data.mv_polynomial.derivation ⟷ Mathlib.Data.MvPolynomial.Derivation

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Data.MvPolynomial.Supported
+import Algebra.MvPolynomial.Supported
 import RingTheory.Derivation.Basic
 
 #align_import data.mv_polynomial.derivation from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"

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

@@ -84,7 +84,7 @@ theorem derivation_c_hMul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f :
 theorem derivation_eqOn_supported {D₁ D₂ : Derivation R (MvPolynomial σ R) A} {s : Set σ}
     (h : Set.EqOn (D₁ ∘ X) (D₂ ∘ X) s) {f : MvPolynomial σ R} (hf : f ∈ supported R s) :
     D₁ f = D₂ f :=
-  Derivation.eqOn_adjoin (Set.ball_image_iff.2 h) hf
+  Derivation.eqOn_adjoin (Set.forall_mem_image.2 h) hf
 #align mv_polynomial.derivation_eq_on_supported MvPolynomial.derivation_eqOn_supported
 -/
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Data.MvPolynomial.Supported
-import Mathbin.RingTheory.Derivation.Basic
+import Data.MvPolynomial.Supported
+import RingTheory.Derivation.Basic
 
 #align_import data.mv_polynomial.derivation from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
 

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

@@ -74,9 +74,9 @@ theorem derivation_C (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a)
 -/
 
 @[simp]
-theorem derivation_c_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
+theorem derivation_c_hMul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
     D (C a * f) = a • D f := by rw [C_mul', D.map_smul]
-#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_c_mul
+#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_c_hMul
 
 #print MvPolynomial.derivation_eqOn_supported /-
 /-- If two derivations agree on `X i`, `i ∈ s`, then they agree on all polynomials from

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

@@ -73,12 +73,10 @@ theorem derivation_C (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a)
 #align mv_polynomial.derivation_C MvPolynomial.derivation_C
 -/
 
-#print MvPolynomial.derivation_C_mul /-
 @[simp]
-theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
+theorem derivation_c_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
     D (C a * f) = a • D f := by rw [C_mul', D.map_smul]
-#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_C_mul
--/
+#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_c_mul
 
 #print MvPolynomial.derivation_eqOn_supported /-
 /-- If two derivations agree on `X i`, `i ∈ s`, then they agree on all polynomials from

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module data.mv_polynomial.derivation
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Supported
 import Mathbin.RingTheory.Derivation.Basic
 
+#align_import data.mv_polynomial.derivation from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # Derivations of multivariate polynomials
 

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

@@ -49,30 +49,41 @@ def mkDerivationₗ (f : σ → A) : MvPolynomial σ R →ₗ[R] A :=
 
 end
 
+#print MvPolynomial.mkDerivationₗ_monomial /-
 theorem mkDerivationₗ_monomial (f : σ → A) (s : σ →₀ ℕ) (r : R) :
     mkDerivationₗ R f (monomial s r) =
       r • s.Sum fun i k => monomial (s - Finsupp.single i 1) (k : R) • f i :=
   sum_monomial_eq <| LinearMap.map_zero _
 #align mv_polynomial.mk_derivationₗ_monomial MvPolynomial.mkDerivationₗ_monomial
+-/
 
+#print MvPolynomial.mkDerivationₗ_C /-
 theorem mkDerivationₗ_C (f : σ → A) (r : R) : mkDerivationₗ R f (C r) = 0 :=
   (mkDerivationₗ_monomial f _ _).trans (smul_zero _)
 #align mv_polynomial.mk_derivationₗ_C MvPolynomial.mkDerivationₗ_C
+-/
 
+#print MvPolynomial.mkDerivationₗ_X /-
 theorem mkDerivationₗ_X (f : σ → A) (i : σ) : mkDerivationₗ R f (X i) = f i :=
   (mkDerivationₗ_monomial f _ _).trans <| by simp
 #align mv_polynomial.mk_derivationₗ_X MvPolynomial.mkDerivationₗ_X
+-/
 
+#print MvPolynomial.derivation_C /-
 @[simp]
 theorem derivation_C (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a) = 0 :=
   D.map_algebraMap a
 #align mv_polynomial.derivation_C MvPolynomial.derivation_C
+-/
 
+#print MvPolynomial.derivation_C_mul /-
 @[simp]
 theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
     D (C a * f) = a • D f := by rw [C_mul', D.map_smul]
 #align mv_polynomial.derivation_C_mul MvPolynomial.derivation_C_mul
+-/
 
