePresentation.of_finiteType
 #align alg_hom.finite_presentation.of_finite_type AlgHom.FinitePresentation.of_finiteType
+-/
 
+#print AlgHom.FinitePresentation.of_comp_finiteType /-
 theorem of_comp_finiteType (f : A →ₐ[R] B) {g : B →ₐ[R] C} (h : (g.comp f).FinitePresentation)
     (h' : f.FiniteType) : g.FinitePresentation :=
   h.of_comp_finiteType _ h'
 #align alg_hom.finite_presentation.of_comp_finite_type AlgHom.FinitePresentation.of_comp_finiteType
+-/
 
 end FinitePresentation
 

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

@@ -202,18 +202,18 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι :
   by
   rw [iff_quotient_mv_polynomial'] at hfp ⊢
   classical
-    obtain ⟨ι', _, f, hf_surj, hf_ker⟩ := hfp
-    skip
-    let g := (MvPolynomial.mapAlgHom f).comp (MvPolynomial.sumAlgEquiv R ι ι').toAlgHom
-    cases nonempty_fintype (Sum ι ι')
-    refine'
-      ⟨Sum ι ι', by infer_instance, g,
-        (MvPolynomial.map_surjective f.to_ring_hom hf_surj).comp (AlgEquiv.surjective _),
-        Ideal.fg_ker_comp _ _ _ _ (AlgEquiv.surjective _)⟩
-    · convert Submodule.fg_bot
-      exact RingHom.ker_coe_equiv (MvPolynomial.sumAlgEquiv R ι ι').toRingEquiv
-    · rw [AlgHom.toRingHom_eq_coe, MvPolynomial.mapAlgHom_coe_ringHom, MvPolynomial.ker_map]
-      exact hf_ker.map MvPolynomial.C
+  obtain ⟨ι', _, f, hf_surj, hf_ker⟩ := hfp
+  skip
+  let g := (MvPolynomial.mapAlgHom f).comp (MvPolynomial.sumAlgEquiv R ι ι').toAlgHom
+  cases nonempty_fintype (Sum ι ι')
+  refine'
+    ⟨Sum ι ι', by infer_instance, g,
+      (MvPolynomial.map_surjective f.to_ring_hom hf_surj).comp (AlgEquiv.surjective _),
+      Ideal.fg_ker_comp _ _ _ _ (AlgEquiv.surjective _)⟩
+  · convert Submodule.fg_bot
+    exact RingHom.ker_coe_equiv (MvPolynomial.sumAlgEquiv R ι ι').toRingEquiv
+  · rw [AlgHom.toRingHom_eq_coe, MvPolynomial.mapAlgHom_coe_ringHom, MvPolynomial.ker_map]
+    exact hf_ker.map MvPolynomial.C
 #align algebra.finite_presentation.mv_polynomial_of_finite_presentation Algebra.FinitePresentation.mvPolynomial_of_finitePresentation
 -/
 
@@ -235,146 +235,144 @@ open MvPolynomial
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
     (hRB : FinitePresentation R B) [hRA : FiniteType R A] : FinitePresentation A B := by
   classical
-    obtain ⟨n, f, hf, s, hs⟩ := hRB
-    let RX := MvPolynomial (Fin n) R
-    let AX := MvPolynomial (Fin n) A
-    refine' ⟨n, MvPolynomial.aeval (f ∘ X), _, _⟩
-    · rw [← Algebra.range_top_iff_surjective, ← Algebra.adjoin_range_eq_range_aeval, Set.range_comp,
-        _root_.eq_top_iff, ← @adjoin_adjoin_of_tower R A B, adjoin_image, adjoin_range_X,
-        Algebra.map_top, (Algebra.range_top_iff_surjective _).mpr hf]
-      exact subset_adjoin
-    · obtain ⟨t, ht⟩ := hRA.out
-      have := fun i : t => hf (algebraMap A B i)
-      choose t' ht'
-      have ht'' : Algebra.adjoin R (algebraMap A AX '' t ∪ Set.range (X : _ → AX)) = ⊤ :=
-        by
-        rw [adjoin_union_eq_adjoin_adjoin, ← Subalgebra.restrictScalars_top R]
-        congr 1
-        swap; · exact Subalgebra.isScalarTower_mid _
-        rw [adjoin_algebra_map, ht]
-        apply Subalgebra.restrictScalars_injective R
-        rw [← adjoin_restrict_scalars, adjoin_range_X, Subalgebra.restrictScalars_top,
-          Subalgebra.restrictScalars_top]
-      let g : t → AX := fun x => C (x : A) - map (algebraMap R A) (t' x)
-      refine' ⟨s.image (map (algebraMap R A)) ∪ t.attach.image g, _⟩
-      rw [Finset.coe_union, Finset.coe_image, Finset.coe_image, Finset.attach_eq_univ,
-        Finset.coe_univ, Set.image_univ]
-      let s₀ := _; let I := _; change Ideal.span s₀ = I
-      have leI : Ideal.span s₀ ≤ I := by
-        rw [Ideal.span_le]
-        rintro _ (⟨x, hx, rfl⟩ | ⟨⟨x, hx⟩, rfl⟩)
-        all_goals dsimp [g]; rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom]
-        · rw [MvPolynomial.aeval_map_algebraMap, ← aeval_unique]
-          have := Ideal.subset_span hx
-          rwa [hs] at this 
-        ·
-          rw [map_sub, MvPolynomial.aeval_map_algebraMap, ← aeval_unique, aeval_C, ht',
-            Subtype.coe_mk, sub_self]
-      apply leI.antisymm
-      intro x hx
-      rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx 
-      let s₀ := _; change x ∈ Ideal.span s₀
-      have :
-        x ∈
-          (map (algebraMap R A) : _ →+* AX).srange.toAddSubmonoid ⊔
-            (Ideal.span s₀).toAddSubmonoid :=
-        by
-        have : x ∈ (⊤ : Subalgebra R AX) := trivial
-        rw [← ht''] at this 
-        apply adjoin_induction this
-        · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
-          · rw [algebra_map_eq, ← sub_add_cancel (C x) (map (algebraMap R A) (t' ⟨x, hx⟩)),
-              add_comm]
-            apply AddSubmonoid.add_mem_sup
-            · exact Set.mem_range_self _
-            · apply Ideal.subset_span
-              apply Set.mem_union_right
-              exact Set.mem_range_self ⟨x, hx⟩
-          · apply AddSubmonoid.mem_sup_left
-            exact ⟨X i, map_X _ _⟩
-        · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, map_C _ _⟩
-        · intro _ _ h₁ h₂; exact add_mem h₁ h₂
-        · intro x₁ x₂ h₁ h₂
-          obtain ⟨_, ⟨p₁, rfl⟩, q₁, hq₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
-          obtain ⟨_, ⟨p₂, rfl⟩, q₂, hq₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
-          rw [add_mul, mul_add, add_assoc, ← map_mul]
-          apply AddSubmonoid.add_mem_sup
-          · exact Set.mem_range_self _
-          · refine' add_mem (Ideal.mul_mem_left _ _ hq₂) (Ideal.mul_mem_right _ _ hq₁)
-      obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
-      rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
-        add_zero] at hx 
-      suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
-        refine' add_mem _ hq; rw [hs] at this ; exact this hx
-      rw [Ideal.span_le]
-      intro x hx
-      apply Ideal.subset_span
-      apply Set.mem_union_left
-      exact Set.mem_image_of_mem _ hx
-#align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
-
--- TODO: extract out helper lemmas and tidy proof.
-/-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
-theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
-    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
-  classical
-    obtain ⟨m, f', hf', s, hs⟩ := hfp
-    let RXn := MvPolynomial (Fin n) R
-    let RXm := MvPolynomial (Fin m) R
-    have := fun i : Fin n => hf' (f <| X i)
-    choose g hg
-    have := fun i : Fin m => hf (f' <| X i)
-    choose h hh
-    let aeval_h : RXm →ₐ[R] RXn := aeval h
-    let g' : Fin n → RXn := fun i => X i - aeval_h (g i)
-    refine' ⟨finset.univ.image g' ∪ s.image aeval_h, _⟩
-    simp only [Finset.coe_image, Finset.coe_union, Finset.coe_univ, Set.image_univ]
-    have hh' : ∀ x, f (aeval_h x) = f' x := by
-      intro x; rw [← f.coe_to_ring_hom, map_aeval]; simp_rw [AlgHom.coe_toRingHom, hh]
-      rw [AlgHom.comp_algebraMap, ← aeval_eq_eval₂_hom, ← aeval_unique]
-    let s' := Set.range g' ∪ aeval_h '' s
-    have leI : Ideal.span s' ≤ f.to_ring_hom.ker :=
+  obtain ⟨n, f, hf, s, hs⟩ := hRB
+  let RX := MvPolynomial (Fin n) R
+  let AX := MvPolynomial (Fin n) A
+  refine' ⟨n, MvPolynomial.aeval (f ∘ X), _, _⟩
+  · rw [← Algebra.range_top_iff_surjective, ← Algebra.adjoin_range_eq_range_aeval, Set.range_comp,
+      _root_.eq_top_iff, ← @adjoin_adjoin_of_tower R A B, adjoin_image, adjoin_range_X,
+      Algebra.map_top, (Algebra.range_top_iff_surjective _).mpr hf]
+    exact subset_adjoin
+  · obtain ⟨t, ht⟩ := hRA.out
+    have := fun i : t => hf (algebraMap A B i)
+    choose t' ht'
+    have ht'' : Algebra.adjoin R (algebraMap A AX '' t ∪ Set.range (X : _ → AX)) = ⊤ :=
       by
+      rw [adjoin_union_eq_adjoin_adjoin, ← Subalgebra.restrictScalars_top R]
+      congr 1
+      swap; · exact Subalgebra.isScalarTower_mid _
+      rw [adjoin_algebra_map, ht]
+      apply Subalgebra.restrictScalars_injective R
+      rw [← adjoin_restrict_scalars, adjoin_range_X, Subalgebra.restrictScalars_top,
+        Subalgebra.restrictScalars_top]
+    let g : t → AX := fun x => C (x : A) - map (algebraMap R A) (t' x)
+    refine' ⟨s.image (map (algebraMap R A)) ∪ t.attach.image g, _⟩
+    rw [Finset.coe_union, Finset.coe_image, Finset.coe_image, Finset.attach_eq_univ,
+      Finset.coe_univ, Set.image_univ]
+    let s₀ := _; let I := _; change Ideal.span s₀ = I
+    have leI : Ideal.span s₀ ≤ I := by
       rw [Ideal.span_le]
-      rintro _ (⟨i, rfl⟩ | ⟨x, hx, rfl⟩)
-      · change f (g' i) = 0; rw [map_sub, ← hg, hh', sub_self]
-      · change f (aeval_h x) = 0
-        rw [hh']
-        change x ∈ f'.to_ring_hom.ker
-        rw [← hs]
-        exact Ideal.subset_span hx
+      rintro _ (⟨x, hx, rfl⟩ | ⟨⟨x, hx⟩, rfl⟩)
+      all_goals dsimp [g]; rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom]
+      · rw [MvPolynomial.aeval_map_algebraMap, ← aeval_unique]
+        have := Ideal.subset_span hx
+        rwa [hs] at this 
+      ·
+        rw [map_sub, MvPolynomial.aeval_map_algebraMap, ← aeval_unique, aeval_C, ht',
+          Subtype.coe_mk, sub_self]
     apply leI.antisymm
     intro x hx
-    have : x ∈ aeval_h.range.to_add_submonoid ⊔ (Ideal.span s').toAddSubmonoid :=
+    rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx 
+    let s₀ := _; change x ∈ Ideal.span s₀
+    have :
+      x ∈
+        (map (algebraMap R A) : _ →+* AX).srange.toAddSubmonoid ⊔ (Ideal.span s₀).toAddSubmonoid :=
       by
-      have : x ∈ adjoin R (Set.range X : Set RXn) := by rw [adjoin_range_X]; trivial
+      have : x ∈ (⊤ : Subalgebra R AX) := trivial
+      rw [← ht''] at this 
       apply adjoin_induction this
-      · rintro _ ⟨i, rfl⟩
-        rw [← sub_add_cancel (X i) (aeval h (g i)), add_comm]
-        apply AddSubmonoid.add_mem_sup
-        · exact Set.mem_range_self _
-        · apply Submodule.subset_span
-          apply Set.mem_union_left
-          exact Set.mem_range_self _
-      · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, aeval_C _ _⟩
+      · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
+        · rw [algebra_map_eq, ← sub_add_cancel (C x) (map (algebraMap R A) (t' ⟨x, hx⟩)), add_comm]
+          apply AddSubmonoid.add_mem_sup
+          · exact Set.mem_range_self _
+          · apply Ideal.subset_span
+            apply Set.mem_union_right
+            exact Set.mem_range_self ⟨x, hx⟩
+        · apply AddSubmonoid.mem_sup_left
+          exact ⟨X i, map_X _ _⟩
+      · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, map_C _ _⟩
       · intro _ _ h₁ h₂; exact add_mem h₁ h₂
-      · intro p₁ p₂ h₁ h₂
-        obtain ⟨_, ⟨x₁, rfl⟩, y₁, hy₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
-        obtain ⟨_, ⟨x₂, rfl⟩, y₂, hy₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
-        rw [mul_add, add_mul, add_assoc, ← map_mul]
+      · intro x₁ x₂ h₁ h₂
+        obtain ⟨_, ⟨p₁, rfl⟩, q₁, hq₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
+        obtain ⟨_, ⟨p₂, rfl⟩, q₂, hq₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
+        rw [add_mul, mul_add, add_assoc, ← map_mul]
         apply AddSubmonoid.add_mem_sup
         · exact Set.mem_range_self _
-        · exact add_mem (Ideal.mul_mem_right _ _ hy₁) (Ideal.mul_mem_left _ _ hy₂)
-    obtain ⟨_, ⟨x, rfl⟩, y, hy, rfl⟩ := add_submonoid.mem_sup.mp this
-    refine' add_mem _ hy
-    simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
-      show f y = 0 from leI hy, add_zero, hh'] at hx 
-    suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
+        · refine' add_mem (Ideal.mul_mem_left _ _ hq₂) (Ideal.mul_mem_right _ _ hq₁)
+    obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
+    rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
+      add_zero] at hx 
+    suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
+      refine' add_mem _ hq; rw [hs] at this ; exact this hx
     rw [Ideal.span_le]
     intro x hx
-    apply Submodule.subset_span
-    apply Set.mem_union_right
+    apply Ideal.subset_span
+    apply Set.mem_union_left
     exact Set.mem_image_of_mem _ hx
+#align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
+
+-- TODO: extract out helper lemmas and tidy proof.
+/-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
+theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
+    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
+  classical
+  obtain ⟨m, f', hf', s, hs⟩ := hfp
+  let RXn := MvPolynomial (Fin n) R
+  let RXm := MvPolynomial (Fin m) R
+  have := fun i : Fin n => hf' (f <| X i)
+  choose g hg
+  have := fun i : Fin m => hf (f' <| X i)
+  choose h hh
+  let aeval_h : RXm →ₐ[R] RXn := aeval h
+  let g' : Fin n → RXn := fun i => X i - aeval_h (g i)
+  refine' ⟨finset.univ.image g' ∪ s.image aeval_h, _⟩
+  simp only [Finset.coe_image, Finset.coe_union, Finset.coe_univ, Set.image_univ]
+  have hh' : ∀ x, f (aeval_h x) = f' x := by
+    intro x; rw [← f.coe_to_ring_hom, map_aeval]; simp_rw [AlgHom.coe_toRingHom, hh]
+    rw [AlgHom.comp_algebraMap, ← aeval_eq_eval₂_hom, ← aeval_unique]
+  let s' := Set.range g' ∪ aeval_h '' s
+  have leI : Ideal.span s' ≤ f.to_ring_hom.ker :=
+    by
+    rw [Ideal.span_le]
+    rintro _ (⟨i, rfl⟩ | ⟨x, hx, rfl⟩)
+    · change f (g' i) = 0; rw [map_sub, ← hg, hh', sub_self]
+    · change f (aeval_h x) = 0
+      rw [hh']
+      change x ∈ f'.to_ring_hom.ker
+      rw [← hs]
+      exact Ideal.subset_span hx
+  apply leI.antisymm
+  intro x hx
+  have : x ∈ aeval_h.range.to_add_submonoid ⊔ (Ideal.span s').toAddSubmonoid :=
+    by
+    have : x ∈ adjoin R (Set.range X : Set RXn) := by rw [adjoin_range_X]; trivial
+    apply adjoin_induction this
+    · rintro _ ⟨i, rfl⟩
+      rw [← sub_add_cancel (X i) (aeval h (g i)), add_comm]
+      apply AddSubmonoid.add_mem_sup
+      · exact Set.mem_range_self _
+      · apply Submodule.subset_span
+        apply Set.mem_union_left
+        exact Set.mem_range_self _
+    · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, aeval_C _ _⟩
+    · intro _ _ h₁ h₂; exact add_mem h₁ h₂
+    · intro p₁ p₂ h₁ h₂
+      obtain ⟨_, ⟨x₁, rfl⟩, y₁, hy₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
+      obtain ⟨_, ⟨x₂, rfl⟩, y₂, hy₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
+      rw [mul_add, add_mul, add_assoc, ← map_mul]
+      apply AddSubmonoid.add_mem_sup
+      · exact Set.mem_range_self _
+      · exact add_mem (Ideal.mul_mem_right _ _ hy₁) (Ideal.mul_mem_left _ _ hy₂)
+  obtain ⟨_, ⟨x, rfl⟩, y, hy, rfl⟩ := add_submonoid.mem_sup.mp this
+  refine' add_mem _ hy
+  simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
+    show f y = 0 from leI hy, add_zero, hh'] at hx 
+  suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
+  rw [Ideal.span_le]
+  intro x hx
+  apply Submodule.subset_span
+  apply Set.mem_union_right
+  exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
 
