field_theory.ax_grothendieck ⟷ Mathlib.FieldTheory.AxGrothendieck

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

@@ -3,7 +3,7 @@ Copyright (c) 2023 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Data.MvPolynomial.Basic
+import Algebra.MvPolynomial.Basic
 import RingTheory.Algebraic
 import Data.Fintype.Card
 

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

@@ -65,7 +65,7 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
   have hres_inj : injective res := by
     intro x y hxy
     ext i
-    simp only [res, Subtype.ext_iff, funext_iff] at hxy 
+    simp only [res, Subtype.ext_iff, funext_iff] at hxy
     exact congr_fun (hinj (funext hxy)) i
   have hres_surj : surjective res := Finite.injective_iff_surjective.1 hres_inj
   cases' hres_surj fun i => ⟨v i, hv i⟩ with w hw

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

@@ -40,9 +40,37 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
   by
   have is_int : ∀ x : R, IsIntegral K x := fun x => isAlgebraic_iff_isIntegral.1 (alg x)
   classical
+  intro v
+  cases nonempty_fintype ι
+  /- `s` is the set of all coefficients of the polynomial, as well as all of
+    the coordinates of `v`, the point I am trying to find the preimage of. -/
+  let s : Finset R :=
+    (Finset.biUnion (univ : Finset ι) fun i => (ps i).support.image fun x => coeff x (ps i)) ∪
+      (univ : Finset ι).image v
+  have hv : ∀ i, v i ∈ Algebra.adjoin K (s : Set R) := fun j =>
+    Algebra.subset_adjoin (mem_union_right _ (mem_image.2 ⟨j, mem_univ _, rfl⟩))
+  have hs₁ :
+    ∀ (i : ι) (k : ι →₀ ℕ), k ∈ (ps i).support → coeff k (ps i) ∈ Algebra.adjoin K (s : Set R) :=
+    fun i k hk =>
+    Algebra.subset_adjoin (mem_union_left _ (mem_bUnion.2 ⟨i, mem_univ _, mem_image_of_mem _ hk⟩))
+  have hs : ∀ i, MvPolynomial.eval v (ps i) ∈ Algebra.adjoin K (s : Set R) := fun i =>
+    eval_mem (hs₁ _) hv
+  letI := isNoetherian_adjoin_finset s fun x _ => is_int x
+  letI := Module.IsNoetherian.finite K (Algebra.adjoin K (s : Set R))
+  letI : Finite (Algebra.adjoin K (s : Set R)) :=
+    FiniteDimensional.finite_of_finite K (Algebra.adjoin K (s : Set R))
+  -- The restriction of the polynomial map, `ps`, to the subalgebra generated by `s`
+  let res : (ι → Algebra.adjoin K (s : Set R)) → ι → Algebra.adjoin K (s : Set R) := fun x i =>
+    ⟨eval (fun j : ι => (x j : R)) (ps i), eval_mem (hs₁ _) fun i => (x i).2⟩
+  have hres_inj : injective res := by
+    intro x y hxy
+    ext i
+    simp only [res, Subtype.ext_iff, funext_iff] at hxy 
+    exact congr_fun (hinj (funext hxy)) i
+  have hres_surj : surjective res := Finite.injective_iff_surjective.1 hres_inj
+  cases' hres_surj fun i => ⟨v i, hv i⟩ with w hw
+  use fun i => w i
+  simpa only [res, Subtype.ext_iff, funext_iff] using hw
 #align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finite
 -/
 
-/- `s` is the set of all coefficients of the polynomial, as well as all of
-  the coordinates of `v`, the point I am trying to find the preimage of. -/
--- The restriction of the polynomial map, `ps`, to the subalgebra generated by `s` 