+#print MvPolynomial.derivation_eqOn_supported /-
 /-- If two derivations agree on `X i`, `i ∈ s`, then they agree on all polynomials from
 `mv_polynomial.supported R s`. -/
 theorem derivation_eqOn_supported {D₁ D₂ : Derivation R (MvPolynomial σ R) A} {s : Set σ}
@@ -80,25 +91,33 @@ theorem derivation_eqOn_supported {D₁ D₂ : Derivation R (MvPolynomial σ R)
     D₁ f = D₂ f :=
   Derivation.eqOn_adjoin (Set.ball_image_iff.2 h) hf
 #align mv_polynomial.derivation_eq_on_supported MvPolynomial.derivation_eqOn_supported
+-/
 
+#print MvPolynomial.derivation_eq_of_forall_mem_vars /-
 theorem derivation_eq_of_forall_mem_vars {D₁ D₂ : Derivation R (MvPolynomial σ R) A}
     {f : MvPolynomial σ R} (h : ∀ i ∈ f.vars, D₁ (X i) = D₂ (X i)) : D₁ f = D₂ f :=
   derivation_eqOn_supported h f.mem_supported_vars
 #align mv_polynomial.derivation_eq_of_forall_mem_vars MvPolynomial.derivation_eq_of_forall_mem_vars
+-/
 
+#print MvPolynomial.derivation_eq_zero_of_forall_mem_vars /-
 theorem derivation_eq_zero_of_forall_mem_vars {D : Derivation R (MvPolynomial σ R) A}
     {f : MvPolynomial σ R} (h : ∀ i ∈ f.vars, D (X i) = 0) : D f = 0 :=
   show D f = (0 : Derivation R (MvPolynomial σ R) A) f from derivation_eq_of_forall_mem_vars h
 #align mv_polynomial.derivation_eq_zero_of_forall_mem_vars MvPolynomial.derivation_eq_zero_of_forall_mem_vars
+-/
 
+#print MvPolynomial.derivation_ext /-
 @[ext]
 theorem derivation_ext {D₁ D₂ : Derivation R (MvPolynomial σ R) A} (h : ∀ i, D₁ (X i) = D₂ (X i)) :
     D₁ = D₂ :=
   Derivation.ext fun f => derivation_eq_of_forall_mem_vars fun i _ => h i
 #align mv_polynomial.derivation_ext MvPolynomial.derivation_ext
+-/
 
 variable [IsScalarTower R (MvPolynomial σ R) A]
 
+#print MvPolynomial.leibniz_iff_X /-
 theorem leibniz_iff_X (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
     (∀ p q, D (p * q) = p • D q + q • D p) ↔
       ∀ s i,
@@ -124,6 +143,7 @@ theorem leibniz_iff_X (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
   case h_X q i hq =>
     simp only [this, ← mul_assoc, hq, mul_smul, smul_add, smul_comm (X i), add_assoc]
 #align mv_polynomial.leibniz_iff_X MvPolynomial.leibniz_iff_X
+-/
 
 variable (R)
 
@@ -148,17 +168,22 @@ def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
 #align mv_polynomial.mk_derivation MvPolynomial.mkDerivation
 -/
 
+#print MvPolynomial.mkDerivation_X /-
 @[simp]
 theorem mkDerivation_X (f : σ → A) (i : σ) : mkDerivation R f (X i) = f i :=
   mkDerivationₗ_X f i
 #align mv_polynomial.mk_derivation_X MvPolynomial.mkDerivation_X
+-/
 
+#print MvPolynomial.mkDerivation_monomial /-
 theorem mkDerivation_monomial (f : σ → A) (s : σ →₀ ℕ) (r : R) :
     mkDerivation R f (monomial s r) =
       r • s.Sum fun i k => monomial (s - Finsupp.single i 1) (k : R) • f i :=
   mkDerivationₗ_monomial f s r
 #align mv_polynomial.mk_derivation_monomial MvPolynomial.mkDerivation_monomial
+-/
 