 /-- If `f : A →ₐ[R] B` is a sujection between finitely-presented `R`-algebras, then the kernel of
@@ -383,7 +381,7 @@ theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
     (hRA : FinitePresentation R A) (hRB : FinitePresentation R B) : f.toRingHom.ker.FG :=
   by
   obtain ⟨n, g, hg, hg'⟩ := hRA
-  convert(ker_fg_of_mv_polynomial (f.comp g) (hf.comp hg) hRB).map g.to_ring_hom
+  convert (ker_fg_of_mv_polynomial (f.comp g) (hf.comp hg) hRB).map g.to_ring_hom
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 #align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fG_of_surjective

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

@@ -44,7 +44,7 @@ variable (R A B M N : Type _)
 /-- An algebra over a commutative semiring is `finite_presentation` if it is the quotient of a
 polynomial ring in `n` variables by a finitely generated ideal. -/
 def Algebra.FinitePresentation [CommSemiring R] [Semiring A] [Algebra R A] : Prop :=
-  ∃ (n : ℕ)(f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.FG
+  ∃ (n : ℕ) (f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.FG
 #align algebra.finite_presentation Algebra.FinitePresentation
 -/
 
@@ -159,7 +159,7 @@ theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f
 #print Algebra.FinitePresentation.iff /-
 theorem iff :
     FinitePresentation R A ↔
-      ∃ (n : _)(I : Ideal (MvPolynomial (Fin n) R))(e : (_ ⧸ I) ≃ₐ[R] A), I.FG :=
+      ∃ (n : _) (I : Ideal (MvPolynomial (Fin n) R)) (e : (_ ⧸ I) ≃ₐ[R] A), I.FG :=
   by
   constructor
   · rintro ⟨n, f, hf⟩
@@ -173,7 +173,7 @@ theorem iff :
 variables are indexed by a fintype by a finitely generated ideal. -/
 theorem iff_quotient_mvPolynomial' :
     FinitePresentation R A ↔
-      ∃ (ι : Type u_2)(_ : Fintype ι)(f : MvPolynomial ι R →ₐ[R] A),
+      ∃ (ι : Type u_2) (_ : Fintype ι) (f : MvPolynomial ι R →ₐ[R] A),
         Surjective f ∧ f.toRingHom.ker.FG :=
   by
   constructor
@@ -200,7 +200,7 @@ as `R`-algebra. -/
 theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι : Type _) [Finite ι] :
     FinitePresentation R (MvPolynomial ι A) :=
   by
-  rw [iff_quotient_mv_polynomial'] at hfp⊢
+  rw [iff_quotient_mv_polynomial'] at hfp ⊢
   classical
     obtain ⟨ι', _, f, hf_surj, hf_ker⟩ := hfp
     skip
@@ -266,13 +266,13 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
         all_goals dsimp [g]; rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom]
         · rw [MvPolynomial.aeval_map_algebraMap, ← aeval_unique]
           have := Ideal.subset_span hx
-          rwa [hs] at this
+          rwa [hs] at this 
         ·
           rw [map_sub, MvPolynomial.aeval_map_algebraMap, ← aeval_unique, aeval_C, ht',
             Subtype.coe_mk, sub_self]
       apply leI.antisymm
       intro x hx
-      rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx
+      rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx 
       let s₀ := _; change x ∈ Ideal.span s₀
       have :
         x ∈
@@ -280,7 +280,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
             (Ideal.span s₀).toAddSubmonoid :=
         by
         have : x ∈ (⊤ : Subalgebra R AX) := trivial
-        rw [← ht''] at this
+        rw [← ht''] at this 
         apply adjoin_induction this
         · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
           · rw [algebra_map_eq, ← sub_add_cancel (C x) (map (algebraMap R A) (t' ⟨x, hx⟩)),
@@ -303,9 +303,9 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
           · refine' add_mem (Ideal.mul_mem_left _ _ hq₂) (Ideal.mul_mem_right _ _ hq₁)
       obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
       rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
-        add_zero] at hx
+        add_zero] at hx 
       suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
-        refine' add_mem _ hq; rw [hs] at this; exact this hx
+        refine' add_mem _ hq; rw [hs] at this ; exact this hx
       rw [Ideal.span_le]
       intro x hx
       apply Ideal.subset_span
@@ -368,7 +368,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     obtain ⟨_, ⟨x, rfl⟩, y, hy, rfl⟩ := add_submonoid.mem_sup.mp this
     refine' add_mem _ hy
     simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
-      show f y = 0 from leI hy, add_zero, hh'] at hx
+      show f y = 0 from leI hy, add_zero, hh'] at hx 
     suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
     rw [Ideal.span_le]
     intro x hx

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

@@ -149,14 +149,12 @@ protected theorem quotient {I : Ideal A} (h : I.FG) (hfp : FinitePresentation R
 #align algebra.finite_presentation.quotient Algebra.FinitePresentation.quotient
 -/
 
-#print Algebra.FinitePresentation.of_surjective /-
 /-- If `f : A →ₐ[R] B` is surjective with finitely generated kernel and `A` is finitely presented,
 then so is `B`. -/
 theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f.toRingHom.ker.FG)
     (hfp : FinitePresentation R A) : FinitePresentation R B :=
   equiv (hfp.Quotient hker) (Ideal.quotientKerAlgEquivOfSurjective hf)
 #align algebra.finite_presentation.of_surjective Algebra.FinitePresentation.of_surjective
--/
 
 #print Algebra.FinitePresentation.iff /-
 theorem iff :
@@ -315,7 +313,6 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
 
-#print Algebra.FinitePresentation.ker_fg_of_mvPolynomial /-
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
 theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
@@ -379,9 +376,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     apply Set.mem_union_right
     exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
--/
 
-#print Algebra.FinitePresentation.ker_fG_of_surjective /-
 /-- If `f : A →ₐ[R] B` is a sujection between finitely-presented `R`-algebras, then the kernel of
 `f` is finitely generated. -/
 theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
@@ -392,7 +387,6 @@ theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 #align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fG_of_surjective
--/
 
 end FinitePresentation
 

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

@@ -34,7 +34,7 @@ In this file we define several notions of finiteness that are common in commutat
 
 open Function (Surjective)
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 section ModuleAndAlgebra
 

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

@@ -60,12 +60,6 @@ namespace FiniteType
 
 variable {R A B}
 
-/- warning: algebra.finite_type.of_finite_presentation -> Algebra.FiniteType.of_finitePresentation is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], (Algebra.FinitePresentation.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) -> (Algebra.FiniteType.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)
-but is expected to have type
-  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))], (Algebra.FinitePresentation.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) -> (Algebra.FiniteType.{u2, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3)
-Case conversion may be inaccurate. Consider using '#align algebra.finite_type.of_finite_presentation Algebra.FiniteType.of_finitePresentationₓ'. -/
 /-- A finitely presented algebra is of finite type. -/
 theorem of_finitePresentation : FinitePresentation R A → FiniteType R A :=
   by
@@ -80,12 +74,6 @@ namespace FinitePresentation
 
 variable {R A B}
 
-/- warning: algebra.finite_presentation.of_finite_type -> Algebra.FinitePresentation.of_finiteType is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.of_finite_type Algebra.FinitePresentation.of_finiteTypeₓ'. -/
 /-- An algebra over a Noetherian ring is finitely generated if and only if it is finitely
 presented. -/
 theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentation R A :=
@@ -183,9 +171,6 @@ theorem iff :
 #align algebra.finite_presentation.iff Algebra.FinitePresentation.iff
 -/
 
-/- warning: algebra.finite_presentation.iff_quotient_mv_polynomial' -> Algebra.FinitePresentation.iff_quotient_mvPolynomial' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'ₓ'. -/
 /-- An algebra is finitely presented if and only if it is a quotient of a polynomial ring whose
 variables are indexed by a fintype by a finitely generated ideal. -/
 theorem iff_quotient_mvPolynomial' :
@@ -247,12 +232,6 @@ theorem trans [Algebra A B] [IsScalarTower R A B] (hfpA : FinitePresentation R A
 
 open MvPolynomial
 
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(MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B 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u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)))))], (Algebra.FinitePresentation.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5) -> (forall [hRA : Algebra.FiniteType.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3], Algebra.FinitePresentation.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_10)
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-Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentationₓ'. -/
 -- We follow the proof of https://stacks.math.columbia.edu/tag/0561
 -- TODO: extract out helper lemmas and tidy proof.
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
@@ -435,12 +414,6 @@ def FinitePresentation (f : A →+* B) : Prop :=
 
 namespace FiniteType
 
-/- warning: ring_hom.finite_type.of_finite_presentation -> RingHom.FiniteType.of_finitePresentation is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ring_hom.finite_type.of_finite_presentation RingHom.FiniteType.of_finitePresentationₓ'. -/
 theorem of_finitePresentation {f : A →+* B} (hf : f.FinitePresentation) : f.FiniteType :=
   @Algebra.FiniteType.of_finitePresentation A B _ _ f.toAlgebra hf
 #align ring_hom.finite_type.of_finite_presentation RingHom.FiniteType.of_finitePresentation
@@ -459,12 +432,6 @@ theorem id : FinitePresentation (RingHom.id A) :=
 
 variable {A}
 
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 theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentation) (hg : Surjective g)
     (hker : g.ker.FG) : (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.of_surjective A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra
@@ -474,32 +441,14 @@ theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentati
     hg hker hf
 #align ring_hom.finite_presentation.comp_surjective RingHom.FinitePresentation.comp_surjective
 
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 theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.FG) : f.FinitePresentation :=
   by rw [← f.comp_id]; exact (id A).comp_surjective hf hker
 #align ring_hom.finite_presentation.of_surjective RingHom.FinitePresentation.of_surjective
 
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 theorem of_finiteType [IsNoetherianRing A] {f : A →+* B} : f.FiniteType ↔ f.FinitePresentation :=
   @Algebra.FinitePresentation.of_finiteType A B _ _ f.toAlgebra _
 #align ring_hom.finite_presentation.of_finite_type RingHom.FinitePresentation.of_finiteType
 
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 theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f.FinitePresentation) :
     (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.trans A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra g.toAlgebra
@@ -511,12 +460,6 @@ theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f
     hf hg
 #align ring_hom.finite_presentation.comp RingHom.FinitePresentation.comp
 
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 theorem of_comp_finiteType (f : A →+* B) {g : B →+* C} (hg : (g.comp f).FinitePresentation)
     (hf : f.FiniteType) : g.FinitePresentation :=
   @Algebra.FinitePresentation.of_restrict_scalars_finitePresentation _ _ f.toAlgebra _
@@ -548,12 +491,6 @@ namespace FiniteType
 
 variable {R A}
 
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 theorem of_finitePresentation {f : A →ₐ[R] B} (hf : f.FinitePresentation) : f.FiniteType :=
   RingHom.FiniteType.of_finitePresentation hf
 #align alg_hom.finite_type.of_finite_presentation AlgHom.FiniteType.of_finitePresentation
@@ -564,61 +501,31 @@ namespace FinitePresentation
 
 variable (R A)
 
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 theorem id : FinitePresentation (AlgHom.id R A) :=
   RingHom.FinitePresentation.id A
 #align alg_hom.finite_presentation.id AlgHom.FinitePresentation.id
 
 variable {R A}
 
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 theorem comp {g : B →ₐ[R] C} {f : A →ₐ[R] B} (hg : g.FinitePresentation)
     (hf : f.FinitePresentation) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp hg hf
 #align alg_hom.finite_presentation.comp AlgHom.FinitePresentation.comp
 
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-<too large>
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 theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePresentation)
     (hg : Surjective g) (hker : g.toRingHom.ker.FG) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp_surjective hf hg hker
 #align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjective
 
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-<too large>
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 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation :=
   RingHom.FinitePresentation.of_surjective f hf hker
 #align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjective
 
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 theorem of_finiteType [IsNoetherianRing A] {f : A →ₐ[R] B} : f.FiniteType ↔ f.FinitePresentation :=
   RingHom.FinitePresentation.of_finiteType
 #align alg_hom.finite_presentation.of_finite_type AlgHom.FinitePresentation.of_finiteType
 
-/- warning: alg_hom.finite_presentation.of_comp_finite_type -> AlgHom.FinitePresentation.of_comp_finiteType is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_4 : CommRing.{u4} C] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] [_inst_7 : Algebra.{u1, u4} R C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4))] (f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) {g : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_5 _inst_6 _inst_7 g f)) -> (AlgHom.FiniteType.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FinitePresentation.{u1, u3, u4} R B C _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g)
-but is expected to have type
-  forall {R : Type.{u4}} {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} B] [_inst_4 : CommRing.{u1} C] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))] [_inst_7 : Algebra.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))] (f : AlgHom.{u4, u3, u2} R A B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_5 _inst_6) {g : AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u3, u2, u1} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_5 _inst_6 _inst_7 g f)) -> (AlgHom.FiniteType.{u4, u3, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FinitePresentation.{u4, u2, u1} R B C _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g)
-Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.of_comp_finite_type AlgHom.FinitePresentation.of_comp_finiteTypeₓ'. -/
 theorem of_comp_finiteType (f : A →ₐ[R] B) {g : B →ₐ[R] C} (h : (g.comp f).FinitePresentation)
     (h' : f.FiniteType) : g.FinitePresentation :=
   h.of_comp_finiteType _ h'

