field_theory.chevalley_warning | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

e001509c

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

5c1efce1

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -140,7 +140,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     split_ifs with hx hx
     · apply Finset.prod_eq_one
       intro i hi
-      rw [hS] at hx 
+      rw [hS] at hx
       rw [hx i hi, zero_pow hq, sub_zero]
     · obtain ⟨i, hi, hx⟩ : ∃ i : ι, i ∈ s ∧ eval x (f i) ≠ 0 := by
         simpa only [hS, Classical.not_forall, not_imp] using hx

5c1efce1

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -143,7 +143,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
       rw [hS] at hx 
       rw [hx i hi, zero_pow hq, sub_zero]
     · obtain ⟨i, hi, hx⟩ : ∃ i : ι, i ∈ s ∧ eval x (f i) ≠ 0 := by
-        simpa only [hS, not_forall, not_imp] using hx
+        simpa only [hS, Classical.not_forall, not_imp] using hx
       apply Finset.prod_eq_zero hi
       rw [pow_card_sub_one_eq_one (eval x (f i)) hx, sub_self]
   -- In particular, we can now show:

5c1efce1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.FieldTheory.Finite.Basic
+import FieldTheory.Finite.Basic
 
 #align_import field_theory.chevalley_warning from "leanprover-community/mathlib"@"5c1efce12ba86d4901463f61019832f6a4b1a0d0"

5c1efce1

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 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 field_theory.chevalley_warning
-! leanprover-community/mathlib commit 5c1efce12ba86d4901463f61019832f6a4b1a0d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.FieldTheory.Finite.Basic
 
+#align_import field_theory.chevalley_warning from "leanprover-community/mathlib"@"5c1efce12ba86d4901463f61019832f6a4b1a0d0"
+
 /-!
 # The Chevalley–Warning theorem

5c1efce1

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -56,9 +56,9 @@ open Finset FiniteField
 
 variable {K σ ι : Type _} [Fintype K] [Field K] [Fintype σ] [DecidableEq σ]
 
--- mathport name: exprq
 local notation "q" => Fintype.card K
 
+#print MvPolynomial.sum_eval_eq_zero /-
 theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
     (h : f.totalDegree < (q - 1) * Fintype.card σ) : ∑ x, eval x f = 0 :=
   by
@@ -109,9 +109,11 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
     show (e a : σ → K) j ^ d j = x₀ ⟨j, hj⟩ ^ d j
     rw [Equiv.subtypeEquivCodomain_symm_apply_ne]
 #align mv_polynomial.sum_eval_eq_zero MvPolynomial.sum_eval_eq_zero
+-/
 
 variable [DecidableEq K] (p : ℕ) [CharP K p]
 
+#print char_dvd_card_solutions_of_sum_lt /-
 /-- The **Chevalley–Warning theorem**, finitary version.
 Let `(f i)` be a finite family of multivariate polynomials
 in finitely many variables (`X s`, `s : σ`) over a finite field of characteristic `p`.
@@ -176,7 +178,9 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     _ ≤ (f i ^ (q - 1)).totalDegree := by simp only [max_eq_right, Nat.zero_le, total_degree_one]
     _ ≤ (q - 1) * (f i).totalDegree := total_degree_pow _ _
 #align char_dvd_card_solutions_of_sum_lt char_dvd_card_solutions_of_sum_lt
+-/
 
+#print char_dvd_card_solutions_of_fintype_sum_lt /-
 /-- The **Chevalley–Warning theorem**, fintype version.
 Let `(f i)` be a finite family of multivariate polynomials
 in finitely many variables (`X s`, `s : σ`) over a finite field of characteristic `p`.
@@ -187,7 +191,9 @@ theorem char_dvd_card_solutions_of_fintype_sum_lt [Fintype ι] {f : ι → MvPol
     p ∣ Fintype.card { x : σ → K // ∀ i, eval x (f i) = 0 } := by
   simpa using char_dvd_card_solutions_of_sum_lt p h
 #align char_dvd_card_solutions_of_fintype_sum_lt char_dvd_card_solutions_of_fintype_sum_lt
+-/
 