+#print MvPolynomial.mkDerivationEquiv /-
 /-- `mv_polynomial.mk_derivation` as a linear equivalence. -/
 def mkDerivationEquiv : (σ → A) ≃ₗ[R] Derivation R (MvPolynomial σ R) A :=
   LinearEquiv.symm <|
@@ -169,6 +194,7 @@ def mkDerivationEquiv : (σ → A) ≃ₗ[R] Derivation R (MvPolynomial σ R) A
       left_inv := fun D => derivation_ext <| mkDerivation_X _ _
       right_inv := fun f => funext <| mkDerivation_X _ _ }
 #align mv_polynomial.mk_derivation_equiv MvPolynomial.mkDerivationEquiv
+-/
 
 end MvPolynomial
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.derivation
-! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.Derivation.Basic
 /-!
 # Derivations of multivariate polynomials
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove that a derivation of `mv_polynomial σ R` is determined by its values on all
 monomials `mv_polynomial.X i`. We also provide a constructor `mv_polynomial.mk_derivation` that
 builds a derivation from its values on `X i`s and a linear equivalence
@@ -34,6 +37,7 @@ section
 
 variable (R)
 
+#print MvPolynomial.mkDerivationₗ /-
 /-- The derivation on `mv_polynomial σ R` that takes value `f i` on `X i`, as a linear map.
 Use `mv_polynomial.mk_derivation` instead. -/
 def mkDerivationₗ (f : σ → A) : MvPolynomial σ R →ₗ[R] A :=
@@ -41,6 +45,7 @@ def mkDerivationₗ (f : σ → A) : MvPolynomial σ R →ₗ[R] A :=
     (LinearMap.ringLmapEquivSelf R R A).symm <|
       xs.Sum fun i k => monomial (xs - Finsupp.single i 1) (k : R) • f i
 #align mv_polynomial.mk_derivationₗ MvPolynomial.mkDerivationₗ
+-/
 
 end
 
@@ -50,23 +55,23 @@ theorem mkDerivationₗ_monomial (f : σ → A) (s : σ →₀ ℕ) (r : R) :
   sum_monomial_eq <| LinearMap.map_zero _
 #align mv_polynomial.mk_derivationₗ_monomial MvPolynomial.mkDerivationₗ_monomial
 
-theorem mkDerivationₗ_c (f : σ → A) (r : R) : mkDerivationₗ R f (C r) = 0 :=
+theorem mkDerivationₗ_C (f : σ → A) (r : R) : mkDerivationₗ R f (C r) = 0 :=
   (mkDerivationₗ_monomial f _ _).trans (smul_zero _)
-#align mv_polynomial.mk_derivationₗ_C MvPolynomial.mkDerivationₗ_c
+#align mv_polynomial.mk_derivationₗ_C MvPolynomial.mkDerivationₗ_C
 
-theorem mkDerivationₗ_x (f : σ → A) (i : σ) : mkDerivationₗ R f (X i) = f i :=
+theorem mkDerivationₗ_X (f : σ → A) (i : σ) : mkDerivationₗ R f (X i) = f i :=
   (mkDerivationₗ_monomial f _ _).trans <| by simp
-#align mv_polynomial.mk_derivationₗ_X MvPolynomial.mkDerivationₗ_x
+#align mv_polynomial.mk_derivationₗ_X MvPolynomial.mkDerivationₗ_X
 
 @[simp]
-theorem derivation_c (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a) = 0 :=
+theorem derivation_C (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a) = 0 :=
   D.map_algebraMap a
-#align mv_polynomial.derivation_C MvPolynomial.derivation_c
+#align mv_polynomial.derivation_C MvPolynomial.derivation_C
 
 @[simp]
-theorem derivation_c_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
+theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
     D (C a * f) = a • D f := by rw [C_mul', D.map_smul]
-#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_c_mul
+#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_C_mul
 
 /-- If two derivations agree on `X i`, `i ∈ s`, then they agree on all polynomials from
 `mv_polynomial.supported R s`. -/
@@ -94,7 +99,7 @@ theorem derivation_ext {D₁ D₂ : Derivation R (MvPolynomial σ R) A} (h : ∀
 
 variable [IsScalarTower R (MvPolynomial σ R) A]
 
-theorem leibniz_iff_x (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
+theorem leibniz_iff_X (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
     (∀ p q, D (p * q) = p • D q + q • D p) ↔
       ∀ s i,
         D (monomial s 1 * X i) =
@@ -118,17 +123,18 @@ theorem leibniz_iff_x (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
   case h_add q₁ q₂ h₁ h₂ => simp only [mul_add, map_add, h₁, h₂, smul_add, add_smul]; abel
   case h_X q i hq =>
     simp only [this, ← mul_assoc, hq, mul_smul, smul_add, smul_comm (X i), add_assoc]
-#align mv_polynomial.leibniz_iff_X MvPolynomial.leibniz_iff_x
+#align mv_polynomial.leibniz_iff_X MvPolynomial.leibniz_iff_X
 
 variable (R)
 
