ring_theory.witt_vector.frobenius_fraction_field

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

cead9313

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

d0b19368

bump to nightly-2024-04-10-08

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

cd0c1af5

Diff

@@ -148,8 +148,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   have := succ_nth_val_spec p n a₁ a₂ bs ha₁ ha₂
   simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succ_nth_defining_poly, Polynomial.eval_mul, Polynomial.eval_add,
-    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.definition] at
-    this
+    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this
   convert this using 1
   ring
 #align witt_vector.recursion_main.succ_nth_val_spec' WittVector.RecursionMain.succNthVal_spec'

d0b19368

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -148,7 +148,8 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   have := succ_nth_val_spec p n a₁ a₂ bs ha₁ ha₂
   simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succ_nth_defining_poly, Polynomial.eval_mul, Polynomial.eval_add,
-    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this
+    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.definition] at
+    this
   convert this using 1
   ring
 #align witt_vector.recursion_main.succ_nth_val_spec' WittVector.RecursionMain.succNthVal_spec'
@@ -204,7 +205,7 @@ theorem solution_spec' {a₁ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (a₂ : 𝕎
     congr
     skip
     rw [hq]
-  rw [pow_succ', hq', this]
+  rw [pow_succ, hq', this]
   field_simp [ha₁, mul_comm]
 #align witt_vector.recursion_base.solution_spec' WittVector.RecursionBase.solution_spec'
 -/

d0b19368

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -148,7 +148,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   have := succ_nth_val_spec p n a₁ a₂ bs ha₁ ha₂
   simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succ_nth_defining_poly, Polynomial.eval_mul, Polynomial.eval_add,
-    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this 
+    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this
   convert this using 1
   ring
 #align witt_vector.recursion_main.succ_nth_val_spec' WittVector.RecursionMain.succNthVal_spec'
@@ -186,7 +186,7 @@ theorem solution_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha
     solution p a₁ a₂ ≠ 0 := by
   intro h
   have := solution_spec p a₁ a₂
-  rw [h, zero_pow] at this 
+  rw [h, zero_pow] at this
   · simpa [ha₁, ha₂] using _root_.div_eq_zero_iff.mp this.symm
   · linarith [hp.out.one_lt, le_of_lt hp.out.one_lt]
 #align witt_vector.recursion_base.solution_nonzero WittVector.RecursionBase.solution_nonzero
@@ -262,7 +262,7 @@ theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 
     have :=
       succ_nth_val_spec' p n a₁ a₂ (fun i : Fin (n + 1) => frobenius_rotation_coeff p ha₁ ha₂ i.val)
         ha₁ ha₂
-    simp only [frobenius_rotation_coeff, Fin.val_eq_coe, Fin.val_zero] at this 
+    simp only [frobenius_rotation_coeff, Fin.val_eq_coe, Fin.val_zero] at this
     convert this using 4
     apply TruncatedWittVector.ext
     intro i
@@ -286,7 +286,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
   have key : WittVector.frobenius b * p ^ m * r' * p ^ n = p ^ m * b * (p ^ n * q') :=
     by
     have H := congr_arg (fun x : 𝕎 k => x * p ^ m * p ^ n) (frobenius_frobenius_rotation p hr' hq')
-    dsimp at H 
+    dsimp at H
     refine' (Eq.trans _ H).trans _ <;> ring
   have hq'' : algebraMap (𝕎 k) (FractionRing (𝕎 k)) q' ≠ 0 :=
     by

d0b19368

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Heather Macbeth
 -/
-import Mathbin.Data.Nat.Cast.WithTop
-import Mathbin.FieldTheory.IsAlgClosed.Basic
-import Mathbin.RingTheory.WittVector.DiscreteValuationRing
+import Data.Nat.Cast.WithTop
+import FieldTheory.IsAlgClosed.Basic
+import RingTheory.WittVector.DiscreteValuationRing
 