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

@@ -40,37 +40,9 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
   by
   have is_int : ∀ x : R, IsIntegral K x := fun x => isAlgebraic_iff_isIntegral.1 (alg x)
   classical
-  intro v
-  cases nonempty_fintype ι
-  /- `s` is the set of all coefficients of the polynomial, as well as all of
-    the coordinates of `v`, the point I am trying to find the preimage of. -/
-  let s : Finset R :=
-    (Finset.biUnion (univ : Finset ι) fun i => (ps i).support.image fun x => coeff x (ps i)) ∪
-      (univ : Finset ι).image v
-  have hv : ∀ i, v i ∈ Algebra.adjoin K (s : Set R) := fun j =>
-    Algebra.subset_adjoin (mem_union_right _ (mem_image.2 ⟨j, mem_univ _, rfl⟩))
-  have hs₁ :
-    ∀ (i : ι) (k : ι →₀ ℕ), k ∈ (ps i).support → coeff k (ps i) ∈ Algebra.adjoin K (s : Set R) :=
-    fun i k hk =>
-    Algebra.subset_adjoin (mem_union_left _ (mem_bUnion.2 ⟨i, mem_univ _, mem_image_of_mem _ hk⟩))
-  have hs : ∀ i, MvPolynomial.eval v (ps i) ∈ Algebra.adjoin K (s : Set R) := fun i =>
-    eval_mem (hs₁ _) hv
-  letI := isNoetherian_adjoin_finset s fun x _ => is_int x
-  letI := Module.IsNoetherian.finite K (Algebra.adjoin K (s : Set R))
-  letI : Finite (Algebra.adjoin K (s : Set R)) :=
-    FiniteDimensional.finite_of_finite K (Algebra.adjoin K (s : Set R))
-  -- The restriction of the polynomial map, `ps`, to the subalgebra generated by `s`
-  let res : (ι → Algebra.adjoin K (s : Set R)) → ι → Algebra.adjoin K (s : Set R) := fun x i =>
-    ⟨eval (fun j : ι => (x j : R)) (ps i), eval_mem (hs₁ _) fun i => (x i).2⟩
-  have hres_inj : injective res := by
-    intro x y hxy
-    ext i
-    simp only [res, Subtype.ext_iff, funext_iff] at hxy 
-    exact congr_fun (hinj (funext hxy)) i
-  have hres_surj : surjective res := Finite.injective_iff_surjective.1 hres_inj
-  cases' hres_surj fun i => ⟨v i, hv i⟩ with w hw
-  use fun i => w i
-  simpa only [res, Subtype.ext_iff, funext_iff] using hw
 #align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finite
 -/
 
+/- `s` is the set of all coefficients of the polynomial, as well as all of
+  the coordinates of `v`, the point I am trying to find the preimage of. -/
+-- The restriction of the polynomial map, `ps`, to the subalgebra generated by `s` 

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

@@ -3,9 +3,9 @@ Copyright (c) 2023 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.Data.MvPolynomial.Basic
-import Mathbin.RingTheory.Algebraic
-import Mathbin.Data.Fintype.Card
+import Data.MvPolynomial.Basic
+import RingTheory.Algebraic
+import Data.Fintype.Card
 
 #align_import field_theory.ax_grothendieck from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2023 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module field_theory.ax_grothendieck
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Basic
 import Mathbin.RingTheory.Algebraic
 import Mathbin.Data.Fintype.Card
 
+#align_import field_theory.ax_grothendieck from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 # Ax-Grothendieck for algebraic extensions of `zmod p`
 

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

@@ -35,6 +35,7 @@ noncomputable section
 
 open MvPolynomial Finset Function
 
+#print ax_grothendieck_of_locally_finite /-
 /-- Any injective polynomial map over an algebraic extension of a finite field is surjective. -/
 theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K] [CommRing R]
     [Finite ι] [Algebra K R] (alg : Algebra.IsAlgebraic K R) (ps : ι → MvPolynomial ι R)
@@ -74,4 +75,5 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
   use fun i => w i
   simpa only [res, Subtype.ext_iff, funext_iff] using hw
 #align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finite
+-/
 