+#print char_dvd_card_solutions /-
 /-- The **Chevalley–Warning theorem**, unary version.
 Let `f` be a multivariate polynomial in finitely many variables (`X s`, `s : σ`)
 over a finite field of characteristic `p`.
@@ -202,7 +208,9 @@ theorem char_dvd_card_solutions {f : MvPolynomial σ K} (h : f.totalDegree < Fin
   simpa only [F, Fintype.univ_punit, forall_eq, mem_singleton] using
     char_dvd_card_solutions_of_sum_lt p this
 #align char_dvd_card_solutions char_dvd_card_solutions
+-/
 
+#print char_dvd_card_solutions_of_add_lt /-
 /-- The **Chevalley–Warning theorem**, binary version.
 Let `f₁`, `f₂` be two multivariate polynomials in finitely many variables (`X s`, `s : σ`) over a
 finite field of characteristic `p`.
@@ -216,6 +224,7 @@ theorem char_dvd_card_solutions_of_add_lt {f₁ f₂ : MvPolynomial σ K}
   have : ∑ b : Bool, (F b).totalDegree < Fintype.card σ := (add_comm _ _).trans_lt h
   simpa only [F, Bool.forall_bool] using char_dvd_card_solutions_of_fintype_sum_lt p this
 #align char_dvd_card_solutions_of_add_lt char_dvd_card_solutions_of_add_lt
+-/
 
 end FiniteField

5c1efce1

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -60,29 +60,29 @@ variable {K σ ι : Type _} [Fintype K] [Field K] [Fintype σ] [DecidableEq σ]
 local notation "q" => Fintype.card K
 
 theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
-    (h : f.totalDegree < (q - 1) * Fintype.card σ) : (∑ x, eval x f) = 0 :=
+    (h : f.totalDegree < (q - 1) * Fintype.card σ) : ∑ x, eval x f = 0 :=
   by
   haveI : DecidableEq K := Classical.decEq K
   calc
-    (∑ x, eval x f) = ∑ x : σ → K, ∑ d in f.support, f.coeff d * ∏ i, x i ^ d i := by
+    ∑ x, eval x f = ∑ x : σ → K, ∑ d in f.support, f.coeff d * ∏ i, x i ^ d i := by
       simp only [eval_eq']
     _ = ∑ d in f.support, ∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i := sum_comm
     _ = 0 := sum_eq_zero _
   intro d hd
   obtain ⟨i, hi⟩ : ∃ i, d i < q - 1; exact f.exists_degree_lt (q - 1) h hd
   calc
-    (∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i) = f.coeff d * ∑ x : σ → K, ∏ i, x i ^ d i :=
+    ∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i = f.coeff d * ∑ x : σ → K, ∏ i, x i ^ d i :=
       mul_sum.symm
     _ = 0 := (mul_eq_zero.mpr ∘ Or.inr) _
   calc
-    (∑ x : σ → K, ∏ i, x i ^ d i) =
+    ∑ x : σ → K, ∏ i, x i ^ d i =
         ∑ (x₀ : { j // j ≠ i } → K) (x : { x : σ → K // x ∘ coe = x₀ }), ∏ j, (x : σ → K) j ^ d j :=
       (Fintype.sum_fiberwise _ _).symm
     _ = 0 := Fintype.sum_eq_zero _ _
   intro x₀
   let e : K ≃ { x // x ∘ coe = x₀ } := (Equiv.subtypeEquivCodomain _).symm
   calc
-    (∑ x : { x : σ → K // x ∘ coe = x₀ }, ∏ j, (x : σ → K) j ^ d j) =
+    ∑ x : { x : σ → K // x ∘ coe = x₀ }, ∏ j, (x : σ → K) j ^ d j =
         ∑ a : K, ∏ j : σ, (e a : σ → K) j ^ d j :=
       (e.sum_comp _).symm
     _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := (Fintype.sum_congr _ _ _)
@@ -94,7 +94,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
     { default := ⟨i, rfl⟩
       uniq := fun ⟨j, h⟩ => Subtype.val_injective h }
   calc
-    (∏ j : σ, (e a : σ → K) j ^ d j) =
+    ∏ j : σ, (e a : σ → K) j ^ d j =
         (e a : σ → K) i ^ d i * ∏ j : { j // j ≠ i }, (e a : σ → K) j ^ d j :=
       by rw [← e'.prod_comp, Fintype.prod_sum_type, univ_unique, prod_singleton]; rfl
     _ = a ^ d i * ∏ j : { j // j ≠ i }, (e a : σ → K) j ^ d j := by
@@ -118,7 +118,7 @@ in finitely many variables (`X s`, `s : σ`) over a finite field of characterist
 Assume that the sum of the total degrees of the `f i` is less than the cardinality of `σ`.
 Then the number of common solutions of the `f i` is divisible by `p`. -/
 theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomial σ K}
-    (h : (∑ i in s, (f i).totalDegree) < Fintype.card σ) :
+    (h : ∑ i in s, (f i).totalDegree < Fintype.card σ) :
     p ∣ Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 } :=
   by
   have hq : 0 < q - 1 := by rw [← Fintype.card_units, Fintype.card_pos_iff]; exact ⟨1⟩
@@ -130,7 +130,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     while it is `0` outside that locus.
     Hence the sum of its values is equal to the cardinality of
     `{x : σ → K // ∀ i ∈ s, (f i).eval x = 0}` modulo `p`. -/
-  let F : MvPolynomial σ K := ∏ i in s, 1 - f i ^ (q - 1)
+  let F : MvPolynomial σ K := ∏ i in s, (1 - f i ^ (q - 1))
   have hF : ∀ x, eval x F = if x ∈ S then 1 else 0 :=
     by
     intro x
@@ -148,13 +148,13 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
       apply Finset.prod_eq_zero hi
       rw [pow_card_sub_one_eq_one (eval x (f i)) hx, sub_self]
   -- In particular, we can now show:
-  have key : (∑ x, eval x F) = Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 }
+  have key : ∑ x, eval x F = Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 }
   rw [Fintype.card_of_subtype S hS, card_eq_sum_ones, Nat.cast_sum, Nat.cast_one, ←
     Fintype.sum_extend_by_zero S, sum_congr rfl fun x hx => hF x]
   -- With these preparations under our belt, we will approach the main goal.
   show p ∣ Fintype.card { x // ∀ i : ι, i ∈ s → eval x (f i) = 0 }
   rw [← CharP.cast_eq_zero_iff K, ← key]
-  show (∑ x, eval x F) = 0
+  show ∑ x, eval x F = 0
   -- We are now ready to apply the main machine, proven before.
   apply F.sum_eval_eq_zero
   -- It remains to verify the crucial assumption of this machine
@@ -183,7 +183,7 @@ in finitely many variables (`X s`, `s : σ`) over a finite field of characterist
 Assume that the sum of the total degrees of the `f i` is less than the cardinality of `σ`.
 Then the number of common solutions of the `f i` is divisible by `p`. -/
 theorem char_dvd_card_solutions_of_fintype_sum_lt [Fintype ι] {f : ι → MvPolynomial σ K}
-    (h : (∑ i, (f i).totalDegree) < Fintype.card σ) :
+    (h : ∑ i, (f i).totalDegree < Fintype.card σ) :
     p ∣ Fintype.card { x : σ → K // ∀ i, eval x (f i) = 0 } := by
   simpa using char_dvd_card_solutions_of_sum_lt p h
 #align char_dvd_card_solutions_of_fintype_sum_lt char_dvd_card_solutions_of_fintype_sum_lt
@@ -198,7 +198,7 @@ theorem char_dvd_card_solutions {f : MvPolynomial σ K} (h : f.totalDegree < Fin
     p ∣ Fintype.card { x : σ → K // eval x f = 0 } :=
   by
   let F : Unit → MvPolynomial σ K := fun _ => f
-  have : (∑ i : Unit, (F i).totalDegree) < Fintype.card σ := h
+  have : ∑ i : Unit, (F i).totalDegree < Fintype.card σ := h
   simpa only [F, Fintype.univ_punit, forall_eq, mem_singleton] using
     char_dvd_card_solutions_of_sum_lt p this
 #align char_dvd_card_solutions char_dvd_card_solutions
@@ -213,7 +213,7 @@ theorem char_dvd_card_solutions_of_add_lt {f₁ f₂ : MvPolynomial σ K}
     p ∣ Fintype.card { x : σ → K // eval x f₁ = 0 ∧ eval x f₂ = 0 } :=
   by
   let F : Bool → MvPolynomial σ K := fun b => cond b f₂ f₁
-  have : (∑ b : Bool, (F b).totalDegree) < Fintype.card σ := (add_comm _ _).trans_lt h
+  have : ∑ b : Bool, (F b).totalDegree < Fintype.card σ := (add_comm _ _).trans_lt h
   simpa only [F, Bool.forall_bool] using char_dvd_card_solutions_of_fintype_sum_lt p this
 #align char_dvd_card_solutions_of_add_lt char_dvd_card_solutions_of_add_lt