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

@@ -107,8 +107,7 @@ theorem equiv (hfp : FinitePresentation R A) (e : A ≃ₐ[R] B) : FinitePresent
   constructor
   · exact Function.Surjective.comp e.surjective hf.1
   suffices hker : (AlgHom.comp (↑e) f).toRingHom.ker = f.to_ring_hom.ker
-  · rw [hker]
-    exact hf.2
+  · rw [hker]; exact hf.2
   · have hco : (AlgHom.comp (↑e) f).toRingHom = RingHom.comp (↑e.to_ring_equiv) f.to_ring_hom :=
       by
       have h : (AlgHom.comp (↑e) f).toRingHom = e.to_alg_hom.to_ring_hom.comp f.to_ring_hom := rfl
@@ -274,8 +273,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
         by
         rw [adjoin_union_eq_adjoin_adjoin, ← Subalgebra.restrictScalars_top R]
         congr 1
-        swap
-        · exact Subalgebra.isScalarTower_mid _
+        swap; · exact Subalgebra.isScalarTower_mid _
         rw [adjoin_algebra_map, ht]
         apply Subalgebra.restrictScalars_injective R
         rw [← adjoin_restrict_scalars, adjoin_range_X, Subalgebra.restrictScalars_top,
@@ -284,9 +282,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       refine' ⟨s.image (map (algebraMap R A)) ∪ t.attach.image g, _⟩
       rw [Finset.coe_union, Finset.coe_image, Finset.coe_image, Finset.attach_eq_univ,
         Finset.coe_univ, Set.image_univ]
-      let s₀ := _
-      let I := _
-      change Ideal.span s₀ = I
+      let s₀ := _; let I := _; change Ideal.span s₀ = I
       have leI : Ideal.span s₀ ≤ I := by
         rw [Ideal.span_le]
         rintro _ (⟨x, hx, rfl⟩ | ⟨⟨x, hx⟩, rfl⟩)
@@ -300,8 +296,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       apply leI.antisymm
       intro x hx
       rw [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom] at hx
-      let s₀ := _
-      change x ∈ Ideal.span s₀
+      let s₀ := _; change x ∈ Ideal.span s₀
       have :
         x ∈
           (map (algebraMap R A) : _ →+* AX).srange.toAddSubmonoid ⊔
@@ -320,11 +315,8 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
               exact Set.mem_range_self ⟨x, hx⟩
           · apply AddSubmonoid.mem_sup_left
             exact ⟨X i, map_X _ _⟩
-        · intro r
-          apply AddSubmonoid.mem_sup_left
-          exact ⟨C r, map_C _ _⟩
-        · intro _ _ h₁ h₂
-          exact add_mem h₁ h₂
+        · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, map_C _ _⟩
+        · intro _ _ h₁ h₂; exact add_mem h₁ h₂
         · intro x₁ x₂ h₁ h₂
           obtain ⟨_, ⟨p₁, rfl⟩, q₁, hq₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
           obtain ⟨_, ⟨p₂, rfl⟩, q₂, hq₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
@@ -335,11 +327,8 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       obtain ⟨_, ⟨p, rfl⟩, q, hq, rfl⟩ := add_submonoid.mem_sup.mp this
       rw [map_add, aeval_map_algebra_map, ← aeval_unique, show aeval (f ∘ X) q = 0 from leI hq,
         add_zero] at hx
-      suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A)
-        by
-        refine' add_mem _ hq
-        rw [hs] at this
-        exact this hx
+      suffices Ideal.span (s : Set RX) ≤ (Ideal.span s₀).comap (map <| algebraMap R A) by
+        refine' add_mem _ hq; rw [hs] at this; exact this hx
       rw [Ideal.span_le]
       intro x hx
       apply Ideal.subset_span
@@ -365,17 +354,14 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     refine' ⟨finset.univ.image g' ∪ s.image aeval_h, _⟩
     simp only [Finset.coe_image, Finset.coe_union, Finset.coe_univ, Set.image_univ]
     have hh' : ∀ x, f (aeval_h x) = f' x := by
-      intro x
-      rw [← f.coe_to_ring_hom, map_aeval]
-      simp_rw [AlgHom.coe_toRingHom, hh]
+      intro x; rw [← f.coe_to_ring_hom, map_aeval]; simp_rw [AlgHom.coe_toRingHom, hh]
       rw [AlgHom.comp_algebraMap, ← aeval_eq_eval₂_hom, ← aeval_unique]
     let s' := Set.range g' ∪ aeval_h '' s
     have leI : Ideal.span s' ≤ f.to_ring_hom.ker :=
       by
       rw [Ideal.span_le]
       rintro _ (⟨i, rfl⟩ | ⟨x, hx, rfl⟩)
-      · change f (g' i) = 0
-        rw [map_sub, ← hg, hh', sub_self]
+      · change f (g' i) = 0; rw [map_sub, ← hg, hh', sub_self]
       · change f (aeval_h x) = 0
         rw [hh']
         change x ∈ f'.to_ring_hom.ker
@@ -385,10 +371,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     intro x hx
     have : x ∈ aeval_h.range.to_add_submonoid ⊔ (Ideal.span s').toAddSubmonoid :=
       by
-      have : x ∈ adjoin R (Set.range X : Set RXn) :=
-        by
-        rw [adjoin_range_X]
-        trivial
+      have : x ∈ adjoin R (Set.range X : Set RXn) := by rw [adjoin_range_X]; trivial
       apply adjoin_induction this
       · rintro _ ⟨i, rfl⟩
         rw [← sub_add_cancel (X i) (aeval h (g i)), add_comm]
@@ -397,11 +380,8 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
         · apply Submodule.subset_span
           apply Set.mem_union_left
           exact Set.mem_range_self _
-      · intro r
-        apply AddSubmonoid.mem_sup_left
-        exact ⟨C r, aeval_C _ _⟩
-      · intro _ _ h₁ h₂
-        exact add_mem h₁ h₂
+      · intro r; apply AddSubmonoid.mem_sup_left; exact ⟨C r, aeval_C _ _⟩
+      · intro _ _ h₁ h₂; exact add_mem h₁ h₂
       · intro p₁ p₂ h₁ h₂
         obtain ⟨_, ⟨x₁, rfl⟩, y₁, hy₁, rfl⟩ := add_submonoid.mem_sup.mp h₁
         obtain ⟨_, ⟨x₂, rfl⟩, y₂, hy₂, rfl⟩ := add_submonoid.mem_sup.mp h₂
@@ -413,10 +393,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     refine' add_mem _ hy
     simp only [RingHom.mem_ker, AlgHom.toRingHom_eq_coe, AlgHom.coe_toRingHom, map_add,
       show f y = 0 from leI hy, add_zero, hh'] at hx
-    suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h
-      by
-      apply this
-      rwa [hs]
+    suffices Ideal.span (s : Set RXm) ≤ (Ideal.span s').comap aeval_h by apply this; rwa [hs]
     rw [Ideal.span_le]
     intro x hx
     apply Submodule.subset_span
@@ -504,9 +481,7 @@ but is expected to have type
   forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] (f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))), (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : A) => B) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonUnitalNonAssocSemiring.toMul.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))))) (NonUnitalNonAssocSemiring.toMul.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2))))))) f)) -> (Ideal.FG.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (RingHom.ker.{u2, u1, max u2 u1} A B (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))) f)) -> (RingHom.FinitePresentation.{u2, u1} A B _inst_1 _inst_2 f)
 Case conversion may be inaccurate. Consider using '#align ring_hom.finite_presentation.of_surjective RingHom.FinitePresentation.of_surjectiveₓ'. -/
 theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.FG) : f.FinitePresentation :=
-  by
-  rw [← f.comp_id]
-  exact (id A).comp_surjective hf hker
+  by rw [← f.comp_id]; exact (id A).comp_surjective hf hker
 #align ring_hom.finite_presentation.of_surjective RingHom.FinitePresentation.of_surjective
 
 /- warning: ring_hom.finite_presentation.of_finite_type -> RingHom.FinitePresentation.of_finiteType is a dubious translation:

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

@@ -185,10 +185,7 @@ theorem iff :
 -/
 
 /- warning: algebra.finite_presentation.iff_quotient_mv_polynomial' -> Algebra.FinitePresentation.iff_quotient_mvPolynomial' is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u_1}} {A : Type.{u_2}} [_inst_1 : CommRing.{u_1} R] [_inst_2 : CommRing.{u_2} A] [_inst_3 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2))], Iff (Algebra.FinitePresentation.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) _inst_3) (Exists.{succ (succ u_2)} Type.{u_2} (fun (ι : Type.{u_2}) => Exists.{succ u_2} (Fintype.{u_2} ι) (fun (_x : Fintype.{u_2} ι) => Exists.{max (succ (max u_2 u_1)) (succ u_2)} (AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) (fun (f : AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ u_2) (succ u_1), succ u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (coeFn.{max (succ (max u_2 u_1)) (succ u_2), max (succ (max u_2 u_1)) (succ u_2)} (AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) (fun (_x : AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) => (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) -> A) ([anonymous].{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) f)) (Ideal.FG.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (RingHom.ker.{max u_2 u_1, u_2, max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (RingHom.{max u_2 u_1, u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)))) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (RingHom.ringHomClass.{max u_2 u_1, u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)))) (AlgHom.toRingHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3 f)))))))
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_inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (fun (f : AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ w₁) (succ u_1), succ w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (FunLike.coe.{max (max (succ w₁) (succ w₂)) 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(NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max w₁ w₂) u_1, w₁, max w₁ u_1, w₂} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{w₁, max w₁ u_1, w₂, max (max w₁ w₂) u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (AlgHom.algHomClass.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3))))) f)) (Ideal.FG.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (RingHom.ker.{max w₁ u_1, w₂, max (max w₁ w₂) u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (RingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (RingHom.instRingHomClassRingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (AlgHom.toRingHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 f)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'ₓ'. -/
 /-- An algebra is finitely presented if and only if it is a quotient of a polynomial ring whose
 variables are indexed by a fintype by a finitely generated ideal. -/
@@ -616,10 +613,7 @@ theorem comp {g : B →ₐ[R] C} {f : A →ₐ[R] B} (hg : g.FinitePresentation)
 #align alg_hom.finite_presentation.comp AlgHom.FinitePresentation.comp
 
 /- warning: alg_hom.finite_presentation.comp_surjective -> AlgHom.FinitePresentation.comp_surjective is a dubious translation:
-lean 3 declaration is
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_inst_6 _inst_7 g))) -> (AlgHom.FinitePresentation.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u3, u2, u1} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjectiveₓ'. -/
 theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePresentation)
     (hg : Surjective g) (hker : g.toRingHom.ker.FG) : (g.comp f).FinitePresentation :=
@@ -627,10 +621,7 @@ theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePr
 #align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjective
 
 /- warning: alg_hom.finite_presentation.of_surjective -> AlgHom.FinitePresentation.of_surjective is a dubious translation:
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-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u1} B] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_6 : Algebra.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))] (f : AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6))))) f)) -> (Ideal.FG.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ker.{u2, u1, max u2 u1} A B (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (AlgHom.toRingHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 f))) -> (AlgHom.FinitePresentation.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjectiveₓ'. -/
 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation :=

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

@@ -188,7 +188,7 @@ theorem iff :
 lean 3 declaration is
   forall {R : Type.{u_1}} {A : Type.{u_2}} [_inst_1 : CommRing.{u_1} R] [_inst_2 : CommRing.{u_2} A] [_inst_3 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2))], Iff (Algebra.FinitePresentation.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) _inst_3) (Exists.{succ (succ u_2)} Type.{u_2} (fun (ι : Type.{u_2}) => Exists.{succ u_2} (Fintype.{u_2} ι) (fun (_x : Fintype.{u_2} ι) => Exists.{max (succ (max u_2 u_1)) (succ u_2)} (AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) (fun (f : AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ u_2) (succ u_1), succ u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (coeFn.{max (succ (max u_2 u_1)) (succ u_2), max (succ (max u_2 u_1)) (succ u_2)} (AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) (fun (_x : AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) => (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) -> A) ([anonymous].{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) f)) (Ideal.FG.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (RingHom.ker.{max u_2 u_1, u_2, max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (RingHom.{max u_2 u_1, u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)))) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (RingHom.ringHomClass.{max u_2 u_1, u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)))) (AlgHom.toRingHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3 f)))))))
 but is expected to have type
-  forall {R : Type.{w₁}} {A : Type.{w₂}} [_inst_1 : CommRing.{w₁} R] [_inst_2 : CommRing.{w₂} A] [_inst_3 : Algebra.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))], Iff (Algebra.FinitePresentation.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3) (Exists.{succ (succ u_1)} Type.{u_1} (fun (ι : Type.{u_1}) => Exists.{succ u_1} (Fintype.{u_1} ι) (fun (_x : Fintype.{u_1} ι) => Exists.{max (max (succ w₁) (succ w₂)) (succ u_1)} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (fun (f : AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ w₁) (succ u_1), succ w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (FunLike.coe.{max (max (succ w₁) (succ w₂)) 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))))))) (SMulZeroClass.toSMul.{w₁, w₂} R A (AddMonoid.toZero.{w₂} A (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{w₁, w₂} R A (AddMonoid.toAddZeroClass.{w₂} A (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))))) (DistribMulAction.toDistribSMul.{w₁, w₂} R A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max (max w₁ w₂) u_1, w₁, max w₁ u_1, w₂} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max w₁ w₂) u_1, w₁, max w₁ u_1, w₂} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{w₁, max w₁ u_1, w₂, max (max w₁ w₂) u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (AlgHom.algHomClass.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3))))) f)) (Ideal.FG.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (RingHom.ker.{max w₁ u_1, w₂, max (max w₁ w₂) u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (RingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (RingHom.instRingHomClassRingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (AlgHom.toRingHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 f)))))))
+  forall {R : Type.{w₁}} {A : Type.{w₂}} [_inst_1 : CommRing.{w₁} R] [_inst_2 : CommRing.{w₂} A] [_inst_3 : Algebra.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))], Iff (Algebra.FinitePresentation.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3) (Exists.{succ (succ u_1)} Type.{u_1} (fun (ι : Type.{u_1}) => Exists.{succ u_1} (Fintype.{u_1} ι) (fun (_x : Fintype.{u_1} ι) => Exists.{max (max (succ w₁) (succ w₂)) (succ u_1)} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (fun (f : AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ w₁) (succ u_1), succ w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (FunLike.coe.{max (max (succ w₁) (succ w₂)) 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(MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{w₁, max w₁ u_1, w₂, max (max w₁ w₂) u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (AlgHom.algHomClass.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3))))) f)) (Ideal.FG.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (RingHom.ker.{max w₁ u_1, w₂, max (max w₁ w₂) u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (RingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (RingHom.instRingHomClassRingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (AlgHom.toRingHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 f)))))))
 Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'ₓ'. -/
 /-- An algebra is finitely presented if and only if it is a quotient of a polynomial ring whose
 variables are indexed by a fintype by a finitely generated ideal. -/
@@ -619,7 +619,7 @@ theorem comp {g : B →ₐ[R] C} {f : A →ₐ[R] B} (hg : g.FinitePresentation)
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_4 : CommRing.{u4} C] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] [_inst_7 : Algebra.{u1, u4} R C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4))] {f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6} {g : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (Function.Surjective.{succ u3, succ u4} B C (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7) (fun (_x : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7) => B -> C) ([anonymous].{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7) g)) -> (Ideal.FG.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (RingHom.ker.{u3, u4, max u3 u4} B C (RingHom.{u3, u4} B C (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))) (Semiring.toNonAssocSemiring.{u4} C (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)))) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) (RingHom.ringHomClass.{u3, u4} B C (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))) (Semiring.toNonAssocSemiring.{u4} C (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)))) (AlgHom.toRingHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7 g))) -> (AlgHom.FinitePresentation.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
 but is expected to have type
-  forall {R : Type.{u4}} {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} B] [_inst_4 : CommRing.{u1} C] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))] [_inst_7 : Algebra.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))] {f : AlgHom.{u4, u3, u2} R A B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_5 _inst_6} {g : AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u4, u3, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (Function.Surjective.{succ u2, succ u1} B C (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : B) => C) _x) (SMulHomClass.toFunLike.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (SMulZeroClass.toSMul.{u4, u2} R B (AddMonoid.toZero.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R B (AddMonoid.toAddZeroClass.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R B (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6))))) (SMulZeroClass.toSMul.{u4, u1} R C (AddMonoid.toZero.{u1} C (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u1} R C (AddMonoid.toAddZeroClass.{u1} C (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u1} R C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))))) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))))) (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6)) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6)) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u2, u1, max u2 u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7 (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) (AlgHom.algHomClass.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7))))) g)) -> (Ideal.FG.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (RingHom.ker.{u2, u1, max u2 u1} B C (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (AlgHom.toRingHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7 g))) -> (AlgHom.FinitePresentation.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u3, u2, u1} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
+  forall {R : Type.{u4}} {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} B] [_inst_4 : CommRing.{u1} C] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))] [_inst_7 : Algebra.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))] {f : AlgHom.{u4, u3, u2} R A B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_5 _inst_6} {g : AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u4, u3, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (Function.Surjective.{succ u2, succ u1} B C (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : B) => C) _x) (SMulHomClass.toFunLike.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (SMulZeroClass.toSMul.{u4, u2} R B (AddMonoid.toZero.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R B (AddMonoid.toAddZeroClass.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R B (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6))))) (SMulZeroClass.toSMul.{u4, u1} R C (AddMonoid.toZero.{u1} C (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u1} R C (AddMonoid.toAddZeroClass.{u1} C (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u1} R C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))))) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))))) (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6)) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6)) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u2, u1, max u2 u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7 (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) (AlgHom.algHomClass.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7))))) g)) -> (Ideal.FG.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (RingHom.ker.{u2, u1, max u2 u1} B C (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (AlgHom.toRingHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7 g))) -> (AlgHom.FinitePresentation.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u3, u2, u1} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
 Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjectiveₓ'. -/
 theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePresentation)
     (hg : Surjective g) (hker : g.toRingHom.ker.FG) : (g.comp f).FinitePresentation :=
@@ -630,7 +630,7 @@ theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePr
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] (f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) => A -> B) ([anonymous].{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) f)) -> (Ideal.FG.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (RingHom.ker.{u2, u3, max u2 u3} A B (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (RingHom.ringHomClass.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)))) (AlgHom.toRingHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6 f))) -> (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
 but is expected to have type
-  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u1} B] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_6 : Algebra.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))] (f : AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6))))) f)) -> (Ideal.FG.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ker.{u2, u1, max u2 u1} A B (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (AlgHom.toRingHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 f))) -> (AlgHom.FinitePresentation.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u1} B] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_6 : Algebra.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))] (f : AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6))))) f)) -> (Ideal.FG.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ker.{u2, u1, max u2 u1} A B (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (AlgHom.toRingHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 f))) -> (AlgHom.FinitePresentation.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
 Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjectiveₓ'. -/
 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module ring_theory.finite_presentation
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
+! leanprover-community/mathlib commit 33c67ae661dd8988516ff7f247b0be3018cdd952
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Ideal.QuotientOperations
 /-!
 # Finiteness conditions in commutative algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define several notions of finiteness that are common in commutative algebra.
 