 #align_import ring_theory.witt_vector.frobenius_fraction_field from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"

d0b19368

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Heather Macbeth
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.frobenius_fraction_field
-! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Nat.Cast.WithTop
 import Mathbin.FieldTheory.IsAlgClosed.Basic
 import Mathbin.RingTheory.WittVector.DiscreteValuationRing
 
+#align_import ring_theory.witt_vector.frobenius_fraction_field from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
+
 /-!
 # Solving equations about the Frobenius map on the field of fractions of `𝕎 k`

d0b19368

bump to nightly-2023-07-04-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

05318d71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Heather Macbeth
 
 ! This file was ported from Lean 3 source module ring_theory.witt_vector.frobenius_fraction_field
-! leanprover-community/mathlib commit cead93130da7100f8a9fe22ee210f7636a91168f
+! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.WittVector.DiscreteValuationRing
 /-!
 # Solving equations about the Frobenius map on the field of fractions of `𝕎 k`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The goal of this file is to prove `witt_vector.exists_frobenius_solution_fraction_ring`,
 which says that for an algebraically closed field `k` of characteristic `p` and `a, b` in the
 field of fractions of Witt vectors over `k`,

cead9313

bump to nightly-2023-06-29-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

f2d78e63

Diff

@@ -69,6 +69,7 @@ variable {k : Type _} [CommRing k] [CharP k p]
 
 open Polynomial
 
+#print WittVector.RecursionMain.succNthDefiningPoly /-
 /-- The root of this polynomial determines the `n+1`st coefficient of our solution. -/
 def succNthDefiningPoly (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) : Polynomial k :=
   X ^ p * C (a₁.coeff 0 ^ p ^ (n + 1)) - X * C (a₂.coeff 0 ^ p ^ (n + 1)) +
@@ -78,7 +79,9 @@ def succNthDefiningPoly (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
           a₂.coeff (n + 1) * bs 0 ^ p ^ (n + 1) -
         nthRemainder p n bs (truncateFun (n + 1) a₂))
 #align witt_vector.recursion_main.succ_nth_defining_poly WittVector.RecursionMain.succNthDefiningPoly
+-/
 
+#print WittVector.RecursionMain.succNthDefiningPoly_degree /-
 theorem succNthDefiningPoly_degree [IsDomain k] (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
     (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) : (succNthDefiningPoly p n a₁ a₂ bs).degree = p :=
   by
@@ -98,6 +101,7 @@ theorem succNthDefiningPoly_degree [IsDomain k] (n : ℕ) (a₁ a₂ : 𝕎 k) (
   rw [this]
   exact_mod_cast hp.out.pos
 #align witt_vector.recursion_main.succ_nth_defining_poly_degree WittVector.RecursionMain.succNthDefiningPoly_degree
+-/
 
 end CommRing
 
@@ -105,25 +109,32 @@ section IsAlgClosed
 
 variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
 
+#print WittVector.RecursionMain.root_exists /-
 theorem root_exists (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) (ha₁ : a₁.coeff 0 ≠ 0)
     (ha₂ : a₂.coeff 0 ≠ 0) : ∃ b : k, (succNthDefiningPoly p n a₁ a₂ bs).IsRoot b :=
   IsAlgClosed.exists_root _ <| by
     simp only [succ_nth_defining_poly_degree p n a₁ a₂ bs ha₁ ha₂, hp.out.ne_zero,
       WithTop.coe_eq_zero, Ne.def, not_false_iff]
 #align witt_vector.recursion_main.root_exists WittVector.RecursionMain.root_exists
+-/
 
+#print WittVector.RecursionMain.succNthVal /-
 /-- This is the `n+1`st coefficient of our solution, projected from `root_exists`. -/
 def succNthVal (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) (ha₁ : a₁.coeff 0 ≠ 0)
     (ha₂ : a₂.coeff 0 ≠ 0) : k :=
   Classical.choose (root_exists p n a₁ a₂ bs ha₁ ha₂)
 #align witt_vector.recursion_main.succ_nth_val WittVector.RecursionMain.succNthVal
+-/
 