+#print MvPolynomial.mkDerivation /-
 /-- The derivation on `mv_polynomial σ R` that takes value `f i` on `X i`. -/
 def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
     where
   toLinearMap := mkDerivationₗ R f
-  map_one_eq_zero' := mkDerivationₗ_c _ 1
+  map_one_eq_zero' := mkDerivationₗ_C _ 1
   leibniz' :=
-    (leibniz_iff_x (mkDerivationₗ R f) (mkDerivationₗ_c _ 1)).2 fun s i =>
+    (leibniz_iff_X (mkDerivationₗ R f) (mkDerivationₗ_C _ 1)).2 fun s i =>
       by
       simp only [mk_derivationₗ_monomial, X, monomial_mul, one_smul, one_mul]
       rw [Finsupp.sum_add_index'] <;> [skip; · simp;
@@ -140,11 +146,12 @@ def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
       rw [smul_smul, monomial_mul, one_mul, add_comm s, add_tsub_assoc_of_le]
       rwa [Finsupp.single_le_iff, Nat.succ_le_iff, pos_iff_ne_zero, ← Finsupp.mem_support_iff]
 #align mv_polynomial.mk_derivation MvPolynomial.mkDerivation
+-/
 
 @[simp]
-theorem mkDerivation_x (f : σ → A) (i : σ) : mkDerivation R f (X i) = f i :=
-  mkDerivationₗ_x f i
-#align mv_polynomial.mk_derivation_X MvPolynomial.mkDerivation_x
+theorem mkDerivation_X (f : σ → A) (i : σ) : mkDerivation R f (X i) = f i :=
+  mkDerivationₗ_X f i
+#align mv_polynomial.mk_derivation_X MvPolynomial.mkDerivation_X
 
 theorem mkDerivation_monomial (f : σ → A) (s : σ →₀ ℕ) (r : R) :
     mkDerivation R f (monomial s r) =
@@ -159,8 +166,8 @@ def mkDerivationEquiv : (σ → A) ≃ₗ[R] Derivation R (MvPolynomial σ R) A
       toFun := fun D i => D (X i)
       map_add' := fun D₁ D₂ => rfl
       map_smul' := fun c D => rfl
-      left_inv := fun D => derivation_ext <| mkDerivation_x _ _
-      right_inv := fun f => funext <| mkDerivation_x _ _ }
+      left_inv := fun D => derivation_ext <| mkDerivation_X _ _
+      right_inv := fun f => funext <| mkDerivation_X _ _ }
 #align mv_polynomial.mk_derivation_equiv MvPolynomial.mkDerivationEquiv
 
 end MvPolynomial

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.mv_polynomial.derivation
-! leanprover-community/mathlib commit 6e492fdbed778ea815798a5a0c6cb83df8486265
+! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.MvPolynomial.Supported
-import Mathbin.RingTheory.Derivation
+import Mathbin.RingTheory.Derivation.Basic
 
 /-!
 # Derivations of multivariate polynomials

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

@@ -131,9 +131,9 @@ def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
     (leibniz_iff_x (mkDerivationₗ R f) (mkDerivationₗ_c _ 1)).2 fun s i =>
       by
       simp only [mk_derivationₗ_monomial, X, monomial_mul, one_smul, one_mul]
-      rw [Finsupp.sum_add_index'] <;>
-        [skip;· simp;· intros ; simp only [Nat.cast_add, (monomial _).map_add, add_smul]]
-      rw [Finsupp.sum_single_index, Finsupp.sum_single_index] <;> [skip;· simp;· simp]
+      rw [Finsupp.sum_add_index'] <;> [skip; · simp;
+        · intros; simp only [Nat.cast_add, (monomial _).map_add, add_smul]]
+      rw [Finsupp.sum_single_index, Finsupp.sum_single_index] <;> [skip; · simp; · simp]
       rw [tsub_self, add_tsub_cancel_right, Nat.cast_one, ← C_apply, C_1, one_smul, add_comm,
         Finsupp.smul_sum]
       refine' congr_arg₂ (· + ·) rfl (Finset.sum_congr rfl fun j hj => _); dsimp only