 ## Main declarations

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

@@ -37,11 +37,13 @@ section ModuleAndAlgebra
 
 variable (R A B M N : Type _)
 
+#print Algebra.FinitePresentation /-
 /-- An algebra over a commutative semiring is `finite_presentation` if it is the quotient of a
 polynomial ring in `n` variables by a finitely generated ideal. -/
 def Algebra.FinitePresentation [CommSemiring R] [Semiring A] [Algebra R A] : Prop :=
   ∃ (n : ℕ)(f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.FG
 #align algebra.finite_presentation Algebra.FinitePresentation
+-/
 
 namespace Algebra
 
@@ -55,6 +57,12 @@ namespace FiniteType
 
 variable {R A B}
 
+/- warning: algebra.finite_type.of_finite_presentation -> Algebra.FiniteType.of_finitePresentation is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], (Algebra.FinitePresentation.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) -> (Algebra.FiniteType.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))], (Algebra.FinitePresentation.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) -> (Algebra.FiniteType.{u2, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3)
+Case conversion may be inaccurate. Consider using '#align algebra.finite_type.of_finite_presentation Algebra.FiniteType.of_finitePresentationₓ'. -/
 /-- A finitely presented algebra is of finite type. -/
 theorem of_finitePresentation : FinitePresentation R A → FiniteType R A :=
   by
@@ -69,6 +77,12 @@ namespace FinitePresentation
 
 variable {R A B}
 
+/- warning: algebra.finite_presentation.of_finite_type -> Algebra.FinitePresentation.of_finiteType is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_10 : IsNoetherianRing.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))], Iff (Algebra.FiniteType.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3) (Algebra.FinitePresentation.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_10 : IsNoetherianRing.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))], Iff (Algebra.FiniteType.{u2, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Algebra.FinitePresentation.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3)
+Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.of_finite_type Algebra.FinitePresentation.of_finiteTypeₓ'. -/
 /-- An algebra over a Noetherian ring is finitely generated if and only if it is finitely
 presented. -/
 theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentation R A :=
@@ -81,6 +95,7 @@ theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentati
   exact hnoet f.to_ring_hom.ker
 #align algebra.finite_presentation.of_finite_type Algebra.FinitePresentation.of_finiteType
 
+#print Algebra.FinitePresentation.equiv /-
 /-- If `e : A ≃ₐ[R] B` and `A` is finitely presented, then so is `B`. -/
 theorem equiv (hfp : FinitePresentation R A) (e : A ≃ₐ[R] B) : FinitePresentation R B :=
   by
@@ -99,9 +114,11 @@ theorem equiv (hfp : FinitePresentation R A) (e : A ≃ₐ[R] B) : FinitePresent
     rw [RingHom.ker_eq_comap_bot, hco, ← Ideal.comap_comap, ← RingHom.ker_eq_comap_bot,
       RingHom.ker_coe_equiv (AlgEquiv.toRingEquiv e), RingHom.ker_eq_comap_bot]
 #align algebra.finite_presentation.equiv Algebra.FinitePresentation.equiv
+-/
 
 variable (R)
 
+#print Algebra.FinitePresentation.mvPolynomial /-
 /-- The ring of polynomials in finitely many variables is finitely presented. -/
 protected theorem mvPolynomial (ι : Type u_2) [Finite ι] :
     FinitePresentation R (MvPolynomial ι R) := by
@@ -111,19 +128,25 @@ protected theorem mvPolynomial (ι : Type u_2) [Finite ι] :
       ⟨Fintype.card ι, eqv, eqv.Surjective,
         ((RingHom.injective_iff_ker_eq_bot _).1 eqv.Injective).symm ▸ Submodule.fg_bot⟩
 #align algebra.finite_presentation.mv_polynomial Algebra.FinitePresentation.mvPolynomial
+-/
 
+#print Algebra.FinitePresentation.self /-
 /-- `R` is finitely presented as `R`-algebra. -/
 theorem self : FinitePresentation R R :=
   equiv (FinitePresentation.mvPolynomial R PEmpty) (MvPolynomial.isEmptyAlgEquiv R PEmpty)
 #align algebra.finite_presentation.self Algebra.FinitePresentation.self
+-/
 
+#print Algebra.FinitePresentation.polynomial /-
 /-- `R[X]` is finitely presented as `R`-algebra. -/
 theorem polynomial : FinitePresentation R R[X] :=
   equiv (FinitePresentation.mvPolynomial R PUnit) (MvPolynomial.pUnitAlgEquiv R)
 #align algebra.finite_presentation.polynomial Algebra.FinitePresentation.polynomial
+-/
 
 variable {R}
 
+#print Algebra.FinitePresentation.quotient /-
 /-- The quotient of a finitely presented algebra by a finitely generated ideal is finitely
 presented. -/
 protected theorem quotient {I : Ideal A} (h : I.FG) (hfp : FinitePresentation R A) :
@@ -134,14 +157,18 @@ protected theorem quotient {I : Ideal A} (h : I.FG) (hfp : FinitePresentation R
   · refine' Ideal.fg_ker_comp _ _ hf.2 _ hf.1
     simp [h]
 #align algebra.finite_presentation.quotient Algebra.FinitePresentation.quotient
+-/
 
+#print Algebra.FinitePresentation.of_surjective /-
 /-- If `f : A →ₐ[R] B` is surjective with finitely generated kernel and `A` is finitely presented,
 then so is `B`. -/
 theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f.toRingHom.ker.FG)
     (hfp : FinitePresentation R A) : FinitePresentation R B :=
   equiv (hfp.Quotient hker) (Ideal.quotientKerAlgEquivOfSurjective hf)
 #align algebra.finite_presentation.of_surjective Algebra.FinitePresentation.of_surjective
+-/
 
+#print Algebra.FinitePresentation.iff /-
 theorem iff :
     FinitePresentation R A ↔
       ∃ (n : _)(I : Ideal (MvPolynomial (Fin n) R))(e : (_ ⧸ I) ≃ₐ[R] A), I.FG :=
@@ -152,10 +179,17 @@ theorem iff :
   · rintro ⟨n, I, e, hfg⟩
     exact Equiv ((finite_presentation.mv_polynomial R _).Quotient hfg) e
 #align algebra.finite_presentation.iff Algebra.FinitePresentation.iff
+-/
 
+/- warning: algebra.finite_presentation.iff_quotient_mv_polynomial' -> Algebra.FinitePresentation.iff_quotient_mvPolynomial' is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u_1}} {A : Type.{u_2}} [_inst_1 : CommRing.{u_1} R] [_inst_2 : CommRing.{u_2} A] [_inst_3 : Algebra.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2))], Iff (Algebra.FinitePresentation.{u_1, u_2} R A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) _inst_3) (Exists.{succ (succ u_2)} Type.{u_2} (fun (ι : Type.{u_2}) => Exists.{succ u_2} (Fintype.{u_2} ι) (fun (_x : Fintype.{u_2} ι) => Exists.{max (succ (max u_2 u_1)) (succ u_2)} (AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) (fun (f : AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ u_2) (succ u_1), succ u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (coeFn.{max (succ (max u_2 u_1)) (succ u_2), max (succ (max u_2 u_1)) (succ u_2)} (AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) (fun (_x : AlgHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) => (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) -> A) ([anonymous].{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3) f)) (Ideal.FG.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (RingHom.ker.{max u_2 u_1, u_2, max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (RingHom.{max u_2 u_1, u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)))) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (RingHom.ringHomClass.{max u_2 u_1, u_2} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (Semiring.toNonAssocSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1)))) (Semiring.toNonAssocSemiring.{u_2} A (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)))) (AlgHom.toRingHom.{u_1, max u_2 u_1, u_2} R (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) A (CommRing.toCommSemiring.{u_1} R _inst_1) (Ring.toSemiring.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (CommRing.toRing.{max u_2 u_1} (MvPolynomial.{u_2, u_1} ι R (CommRing.toCommSemiring.{u_1} R _inst_1)) (MvPolynomial.commRing.{u_1, u_2} R ι _inst_1))) (Ring.toSemiring.{u_2} A (CommRing.toRing.{u_2} A _inst_2)) (MvPolynomial.algebra.{u_1, u_1, u_2} R R ι (CommRing.toCommSemiring.{u_1} R _inst_1) (CommRing.toCommSemiring.{u_1} R _inst_1) (Algebra.id.{u_1} R (CommRing.toCommSemiring.{u_1} R _inst_1))) _inst_3 f)))))))
+but is expected to have type
+  forall {R : Type.{w₁}} {A : Type.{w₂}} [_inst_1 : CommRing.{w₁} R] [_inst_2 : CommRing.{w₂} A] [_inst_3 : Algebra.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))], Iff (Algebra.FinitePresentation.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3) (Exists.{succ (succ u_1)} Type.{u_1} (fun (ι : Type.{u_1}) => Exists.{succ u_1} (Fintype.{u_1} ι) (fun (_x : Fintype.{u_1} ι) => Exists.{max (max (succ w₁) (succ w₂)) (succ u_1)} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (fun (f : AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) => And (Function.Surjective.{max (succ w₁) (succ u_1), succ w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (FunLike.coe.{max (max (succ w₁) (succ w₂)) (succ u_1), max (succ w₁) (succ u_1), succ w₂} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (fun (_x : MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max (max w₁ w₂) u_1, w₁, max w₁ u_1, 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(NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))))))) (SMulZeroClass.toSMul.{w₁, w₂} R A (AddMonoid.toZero.{w₂} A (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{w₁, w₂} R A (AddMonoid.toAddZeroClass.{w₂} A (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))))) (DistribMulAction.toDistribSMul.{w₁, w₂} R A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max (max w₁ w₂) u_1, w₁, max w₁ u_1, w₂} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))))) (AddCommMonoid.toAddMonoid.{w₂} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max (max w₁ w₂) u_1, w₁, max w₁ u_1, w₂} (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (MonoidWithZero.toMonoid.{w₁} R (Semiring.toMonoidWithZero.{w₁} R (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (Module.toDistribMulAction.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))))) (Algebra.toModule.{w₁, max w₁ u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))))) (Module.toDistribMulAction.{w₁, w₂} R A (CommSemiring.toSemiring.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{w₂} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{w₂} A (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2))))) (Algebra.toModule.{w₁, w₂} R A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{w₁, max w₁ u_1, w₂, max (max w₁ w₂) u_1} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 (AlgHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3) (AlgHom.algHomClass.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3))))) f)) (Ideal.FG.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (RingHom.ker.{max w₁ u_1, w₂, max (max w₁ w₂) u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (RingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (RingHom.instRingHomClassRingHom.{max w₁ u_1, w₂} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (Semiring.toNonAssocSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1)))) (Semiring.toNonAssocSemiring.{w₂} A (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)))) (AlgHom.toRingHom.{w₁, max w₁ u_1, w₂} R (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) A (CommRing.toCommSemiring.{w₁} R _inst_1) (CommSemiring.toSemiring.{max w₁ u_1} (MvPolynomial.{u_1, w₁} ι R (CommRing.toCommSemiring.{w₁} R _inst_1)) (MvPolynomial.commSemiring.{w₁, u_1} R ι (CommRing.toCommSemiring.{w₁} R _inst_1))) (CommSemiring.toSemiring.{w₂} A (CommRing.toCommSemiring.{w₂} A _inst_2)) (MvPolynomial.algebra.{w₁, w₁, u_1} R R ι (CommRing.toCommSemiring.{w₁} R _inst_1) (CommRing.toCommSemiring.{w₁} R _inst_1) (Algebra.id.{w₁} R (CommRing.toCommSemiring.{w₁} R _inst_1))) _inst_3 f)))))))
+Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'ₓ'. -/
 /-- An algebra is finitely presented if and only if it is a quotient of a polynomial ring whose
 variables are indexed by a fintype by a finitely generated ideal. -/
-theorem iff_quotient_mv_polynomial' :
+theorem iff_quotient_mvPolynomial' :
     FinitePresentation R A ↔
       ∃ (ι : Type u_2)(_ : Fintype ι)(f : MvPolynomial ι R →ₐ[R] A),
         Surjective f ∧ f.toRingHom.ker.FG :=
@@ -176,8 +210,9 @@ theorem iff_quotient_mv_polynomial' :
         Ideal.fg_ker_comp _ f _ hf.2 equiv.symm.surjective⟩
     convert Submodule.fg_bot
     exact RingHom.ker_coe_equiv equiv.symm.to_ring_equiv
-#align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mv_polynomial'
+#align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'
 
+#print Algebra.FinitePresentation.mvPolynomial_of_finitePresentation /-
 /-- If `A` is a finitely presented `R`-algebra, then `mv_polynomial (fin n) A` is finitely presented
 as `R`-algebra. -/
 theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι : Type _) [Finite ι] :
@@ -198,7 +233,9 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι :
     · rw [AlgHom.toRingHom_eq_coe, MvPolynomial.mapAlgHom_coe_ringHom, MvPolynomial.ker_map]
       exact hf_ker.map MvPolynomial.C
 #align algebra.finite_presentation.mv_polynomial_of_finite_presentation Algebra.FinitePresentation.mvPolynomial_of_finitePresentation
+-/
 