+#print WittVector.RecursionMain.succNthVal_spec /-
 theorem succNthVal_spec (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) (ha₁ : a₁.coeff 0 ≠ 0)
     (ha₂ : a₂.coeff 0 ≠ 0) :
     (succNthDefiningPoly p n a₁ a₂ bs).IsRoot (succNthVal p n a₁ a₂ bs ha₁ ha₂) :=
   Classical.choose_spec (root_exists p n a₁ a₂ bs ha₁ ha₂)
 #align witt_vector.recursion_main.succ_nth_val_spec WittVector.RecursionMain.succNthVal_spec
+-/
 
+#print WittVector.RecursionMain.succNthVal_spec' /-
 theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) (ha₁ : a₁.coeff 0 ≠ 0)
     (ha₂ : a₂.coeff 0 ≠ 0) :
     succNthVal p n a₁ a₂ bs ha₁ ha₂ ^ p * a₁.coeff 0 ^ p ^ (n + 1) +
@@ -141,6 +152,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   convert this using 1
   ring
 #align witt_vector.recursion_main.succ_nth_val_spec' WittVector.RecursionMain.succNthVal_spec'
+-/
 
 end IsAlgClosed
 
@@ -150,19 +162,26 @@ namespace RecursionBase
 
 variable {k : Type _} [Field k] [IsAlgClosed k]
 
+#print WittVector.RecursionBase.solution_pow /-
 theorem solution_pow (a₁ a₂ : 𝕎 k) : ∃ x : k, x ^ (p - 1) = a₂.coeff 0 / a₁.coeff 0 :=
   IsAlgClosed.exists_pow_nat_eq _ <| by linarith [hp.out.one_lt, le_of_lt hp.out.one_lt]
 #align witt_vector.recursion_base.solution_pow WittVector.RecursionBase.solution_pow
+-/
 
+#print WittVector.RecursionBase.solution /-
 /-- The base case (0th coefficient) of our solution vector. -/
 def solution (a₁ a₂ : 𝕎 k) : k :=
   Classical.choose <| solution_pow p a₁ a₂
 #align witt_vector.recursion_base.solution WittVector.RecursionBase.solution
+-/
 
+#print WittVector.RecursionBase.solution_spec /-
 theorem solution_spec (a₁ a₂ : 𝕎 k) : solution p a₁ a₂ ^ (p - 1) = a₂.coeff 0 / a₁.coeff 0 :=
   Classical.choose_spec <| solution_pow p a₁ a₂
 #align witt_vector.recursion_base.solution_spec WittVector.RecursionBase.solution_spec
+-/
 
+#print WittVector.RecursionBase.solution_nonzero /-
 theorem solution_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) :
     solution p a₁ a₂ ≠ 0 := by
   intro h
@@ -171,7 +190,9 @@ theorem solution_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha
   · simpa [ha₁, ha₂] using _root_.div_eq_zero_iff.mp this.symm
   · linarith [hp.out.one_lt, le_of_lt hp.out.one_lt]
 #align witt_vector.recursion_base.solution_nonzero WittVector.RecursionBase.solution_nonzero
+-/
 
+#print WittVector.RecursionBase.solution_spec' /-
 theorem solution_spec' {a₁ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (a₂ : 𝕎 k) :
     solution p a₁ a₂ ^ p * a₁.coeff 0 = solution p a₁ a₂ * a₂.coeff 0 :=
   by
@@ -186,6 +207,7 @@ theorem solution_spec' {a₁ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (a₂ : 𝕎
   rw [pow_succ', hq', this]
   field_simp [ha₁, mul_comm]
 #align witt_vector.recursion_base.solution_spec' WittVector.RecursionBase.solution_spec'
+-/
 
 end RecursionBase
 
@@ -197,6 +219,7 @@ section IsAlgClosed
 
 variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
 
+#print WittVector.frobeniusRotationCoeff /-
 /-- Recursively defines the sequence of coefficients for `witt_vector.frobenius_rotation`.
 -/
 noncomputable def frobeniusRotationCoeff {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0)
@@ -205,21 +228,27 @@ noncomputable def frobeniusRotationCoeff {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coef
   | n + 1 => succNthVal p n a₁ a₂ (fun i => frobenius_rotation_coeff i.val) ha₁ ha₂
 decreasing_by apply Fin.is_lt
 #align witt_vector.frobenius_rotation_coeff WittVector.frobeniusRotationCoeff
+-/
 