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

@@ -42,36 +42,36 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
   by
   have is_int : ∀ x : R, IsIntegral K x := fun x => isAlgebraic_iff_isIntegral.1 (alg x)
   classical
-    intro v
-    cases nonempty_fintype ι
-    /- `s` is the set of all coefficients of the polynomial, as well as all of
-      the coordinates of `v`, the point I am trying to find the preimage of. -/
-    let s : Finset R :=
-      (Finset.biUnion (univ : Finset ι) fun i => (ps i).support.image fun x => coeff x (ps i)) ∪
-        (univ : Finset ι).image v
-    have hv : ∀ i, v i ∈ Algebra.adjoin K (s : Set R) := fun j =>
-      Algebra.subset_adjoin (mem_union_right _ (mem_image.2 ⟨j, mem_univ _, rfl⟩))
-    have hs₁ :
-      ∀ (i : ι) (k : ι →₀ ℕ), k ∈ (ps i).support → coeff k (ps i) ∈ Algebra.adjoin K (s : Set R) :=
-      fun i k hk =>
-      Algebra.subset_adjoin (mem_union_left _ (mem_bUnion.2 ⟨i, mem_univ _, mem_image_of_mem _ hk⟩))
-    have hs : ∀ i, MvPolynomial.eval v (ps i) ∈ Algebra.adjoin K (s : Set R) := fun i =>
-      eval_mem (hs₁ _) hv
-    letI := isNoetherian_adjoin_finset s fun x _ => is_int x
-    letI := Module.IsNoetherian.finite K (Algebra.adjoin K (s : Set R))
-    letI : Finite (Algebra.adjoin K (s : Set R)) :=
-      FiniteDimensional.finite_of_finite K (Algebra.adjoin K (s : Set R))
-    -- The restriction of the polynomial map, `ps`, to the subalgebra generated by `s`
-    let res : (ι → Algebra.adjoin K (s : Set R)) → ι → Algebra.adjoin K (s : Set R) := fun x i =>
-      ⟨eval (fun j : ι => (x j : R)) (ps i), eval_mem (hs₁ _) fun i => (x i).2⟩
-    have hres_inj : injective res := by
-      intro x y hxy
-      ext i
-      simp only [res, Subtype.ext_iff, funext_iff] at hxy 
-      exact congr_fun (hinj (funext hxy)) i
-    have hres_surj : surjective res := Finite.injective_iff_surjective.1 hres_inj
-    cases' hres_surj fun i => ⟨v i, hv i⟩ with w hw
-    use fun i => w i
-    simpa only [res, Subtype.ext_iff, funext_iff] using hw
+  intro v
+  cases nonempty_fintype ι
+  /- `s` is the set of all coefficients of the polynomial, as well as all of
+    the coordinates of `v`, the point I am trying to find the preimage of. -/
+  let s : Finset R :=
+    (Finset.biUnion (univ : Finset ι) fun i => (ps i).support.image fun x => coeff x (ps i)) ∪
+      (univ : Finset ι).image v
+  have hv : ∀ i, v i ∈ Algebra.adjoin K (s : Set R) := fun j =>
+    Algebra.subset_adjoin (mem_union_right _ (mem_image.2 ⟨j, mem_univ _, rfl⟩))
+  have hs₁ :
+    ∀ (i : ι) (k : ι →₀ ℕ), k ∈ (ps i).support → coeff k (ps i) ∈ Algebra.adjoin K (s : Set R) :=
+    fun i k hk =>
+    Algebra.subset_adjoin (mem_union_left _ (mem_bUnion.2 ⟨i, mem_univ _, mem_image_of_mem _ hk⟩))
+  have hs : ∀ i, MvPolynomial.eval v (ps i) ∈ Algebra.adjoin K (s : Set R) := fun i =>
+    eval_mem (hs₁ _) hv
+  letI := isNoetherian_adjoin_finset s fun x _ => is_int x
+  letI := Module.IsNoetherian.finite K (Algebra.adjoin K (s : Set R))
+  letI : Finite (Algebra.adjoin K (s : Set R)) :=
+    FiniteDimensional.finite_of_finite K (Algebra.adjoin K (s : Set R))
+  -- The restriction of the polynomial map, `ps`, to the subalgebra generated by `s`
+  let res : (ι → Algebra.adjoin K (s : Set R)) → ι → Algebra.adjoin K (s : Set R) := fun x i =>
+    ⟨eval (fun j : ι => (x j : R)) (ps i), eval_mem (hs₁ _) fun i => (x i).2⟩
+  have hres_inj : injective res := by
+    intro x y hxy
+    ext i
+    simp only [res, Subtype.ext_iff, funext_iff] at hxy 
+    exact congr_fun (hinj (funext hxy)) i
+  have hres_surj : surjective res := Finite.injective_iff_surjective.1 hres_inj
+  cases' hres_surj fun i => ⟨v i, hv i⟩ with w hw
+  use fun i => w i
+  simpa only [res, Subtype.ext_iff, funext_iff] using hw
 #align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finite
 