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

@@ -23,7 +23,7 @@ builds a derivation from its values on `X i`s and a linear equivalence
 
 namespace MvPolynomial
 
-open BigOperators
+open scoped BigOperators
 
 noncomputable section
 

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

@@ -102,9 +102,7 @@ theorem leibniz_iff_x (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
             (X i : MvPolynomial σ R) • D (monomial s 1) :=
   by
   refine' ⟨fun H p i => H _ _, fun H => _⟩
-  have hC : ∀ r, D (C r) = 0 := by
-    intro r
-    rw [C_eq_smul_one, D.map_smul, h₁, smul_zero]
+  have hC : ∀ r, D (C r) = 0 := by intro r; rw [C_eq_smul_one, D.map_smul, h₁, smul_zero]
   have : ∀ p i, D (p * X i) = p • D (X i) + (X i : MvPolynomial σ R) • D p :=
     by
     intro p i
@@ -134,9 +132,7 @@ def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
       by
       simp only [mk_derivationₗ_monomial, X, monomial_mul, one_smul, one_mul]
       rw [Finsupp.sum_add_index'] <;>
-        [skip;· simp;·
-          intros
-          simp only [Nat.cast_add, (monomial _).map_add, add_smul]]
+        [skip;· simp;· intros ; simp only [Nat.cast_add, (monomial _).map_add, add_smul]]
       rw [Finsupp.sum_single_index, Finsupp.sum_single_index] <;> [skip;· simp;· simp]
       rw [tsub_self, add_tsub_cancel_right, Nat.cast_one, ← C_apply, C_1, one_smul, add_comm,
         Finsupp.smul_sum]

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

@@ -133,10 +133,11 @@ def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
     (leibniz_iff_x (mkDerivationₗ R f) (mkDerivationₗ_c _ 1)).2 fun s i =>
       by
       simp only [mk_derivationₗ_monomial, X, monomial_mul, one_smul, one_mul]
-      rw [Finsupp.sum_add_index'] <;> [skip, · simp,
-        · intros
+      rw [Finsupp.sum_add_index'] <;>
+        [skip;· simp;·
+          intros
           simp only [Nat.cast_add, (monomial _).map_add, add_smul]]
-      rw [Finsupp.sum_single_index, Finsupp.sum_single_index] <;> [skip, · simp, · simp]
+      rw [Finsupp.sum_single_index, Finsupp.sum_single_index] <;> [skip;· simp;· simp]
       rw [tsub_self, add_tsub_cancel_right, Nat.cast_one, ← C_apply, C_1, one_smul, add_comm,
         Finsupp.smul_sum]
       refine' congr_arg₂ (· + ·) rfl (Finset.sum_congr rfl fun j hj => _); dsimp only

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

@@ -50,44 +50,44 @@ theorem mkDerivationₗ_monomial (f : σ → A) (s : σ →₀ ℕ) (r : R) :
   sum_monomial_eq <| LinearMap.map_zero _
 #align mv_polynomial.mk_derivationₗ_monomial MvPolynomial.mkDerivationₗ_monomial
 
-theorem mkDerivationₗ_c (f : σ → A) (r : R) : mkDerivationₗ R f (c r) = 0 :=
+theorem mkDerivationₗ_c (f : σ → A) (r : R) : mkDerivationₗ R f (C r) = 0 :=
   (mkDerivationₗ_monomial f _ _).trans (smul_zero _)
 #align mv_polynomial.mk_derivationₗ_C MvPolynomial.mkDerivationₗ_c
 
-theorem mkDerivationₗ_x (f : σ → A) (i : σ) : mkDerivationₗ R f (x i) = f i :=
+theorem mkDerivationₗ_x (f : σ → A) (i : σ) : mkDerivationₗ R f (X i) = f i :=
   (mkDerivationₗ_monomial f _ _).trans <| by simp
 #align mv_polynomial.mk_derivationₗ_X MvPolynomial.mkDerivationₗ_x
 
 @[simp]
-theorem derivation_c (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (c a) = 0 :=
+theorem derivation_c (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a) = 0 :=
   D.map_algebraMap a
 #align mv_polynomial.derivation_C MvPolynomial.derivation_c
 
 @[simp]
 theorem derivation_c_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
-    D (c a * f) = a • D f := by rw [C_mul', D.map_smul]
+    D (C a * f) = a • D f := by rw [C_mul', D.map_smul]
 #align mv_polynomial.derivation_C_mul MvPolynomial.derivation_c_mul
 