+#print WittVector.frobeniusRotation /-
 /-- For nonzero `a₁` and `a₂`, `frobenius_rotation a₁ a₂` is a Witt vector that satisfies the
 equation `frobenius (frobenius_rotation a₁ a₂) * a₁ = (frobenius_rotation a₁ a₂) * a₂`.
 -/
 def frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) : 𝕎 k :=
   WittVector.mk' p (frobeniusRotationCoeff p ha₁ ha₂)
 #align witt_vector.frobenius_rotation WittVector.frobeniusRotation
+-/
 
+#print WittVector.frobeniusRotation_nonzero /-
 theorem frobeniusRotation_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) :
     frobeniusRotation p ha₁ ha₂ ≠ 0 := by
   intro h
   apply solution_nonzero p ha₁ ha₂
   simpa [← h, frobenius_rotation, frobenius_rotation_coeff] using WittVector.zero_coeff p k 0
 #align witt_vector.frobenius_rotation_nonzero WittVector.frobeniusRotation_nonzero
+-/
 
+#print WittVector.frobenius_frobeniusRotation /-
 theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) :
     frobenius (frobeniusRotation p ha₁ ha₂) * a₁ = frobeniusRotation p ha₁ ha₂ * a₂ :=
   by
@@ -240,9 +269,11 @@ theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 
     simp only [Fin.val_eq_coe, WittVector.coeff_truncateFun, WittVector.coeff_frobenius_charP]
     rfl
 #align witt_vector.frobenius_frobenius_rotation WittVector.frobenius_frobeniusRotation
+-/
 
 local notation "φ" => IsFractionRing.fieldEquivOfRingEquiv (frobeniusEquiv p k)
 
+#print WittVector.exists_frobenius_solution_fractionRing_aux /-
 theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k) (hr' : r'.coeff 0 ≠ 0)
     (hq' : q'.coeff 0 ≠ 0) (hq : ↑p ^ n * q' ∈ nonZeroDivisors (𝕎 k)) :
     let b : 𝕎 k := frobeniusRotation p hr' hq'
@@ -271,7 +302,9 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
     ring
   · simp only [RingHom.map_mul, RingHom.map_pow, map_natCast]
 #align witt_vector.exists_frobenius_solution_fraction_ring_aux WittVector.exists_frobenius_solution_fractionRing_aux
+-/
 
+#print WittVector.exists_frobenius_solution_fractionRing /-
 theorem exists_frobenius_solution_fractionRing {a : FractionRing (𝕎 k)} (ha : a ≠ 0) :
     ∃ (b : FractionRing (𝕎 k)) (hb : b ≠ 0) (m : ℤ), φ b * a = p ^ m * b :=
   by
@@ -290,6 +323,7 @@ theorem exists_frobenius_solution_fractionRing {a : FractionRing (𝕎 k)} (ha :
         (frobenius_rotation_nonzero p hr' hq')
   exact exists_frobenius_solution_fraction_ring_aux p m n r' q' hr' hq' hq
 #align witt_vector.exists_frobenius_solution_fraction_ring WittVector.exists_frobenius_solution_fractionRing
+-/
 
 end IsAlgClosed

cead9313

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -47,7 +47,6 @@ namespace WittVector
 
 variable (p : ℕ) [hp : Fact p.Prime]
 
--- mathport name: expr𝕎
 local notation "𝕎" => WittVector p
 
 namespace RecursionMain
@@ -66,8 +65,6 @@ whose variable represents the `n`th coefficient of `x` in `x * a`.
 