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

@@ -67,7 +67,7 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
     have hres_inj : injective res := by
       intro x y hxy
       ext i
-      simp only [res, Subtype.ext_iff, funext_iff] at hxy
+      simp only [res, Subtype.ext_iff, funext_iff] at hxy 
       exact congr_fun (hinj (funext hxy)) i
     have hres_surj : surjective res := Finite.injective_iff_surjective.1 hres_inj
     cases' hres_surj fun i => ⟨v i, hv i⟩ with w hw

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

@@ -35,9 +35,6 @@ noncomputable section
 
 open MvPolynomial Finset Function
 
-/- warning: ax_grothendieck_of_locally_finite -> ax_grothendieck_of_locally_finite is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finiteₓ'. -/
 /-- Any injective polynomial map over an algebraic extension of a finite field is surjective. -/
 theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K] [CommRing R]
     [Finite ι] [Algebra K R] (alg : Algebra.IsAlgebraic K R) (ps : ι → MvPolynomial ι R)

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

@@ -36,10 +36,7 @@ noncomputable section
 open MvPolynomial Finset Function
 
 /- warning: ax_grothendieck_of_locally_finite -> ax_grothendieck_of_locally_finite is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {K : Type.{u2}} {R : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Finite.{succ u2} K] [_inst_3 : CommRing.{u3} R] [_inst_4 : Finite.{succ u1} ι] [_inst_5 : Algebra.{u2, u3} K R (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))], (Algebra.IsAlgebraic.{u2, u3} K R (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u3} R _inst_3) _inst_5) -> (forall (ps : ι -> (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3))), (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (ι -> R) (ι -> R) (fun (v : ι -> R) (i : ι) => coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (fun (_x : RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) => (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) -> R) (RingHom.hasCoeToFun.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (MvPolynomial.eval.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3) v) (ps i))) -> (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (ι -> R) (ι -> R) (fun (v : ι -> R) (i : ι) => coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (fun (_x : RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) => (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) -> R) (RingHom.hasCoeToFun.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (MvPolynomial.eval.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3) v) (ps i))))
-but is expected to have type
-  forall {ι : Type.{u3}} {K : Type.{u2}} {R : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Finite.{succ u2} K] [_inst_3 : CommRing.{u1} R] [_inst_4 : Finite.{succ u3} ι] [_inst_5 : Algebra.{u2, u1} K R (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))], (Algebra.IsAlgebraic.{u2, u1} K R (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u1} R _inst_3) _inst_5) -> (forall (ps : ι -> (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3))), (Function.Injective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (ι -> R) (forall (i : ι), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) (ps i)) (fun (v : ι -> R) (i : ι) => FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), succ u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (fun (_x : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) _x) (MulHomClass.toFunLike.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (RingHom.instRingHomClassRingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))))) (MvPolynomial.eval.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3) v) (ps i))) -> (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (ι -> R) (forall (i : ι), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) (ps i)) (fun (v : ι -> R) (i : ι) => FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), succ u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (fun (_x : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) _x) (MulHomClass.toFunLike.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (RingHom.instRingHomClassRingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))))) (MvPolynomial.eval.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3) v) (ps i))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finiteₓ'. -/
 /-- Any injective polynomial map over an algebraic extension of a finite field is surjective. -/
 theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K] [CommRing R]