5c1efce1

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -68,20 +68,17 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
       simp only [eval_eq']
     _ = ∑ d in f.support, ∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i := sum_comm
     _ = 0 := sum_eq_zero _
-    
   intro d hd
   obtain ⟨i, hi⟩ : ∃ i, d i < q - 1; exact f.exists_degree_lt (q - 1) h hd
   calc
     (∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i) = f.coeff d * ∑ x : σ → K, ∏ i, x i ^ d i :=
       mul_sum.symm
     _ = 0 := (mul_eq_zero.mpr ∘ Or.inr) _
-    
   calc
     (∑ x : σ → K, ∏ i, x i ^ d i) =
         ∑ (x₀ : { j // j ≠ i } → K) (x : { x : σ → K // x ∘ coe = x₀ }), ∏ j, (x : σ → K) j ^ d j :=
       (Fintype.sum_fiberwise _ _).symm
     _ = 0 := Fintype.sum_eq_zero _ _
-    
   intro x₀
   let e : K ≃ { x // x ∘ coe = x₀ } := (Equiv.subtypeEquivCodomain _).symm
   calc
@@ -91,7 +88,6 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
     _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := (Fintype.sum_congr _ _ _)
     _ = (∏ j, x₀ j ^ d j) * ∑ a : K, a ^ d i := by rw [mul_sum]
     _ = 0 := by rw [sum_pow_lt_card_sub_one _ hi, MulZeroClass.mul_zero]
-    
   intro a
   let e' : Sum { j // j = i } { j // j ≠ i } ≃ σ := Equiv.sumCompl _
   letI : Unique { j // j = i } :=
@@ -108,7 +104,6 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
         _ =
         (∏ j, x₀ j ^ d j) * a ^ d i :=
       mul_comm _ _
-    
   · -- the remaining step of the calculation above
     rintro ⟨j, hj⟩
     show (e a : σ → K) j ^ d j = x₀ ⟨j, hj⟩ ^ d j
@@ -142,7 +137,6 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     calc
       eval x F = ∏ i in s, eval x (1 - f i ^ (q - 1)) := eval_prod s _ x
       _ = if x ∈ S then 1 else 0 := _
-      
     simp only [(eval x).map_sub, (eval x).map_pow, (eval x).map_one]
     split_ifs with hx hx
     · apply Finset.prod_eq_one
@@ -173,7 +167,6 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
         (q - 1) * ∑ i in s, (f i).totalDegree :=
       mul_sum.symm
     _ < (q - 1) * Fintype.card σ := by rwa [mul_lt_mul_left hq]
-    
   -- Now we prove the remaining step from the preceding calculation
   show (1 - f i ^ (q - 1)).totalDegree ≤ (q - 1) * (f i).totalDegree
   calc
@@ -182,7 +175,6 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
       total_degree_sub _ _
     _ ≤ (f i ^ (q - 1)).totalDegree := by simp only [max_eq_right, Nat.zero_le, total_degree_one]
     _ ≤ (q - 1) * (f i).totalDegree := total_degree_pow _ _
-    
 #align char_dvd_card_solutions_of_sum_lt char_dvd_card_solutions_of_sum_lt
 
 /-- The **Chevalley–Warning theorem**, fintype version.