 section CommRing
 
-include hp
-
 variable {k : Type _} [CommRing k] [CharP k p]
 
 open Polynomial
@@ -106,8 +103,6 @@ end CommRing
 
 section IsAlgClosed
 
-include hp
-
 variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
 
 theorem root_exists (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) (ha₁ : a₁.coeff 0 ≠ 0)
@@ -153,8 +148,6 @@ end RecursionMain
 
 namespace RecursionBase
 
-include hp
-
 variable {k : Type _} [Field k] [IsAlgClosed k]
 
 theorem solution_pow (a₁ a₂ : 𝕎 k) : ∃ x : k, x ^ (p - 1) = a₂.coeff 0 / a₁.coeff 0 :=
@@ -202,8 +195,6 @@ section FrobeniusRotation
 
 section IsAlgClosed
 
-include hp
-
 variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
 
 /-- Recursively defines the sequence of coefficients for `witt_vector.frobenius_rotation`.
@@ -250,7 +241,6 @@ theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 
     rfl
 #align witt_vector.frobenius_frobenius_rotation WittVector.frobenius_frobeniusRotation
 
--- mathport name: exprφ
 local notation "φ" => IsFractionRing.fieldEquivOfRingEquiv (frobeniusEquiv p k)
 
 theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k) (hr' : r'.coeff 0 ≠ 0)

cead9313

bump to nightly-2023-06-05-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

d07076be

Diff

@@ -219,7 +219,7 @@ decreasing_by apply Fin.is_lt
 equation `frobenius (frobenius_rotation a₁ a₂) * a₁ = (frobenius_rotation a₁ a₂) * a₂`.
 -/
 def frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) : 𝕎 k :=
-  WittVector.mk p (frobeniusRotationCoeff p ha₁ ha₂)
+  WittVector.mk' p (frobeniusRotationCoeff p ha₁ ha₂)
 #align witt_vector.frobenius_rotation WittVector.frobeniusRotation
 
 theorem frobeniusRotation_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) :

cead9313

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -142,7 +142,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   have := succ_nth_val_spec p n a₁ a₂ bs ha₁ ha₂
   simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succ_nth_defining_poly, Polynomial.eval_mul, Polynomial.eval_add,
-    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this
+    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this 
   convert this using 1
   ring
 #align witt_vector.recursion_main.succ_nth_val_spec' WittVector.RecursionMain.succNthVal_spec'
@@ -174,7 +174,7 @@ theorem solution_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha
     solution p a₁ a₂ ≠ 0 := by
   intro h
   have := solution_spec p a₁ a₂
-  rw [h, zero_pow] at this
+  rw [h, zero_pow] at this 
   · simpa [ha₁, ha₂] using _root_.div_eq_zero_iff.mp this.symm
   · linarith [hp.out.one_lt, le_of_lt hp.out.one_lt]
 #align witt_vector.recursion_base.solution_nonzero WittVector.RecursionBase.solution_nonzero
@@ -211,8 +211,8 @@ variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
 noncomputable def frobeniusRotationCoeff {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0)
     (ha₂ : a₂.coeff 0 ≠ 0) : ℕ → k
   | 0 => solution p a₁ a₂
-  | n + 1 => succNthVal p n a₁ a₂ (fun i => frobenius_rotation_coeff i.val) ha₁ ha₂ decreasing_by
-  apply Fin.is_lt
+  | n + 1 => succNthVal p n a₁ a₂ (fun i => frobenius_rotation_coeff i.val) ha₁ ha₂
+decreasing_by apply Fin.is_lt
 #align witt_vector.frobenius_rotation_coeff WittVector.frobeniusRotationCoeff
 