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module field_theory.ax_grothendieck
-! leanprover-community/mathlib commit 4e529b03dd62b7b7d13806c3fb974d9d4848910e
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Data.Fintype.Card
 /-!
 # Ax-Grothendieck for algebraic extensions of `zmod p`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves that if `R` is an algebraic extension of a finite field,
 then any injective polynomial map `R^n -> R^n` is also surjective.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -32,6 +32,12 @@ noncomputable section
 
 open MvPolynomial Finset Function
 
+/- warning: ax_grothendieck_of_locally_finite -> ax_grothendieck_of_locally_finite is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {K : Type.{u2}} {R : Type.{u3}} [_inst_1 : Field.{u2} K] [_inst_2 : Finite.{succ u2} K] [_inst_3 : CommRing.{u3} R] [_inst_4 : Finite.{succ u1} ι] [_inst_5 : Algebra.{u2, u3} K R (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (Ring.toSemiring.{u3} R (CommRing.toRing.{u3} R _inst_3))], (Algebra.IsAlgebraic.{u2, u3} K R (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u3} R _inst_3) _inst_5) -> (forall (ps : ι -> (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3))), (Function.Injective.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (ι -> R) (ι -> R) (fun (v : ι -> R) (i : ι) => coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (fun (_x : RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) => (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) -> R) (RingHom.hasCoeToFun.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (MvPolynomial.eval.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3) v) (ps i))) -> (Function.Surjective.{max (succ u1) (succ u3), max (succ u1) (succ u3)} (ι -> R) (ι -> R) (fun (v : ι -> R) (i : ι) => coeFn.{max (succ (max u1 u3)) (succ u3), max (succ (max u1 u3)) (succ u3)} (RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (fun (_x : RingHom.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) => (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) -> R) (RingHom.hasCoeToFun.{max u1 u3, u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u1, u3} ι R (CommRing.toCommSemiring.{u3} R _inst_3)) (MvPolynomial.commSemiring.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3)))) (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_3)))) (MvPolynomial.eval.{u3, u1} R ι (CommRing.toCommSemiring.{u3} R _inst_3) v) (ps i))))
+but is expected to have type
+  forall {ι : Type.{u3}} {K : Type.{u2}} {R : Type.{u1}} [_inst_1 : Field.{u2} K] [_inst_2 : Finite.{succ u2} K] [_inst_3 : CommRing.{u1} R] [_inst_4 : Finite.{succ u3} ι] [_inst_5 : Algebra.{u2, u1} K R (Semifield.toCommSemiring.{u2} K (Field.toSemifield.{u2} K _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))], (Algebra.IsAlgebraic.{u2, u1} K R (EuclideanDomain.toCommRing.{u2} K (Field.toEuclideanDomain.{u2} K _inst_1)) (CommRing.toRing.{u1} R _inst_3) _inst_5) -> (forall (ps : ι -> (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3))), (Function.Injective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (ι -> R) (forall (i : ι), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) (ps i)) (fun (v : ι -> R) (i : ι) => FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), succ u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (fun (_x : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) _x) (MulHomClass.toFunLike.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (RingHom.instRingHomClassRingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))))) (MvPolynomial.eval.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3) v) (ps i))) -> (Function.Surjective.{max (succ u3) (succ u1), max (succ u3) (succ u1)} (ι -> R) (forall (i : ι), (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) (ps i)) (fun (v : ι -> R) (i : ι) => FunLike.coe.{max (succ u3) (succ u1), max (succ u3) (succ u1), succ u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (fun (_x : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) => R) _x) (MulHomClass.toFunLike.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonUnitalNonAssocSemiring.toMul.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonUnitalRingHomClass.toMulHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u3 u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (RingHomClass.toNonUnitalRingHomClass.{max u3 u1, max u3 u1, u1} (RingHom.{max u1 u3, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3)))) (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))) (RingHom.instRingHomClassRingHom.{max u3 u1, u1} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) R (Semiring.toNonAssocSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (CommSemiring.toSemiring.{max u1 u3} (MvPolynomial.{u3, u1} ι R (CommRing.toCommSemiring.{u1} R _inst_3)) (MvPolynomial.commSemiring.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_3))))))) (MvPolynomial.eval.{u1, u3} R ι (CommRing.toCommSemiring.{u1} R _inst_3) v) (ps i))))
+Case conversion may be inaccurate. Consider using '#align ax_grothendieck_of_locally_finite ax_grothendieck_of_locally_finiteₓ'. -/
 /-- Any injective polynomial map over an algebraic extension of a finite field is surjective. -/
 theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K] [CommRing R]
     [Finite ι] [Algebra K R] (alg : Algebra.IsAlgebraic K R) (ps : ι → MvPolynomial ι R)