+#print Algebra.FinitePresentation.trans /-
 /-- If `A` is an `R`-algebra and `S` is an `A`-algebra, both finitely presented, then `S` is
   finitely presented as `R`-algebra. -/
 theorem trans [Algebra A B] [IsScalarTower R A B] (hfpA : FinitePresentation R A)
@@ -207,9 +244,16 @@ theorem trans [Algebra A B] [IsScalarTower R A B] (hfpA : FinitePresentation R A
   obtain ⟨n, I, e, hfg⟩ := Iff.1 hfpB
   exact Equiv ((mv_polynomial_of_finite_presentation hfpA _).Quotient hfg) (e.restrict_scalars R)
 #align algebra.finite_presentation.trans Algebra.FinitePresentation.trans
+-/
 
 open MvPolynomial
 
+/- warning: algebra.finite_presentation.of_restrict_scalars_finite_presentation -> Algebra.FinitePresentation.of_restrict_scalars_finitePresentation is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_4 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))] [_inst_10 : Algebra.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))] [_inst_11 : IsScalarTower.{u1, u2, u3} R A B (SMulZeroClass.toHasSmul.{u1, u2} R A (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (SMulWithZero.toSmulZeroClass.{u1, u2} R A (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (MulActionWithZero.toSMulWithZero.{u1, u2} R A (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u2} A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)))))))) (Module.toMulActionWithZero.{u1, u2} R A (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))))) (Algebra.toModule.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3))))) (SMulZeroClass.toHasSmul.{u2, u3} A B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u2, u3} A B (MulZeroClass.toHasZero.{u2} A (MulZeroOneClass.toMulZeroClass.{u2} A (MonoidWithZero.toMulZeroOneClass.{u2} A (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u2, u3} A B (Semiring.toMonoidWithZero.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (Module.toMulActionWithZero.{u2, u3} A B (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_10))))) (SMulZeroClass.toHasSmul.{u1, u3} R B (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (SMulWithZero.toSmulZeroClass.{u1, u3} R B (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (MulActionWithZero.toSMulWithZero.{u1, u3} R B (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddZeroClass.toHasZero.{u3} B (AddMonoid.toAddZeroClass.{u3} B (AddCommMonoid.toAddMonoid.{u3} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)))))))) (Module.toMulActionWithZero.{u1, u3} R B (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} B (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4))))) (Algebra.toModule.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5)))))], (Algebra.FinitePresentation.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_5) -> (forall [hRA : Algebra.FiniteType.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_3], Algebra.FinitePresentation.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_4)) _inst_10)
+but is expected to have type
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_4 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4))] [_inst_10 : Algebra.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4))] [_inst_11 : IsScalarTower.{u1, u2, u3} R A B (Algebra.toSMul.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3) (Algebra.toSMul.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_10) (Algebra.toSMul.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5)], (Algebra.FinitePresentation.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_5) -> (forall [hRA : Algebra.FiniteType.{u2, u1} R A (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_3], Algebra.FinitePresentation.{u2, u3} A B (CommRing.toCommSemiring.{u2} A _inst_2) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_4)) _inst_10)
+Case conversion may be inaccurate. Consider using '#align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentationₓ'. -/
 -- We follow the proof of https://stacks.math.columbia.edu/tag/0561
 -- TODO: extract out helper lemmas and tidy proof.
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
@@ -303,9 +347,10 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
 
+#print Algebra.FinitePresentation.ker_fg_of_mvPolynomial /-
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
-theorem ker_fG_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
+theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
     (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
   classical
     obtain ⟨m, f', hf', s, hs⟩ := hfp
@@ -377,8 +422,10 @@ theorem ker_fG_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     apply Submodule.subset_span
     apply Set.mem_union_right
     exact Set.mem_image_of_mem _ hx
-#align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fG_of_mvPolynomial
+#align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
+-/
 
+#print Algebra.FinitePresentation.ker_fG_of_surjective /-
 /-- If `f : A →ₐ[R] B` is a sujection between finitely-presented `R`-algebras, then the kernel of
 `f` is finitely generated. -/
 theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
@@ -389,6 +436,7 @@ theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 #align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fG_of_surjective
+-/
 
 end FinitePresentation
 
@@ -400,14 +448,22 @@ namespace RingHom
 
 variable {A B C : Type _} [CommRing A] [CommRing B] [CommRing C]
 
+#print RingHom.FinitePresentation /-
 /-- A ring morphism `A →+* B` is of `finite_presentation` if `B` is finitely presented as
 `A`-algebra. -/
 def FinitePresentation (f : A →+* B) : Prop :=
   @Algebra.FinitePresentation A B _ _ f.toAlgebra
 #align ring_hom.finite_presentation RingHom.FinitePresentation
+-/
 
 namespace FiniteType
 
+/- warning: ring_hom.finite_type.of_finite_presentation -> RingHom.FiniteType.of_finitePresentation is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (RingHom.FinitePresentation.{u1, u2} A B _inst_1 _inst_2 f) -> (RingHom.FiniteType.{u1, u2} A B _inst_1 _inst_2 f)
+but is expected to have type
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, (RingHom.FinitePresentation.{u2, u1} A B _inst_1 _inst_2 f) -> (RingHom.FiniteType.{u2, u1} A B _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align ring_hom.finite_type.of_finite_presentation RingHom.FiniteType.of_finitePresentationₓ'. -/
 theorem of_finitePresentation {f : A →+* B} (hf : f.FinitePresentation) : f.FiniteType :=
   @Algebra.FiniteType.of_finitePresentation A B _ _ f.toAlgebra hf
 #align ring_hom.finite_type.of_finite_presentation RingHom.FiniteType.of_finitePresentation
@@ -418,12 +474,20 @@ namespace FinitePresentation
 
 variable (A)
 
+#print RingHom.FinitePresentation.id /-
 theorem id : FinitePresentation (RingHom.id A) :=
   Algebra.FinitePresentation.self A
 #align ring_hom.finite_presentation.id RingHom.FinitePresentation.id
+-/
 
 variable {A}
 
+/- warning: ring_hom.finite_presentation.comp_surjective -> RingHom.FinitePresentation.comp_surjective is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {B : Type.{u2}} {C : Type.{u3}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : CommRing.{u3} C] {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))} {g : RingHom.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))}, (RingHom.FinitePresentation.{u1, u2} A B _inst_1 _inst_2 f) -> (Function.Surjective.{succ u2, succ u3} B C (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (RingHom.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))) (fun (_x : RingHom.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))) => B -> C) (RingHom.hasCoeToFun.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))) g)) -> (Ideal.FG.{u2} B (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) (RingHom.ker.{u2, u3, max u2 u3} B C (RingHom.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))) (Ring.toSemiring.{u2} B (CommRing.toRing.{u2} B _inst_2)) (Ring.toSemiring.{u3} C (CommRing.toRing.{u3} C _inst_3)) (RingHom.ringHomClass.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))) g)) -> (RingHom.FinitePresentation.{u1, u3} A C _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} A B C (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3))) g f))
+but is expected to have type
+  forall {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u3} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : CommRing.{u1} C] {f : RingHom.{u3, u2} A B (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2)))} {g : RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))}, (RingHom.FinitePresentation.{u3, u2} A B _inst_1 _inst_2 f) -> (Function.Surjective.{succ u2, succ u1} B C (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : B) => C) _x) (MulHomClass.toFunLike.{max u2 u1, u2, u1} (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) B C (NonUnitalNonAssocSemiring.toMul.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))))) (NonUnitalNonAssocSemiring.toMul.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) B C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, u1} (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3))) (RingHom.instRingHomClassRingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3))))))) g)) -> (Ideal.FG.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2)) (RingHom.ker.{u2, u1, max u2 u1} B C (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)) (RingHom.instRingHomClassRingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))) g)) -> (RingHom.FinitePresentation.{u3, u1} A C _inst_1 _inst_3 (RingHom.comp.{u3, u2, u1} A B C (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3))) g f))
+Case conversion may be inaccurate. Consider using '#align ring_hom.finite_presentation.comp_surjective RingHom.FinitePresentation.comp_surjectiveₓ'. -/
 theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentation) (hg : Surjective g)
     (hker : g.ker.FG) : (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.of_surjective A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra
@@ -433,16 +497,34 @@ theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentati
     hg hker hf
 #align ring_hom.finite_presentation.comp_surjective RingHom.FinitePresentation.comp_surjective
 
+/- warning: ring_hom.finite_presentation.of_surjective -> RingHom.FinitePresentation.of_surjective is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ring_hom.finite_presentation.of_surjective RingHom.FinitePresentation.of_surjectiveₓ'. -/
 theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.FG) : f.FinitePresentation :=
   by
   rw [← f.comp_id]
   exact (id A).comp_surjective hf hker
 #align ring_hom.finite_presentation.of_surjective RingHom.FinitePresentation.of_surjective
 
+/- warning: ring_hom.finite_presentation.of_finite_type -> RingHom.FinitePresentation.of_finiteType is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {B : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_4 : IsNoetherianRing.{u1} A (Ring.toSemiring.{u1} A (CommRing.toRing.{u1} A _inst_1))] {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, Iff (RingHom.FiniteType.{u1, u2} A B _inst_1 _inst_2 f) (RingHom.FinitePresentation.{u1, u2} A B _inst_1 _inst_2 f)
+but is expected to have type
+  forall {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} A] [_inst_2 : CommRing.{u1} B] [_inst_4 : IsNoetherianRing.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))] {f : RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_1))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_2)))}, Iff (RingHom.FiniteType.{u2, u1} A B _inst_1 _inst_2 f) (RingHom.FinitePresentation.{u2, u1} A B _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align ring_hom.finite_presentation.of_finite_type RingHom.FinitePresentation.of_finiteTypeₓ'. -/
 theorem of_finiteType [IsNoetherianRing A] {f : A →+* B} : f.FiniteType ↔ f.FinitePresentation :=
   @Algebra.FinitePresentation.of_finiteType A B _ _ f.toAlgebra _
 #align ring_hom.finite_presentation.of_finite_type RingHom.FinitePresentation.of_finiteType
 
+/- warning: ring_hom.finite_presentation.comp -> RingHom.FinitePresentation.comp is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {B : Type.{u2}} {C : Type.{u3}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : CommRing.{u3} C] {g : RingHom.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))} {f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))}, (RingHom.FinitePresentation.{u2, u3} B C _inst_2 _inst_3 g) -> (RingHom.FinitePresentation.{u1, u2} A B _inst_1 _inst_2 f) -> (RingHom.FinitePresentation.{u1, u3} A C _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} A B C (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3))) g f))
+but is expected to have type
+  forall {A : Type.{u1}} {B : Type.{u3}} {C : Type.{u2}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u3} B] [_inst_3 : CommRing.{u2} C] {g : RingHom.{u3, u2} B C (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_2))) (Semiring.toNonAssocSemiring.{u2} C (CommSemiring.toSemiring.{u2} C (CommRing.toCommSemiring.{u2} C _inst_3)))} {f : RingHom.{u1, u3} A B (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_2)))}, (RingHom.FinitePresentation.{u3, u2} B C _inst_2 _inst_3 g) -> (RingHom.FinitePresentation.{u1, u3} A B _inst_1 _inst_2 f) -> (RingHom.FinitePresentation.{u1, u2} A C _inst_1 _inst_3 (RingHom.comp.{u1, u3, u2} A B C (Semiring.toNonAssocSemiring.{u1} A (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_1))) (Semiring.toNonAssocSemiring.{u3} B (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_2))) (Semiring.toNonAssocSemiring.{u2} C (CommSemiring.toSemiring.{u2} C (CommRing.toCommSemiring.{u2} C _inst_3))) g f))
+Case conversion may be inaccurate. Consider using '#align ring_hom.finite_presentation.comp RingHom.FinitePresentation.compₓ'. -/
 theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f.FinitePresentation) :
     (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.trans A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra g.toAlgebra
@@ -454,6 +536,12 @@ theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f
     hf hg
 #align ring_hom.finite_presentation.comp RingHom.FinitePresentation.comp
 
+/- warning: ring_hom.finite_presentation.of_comp_finite_type -> RingHom.FinitePresentation.of_comp_finiteType is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {B : Type.{u2}} {C : Type.{u3}} [_inst_1 : CommRing.{u1} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : CommRing.{u3} C] (f : RingHom.{u1, u2} A B (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2)))) {g : RingHom.{u2, u3} B C (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3)))}, (RingHom.FinitePresentation.{u1, u3} A C _inst_1 _inst_3 (RingHom.comp.{u1, u2, u3} A B C (NonAssocRing.toNonAssocSemiring.{u1} A (Ring.toNonAssocRing.{u1} A (CommRing.toRing.{u1} A _inst_1))) (NonAssocRing.toNonAssocSemiring.{u2} B (Ring.toNonAssocRing.{u2} B (CommRing.toRing.{u2} B _inst_2))) (NonAssocRing.toNonAssocSemiring.{u3} C (Ring.toNonAssocRing.{u3} C (CommRing.toRing.{u3} C _inst_3))) g f)) -> (RingHom.FiniteType.{u1, u2} A B _inst_1 _inst_2 f) -> (RingHom.FinitePresentation.{u2, u3} B C _inst_2 _inst_3 g)
+but is expected to have type
+  forall {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u3} A] [_inst_2 : CommRing.{u2} B] [_inst_3 : CommRing.{u1} C] (f : RingHom.{u3, u2} A B (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2)))) {g : RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3)))}, (RingHom.FinitePresentation.{u3, u1} A C _inst_1 _inst_3 (RingHom.comp.{u3, u2, u1} A B C (Semiring.toNonAssocSemiring.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_1))) (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_2))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_3))) g f)) -> (RingHom.FiniteType.{u3, u2} A B _inst_1 _inst_2 f) -> (RingHom.FinitePresentation.{u2, u1} B C _inst_2 _inst_3 g)
+Case conversion may be inaccurate. Consider using '#align ring_hom.finite_presentation.of_comp_finite_type RingHom.FinitePresentation.of_comp_finiteTypeₓ'. -/
 theorem of_comp_finiteType (f : A →+* B) {g : B →+* C} (hg : (g.comp f).FinitePresentation)
     (hf : f.FiniteType) : g.FinitePresentation :=
   @Algebra.FinitePresentation.of_restrict_scalars_finitePresentation _ _ f.toAlgebra _
@@ -473,16 +561,24 @@ variable [CommRing A] [CommRing B] [CommRing C]
 
 variable [Algebra R A] [Algebra R B] [Algebra R C]
 
+#print AlgHom.FinitePresentation /-
 /-- An algebra morphism `A →ₐ[R] B` is of `finite_presentation` if it is of finite presentation as
 ring morphism. In other words, if `B` is finitely presented as `A`-algebra. -/
 def FinitePresentation (f : A →ₐ[R] B) : Prop :=
   f.toRingHom.FinitePresentation
 #align alg_hom.finite_presentation AlgHom.FinitePresentation
+-/
 
 namespace FiniteType
 
 variable {R A}
 
+/- warning: alg_hom.finite_type.of_finite_presentation -> AlgHom.FiniteType.of_finitePresentation is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] {f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6}, (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FiniteType.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u1} B] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_6 : Algebra.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))] {f : AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6}, (AlgHom.FinitePresentation.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FiniteType.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_type.of_finite_presentation AlgHom.FiniteType.of_finitePresentationₓ'. -/
 theorem of_finitePresentation {f : A →ₐ[R] B} (hf : f.FinitePresentation) : f.FiniteType :=
   RingHom.FiniteType.of_finitePresentation hf
 #align alg_hom.finite_type.of_finite_presentation AlgHom.FiniteType.of_finitePresentation
@@ -493,31 +589,67 @@ namespace FinitePresentation
 
 variable (R A)
 