5c1efce1

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -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 field_theory.chevalley_warning
-! leanprover-community/mathlib commit e001509c11c4d0f549d91d89da95b4a0b43c714f
+! leanprover-community/mathlib commit 5c1efce12ba86d4901463f61019832f6a4b1a0d0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.FieldTheory.Finite.Basic
 /-!
 # The Chevalley–Warning theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains a proof of the Chevalley–Warning theorem.
 Throughout most of this file, `K` denotes a finite field
 and `q` is notation for the cardinality of `K`.
@@ -124,7 +127,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     p ∣ Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 } :=
   by
   have hq : 0 < q - 1 := by rw [← Fintype.card_units, Fintype.card_pos_iff]; exact ⟨1⟩
-  let S : Finset (σ → K) := { x ∈ univ | ∀ i ∈ s, eval x (f i) = 0 }
+  let S : Finset (σ → K) := {x ∈ univ | ∀ i ∈ s, eval x (f i) = 0}
   have hS : ∀ x : σ → K, x ∈ S ↔ ∀ i : ι, i ∈ s → eval x (f i) = 0 := by intro x;
     simp only [S, true_and_iff, sep_def, mem_filter, mem_univ]
   /- The polynomial `F = ∏ i in s, (1 - (f i)^(q - 1))` has the nice property

e001509c

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -144,7 +144,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     split_ifs with hx hx
     · apply Finset.prod_eq_one
       intro i hi
-      rw [hS] at hx
+      rw [hS] at hx 
       rw [hx i hi, zero_pow hq, sub_zero]
     · obtain ⟨i, hi, hx⟩ : ∃ i : ι, i ∈ s ∧ eval x (f i) ≠ 0 := by
         simpa only [hS, not_forall, not_imp] using hx

e001509c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -41,7 +41,7 @@ and `q` is notation for the cardinality of `K`.
 
 universe u v
 
-open BigOperators
+open scoped BigOperators
 
 section FiniteField

e001509c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -97,9 +97,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
   calc
     (∏ j : σ, (e a : σ → K) j ^ d j) =
         (e a : σ → K) i ^ d i * ∏ j : { j // j ≠ i }, (e a : σ → K) j ^ d j :=
-      by
-      rw [← e'.prod_comp, Fintype.prod_sum_type, univ_unique, prod_singleton]
-      rfl
+      by rw [← e'.prod_comp, Fintype.prod_sum_type, univ_unique, prod_singleton]; rfl
     _ = a ^ d i * ∏ j : { j // j ≠ i }, (e a : σ → K) j ^ d j := by
       rw [Equiv.subtypeEquivCodomain_symm_apply_eq]
     _ = a ^ d i * ∏ j, x₀ j ^ d j := (congr_arg _ (Fintype.prod_congr _ _ _))
@@ -125,13 +123,9 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     (h : (∑ i in s, (f i).totalDegree) < Fintype.card σ) :
     p ∣ Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 } :=
   by
-  have hq : 0 < q - 1 := by
-    rw [← Fintype.card_units, Fintype.card_pos_iff]
-    exact ⟨1⟩
+  have hq : 0 < q - 1 := by rw [← Fintype.card_units, Fintype.card_pos_iff]; exact ⟨1⟩
   let S : Finset (σ → K) := { x ∈ univ | ∀ i ∈ s, eval x (f i) = 0 }
-  have hS : ∀ x : σ → K, x ∈ S ↔ ∀ i : ι, i ∈ s → eval x (f i) = 0 :=
-    by
-    intro x
+  have hS : ∀ x : σ → K, x ∈ S ↔ ∀ i : ι, i ∈ s → eval x (f i) = 0 := by intro x;
     simp only [S, true_and_iff, sep_def, mem_filter, mem_univ]
   /- The polynomial `F = ∏ i in s, (1 - (f i)^(q - 1))` has the nice property
     that it takes the value `1` on elements of `{x : σ → K // ∀ i ∈ s, (f i).eval x = 0}`

e001509c

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -87,7 +87,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
       (e.sum_comp _).symm
     _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := (Fintype.sum_congr _ _ _)
     _ = (∏ j, x₀ j ^ d j) * ∑ a : K, a ^ d i := by rw [mul_sum]
-    _ = 0 := by rw [sum_pow_lt_card_sub_one _ hi, mul_zero]
+    _ = 0 := by rw [sum_pow_lt_card_sub_one _ hi, MulZeroClass.mul_zero]
     
   intro a
   let e' : Sum { j // j = i } { j // j ≠ i } ≃ σ := Equiv.sumCompl _

e001509c

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -85,7 +85,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
     (∑ x : { x : σ → K // x ∘ coe = x₀ }, ∏ j, (x : σ → K) j ^ d j) =
         ∑ a : K, ∏ j : σ, (e a : σ → K) j ^ d j :=
       (e.sum_comp _).symm
-    _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := Fintype.sum_congr _ _ _
+    _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := (Fintype.sum_congr _ _ _)
     _ = (∏ j, x₀ j ^ d j) * ∑ a : K, a ^ d i := by rw [mul_sum]
     _ = 0 := by rw [sum_pow_lt_card_sub_one _ hi, mul_zero]
     