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

@@ -44,7 +44,7 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K]
     /- `s` is the set of all coefficients of the polynomial, as well as all of
       the coordinates of `v`, the point I am trying to find the preimage of. -/
     let s : Finset R :=
-      (Finset.bunionᵢ (univ : Finset ι) fun i => (ps i).support.image fun x => coeff x (ps i)) ∪
+      (Finset.biUnion (univ : Finset ι) fun i => (ps i).support.image fun x => coeff x (ps i)) ∪
         (univ : Finset ι).image v
     have hv : ∀ i, v i ∈ Algebra.adjoin K (s : Set R) := fun j =>
       Algebra.subset_adjoin (mem_union_right _ (mem_image.2 ⟨j, mem_univ _, rfl⟩))

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

Polynomial and MvPolynomial are algebraic objects, hence should be under Algebra (or at least not under Data)

@@ -3,9 +3,9 @@ Copyright (c) 2023 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathlib.Data.MvPolynomial.Basic
-import Mathlib.RingTheory.Algebraic
+import Mathlib.Algebra.MvPolynomial.Basic
 import Mathlib.Data.Fintype.Card
+import Mathlib.RingTheory.Algebraic
 
 #align_import field_theory.ax_grothendieck from "leanprover-community/mathlib"@"4e529b03dd62b7b7d13806c3fb974d9d4848910e"
 

Zulip

Initially I just wanted to add more dot notations for IsIntegral and IsAlgebraic (done in #8437); then I noticed near-duplicates Algebra.isIntegral_of_finite [Field R] [Ring A] and RingHom.IsIntegral.of_finite [CommRing R] [CommRing A] so I went on to generalize the latter to cover the former, and generalized everything in the IntegralClosure file to the noncommutative case whenever possible.

In the process I noticed more golfs, which result in this PR. Most notably, isIntegral_of_mem_of_FG is now proven using Cayley-Hamilton and doesn't depend on the Noetherian case isIntegral_of_noetherian; the latter is now proven using the former. In total the golfs makes mathlib 227 lines leaner (+487 -714).

The main changes are in the single file RingTheory/IntegralClosure:

• Change the definition of Algebra.IsIntegral which makes it unfold to IsIntegral rather than RingHom.IsIntegralElem because the former has much more APIs.

• Fix lemma names involving is_integral which are actually about IsIntegralElem: RingHom.is_integral_map → RingHom.isIntegralElem_map RingHom.is_integral_of_mem_closure → RingHom.IsIntegralElem.of_mem_closure RingHom.is_integral_zero/one → RingHom.isIntegralElem_zero/one RingHom.is_integral_add/neg/sub/mul/of_mul_unit → RingHom.IsIntegralElem.add/neg/sub/mul/of_mul_unit

• Add a lemma Algebra.IsIntegral.of_injective.

• Move isIntegral_of_(submodule_)noetherian down and golf them.

• Remove (Algebra.)isIntegral_of_finite that work only over fields, in favor of the more general (Algebra.)isIntegral.of_finite.

• Merge duplicate lemmas isIntegral_of_isScalarTower and isIntegral_tower_top_of_isIntegral into IsIntegral.tower_top.

• Golf IsIntegral.of_mem_of_fg by first proving IsIntegral.of_finite using Cayley-Hamilton.

• Add a docstring mentioning the Kurosh problem at Algebra.IsIntegral.finite. The negative solution to the problem means the theorem doesn't generalize to noncommutative algebras.

• Golf IsIntegral.tmul and isField_of_isIntegral_of_isField(').