+/- warning: alg_hom.finite_presentation.id -> AlgHom.FinitePresentation.id is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (A : Type.{u2}) [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))], AlgHom.FinitePresentation.{u1, u2, u2} R A A _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (AlgHom.id.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) _inst_5)
+but is expected to have type
+  forall (R : Type.{u2}) (A : Type.{u1}) [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u1} A] [_inst_5 : Algebra.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))], AlgHom.FinitePresentation.{u2, u1, u1} R A A _inst_1 _inst_2 _inst_2 _inst_5 _inst_5 (AlgHom.id.{u2, u1} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) _inst_5)
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.id AlgHom.FinitePresentation.idₓ'. -/
 theorem id : FinitePresentation (AlgHom.id R A) :=
   RingHom.FinitePresentation.id A
 #align alg_hom.finite_presentation.id AlgHom.FinitePresentation.id
 
 variable {R A}
 
+/- warning: alg_hom.finite_presentation.comp -> AlgHom.FinitePresentation.comp is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_4 : CommRing.{u4} C] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] [_inst_7 : Algebra.{u1, u4} R C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4))] {g : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7} {f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6}, (AlgHom.FinitePresentation.{u1, u3, u4} R B C _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FinitePresentation.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
+but is expected to have type
+  forall {R : Type.{u4}} {A : Type.{u1}} {B : Type.{u3}} {C : Type.{u2}} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u1} A] [_inst_3 : CommRing.{u3} B] [_inst_4 : CommRing.{u2} C] [_inst_5 : Algebra.{u4, u1} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2))] [_inst_6 : Algebra.{u4, u3} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_3))] [_inst_7 : Algebra.{u4, u2} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} C (CommRing.toCommSemiring.{u2} C _inst_4))] {g : AlgHom.{u4, u3, u2} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_3)) (CommSemiring.toSemiring.{u2} C (CommRing.toCommSemiring.{u2} C _inst_4)) _inst_6 _inst_7} {f : AlgHom.{u4, u1, u3} R A B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_3)) _inst_5 _inst_6}, (AlgHom.FinitePresentation.{u4, u3, u2} R B C _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g) -> (AlgHom.FinitePresentation.{u4, u1, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FinitePresentation.{u4, u1, u2} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u1, u3, u2} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} A (CommRing.toCommSemiring.{u1} A _inst_2)) (CommSemiring.toSemiring.{u3} B (CommRing.toCommSemiring.{u3} B _inst_3)) (CommSemiring.toSemiring.{u2} C (CommRing.toCommSemiring.{u2} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.comp AlgHom.FinitePresentation.compₓ'. -/
 theorem comp {g : B →ₐ[R] C} {f : A →ₐ[R] B} (hg : g.FinitePresentation)
     (hf : f.FinitePresentation) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp hg hf
 #align alg_hom.finite_presentation.comp AlgHom.FinitePresentation.comp
 
+/- warning: alg_hom.finite_presentation.comp_surjective -> AlgHom.FinitePresentation.comp_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_4 : CommRing.{u4} C] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] [_inst_7 : Algebra.{u1, u4} R C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4))] {f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6} {g : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (Function.Surjective.{succ u3, succ u4} B C (coeFn.{max (succ u3) (succ u4), max (succ u3) (succ u4)} (AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7) (fun (_x : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7) => B -> C) ([anonymous].{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7) g)) -> (Ideal.FG.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (RingHom.ker.{u3, u4, max u3 u4} B C (RingHom.{u3, u4} B C (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))) (Semiring.toNonAssocSemiring.{u4} C (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)))) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) (RingHom.ringHomClass.{u3, u4} B C (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))) (Semiring.toNonAssocSemiring.{u4} C (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)))) (AlgHom.toRingHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7 g))) -> (AlgHom.FinitePresentation.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
+but is expected to have type
+  forall {R : Type.{u4}} {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} B] [_inst_4 : CommRing.{u1} C] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))] [_inst_7 : Algebra.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))] {f : AlgHom.{u4, u3, u2} R A B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_5 _inst_6} {g : AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u4, u3, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (Function.Surjective.{succ u2, succ u1} B C (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) B (fun (_x : B) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : B) => C) _x) (SMulHomClass.toFunLike.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (SMulZeroClass.toSMul.{u4, u2} R B (AddMonoid.toZero.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u4, u2} R B (AddMonoid.toAddZeroClass.{u2} B (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u4, u2} R B (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6))))) (SMulZeroClass.toSMul.{u4, u1} R C (AddMonoid.toZero.{u1} C (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))))) (DistribSMul.toSMulZeroClass.{u4, u1} R C (AddMonoid.toAddZeroClass.{u1} C (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))))) (DistribMulAction.toDistribSMul.{u4, u1} R C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))))) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))))) (AddCommMonoid.toAddMonoid.{u1} C (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6)) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u4, u2, u1} (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) R B C (MonoidWithZero.toMonoid.{u4} R (Semiring.toMonoidWithZero.{u4} R (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (Module.toDistribMulAction.{u4, u2} R B (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} B (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))))) (Algebra.toModule.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_6)) (Module.toDistribMulAction.{u4, u1} R C (CommSemiring.toSemiring.{u4} R (CommRing.toCommSemiring.{u4} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} C (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} C (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))))) (Algebra.toModule.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_7)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u4, u2, u1, max u2 u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7 (AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7) (AlgHom.algHomClass.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7))))) g)) -> (Ideal.FG.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (RingHom.ker.{u2, u1, max u2 u1} B C (RingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) (RingHom.instRingHomClassRingHom.{u2, u1} B C (Semiring.toNonAssocSemiring.{u2} B (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))) (Semiring.toNonAssocSemiring.{u1} C (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)))) (AlgHom.toRingHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7 g))) -> (AlgHom.FinitePresentation.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u3, u2, u1} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_5 _inst_6 _inst_7 g f))
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjectiveₓ'. -/
 theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePresentation)
     (hg : Surjective g) (hker : g.toRingHom.ker.FG) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp_surjective hf hg hker
 #align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjective
 
+/- warning: alg_hom.finite_presentation.of_surjective -> AlgHom.FinitePresentation.of_surjective is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] (f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u3} A B (coeFn.{max (succ u2) (succ u3), max (succ u2) (succ u3)} (AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) (fun (_x : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) => A -> B) ([anonymous].{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) f)) -> (Ideal.FG.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (RingHom.ker.{u2, u3, max u2 u3} A B (RingHom.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)))) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (RingHom.ringHomClass.{u2, u3} A B (Semiring.toNonAssocSemiring.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u3} B (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)))) (AlgHom.toRingHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6 f))) -> (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+but is expected to have type
+  forall {R : Type.{u3}} {A : Type.{u2}} {B : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u1} B] [_inst_5 : Algebra.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))] [_inst_6 : Algebra.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))] (f : AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6), (Function.Surjective.{succ u2, succ u1} A B (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) A (fun (_x : A) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : A) => B) _x) (SMulHomClass.toFunLike.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (SMulZeroClass.toSMul.{u3, u2} R A (AddMonoid.toZero.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribSMul.toSMulZeroClass.{u3, u2} R A (AddMonoid.toAddZeroClass.{u2} A (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))))) (DistribMulAction.toDistribSMul.{u3, u2} R A (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5))))) (SMulZeroClass.toSMul.{u3, u1} R B (AddMonoid.toZero.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribSMul.toSMulZeroClass.{u3, u1} R B (AddMonoid.toAddZeroClass.{u1} B (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))))) (DistribMulAction.toDistribSMul.{u3, u1} R B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6))))) (DistribMulActionHomClass.toSMulHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))))) (AddCommMonoid.toAddMonoid.{u1} B (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u2 u1, u3, u2, u1} (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) R A B (MonoidWithZero.toMonoid.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (Module.toDistribMulAction.{u3, u2} R A (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))))) (Algebra.toModule.{u3, u2} R A (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) _inst_5)) (Module.toDistribMulAction.{u3, u1} R B (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} B (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} B (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))))) (Algebra.toModule.{u3, u1} R B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_6)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u3, u2, u1, max u2 u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 (AlgHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6) (AlgHom.algHomClass.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6))))) f)) -> (Ideal.FG.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (RingHom.ker.{u2, u1, max u2 u1} A B (RingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) (RingHom.instRingHomClassRingHom.{u2, u1} A B (Semiring.toNonAssocSemiring.{u2} A (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2))) (Semiring.toNonAssocSemiring.{u1} B (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)))) (AlgHom.toRingHom.{u3, u2, u1} R A B (CommRing.toCommSemiring.{u3} R _inst_1) (CommSemiring.toSemiring.{u2} A (CommRing.toCommSemiring.{u2} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6 f))) -> (AlgHom.FinitePresentation.{u3, u2, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjectiveₓ'. -/
 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation :=
   RingHom.FinitePresentation.of_surjective f hf hker
 #align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjective
 
+/- warning: alg_hom.finite_presentation.of_finite_type -> AlgHom.FinitePresentation.of_finiteType is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] [_inst_8 : IsNoetherianRing.{u2} A (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] {f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6}, Iff (AlgHom.FiniteType.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) (AlgHom.FinitePresentation.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+but is expected to have type
+  forall {R : Type.{u2}} {A : Type.{u3}} {B : Type.{u1}} [_inst_1 : CommRing.{u2} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u1} B] [_inst_5 : Algebra.{u2, u3} R A (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u2, u1} R B (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3))] [_inst_8 : IsNoetherianRing.{u3} A (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] {f : AlgHom.{u2, u3, u1} R A B (CommRing.toCommSemiring.{u2} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u1} B (CommRing.toCommSemiring.{u1} B _inst_3)) _inst_5 _inst_6}, Iff (AlgHom.FiniteType.{u2, u3, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) (AlgHom.FinitePresentation.{u2, u3, u1} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f)
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.of_finite_type AlgHom.FinitePresentation.of_finiteTypeₓ'. -/
 theorem of_finiteType [IsNoetherianRing A] {f : A →ₐ[R] B} : f.FiniteType ↔ f.FinitePresentation :=
   RingHom.FinitePresentation.of_finiteType
 #align alg_hom.finite_presentation.of_finite_type AlgHom.FinitePresentation.of_finiteType
 
+/- warning: alg_hom.finite_presentation.of_comp_finite_type -> AlgHom.FinitePresentation.of_comp_finiteType is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {A : Type.{u2}} {B : Type.{u3}} {C : Type.{u4}} [_inst_1 : CommRing.{u1} R] [_inst_2 : CommRing.{u2} A] [_inst_3 : CommRing.{u3} B] [_inst_4 : CommRing.{u4} C] [_inst_5 : Algebra.{u1, u2} R A (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2))] [_inst_6 : Algebra.{u1, u3} R B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3))] [_inst_7 : Algebra.{u1, u4} R C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4))] (f : AlgHom.{u1, u2, u3} R A B (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) _inst_5 _inst_6) {g : AlgHom.{u1, u3, u4} R B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u1, u2, u4} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u1, u2, u3, u4} R A B C (CommRing.toCommSemiring.{u1} R _inst_1) (Ring.toSemiring.{u2} A (CommRing.toRing.{u2} A _inst_2)) (Ring.toSemiring.{u3} B (CommRing.toRing.{u3} B _inst_3)) (Ring.toSemiring.{u4} C (CommRing.toRing.{u4} C _inst_4)) _inst_5 _inst_6 _inst_7 g f)) -> (AlgHom.FiniteType.{u1, u2, u3} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FinitePresentation.{u1, u3, u4} R B C _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g)
+but is expected to have type
+  forall {R : Type.{u4}} {A : Type.{u3}} {B : Type.{u2}} {C : Type.{u1}} [_inst_1 : CommRing.{u4} R] [_inst_2 : CommRing.{u3} A] [_inst_3 : CommRing.{u2} B] [_inst_4 : CommRing.{u1} C] [_inst_5 : Algebra.{u4, u3} R A (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2))] [_inst_6 : Algebra.{u4, u2} R B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3))] [_inst_7 : Algebra.{u4, u1} R C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4))] (f : AlgHom.{u4, u3, u2} R A B (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) _inst_5 _inst_6) {g : AlgHom.{u4, u2, u1} R B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_6 _inst_7}, (AlgHom.FinitePresentation.{u4, u3, u1} R A C _inst_1 _inst_2 _inst_4 _inst_5 _inst_7 (AlgHom.comp.{u4, u3, u2, u1} R A B C (CommRing.toCommSemiring.{u4} R _inst_1) (CommSemiring.toSemiring.{u3} A (CommRing.toCommSemiring.{u3} A _inst_2)) (CommSemiring.toSemiring.{u2} B (CommRing.toCommSemiring.{u2} B _inst_3)) (CommSemiring.toSemiring.{u1} C (CommRing.toCommSemiring.{u1} C _inst_4)) _inst_5 _inst_6 _inst_7 g f)) -> (AlgHom.FiniteType.{u4, u3, u2} R A B _inst_1 _inst_2 _inst_3 _inst_5 _inst_6 f) -> (AlgHom.FinitePresentation.{u4, u2, u1} R B C _inst_1 _inst_3 _inst_4 _inst_6 _inst_7 g)
+Case conversion may be inaccurate. Consider using '#align alg_hom.finite_presentation.of_comp_finite_type AlgHom.FinitePresentation.of_comp_finiteTypeₓ'. -/
 theorem of_comp_finiteType (f : A →ₐ[R] B) {g : B →ₐ[R] C} (h : (g.comp f).FinitePresentation)
     (h' : f.FiniteType) : g.FinitePresentation :=
   h.of_comp_finiteType _ h'

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

@@ -40,7 +40,7 @@ variable (R A B M N : Type _)
 /-- An algebra over a commutative semiring is `finite_presentation` if it is the quotient of a
 polynomial ring in `n` variables by a finitely generated ideal. -/
 def Algebra.FinitePresentation [CommSemiring R] [Semiring A] [Algebra R A] : Prop :=
-  ∃ (n : ℕ)(f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.Fg
+  ∃ (n : ℕ)(f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.FG
 #align algebra.finite_presentation Algebra.FinitePresentation
 
 namespace Algebra
@@ -126,7 +126,7 @@ variable {R}
 
 /-- The quotient of a finitely presented algebra by a finitely generated ideal is finitely
 presented. -/
-protected theorem quotient {I : Ideal A} (h : I.Fg) (hfp : FinitePresentation R A) :
+protected theorem quotient {I : Ideal A} (h : I.FG) (hfp : FinitePresentation R A) :
     FinitePresentation R (A ⧸ I) := by
   obtain ⟨n, f, hf⟩ := hfp
   refine' ⟨n, (Ideal.Quotient.mkₐ R I).comp f, _, _⟩
@@ -137,14 +137,14 @@ protected theorem quotient {I : Ideal A} (h : I.Fg) (hfp : FinitePresentation R
 
 /-- If `f : A →ₐ[R] B` is surjective with finitely generated kernel and `A` is finitely presented,
 then so is `B`. -/
-theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f.toRingHom.ker.Fg)
+theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f.toRingHom.ker.FG)
     (hfp : FinitePresentation R A) : FinitePresentation R B :=
   equiv (hfp.Quotient hker) (Ideal.quotientKerAlgEquivOfSurjective hf)
 #align algebra.finite_presentation.of_surjective Algebra.FinitePresentation.of_surjective
 
 theorem iff :
     FinitePresentation R A ↔
-      ∃ (n : _)(I : Ideal (MvPolynomial (Fin n) R))(e : (_ ⧸ I) ≃ₐ[R] A), I.Fg :=
+      ∃ (n : _)(I : Ideal (MvPolynomial (Fin n) R))(e : (_ ⧸ I) ≃ₐ[R] A), I.FG :=
   by
   constructor
   · rintro ⟨n, f, hf⟩
@@ -158,7 +158,7 @@ variables are indexed by a fintype by a finitely generated ideal. -/
 theorem iff_quotient_mv_polynomial' :
     FinitePresentation R A ↔
       ∃ (ι : Type u_2)(_ : Fintype ι)(f : MvPolynomial ι R →ₐ[R] A),
-        Surjective f ∧ f.toRingHom.ker.Fg :=
+        Surjective f ∧ f.toRingHom.ker.FG :=
   by
   constructor
   · rintro ⟨n, f, hfs, hfk⟩
@@ -305,8 +305,8 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
 
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
-theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
-    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.Fg := by
+theorem ker_fG_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
+    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
   classical
     obtain ⟨m, f', hf', s, hs⟩ := hfp
     let RXn := MvPolynomial (Fin n) R
@@ -377,18 +377,18 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     apply Submodule.subset_span
     apply Set.mem_union_right
     exact Set.mem_image_of_mem _ hx
-#align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
+#align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fG_of_mvPolynomial
 