@@ -102,7 +102,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
       rfl
     _ = a ^ d i * ∏ j : { j // j ≠ i }, (e a : σ → K) j ^ d j := by
       rw [Equiv.subtypeEquivCodomain_symm_apply_eq]
-    _ = a ^ d i * ∏ j, x₀ j ^ d j := congr_arg _ (Fintype.prod_congr _ _ _)
+    _ = a ^ d i * ∏ j, x₀ j ^ d j := (congr_arg _ (Fintype.prod_congr _ _ _))
     -- see below
         _ =
         (∏ j, x₀ j ^ d j) * a ^ d i :=
@@ -170,7 +170,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
   show F.total_degree < (q - 1) * Fintype.card σ
   calc
     F.total_degree ≤ ∑ i in s, (1 - f i ^ (q - 1)).totalDegree := total_degree_finset_prod s _
-    _ ≤ ∑ i in s, (q - 1) * (f i).totalDegree := sum_le_sum fun i hi => _
+    _ ≤ ∑ i in s, (q - 1) * (f i).totalDegree := (sum_le_sum fun i hi => _)
     -- see ↓
         _ =
         (q - 1) * ∑ i in s, (f i).totalDegree :=

e001509c

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e001509c

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -76,7 +76,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
   calc
     (∑ x : { x : σ → K // x ∘ (↑) = x₀ }, ∏ j, (x : σ → K) j ^ d j) =
         ∑ a : K, ∏ j : σ, (e a : σ → K) j ^ d j := (e.sum_comp _).symm
-    _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := (Fintype.sum_congr _ _ ?_)
+    _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := Fintype.sum_congr _ _ ?_
     _ = (∏ j, x₀ j ^ d j) * ∑ a : K, a ^ d i := by rw [mul_sum]
     _ = 0 := by rw [sum_pow_lt_card_sub_one K _ hi, mul_zero]
   intro a
@@ -90,7 +90,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
       by rw [← e'.prod_comp, Fintype.prod_sum_type, univ_unique, prod_singleton]; rfl
     _ = a ^ d i * ∏ j : { j // j ≠ i }, (e a : σ → K) j ^ d j := by
       rw [Equiv.subtypeEquivCodomain_symm_apply_eq]
-    _ = a ^ d i * ∏ j, x₀ j ^ d j := (congr_arg _ (Fintype.prod_congr _ _ ?_))
+    _ = a ^ d i * ∏ j, x₀ j ^ d j := congr_arg _ (Fintype.prod_congr _ _ ?_)
     -- see below
     _ = (∏ j, x₀ j ^ d j) * a ^ d i := mul_comm _ _
   · -- the remaining step of the calculation above
@@ -149,7 +149,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
   show F.totalDegree < (q - 1) * Fintype.card σ
   calc
     F.totalDegree ≤ ∑ i in s, (1 - f i ^ (q - 1)).totalDegree := totalDegree_finset_prod s _
-    _ ≤ ∑ i in s, (q - 1) * (f i).totalDegree := (sum_le_sum fun i _ => ?_)
+    _ ≤ ∑ i in s, (q - 1) * (f i).totalDegree := sum_le_sum fun i _ => ?_
     -- see ↓
     _ = (q - 1) * ∑ i in s, (f i).totalDegree := (mul_sum ..).symm
     _ < (q - 1) * Fintype.card σ := by rwa [mul_lt_mul_left hq]

e001509c

chore: remove stream-of-conciousness syntax for obtain (#11045)