 /-- For nonzero `a₁` and `a₂`, `frobenius_rotation a₁ a₂` is a Witt vector that satisfies the
@@ -242,7 +242,7 @@ theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 
     have :=
       succ_nth_val_spec' p n a₁ a₂ (fun i : Fin (n + 1) => frobenius_rotation_coeff p ha₁ ha₂ i.val)
         ha₁ ha₂
-    simp only [frobenius_rotation_coeff, Fin.val_eq_coe, Fin.val_zero] at this
+    simp only [frobenius_rotation_coeff, Fin.val_eq_coe, Fin.val_zero] at this 
     convert this using 4
     apply TruncatedWittVector.ext
     intro i
@@ -265,7 +265,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
   have key : WittVector.frobenius b * p ^ m * r' * p ^ n = p ^ m * b * (p ^ n * q') :=
     by
     have H := congr_arg (fun x : 𝕎 k => x * p ^ m * p ^ n) (frobenius_frobenius_rotation p hr' hq')
-    dsimp at H
+    dsimp at H 
     refine' (Eq.trans _ H).trans _ <;> ring
   have hq'' : algebraMap (𝕎 k) (FractionRing (𝕎 k)) q' ≠ 0 :=
     by
@@ -283,7 +283,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
 #align witt_vector.exists_frobenius_solution_fraction_ring_aux WittVector.exists_frobenius_solution_fractionRing_aux
 
 theorem exists_frobenius_solution_fractionRing {a : FractionRing (𝕎 k)} (ha : a ≠ 0) :
-    ∃ (b : FractionRing (𝕎 k))(hb : b ≠ 0)(m : ℤ), φ b * a = p ^ m * b :=
+    ∃ (b : FractionRing (𝕎 k)) (hb : b ≠ 0) (m : ℤ), φ b * a = p ^ m * b :=
   by
   revert ha
   refine' Localization.induction_on a _

cead9313

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -238,15 +238,15 @@ theorem frobenius_frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 
       frobenius_rotation_coeff]
     apply solution_spec' _ ha₁
   · simp only [nth_remainder_spec, WittVector.coeff_frobenius_charP, frobenius_rotation_coeff,
-      frobenius_rotation, [anonymous]]
+      frobenius_rotation, Fin.val_eq_coe]
     have :=
       succ_nth_val_spec' p n a₁ a₂ (fun i : Fin (n + 1) => frobenius_rotation_coeff p ha₁ ha₂ i.val)
         ha₁ ha₂
-    simp only [frobenius_rotation_coeff, [anonymous], Fin.val_zero] at this
+    simp only [frobenius_rotation_coeff, Fin.val_eq_coe, Fin.val_zero] at this
     convert this using 4
     apply TruncatedWittVector.ext
     intro i
-    simp only [[anonymous], WittVector.coeff_truncateFun, WittVector.coeff_frobenius_charP]
+    simp only [Fin.val_eq_coe, WittVector.coeff_truncateFun, WittVector.coeff_frobenius_charP]
     rfl
 #align witt_vector.frobenius_frobenius_rotation WittVector.frobenius_frobeniusRotation

cead9313

bump to nightly-2023-03-08-14

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

f7af4b63

Diff

@@ -140,7 +140,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   by
   rw [← sub_eq_zero]
   have := succ_nth_val_spec p n a₁ a₂ bs ha₁ ha₂
-  simp only [Polynomial.map_add, Polynomial.eval_x, Polynomial.map_pow, Polynomial.eval_c,
+  simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succ_nth_defining_poly, Polynomial.eval_mul, Polynomial.eval_add,
     Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this
   convert this using 1

cead9313

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -74,8 +74,8 @@ open Polynomial
 
 /-- The root of this polynomial determines the `n+1`st coefficient of our solution. -/
 def succNthDefiningPoly (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) : Polynomial k :=
-  x ^ p * c (a₁.coeff 0 ^ p ^ (n + 1)) - x * c (a₂.coeff 0 ^ p ^ (n + 1)) +
-    c
+  X ^ p * C (a₁.coeff 0 ^ p ^ (n + 1)) - X * C (a₂.coeff 0 ^ p ^ (n + 1)) +
+    C
       (a₁.coeff (n + 1) * (bs 0 ^ p) ^ p ^ (n + 1) +
             nthRemainder p n (fun v => bs v ^ p) (truncateFun (n + 1) a₁) -
           a₂.coeff (n + 1) * bs 0 ^ p ^ (n + 1) -

cead9313

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

cead9313

chore: rename IsRoot.definition back to IsRoot.def (#11999)