 /-- If `f : A →ₐ[R] B` is a sujection between finitely-presented `R`-algebras, then the kernel of
 `f` is finitely generated. -/
-theorem ker_fg_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
-    (hRA : FinitePresentation R A) (hRB : FinitePresentation R B) : f.toRingHom.ker.Fg :=
+theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
+    (hRA : FinitePresentation R A) (hRB : FinitePresentation R B) : f.toRingHom.ker.FG :=
   by
   obtain ⟨n, g, hg, hg'⟩ := hRA
   convert(ker_fg_of_mv_polynomial (f.comp g) (hf.comp hg) hRB).map g.to_ring_hom
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
-#align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fg_of_surjective
+#align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fG_of_surjective
 
 end FinitePresentation
 
@@ -425,7 +425,7 @@ theorem id : FinitePresentation (RingHom.id A) :=
 variable {A}
 
 theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentation) (hg : Surjective g)
-    (hker : g.ker.Fg) : (g.comp f).FinitePresentation :=
+    (hker : g.ker.FG) : (g.comp f).FinitePresentation :=
   @Algebra.FinitePresentation.of_surjective A B C _ _ f.toAlgebra _ (g.comp f).toAlgebra
     { g with
       toFun := g
@@ -433,7 +433,7 @@ theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentati
     hg hker hf
 #align ring_hom.finite_presentation.comp_surjective RingHom.FinitePresentation.comp_surjective
 
-theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.Fg) : f.FinitePresentation :=
+theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.FG) : f.FinitePresentation :=
   by
   rw [← f.comp_id]
   exact (id A).comp_surjective hf hker
@@ -505,11 +505,11 @@ theorem comp {g : B →ₐ[R] C} {f : A →ₐ[R] B} (hg : g.FinitePresentation)
 #align alg_hom.finite_presentation.comp AlgHom.FinitePresentation.comp
 
 theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePresentation)
-    (hg : Surjective g) (hker : g.toRingHom.ker.Fg) : (g.comp f).FinitePresentation :=
+    (hg : Surjective g) (hker : g.toRingHom.ker.FG) : (g.comp f).FinitePresentation :=
   RingHom.FinitePresentation.comp_surjective hf hg hker
 #align alg_hom.finite_presentation.comp_surjective AlgHom.FinitePresentation.comp_surjective
 
-theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.Fg) :
+theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation :=
   RingHom.FinitePresentation.of_surjective f hf hker
 #align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjective

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

@@ -74,7 +74,7 @@ presented. -/
 theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentation R A :=
   by
   refine' ⟨fun h => _, Algebra.FiniteType.of_finitePresentation⟩
-  obtain ⟨n, f, hf⟩ := Algebra.FiniteType.iff_quotient_mv_polynomial''.1 h
+  obtain ⟨n, f, hf⟩ := Algebra.FiniteType.iff_quotient_mvPolynomial''.1 h
   refine' ⟨n, f, hf, _⟩
   have hnoet : IsNoetherianRing (MvPolynomial (Fin n) R) := by infer_instance
   replace hnoet := (isNoetherianRing_iff.1 hnoet).noetherian

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

@@ -119,7 +119,7 @@ theorem self : FinitePresentation R R :=
 
 /-- `R[X]` is finitely presented as `R`-algebra. -/
 theorem polynomial : FinitePresentation R R[X] :=
-  equiv (FinitePresentation.mvPolynomial R PUnit) (MvPolynomial.punitAlgEquiv R)
+  equiv (FinitePresentation.mvPolynomial R PUnit) (MvPolynomial.pUnitAlgEquiv R)
 #align algebra.finite_presentation.polynomial Algebra.FinitePresentation.polynomial
 
 variable {R}

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

@@ -385,7 +385,7 @@ theorem ker_fg_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
     (hRA : FinitePresentation R A) (hRB : FinitePresentation R B) : f.toRingHom.ker.Fg :=
   by
   obtain ⟨n, g, hg, hg'⟩ := hRA
-  convert (ker_fg_of_mv_polynomial (f.comp g) (hf.comp hg) hRB).map g.to_ring_hom
+  convert(ker_fg_of_mv_polynomial (f.comp g) (hf.comp hg) hRB).map g.to_ring_hom
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 #align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fg_of_surjective

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -196,7 +196,7 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation R A) (ι :
     · convert Submodule.fg_bot
       exact RingHom.ker_coe_equiv (MvPolynomial.sumAlgEquiv R ι ι').toRingEquiv
     · rw [AlgHom.toRingHom_eq_coe, MvPolynomial.mapAlgHom_coe_ringHom, MvPolynomial.ker_map]
-      exact hf_ker.map MvPolynomial.c
+      exact hf_ker.map MvPolynomial.C
 #align algebra.finite_presentation.mv_polynomial_of_finite_presentation Algebra.FinitePresentation.mvPolynomial_of_finitePresentation
 
 /-- If `A` is an `R`-algebra and `S` is an `A`-algebra, both finitely presented, then `S` is

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

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 
 ! This file was ported from Lean 3 source module ring_theory.finite_presentation
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.FiniteType
 import Mathbin.RingTheory.MvPolynomial.Tower
+import Mathbin.RingTheory.Ideal.QuotientOperations
 
 /-!
 # Finiteness conditions in commutative algebra

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

• Adds lemma Polynomial.algebraMap_eq analogous to MvPolynomial.algebraMap_eq
  • Adds some namespace disambiguations in various places to make this possible
• Adds simp to these, and the related {Mv}Polynomial.algebraMap_apply lemmas.
  • Removes simp tag from later lemmas which linter says these additions now allow to be simp-proved

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

@@ -281,7 +281,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       rw [← ht''] at this
       refine adjoin_induction this ?_ ?_ ?_ ?_
       · rintro _ (⟨x, hx, rfl⟩ | ⟨i, rfl⟩)
-        · rw [algebraMap_eq, ← sub_add_cancel (MvPolynomial.C x)
+        · rw [MvPolynomial.algebraMap_eq, ← sub_add_cancel (MvPolynomial.C x)
             (map (algebraMap R A) (t' ⟨x, hx⟩)), add_comm]
           apply AddSubmonoid.add_mem_sup
           · exact Set.mem_range_self _

Makes Algebra.FinitePresentation a class, matching Algebra.FiniteType. Changes theorems to instances where possible.

@@ -40,8 +40,8 @@ variable (R : Type w₁) (A : Type w₂) (B : Type w₃)
 
 /-- An algebra over a commutative semiring is `Algebra.FinitePresentation` if it is the quotient of
 a polynomial ring in `n` variables by a finitely generated ideal. -/
-def Algebra.FinitePresentation [CommSemiring R] [Semiring A] [Algebra R A] : Prop :=
-  ∃ (n : ℕ) (f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.FG
+class Algebra.FinitePresentation [CommSemiring R] [Semiring A] [Algebra R A] : Prop where
+  out : ∃ (n : ℕ) (f : MvPolynomial (Fin n) R →ₐ[R] A), Surjective f ∧ f.toRingHom.ker.FG
 #align algebra.finite_presentation Algebra.FinitePresentation
 
 namespace Algebra
@@ -53,8 +53,8 @@ namespace FiniteType
 variable {R A B}
 
 /-- A finitely presented algebra is of finite type. -/
-theorem of_finitePresentation : FinitePresentation R A → FiniteType R A := by
-  rintro ⟨n, f, hf⟩
+instance of_finitePresentation [FinitePresentation R A] : FiniteType R A := by
+  obtain ⟨n, f, hf⟩ := FinitePresentation.out (R := R) (A := A)
   apply FiniteType.iff_quotient_mvPolynomial''.2
   exact ⟨n, f, hf.1⟩
 #align algebra.finite_type.of_finite_presentation Algebra.FiniteType.of_finitePresentation
@@ -68,7 +68,7 @@ variable {R A B}
 /-- An algebra over a Noetherian ring is finitely generated if and only if it is finitely
 presented. -/
 theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentation R A := by
-  refine' ⟨fun h => _, Algebra.FiniteType.of_finitePresentation⟩
+  refine' ⟨fun h => _, fun hfp => Algebra.FiniteType.of_finitePresentation⟩
   obtain ⟨n, f, hf⟩ := Algebra.FiniteType.iff_quotient_mvPolynomial''.1 h
   refine' ⟨n, f, hf, _⟩
   have hnoet : IsNoetherianRing (MvPolynomial (Fin n) R) := by infer_instance
@@ -80,8 +80,8 @@ theorem of_finiteType [IsNoetherianRing R] : FiniteType R A ↔ FinitePresentati
 #align algebra.finite_presentation.of_finite_type Algebra.FinitePresentation.of_finiteType
 
 /-- If `e : A ≃ₐ[R] B` and `A` is finitely presented, then so is `B`. -/
-theorem equiv (hfp : FinitePresentation R A) (e : A ≃ₐ[R] B) : FinitePresentation R B := by
-  obtain ⟨n, f, hf⟩ := hfp
+theorem equiv [FinitePresentation R A] (e : A ≃ₐ[R] B) : FinitePresentation R B := by
+  obtain ⟨n, f, hf⟩ := FinitePresentation.out (R := R) (A := A)
   use n, AlgHom.comp (↑e) f
   constructor
   · rw [AlgHom.coe_comp]
@@ -102,45 +102,49 @@ theorem equiv (hfp : FinitePresentation R A) (e : A ≃ₐ[R] B) : FinitePresent
 variable (R)
 
 /-- The ring of polynomials in finitely many variables is finitely presented. -/
-protected theorem mvPolynomial (ι : Type u_2) [Finite ι] :
-    FinitePresentation R (MvPolynomial ι R) := by
-  cases nonempty_fintype ι
-  let eqv := (MvPolynomial.renameEquiv R <| Fintype.equivFin ι).symm
-  exact
-    ⟨Fintype.card ι, eqv, eqv.surjective,
-      ((RingHom.injective_iff_ker_eq_bot _).1 eqv.injective).symm ▸ Submodule.fg_bot⟩
+protected instance mvPolynomial (ι : Type u_2) [Finite ι] :
+    FinitePresentation R (MvPolynomial ι R) where
+  out := by
+    cases nonempty_fintype ι
+    let eqv := (MvPolynomial.renameEquiv R <| Fintype.equivFin ι).symm
+    exact
+      ⟨Fintype.card ι, eqv, eqv.surjective,
+        ((RingHom.injective_iff_ker_eq_bot _).1 eqv.injective).symm ▸ Submodule.fg_bot⟩
 #align algebra.finite_presentation.mv_polynomial Algebra.FinitePresentation.mvPolynomial
 
 /-- `R` is finitely presented as `R`-algebra. -/
-theorem self : FinitePresentation R R :=
+instance self : FinitePresentation R R :=
   -- Porting note: replaced `PEmpty` with `Empty`
-  equiv (FinitePresentation.mvPolynomial R Empty) (MvPolynomial.isEmptyAlgEquiv R Empty)
+  equiv (MvPolynomial.isEmptyAlgEquiv R Empty)
 #align algebra.finite_presentation.self Algebra.FinitePresentation.self
 
 /-- `R[X]` is finitely presented as `R`-algebra. -/
-theorem polynomial : FinitePresentation R R[X] :=
+instance polynomial : FinitePresentation R R[X] :=
   -- Porting note: replaced `PUnit` with `Unit`
-  equiv (FinitePresentation.mvPolynomial R Unit) (MvPolynomial.pUnitAlgEquiv R)
+  letI := FinitePresentation.mvPolynomial R Unit
+  equiv (MvPolynomial.pUnitAlgEquiv R)
 #align algebra.finite_presentation.polynomial Algebra.FinitePresentation.polynomial
 
 variable {R}
 
 /-- The quotient of a finitely presented algebra by a finitely generated ideal is finitely
 presented. -/
-protected theorem quotient {I : Ideal A} (h : I.FG) (hfp : FinitePresentation R A) :
-    FinitePresentation R (A ⧸ I) := by
-  obtain ⟨n, f, hf⟩ := hfp
-  refine' ⟨n, (Ideal.Quotient.mkₐ R I).comp f, _, _⟩
-  · exact (Ideal.Quotient.mkₐ_surjective R I).comp hf.1
-  · refine' Ideal.fg_ker_comp _ _ hf.2 _ hf.1
-    simp [h]
+protected theorem quotient {I : Ideal A} (h : I.FG) [FinitePresentation R A] :
+    FinitePresentation R (A ⧸ I) where
+  out := by
+    obtain ⟨n, f, hf⟩ := FinitePresentation.out (R := R) (A := A)
+    refine' ⟨n, (Ideal.Quotient.mkₐ R I).comp f, _, _⟩
+    · exact (Ideal.Quotient.mkₐ_surjective R I).comp hf.1
+    · refine' Ideal.fg_ker_comp _ _ hf.2 _ hf.1
+      simp [h]
 #align algebra.finite_presentation.quotient Algebra.FinitePresentation.quotient
 
 /-- If `f : A →ₐ[R] B` is surjective with finitely generated kernel and `A` is finitely presented,
 then so is `B`. -/
 theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f.toRingHom.ker.FG)
-    (hfp : FinitePresentation R A) : FinitePresentation R B :=
-  equiv (hfp.quotient hker) (Ideal.quotientKerAlgEquivOfSurjective hf)
+    [FinitePresentation R A] : FinitePresentation R B :=
+  letI : FinitePresentation R (A ⧸ RingHom.ker f) := FinitePresentation.quotient hker
+  equiv (Ideal.quotientKerAlgEquivOfSurjective hf)
 #align algebra.finite_presentation.of_surjective Algebra.FinitePresentation.of_surjective
 
 theorem iff :
@@ -150,7 +154,8 @@ theorem iff :
   · rintro ⟨n, f, hf⟩
     exact ⟨n, RingHom.ker f.toRingHom, Ideal.quotientKerAlgEquivOfSurjective hf.1, hf.2⟩
   · rintro ⟨n, I, e, hfg⟩
-    exact equiv ((FinitePresentation.mvPolynomial R _).quotient hfg) e
+    letI := (FinitePresentation.mvPolynomial R _).quotient hfg
+    exact equiv e
 #align algebra.finite_presentation.iff Algebra.FinitePresentation.iff
 
 /-- An algebra is finitely presented if and only if it is a quotient of a polynomial ring whose
@@ -185,9 +190,10 @@ theorem iff_quotient_mvPolynomial' :
 -- Porting note: make universe level explicit to ensure `ι, ι'` has the same universe level
 /-- If `A` is a finitely presented `R`-algebra, then `MvPolynomial (Fin n) A` is finitely presented
 as `R`-algebra. -/
-theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation.{w₁, w₂} R A)
+theorem mvPolynomial_of_finitePresentation [FinitePresentation.{w₁, w₂} R A]
     (ι : Type v) [Finite ι] :
     FinitePresentation.{w₁, max v w₂} R (MvPolynomial ι A) := by
+  have hfp : FinitePresentation.{w₁, w₂} R A := inferInstance
   rw [iff_quotient_mvPolynomial'] at hfp ⊢
   classical
   -- Porting note: use the same universe level
@@ -207,12 +213,17 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation.{w₁, w₂
     exact hf_ker.map MvPolynomial.C
 #align algebra.finite_presentation.mv_polynomial_of_finite_presentation Algebra.FinitePresentation.mvPolynomial_of_finitePresentation
 