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

cd23c669

Diff

@@ -61,7 +61,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
     _ = ∑ d in f.support, ∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i := sum_comm
     _ = 0 := sum_eq_zero ?_
   intro d hd
-  obtain ⟨i, hi⟩ : ∃ i, d i < q - 1; exact f.exists_degree_lt (q - 1) h hd
+  obtain ⟨i, hi⟩ : ∃ i, d i < q - 1 := f.exists_degree_lt (q - 1) h hd
   calc
     (∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i) = f.coeff d * ∑ x : σ → K, ∏ i, x i ^ d i :=
       (mul_sum ..).symm

e001509c

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -113,7 +113,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
   let S : Finset (σ → K) := { x ∈ univ | ∀ i ∈ s, eval x (f i) = 0 }.toFinset
   have hS : ∀ x : σ → K, x ∈ S ↔ ∀ i : ι, i ∈ s → eval x (f i) = 0 := by
     intro x
-    simp only [Set.toFinset_setOf, mem_univ, true_and, mem_filter]
+    simp only [S, Set.toFinset_setOf, mem_univ, true_and, mem_filter]
   /- The polynomial `F = ∏ i in s, (1 - (f i)^(q - 1))` has the nice property
     that it takes the value `1` on elements of `{x : σ → K // ∀ i ∈ s, (f i).eval x = 0}`
     while it is `0` outside that locus.

e001509c

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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>

a13e8040

Diff

@@ -136,9 +136,9 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
       apply Finset.prod_eq_zero hi
       rw [pow_card_sub_one_eq_one (eval x (f i)) hx, sub_self]
   -- In particular, we can now show:
-  have key : ∑ x, eval x F = Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 }
-  rw [Fintype.card_of_subtype S hS, card_eq_sum_ones, Nat.cast_sum, Nat.cast_one, ←
-    Fintype.sum_extend_by_zero S, sum_congr rfl fun x _ => hF x]
+  have key : ∑ x, eval x F = Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 } := by
+    rw [Fintype.card_of_subtype S hS, card_eq_sum_ones, Nat.cast_sum, Nat.cast_one, ←
+      Fintype.sum_extend_by_zero S, sum_congr rfl fun x _ => hF x]
   -- With these preparations under our belt, we will approach the main goal.
   show p ∣ Fintype.card { x // ∀ i : ι, i ∈ s → eval x (f i) = 0 }
   rw [← CharP.cast_eq_zero_iff K, ← key]

e001509c

feat: The support of f ^ n (#9617)

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

9d1a7d26

Diff

@@ -130,7 +130,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     · apply Finset.prod_eq_one
       intro i hi
       rw [hS] at hx
-      rw [hx i hi, zero_pow hq, sub_zero]
+      rw [hx i hi, zero_pow hq.ne', sub_zero]
     · obtain ⟨i, hi, hx⟩ : ∃ i : ι, i ∈ s ∧ eval x (f i) ≠ 0 := by
         simpa only [hS, not_forall, not_imp] using hx
       apply Finset.prod_eq_zero hi

e001509c

chore: Relocate big operator lemmas (#9383)

A bunch of lemmas in Algebra.BigOperators.Ring were not about rings. This PR moves them along with some lemmas from Data.Fintype.BigOperators to their correct place.

I create a new file with the content from #6605 to avoid importing Fin material in finset files as a result.

From LeanAPAP

b8dc3667

Diff

@@ -64,7 +64,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
   obtain ⟨i, hi⟩ : ∃ i, d i < q - 1; exact f.exists_degree_lt (q - 1) h hd
   calc
     (∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i) = f.coeff d * ∑ x : σ → K, ∏ i, x i ^ d i :=
-      mul_sum.symm
+      (mul_sum ..).symm
     _ = 0 := (mul_eq_zero.mpr ∘ Or.inr) ?_
   calc
     (∑ x : σ → K, ∏ i, x i ^ d i) =
@@ -151,7 +151,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
     F.totalDegree ≤ ∑ i in s, (1 - f i ^ (q - 1)).totalDegree := totalDegree_finset_prod s _
     _ ≤ ∑ i in s, (q - 1) * (f i).totalDegree := (sum_le_sum fun i _ => ?_)
     -- see ↓
-    _ = (q - 1) * ∑ i in s, (f i).totalDegree := mul_sum.symm
+    _ = (q - 1) * ∑ i in s, (f i).totalDegree := (mul_sum ..).symm
     _ < (q - 1) * Fintype.card σ := by rwa [mul_lt_mul_left hq]
   -- Now we prove the remaining step from the preceding calculation
   show (1 - f i ^ (q - 1)).totalDegree ≤ (q - 1) * (f i).totalDegree