 /-- If two derivations agree on `X i`, `i ∈ s`, then they agree on all polynomials from
 `mv_polynomial.supported R s`. -/
 theorem derivation_eqOn_supported {D₁ D₂ : Derivation R (MvPolynomial σ R) A} {s : Set σ}
-    (h : Set.EqOn (D₁ ∘ x) (D₂ ∘ x) s) {f : MvPolynomial σ R} (hf : f ∈ supported R s) :
+    (h : Set.EqOn (D₁ ∘ X) (D₂ ∘ X) s) {f : MvPolynomial σ R} (hf : f ∈ supported R s) :
     D₁ f = D₂ f :=
   Derivation.eqOn_adjoin (Set.ball_image_iff.2 h) hf
 #align mv_polynomial.derivation_eq_on_supported MvPolynomial.derivation_eqOn_supported
 
 theorem derivation_eq_of_forall_mem_vars {D₁ D₂ : Derivation R (MvPolynomial σ R) A}
-    {f : MvPolynomial σ R} (h : ∀ i ∈ f.vars, D₁ (x i) = D₂ (x i)) : D₁ f = D₂ f :=
+    {f : MvPolynomial σ R} (h : ∀ i ∈ f.vars, D₁ (X i) = D₂ (X i)) : D₁ f = D₂ f :=
   derivation_eqOn_supported h f.mem_supported_vars
 #align mv_polynomial.derivation_eq_of_forall_mem_vars MvPolynomial.derivation_eq_of_forall_mem_vars
 
 theorem derivation_eq_zero_of_forall_mem_vars {D : Derivation R (MvPolynomial σ R) A}
-    {f : MvPolynomial σ R} (h : ∀ i ∈ f.vars, D (x i) = 0) : D f = 0 :=
+    {f : MvPolynomial σ R} (h : ∀ i ∈ f.vars, D (X i) = 0) : D f = 0 :=
   show D f = (0 : Derivation R (MvPolynomial σ R) A) f from derivation_eq_of_forall_mem_vars h
 #align mv_polynomial.derivation_eq_zero_of_forall_mem_vars MvPolynomial.derivation_eq_zero_of_forall_mem_vars
 
 @[ext]
-theorem derivation_ext {D₁ D₂ : Derivation R (MvPolynomial σ R) A} (h : ∀ i, D₁ (x i) = D₂ (x i)) :
+theorem derivation_ext {D₁ D₂ : Derivation R (MvPolynomial σ R) A} (h : ∀ i, D₁ (X i) = D₂ (X i)) :
     D₁ = D₂ :=
   Derivation.ext fun f => derivation_eq_of_forall_mem_vars fun i _ => h i
 #align mv_polynomial.derivation_ext MvPolynomial.derivation_ext
@@ -97,9 +97,9 @@ variable [IsScalarTower R (MvPolynomial σ R) A]
 theorem leibniz_iff_x (D : MvPolynomial σ R →ₗ[R] A) (h₁ : D 1 = 0) :
     (∀ p q, D (p * q) = p • D q + q • D p) ↔
       ∀ s i,
-        D (monomial s 1 * x i) =
-          (monomial s 1 : MvPolynomial σ R) • D (x i) +
-            (x i : MvPolynomial σ R) • D (monomial s 1) :=
+        D (monomial s 1 * X i) =
+          (monomial s 1 : MvPolynomial σ R) • D (X i) +
+            (X i : MvPolynomial σ R) • D (monomial s 1) :=
   by
   refine' ⟨fun H p i => H _ _, fun H => _⟩
   have hC : ∀ r, D (C r) = 0 := by
@@ -145,7 +145,7 @@ def mkDerivation (f : σ → A) : Derivation R (MvPolynomial σ R) A
 #align mv_polynomial.mk_derivation MvPolynomial.mkDerivation
 
 @[simp]
-theorem mkDerivation_x (f : σ → A) (i : σ) : mkDerivation R f (x i) = f i :=
+theorem mkDerivation_x (f : σ → A) (i : σ) : mkDerivation R f (X i) = f i :=
   mkDerivationₗ_x f i
 #align mv_polynomial.mk_derivation_X MvPolynomial.mkDerivation_x
 