+variable (R A B)
+
 /-- If `A` is an `R`-algebra and `S` is an `A`-algebra, both finitely presented, then `S` is
   finitely presented as `R`-algebra. -/
-theorem trans [Algebra A B] [IsScalarTower R A B] (hfpA : FinitePresentation R A)
-    (hfpB : FinitePresentation A B) : FinitePresentation R B := by
+theorem trans [Algebra A B] [IsScalarTower R A B] [FinitePresentation R A]
+    [FinitePresentation A B] : FinitePresentation R B := by
+  have hfpB : FinitePresentation A B := inferInstance
   obtain ⟨n, I, e, hfg⟩ := iff.1 hfpB
-  exact equiv ((mvPolynomial_of_finitePresentation hfpA _).quotient hfg) (e.restrictScalars R)
+  letI : FinitePresentation R (MvPolynomial (Fin n) A ⧸ I) :=
+    (mvPolynomial_of_finitePresentation _).quotient hfg
+  exact equiv (e.restrictScalars R)
 #align algebra.finite_presentation.trans Algebra.FinitePresentation.trans
 
 open MvPolynomial
@@ -220,10 +231,10 @@ open MvPolynomial
 -- We follow the proof of https://stacks.math.columbia.edu/tag/0561
 -- TODO: extract out helper lemmas and tidy proof.
 theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A B]
-    (hRB : FinitePresentation.{w₁, w₃} R B) [hRA : FiniteType R A] :
+    [FinitePresentation.{w₁, w₃} R B] [FiniteType R A] :
     FinitePresentation.{w₂, w₃} A B := by
   classical
-  obtain ⟨n, f, hf, s, hs⟩ := hRB
+  obtain ⟨n, f, hf, s, hs⟩ := FinitePresentation.out (R := R) (A := B)
   letI RX := MvPolynomial (Fin n) R
   letI AX := MvPolynomial (Fin n) A
   refine' ⟨n, MvPolynomial.aeval (f ∘ X), _, _⟩
@@ -231,7 +242,7 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       Set.range_comp f MvPolynomial.X, eq_top_iff, ← @adjoin_adjoin_of_tower R A B,
       adjoin_image, adjoin_range_X, Algebra.map_top, (Algebra.range_top_iff_surjective _).mpr hf]
     exact fun {x} => subset_adjoin ⟨⟩
-  · obtain ⟨t, ht⟩ := hRA.out
+  · obtain ⟨t, ht⟩ := FiniteType.out (R := R) (A := A)
     have := fun i : t => hf (algebraMap A B i)
     choose t' ht' using this
     have ht'' : Algebra.adjoin R (algebraMap A AX '' t ∪ Set.range (X : _ → AX)) = ⊤ := by
@@ -305,12 +316,14 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
     exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.of_restrict_scalars_finite_presentation Algebra.FinitePresentation.of_restrict_scalars_finitePresentation
 
+variable {R A B}
+
 -- TODO: extract out helper lemmas and tidy proof.
 /-- This is used to prove the strictly stronger `ker_fg_of_surjective`. Use it instead. -/
 theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A)
-    (hf : Function.Surjective f) (hfp : FinitePresentation R A) : f.toRingHom.ker.FG := by
+    (hf : Function.Surjective f) [FinitePresentation R A] : f.toRingHom.ker.FG := by
   classical
-    obtain ⟨m, f', hf', s, hs⟩ := hfp
+    obtain ⟨m, f', hf', s, hs⟩ := FinitePresentation.out (R := R) (A := A)
     let RXn := MvPolynomial (Fin n) R
     let RXm := MvPolynomial (Fin m) R
     have := fun i : Fin n => hf' (f <| X i)
@@ -383,9 +396,9 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
 /-- If `f : A →ₐ[R] B` is a surjection between finitely-presented `R`-algebras, then the kernel of
 `f` is finitely generated. -/
 theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
-    (hRA : FinitePresentation R A) (hRB : FinitePresentation R B) : f.toRingHom.ker.FG := by
-  obtain ⟨n, g, hg, _⟩ := hRA
-  convert (ker_fg_of_mvPolynomial (f.comp g) (hf.comp hg) hRB).map g.toRingHom
+    [FinitePresentation R A] [FinitePresentation R B] : f.toRingHom.ker.FG := by
+  obtain ⟨n, g, hg, _⟩ := FinitePresentation.out (R := R) (A := A)
+  convert (ker_fg_of_mvPolynomial (f.comp g) (hf.comp hg)).map g.toRingHom
   simp_rw [RingHom.ker_eq_comap_bot, AlgHom.toRingHom_eq_coe, AlgHom.comp_toRingHom]
   rw [← Ideal.comap_comap, Ideal.map_comap_of_surjective (g : MvPolynomial (Fin n) R →+* A) hg]
 #align algebra.finite_presentation.ker_fg_of_surjective Algebra.FinitePresentation.ker_fG_of_surjective
@@ -428,12 +441,13 @@ theorem comp_surjective {f : A →+* B} {g : B →+* C} (hf : f.FinitePresentati
     (hker : g.ker.FG) : (g.comp f).FinitePresentation :=
   letI := f.toAlgebra
   letI := (g.comp f).toAlgebra
+  letI : Algebra.FinitePresentation A B := hf
   Algebra.FinitePresentation.of_surjective
     (f :=
       { g with
         toFun := g
         commutes' := fun _ => rfl })
-    hg hker hf
+    hg hker
 #align ring_hom.finite_presentation.comp_surjective RingHom.FinitePresentation.comp_surjective
 
 theorem of_surjective (f : A →+* B) (hf : Surjective f) (hker : f.ker.FG) :
@@ -454,7 +468,9 @@ theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f
   letI ins3 := RingHom.toAlgebra (g.comp f)
   letI ins4 : IsScalarTower A B C :=
     { smul_assoc := fun a b c => by simp [Algebra.smul_def, mul_assoc]; rfl }
-  Algebra.FinitePresentation.trans hf hg
+  letI : Algebra.FinitePresentation A B := hf
+  letI : Algebra.FinitePresentation B C := hg
+  Algebra.FinitePresentation.trans A B C
 #align ring_hom.finite_presentation.comp RingHom.FinitePresentation.comp
 
 theorem of_comp_finiteType (f : A →+* B) {g : B →+* C} (hg : (g.comp f).FinitePresentation)
@@ -465,7 +481,9 @@ theorem of_comp_finiteType (f : A →+* B) {g : B →+* C} (hg : (g.comp f).Fini
   letI ins3 := RingHom.toAlgebra (g.comp f)
   letI ins4 : IsScalarTower A B C :=
     { smul_assoc := fun a b c => by simp [Algebra.smul_def, mul_assoc]; rfl }
-  Algebra.FinitePresentation.of_restrict_scalars_finitePresentation (hRA := hf) hg
+  letI : Algebra.FinitePresentation A C := hg
+  letI : Algebra.FiniteType A B := hf
+  Algebra.FinitePresentation.of_restrict_scalars_finitePresentation A B C
 #align ring_hom.finite_presentation.of_comp_finite_type RingHom.FinitePresentation.of_comp_finiteType
 
 end FinitePresentation

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)

@@ -475,9 +475,7 @@ end RingHom
 namespace AlgHom
 
 variable {R A B C : Type*} [CommRing R]
-
 variable [CommRing A] [CommRing B] [CommRing C]
-
 variable [Algebra R A] [Algebra R B] [Algebra R C]
 
 /-- An algebra morphism `A →ₐ[R] B` is of `AlgHom.FinitePresentation` if it is of finite

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

@@ -238,7 +238,6 @@ theorem of_restrict_scalars_finitePresentation [Algebra A B] [IsScalarTower R A
       rw [adjoin_union_eq_adjoin_adjoin, ← Subalgebra.restrictScalars_top R (A := AX)
         (S := { x // x ∈ adjoin R ((algebraMap A AX) '' t) })]
       refine congrArg (Subalgebra.restrictScalars R) ?_
-      congr 1
       rw [adjoin_algebraMap, ht]
       apply Subalgebra.restrictScalars_injective R
       rw [← adjoin_restrictScalars, adjoin_range_X, Subalgebra.restrictScalars_top,

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

@@ -35,7 +35,7 @@ section ModuleAndAlgebra
 
 universe w₁ w₂ w₃
 
--- Porting Note : `M, N` is never used
+-- Porting note: `M, N` is never used
 variable (R : Type w₁) (A : Type w₂) (B : Type w₃)
 
 /-- An algebra over a commutative semiring is `Algebra.FinitePresentation` if it is the quotient of
@@ -182,7 +182,7 @@ theorem iff_quotient_mvPolynomial' :
     -- exact RingHom.ker_coe_equiv equiv.symm.toRingEquiv
 #align algebra.finite_presentation.iff_quotient_mv_polynomial' Algebra.FinitePresentation.iff_quotient_mvPolynomial'
 
--- Porting note : make universe level explicit to ensure `ι, ι'` has the same universe level
+-- Porting note: make universe level explicit to ensure `ι, ι'` has the same universe level
 /-- If `A` is a finitely presented `R`-algebra, then `MvPolynomial (Fin n) A` is finitely presented
 as `R`-algebra. -/
 theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation.{w₁, w₂} R A)
@@ -190,7 +190,7 @@ theorem mvPolynomial_of_finitePresentation (hfp : FinitePresentation.{w₁, w₂
     FinitePresentation.{w₁, max v w₂} R (MvPolynomial ι A) := by
   rw [iff_quotient_mvPolynomial'] at hfp ⊢
   classical
-  -- Porting note : use the same universe level
+  -- Porting note: use the same universe level
   obtain ⟨(ι' : Type v), _, f, hf_surj, hf_ker⟩ := hfp
   let g := (MvPolynomial.mapAlgHom f).comp (MvPolynomial.sumAlgEquiv R ι ι').toAlgHom
   cases nonempty_fintype (Sum ι ι')
@@ -449,7 +449,7 @@ theorem of_finiteType [IsNoetherianRing A] {f : A →+* B} : f.FiniteType ↔ f.
 
 theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f.FinitePresentation) :
     (g.comp f).FinitePresentation :=
-  -- Porting note : specify `Algebra` instances to get `SMul`
+  -- Porting note: specify `Algebra` instances to get `SMul`
   letI ins1 := RingHom.toAlgebra f
   letI ins2 := RingHom.toAlgebra g
   letI ins3 := RingHom.toAlgebra (g.comp f)
@@ -460,7 +460,7 @@ theorem comp {g : B →+* C} {f : A →+* B} (hg : g.FinitePresentation) (hf : f
 
 theorem of_comp_finiteType (f : A →+* B) {g : B →+* C} (hg : (g.comp f).FinitePresentation)
     (hf : f.FiniteType) : g.FinitePresentation :=
-  -- Porting note : need to specify some instances
+  -- Porting note: need to specify some instances
   letI ins1 := RingHom.toAlgebra f
   letI ins2 := RingHom.toAlgebra g
   letI ins3 := RingHom.toAlgebra (g.comp f)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -86,17 +86,17 @@ theorem equiv (hfp : FinitePresentation R A) (e : A ≃ₐ[R] B) : FinitePresent
   constructor
   · rw [AlgHom.coe_comp]
     exact Function.Surjective.comp e.surjective hf.1
-  suffices hker : (RingHom.ker (AlgHom.comp (e : A →ₐ[R] B) f).toRingHom) = RingHom.ker f.toRingHom
-  · rw [hker]
+  suffices (RingHom.ker (AlgHom.comp (e : A →ₐ[R] B) f).toRingHom) = RingHom.ker f.toRingHom by
+    rw [this]
     exact hf.2
-  · have hco : (AlgHom.comp (e : A →ₐ[R] B) f).toRingHom = RingHom.comp (e.toRingEquiv : A ≃+* B)
-      f.toRingHom := by
-      have h : (AlgHom.comp (e : A →ₐ[R] B) f).toRingHom =
-        e.toAlgHom.toRingHom.comp f.toRingHom := rfl
-      have h1 : ↑e.toRingEquiv = e.toAlgHom.toRingHom := rfl
-      rw [h, h1]
-    rw [RingHom.ker_eq_comap_bot, hco, ← Ideal.comap_comap, ← RingHom.ker_eq_comap_bot,
-      RingHom.ker_coe_equiv (AlgEquiv.toRingEquiv e), RingHom.ker_eq_comap_bot]
+  have hco : (AlgHom.comp (e : A →ₐ[R] B) f).toRingHom = RingHom.comp (e.toRingEquiv : A ≃+* B)
+    f.toRingHom := by
+    have h : (AlgHom.comp (e : A →ₐ[R] B) f).toRingHom =
+      e.toAlgHom.toRingHom.comp f.toRingHom := rfl
+    have h1 : ↑e.toRingEquiv = e.toAlgHom.toRingHom := rfl
+    rw [h, h1]
+  rw [RingHom.ker_eq_comap_bot, hco, ← Ideal.comap_comap, ← RingHom.ker_eq_comap_bot,
+    RingHom.ker_coe_equiv (AlgEquiv.toRingEquiv e), RingHom.ker_eq_comap_bot]
 #align algebra.finite_presentation.equiv Algebra.FinitePresentation.equiv
 
 variable (R)

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -25,6 +25,8 @@ In this file we define several notions of finiteness that are common in commutat
 
 -/
 
+set_option autoImplicit true
+
 open Function (Surjective)
 
 open BigOperators Polynomial

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

This has nice performance benefits.

@@ -155,7 +155,7 @@ theorem iff :
 variables are indexed by a fintype by a finitely generated ideal. -/
 theorem iff_quotient_mvPolynomial' :
     FinitePresentation R A ↔
-      ∃ (ι : Type _) (_ : Fintype ι) (f : MvPolynomial ι R →ₐ[R] A),
+      ∃ (ι : Type*) (_ : Fintype ι) (f : MvPolynomial ι R →ₐ[R] A),
         Surjective f ∧ f.toRingHom.ker.FG := by
   constructor
   · rintro ⟨n, f, hfs, hfk⟩
@@ -397,7 +397,7 @@ end ModuleAndAlgebra
 
 namespace RingHom
 
-variable {A B C : Type _} [CommRing A] [CommRing B] [CommRing C]
+variable {A B C : Type*} [CommRing A] [CommRing B] [CommRing C]
 
 /-- A ring morphism `A →+* B` is of `RingHom.FinitePresentation` if `B` is finitely presented as
 `A`-algebra. -/
@@ -473,7 +473,7 @@ end RingHom
 
 namespace AlgHom
 
-variable {R A B C : Type _} [CommRing R]
+variable {R A B C : Type*} [CommRing R]
 
 variable [CommRing A] [CommRing B] [CommRing C]
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.finite_presentation
-! leanprover-community/mathlib commit da420a8c6dd5bdfb85c4ced85c34388f633bc6ff
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.FiniteType
 import Mathlib.RingTheory.MvPolynomial.Tower
 import Mathlib.RingTheory.Ideal.QuotientOperations
 
+#align_import ring_theory.finite_presentation from "leanprover-community/mathlib"@"da420a8c6dd5bdfb85c4ced85c34388f633bc6ff"
+
 /-!
 # Finiteness conditions in commutative algebra
 

I wrote a script to find lines that contain an odd number of backticks

@@ -518,7 +518,7 @@ theorem comp_surjective {f : A →ₐ[R] B} {g : B →ₐ[R] C} (hf : f.FinitePr
 
 theorem of_surjective (f : A →ₐ[R] B) (hf : Surjective f) (hker : f.toRingHom.ker.FG) :
     f.FinitePresentation := by
-  -- Porting note: added `convert
+  -- Porting note: added `convert`
   convert RingHom.FinitePresentation.of_surjective f hf hker
 #align alg_hom.finite_presentation.of_surjective AlgHom.FinitePresentation.of_surjective
 

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

@@ -146,7 +146,7 @@ theorem of_surjective {f : A →ₐ[R] B} (hf : Function.Surjective f) (hker : f
 
 theorem iff :
     FinitePresentation R A ↔
-      ∃ (n : _)(I : Ideal (MvPolynomial (Fin n) R)) (_ : (_ ⧸ I) ≃ₐ[R] A), I.FG := by
+      ∃ (n : _) (I : Ideal (MvPolynomial (Fin n) R)) (_ : (_ ⧸ I) ≃ₐ[R] A), I.FG := by
   constructor
   · rintro ⟨n, f, hf⟩
     exact ⟨n, RingHom.ker f.toRingHom, Ideal.quotientKerAlgEquivOfSurjective hf.1, hf.2⟩

These are all doc fixes

@@ -382,7 +382,7 @@ theorem ker_fg_of_mvPolynomial {n : ℕ} (f : MvPolynomial (Fin n) R →ₐ[R] A
     exact Set.mem_image_of_mem _ hx
 #align algebra.finite_presentation.ker_fg_of_mv_polynomial Algebra.FinitePresentation.ker_fg_of_mvPolynomial
 
-/-- If `f : A →ₐ[R] B` is a sujection between finitely-presented `R`-algebras, then the kernel of
+/-- If `f : A →ₐ[R] B` is a surjection between finitely-presented `R`-algebras, then the kernel of
 `f` is finitely generated. -/
 theorem ker_fG_of_surjective (f : A →ₐ[R] B) (hf : Function.Surjective f)
     (hRA : FinitePresentation R A) (hRB : FinitePresentation R B) : f.toRingHom.ker.FG := by

Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>