e001509c

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -78,7 +78,7 @@ theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
         ∑ a : K, ∏ j : σ, (e a : σ → K) j ^ d j := (e.sum_comp _).symm
     _ = ∑ a : K, (∏ j, x₀ j ^ d j) * a ^ d i := (Fintype.sum_congr _ _ ?_)
     _ = (∏ j, x₀ j ^ d j) * ∑ a : K, a ^ d i := by rw [mul_sum]
-    _ = 0 := by rw [sum_pow_lt_card_sub_one K _ hi, MulZeroClass.mul_zero]
+    _ = 0 := by rw [sum_pow_lt_card_sub_one K _ hi, mul_zero]
   intro a
   let e' : Sum { j // j = i } { j // j ≠ i } ≃ σ := Equiv.sumCompl _
   letI : Unique { j // j = i } :=

e001509c

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -48,7 +48,7 @@ open Function hiding eval
 
 open Finset FiniteField
 
-variable {K σ ι : Type _} [Fintype K] [Field K] [Fintype σ] [DecidableEq σ]
+variable {K σ ι : Type*} [Fintype K] [Field K] [Fintype σ] [DecidableEq σ]
 
 local notation "q" => Fintype.card K

e001509c

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 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 field_theory.chevalley_warning
-! leanprover-community/mathlib commit e001509c11c4d0f549d91d89da95b4a0b43c714f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.FieldTheory.Finite.Basic
 
+#align_import field_theory.chevalley_warning from "leanprover-community/mathlib"@"e001509c11c4d0f549d91d89da95b4a0b43c714f"
+
 /-!
 # The Chevalley–Warning theorem

e001509c

fix: ∑' precedence (#5615)

Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) $([∑∏][^()∑∏]*,[^()∑∏:]*)$ ([⊂⊆=<≤]) replaced by $1 $2 $3

03fc68aa

Diff

@@ -56,10 +56,10 @@ variable {K σ ι : Type _} [Fintype K] [Field K] [Fintype σ] [DecidableEq σ]
 local notation "q" => Fintype.card K
 
 theorem MvPolynomial.sum_eval_eq_zero (f : MvPolynomial σ K)
-    (h : f.totalDegree < (q - 1) * Fintype.card σ) : (∑ x, eval x f) = 0 := by
+    (h : f.totalDegree < (q - 1) * Fintype.card σ) : ∑ x, eval x f = 0 := by
   haveI : DecidableEq K := Classical.decEq K
   calc
-    (∑ x, eval x f) = ∑ x : σ → K, ∑ d in f.support, f.coeff d * ∏ i, x i ^ d i := by
+    ∑ x, eval x f = ∑ x : σ → K, ∑ d in f.support, f.coeff d * ∏ i, x i ^ d i := by
       simp only [eval_eq']
     _ = ∑ d in f.support, ∑ x : σ → K, f.coeff d * ∏ i, x i ^ d i := sum_comm
     _ = 0 := sum_eq_zero ?_
@@ -139,7 +139,7 @@ theorem char_dvd_card_solutions_of_sum_lt {s : Finset ι} {f : ι → MvPolynomi
       apply Finset.prod_eq_zero hi
       rw [pow_card_sub_one_eq_one (eval x (f i)) hx, sub_self]
   -- In particular, we can now show:
-  have key : (∑ x, eval x F) = Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 }
+  have key : ∑ x, eval x F = Fintype.card { x : σ → K // ∀ i ∈ s, eval x (f i) = 0 }
   rw [Fintype.card_of_subtype S hS, card_eq_sum_ones, Nat.cast_sum, Nat.cast_one, ←
     Fintype.sum_extend_by_zero S, sum_congr rfl fun x _ => hF x]
   -- With these preparations under our belt, we will approach the main goal.

e001509c

feat: port FieldTheory.ChevalleyWarning (#4619)

319e4939

`field_theory.chevalley_warning` ⟷ `Mathlib.FieldTheory.ChevalleyWarning`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 660

field_theory.chevalley_warning ⟷ Mathlib.FieldTheory.ChevalleyWarning

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 660

`field_theory.chevalley_warning` ⟷ `Mathlib.FieldTheory.ChevalleyWarning`