@@ -159,7 +159,7 @@ theorem mkDerivation_monomial (f : σ → A) (s : σ →₀ ℕ) (r : R) :
 def mkDerivationEquiv : (σ → A) ≃ₗ[R] Derivation R (MvPolynomial σ R) A :=
   LinearEquiv.symm <|
     { invFun := mkDerivation R
-      toFun := fun D i => D (x i)
+      toFun := fun D i => D (X i)
       map_add' := fun D₁ D₂ => rfl
       map_smul' := fun c D => rfl
       left_inv := fun D => derivation_ext <| mkDerivation_x _ _

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

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathlib.Data.MvPolynomial.Supported
+import Mathlib.Algebra.MvPolynomial.Supported
 import Mathlib.RingTheory.Derivation.Basic
 
 #align_import data.mv_polynomial.derivation from "leanprover-community/mathlib"@"b608348ffaeb7f557f2fd46876037abafd326ff3"

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -74,7 +74,7 @@ theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : M
 theorem derivation_eqOn_supported {D₁ D₂ : Derivation R (MvPolynomial σ R) A} {s : Set σ}
     (h : Set.EqOn (D₁ ∘ X) (D₂ ∘ X) s) {f : MvPolynomial σ R} (hf : f ∈ supported R s) :
     D₁ f = D₂ f :=
-  Derivation.eqOn_adjoin (Set.ball_image_iff.2 h) hf
+  Derivation.eqOn_adjoin (Set.forall_mem_image.2 h) hf
 #align mv_polynomial.derivation_eq_on_supported MvPolynomial.derivation_eqOn_supported
 
 theorem derivation_eq_of_forall_mem_vars {D₁ D₂ : Derivation R (MvPolynomial σ R) A}

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

This has nice performance benefits.

@@ -24,7 +24,7 @@ open scoped BigOperators
 
 noncomputable section
 
-variable {σ R A : Type _} [CommSemiring R] [AddCommMonoid A] [Module R A]
+variable {σ R A : Type*} [CommSemiring R] [AddCommMonoid A] [Module R A]
   [Module (MvPolynomial σ R) A]
 
 section

An R-derivation from R[X] is determined by its value on X. Joint work with Richard Hill, who needs this stuff for his work on power series. We followed MvPolynomial.Derivation .

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -63,17 +63,11 @@ theorem derivation_C (D : Derivation R (MvPolynomial σ R) A) (a : R) : D (C a)
 set_option linter.uppercaseLean3 false in
 #align mv_polynomial.derivation_C MvPolynomial.derivation_C
 
--- @[simp] -- Porting note: simp normal form is `derivation_C_mul'`
-theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
-    D (C a * f) = a • D f := by rw [C_mul', D.map_smul]
-set_option linter.uppercaseLean3 false in
-#align mv_polynomial.derivation_C_mul MvPolynomial.derivation_C_mul
-
 @[simp]
-theorem derivation_C_mul' (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
+theorem derivation_C_mul (D : Derivation R (MvPolynomial σ R) A) (a : R) (f : MvPolynomial σ R) :
     C (σ := σ) a • D f = a • D f := by
   have : C (σ := σ) a • D f = D (C a * f) := by simp
-  rw [this, derivation_C_mul]
+  rw [this, C_mul', D.map_smul]
 
 /-- If two derivations agree on `X i`, `i ∈ s`, then they agree on all polynomials from
 `MvPolynomial.supported R s`. -/

@@ -14,7 +14,7 @@ import Mathlib.RingTheory.Derivation.Basic
 In this file we prove that a derivation of `MvPolynomial σ R` is determined by its values on all
 monomials `MvPolynomial.X i`. We also provide a constructor `MvPolynomial.mkDerivation` that
 builds a derivation from its values on `X i`s and a linear equivalence
-`MvPolynomial.equivDerivation` between `σ → A` and `Derivation (MvPolynomial σ R) A`.
+`MvPolynomial.mkDerivationEquiv` between `σ → A` and `Derivation (MvPolynomial σ R) A`.
 -/
 
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module data.mv_polynomial.derivation
-! leanprover-community/mathlib commit b608348ffaeb7f557f2fd46876037abafd326ff3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.MvPolynomial.Supported
 import Mathlib.RingTheory.Derivation.Basic
 
+#align_import data.mv_polynomial.derivation from "leanprover-community/mathlib"@"b608348ffaeb7f557f2fd46876037abafd326ff3"
+
 /-!
 # Derivations of multivariate polynomials
 

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>