• Combine isIntegral_trans_aux into isIntegral_trans and golf.

• Add Algebra namespace to isIntegral_sup.

• rename lemmas for dot notation: RingHom.isIntegral_trans → RingHom.IsIntegral.trans RingHom.isIntegral_quotient/tower_bot/top_of_isIntegral → RingHom.IsIntegral.quotient/tower_bot/top isIntegral_of_mem_closure' → IsIntegral.of_mem_closure' (and the '' version) isIntegral_of_surjective → Algebra.isIntegral_of_surjective

The next changed file is RingTheory/Algebraic:

• Rename: of_larger_base → tower_top (for consistency with IsIntegral) Algebra.isAlgebraic_of_finite → Algebra.IsAlgebraic.of_finite Algebra.isAlgebraic_trans → Algebra.IsAlgebraic.trans

• Add new lemmasAlgebra.IsIntegral.isAlgebraic, isAlgebraic_algHom_iff, and Algebra.IsAlgebraic.of_injective to streamline some proofs.

The generalization from CommRing to Ring requires an additional lemma scaleRoots_eval₂_mul_of_commute in Polynomial/ScaleRoots.

A lemma Algebra.lmul_injective is added to Algebra/Bilinear (in order to golf the proof of IsIntegral.of_mem_of_fg).

In all other files, I merely fix the changed names, or use newly available dot notations.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -34,7 +34,6 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type*} [Field K] [Finite K]
     [Finite ι] [Algebra K R] (alg : Algebra.IsAlgebraic K R) (ps : ι → MvPolynomial ι R)
     (hinj : Injective fun v i => MvPolynomial.eval v (ps i)) :
     Surjective fun v i => MvPolynomial.eval v (ps i) := by
-  have is_int : ∀ x : R, IsIntegral K x := fun x => isAlgebraic_iff_isIntegral.1 (alg x)
   classical
     intro v
     cases nonempty_fintype ι
@@ -49,7 +48,7 @@ theorem ax_grothendieck_of_locally_finite {ι K R : Type*} [Field K] [Finite K]
         k ∈ (ps i).support → coeff k (ps i) ∈ Algebra.adjoin K (s : Set R) :=
       fun i k hk => Algebra.subset_adjoin
         (mem_union_left _ (mem_biUnion.2 ⟨i, mem_univ _, mem_image_of_mem _ hk⟩))
-    letI := isNoetherian_adjoin_finset s fun x _ => is_int x
+    letI := isNoetherian_adjoin_finset s fun x _ => alg.isIntegral x
     letI := Module.IsNoetherian.finite K (Algebra.adjoin K (s : Set R))
     letI : Finite (Algebra.adjoin K (s : Set R)) :=
       FiniteDimensional.finite_of_finite K (Algebra.adjoin K (s : Set R))

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

This has nice performance benefits.

@@ -30,7 +30,7 @@ noncomputable section
 open MvPolynomial Finset Function
 
 /-- Any injective polynomial map over an algebraic extension of a finite field is surjective. -/
-theorem ax_grothendieck_of_locally_finite {ι K R : Type _} [Field K] [Finite K] [CommRing R]
+theorem ax_grothendieck_of_locally_finite {ι K R : Type*} [Field K] [Finite K] [CommRing R]
     [Finite ι] [Algebra K R] (alg : Algebra.IsAlgebraic K R) (ps : ι → MvPolynomial ι R)
     (hinj : Injective fun v i => MvPolynomial.eval v (ps i)) :
     Surjective fun v i => MvPolynomial.eval v (ps i) := by

• 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) 2023 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module field_theory.ax_grothendieck
-! leanprover-community/mathlib commit 4e529b03dd62b7b7d13806c3fb974d9d4848910e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.Basic
 import Mathlib.RingTheory.Algebraic
 import Mathlib.Data.Fintype.Card
 
+#align_import field_theory.ax_grothendieck from "leanprover-community/mathlib"@"4e529b03dd62b7b7d13806c3fb974d9d4848910e"
+
 /-!
 # Ax-Grothendieck for algebraic extensions of `ZMod p`