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

1f25ef62

Diff

@@ -132,7 +132,7 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   have := succNthVal_spec p n a₁ a₂ bs ha₁ ha₂
   simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succNthDefiningPoly, Polynomial.eval_mul, Polynomial.eval_add,
-    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.definition]
+    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def]
     at this
   convert this using 1
   ring

cead9313

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -259,7 +259,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
     refine' (Eq.trans _ H).trans _ <;> ring
   have hq'' : algebraMap (𝕎 k) (FractionRing (𝕎 k)) q' ≠ 0 := by
     have hq''' : q' ≠ 0 := fun h => hq' (by simp [h])
-    simpa only [Ne.def, map_zero] using
+    simpa only [Ne, map_zero] using
       (IsFractionRing.injective (𝕎 k) (FractionRing (𝕎 k))).ne hq'''
   rw [zpow_sub₀ (FractionRing.p_nonzero p k)]
   field_simp [FractionRing.p_nonzero p k]

cead9313

chore: rename away from 'def' (#11548)

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

b505e8e9

Diff

@@ -132,7 +132,8 @@ theorem succNthVal_spec' (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k)
   have := succNthVal_spec p n a₁ a₂ bs ha₁ ha₂
   simp only [Polynomial.map_add, Polynomial.eval_X, Polynomial.map_pow, Polynomial.eval_C,
     Polynomial.eval_pow, succNthDefiningPoly, Polynomial.eval_mul, Polynomial.eval_add,
-    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.def] at this
+    Polynomial.eval_sub, Polynomial.map_mul, Polynomial.map_sub, Polynomial.IsRoot.definition]
+    at this
   convert this using 1
   ring
 #align witt_vector.recursion_main.succ_nth_val_spec' WittVector.RecursionMain.succNthVal_spec'

cead9313

chore: remove unneeded decreasing_by and termination_by (#11386)

The termination checker has been getting more capable, and many of the termination_by or decreasing_by clauses in Mathlib are no longer needed.

(Note that termination_by? will show the automatically derived termination expression, so no information is being lost by removing these.)

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

c7950e4e

Diff

@@ -202,7 +202,6 @@ noncomputable def frobeniusRotationCoeff {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coef
     (ha₂ : a₂.coeff 0 ≠ 0) : ℕ → k
   | 0 => solution p a₁ a₂
   | n + 1 => succNthVal p n a₁ a₂ (fun i => frobeniusRotationCoeff ha₁ ha₂ i.val) ha₁ ha₂
-decreasing_by apply Fin.is_lt
 #align witt_vector.frobenius_rotation_coeff WittVector.frobeniusRotationCoeff
 
 /-- For nonzero `a₁` and `a₂`, `frobeniusRotation a₁ a₂` is a Witt vector that satisfies the

cead9313

chore: tidy various files (#10453)

678a9b1b

Diff

@@ -33,7 +33,7 @@ This construction is described in Dupuis, Lewis, and Macbeth,
 We approximately follow an approach sketched on MathOverflow:
 <https://mathoverflow.net/questions/62468/about-frobenius-of-witt-vectors>
 
-The result is a dependency for the proof of `witt_vector.isocrystal_classification`,
+The result is a dependency for the proof of `WittVector.isocrystal_classification`,
 the classification of one-dimensional isocrystals over an algebraically closed field.
 -/
 
@@ -54,7 +54,7 @@ namespace RecursionMain
 
 The first coefficient of our solution vector is easy to define below.
 In this section we focus on the recursive case.
-The goal is to turn `witt_poly_prod n` into a univariate polynomial
+The goal is to turn `WittVector.wittPolyProd n` into a univariate polynomial
 whose variable represents the `n`th coefficient of `x` in `x * a`.
 
 -/
@@ -205,8 +205,8 @@ noncomputable def frobeniusRotationCoeff {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coef
 decreasing_by apply Fin.is_lt
 #align witt_vector.frobenius_rotation_coeff WittVector.frobeniusRotationCoeff
 
-/-- For nonzero `a₁` and `a₂`, `frobenius_rotation a₁ a₂` is a Witt vector that satisfies the
-equation `frobenius (frobenius_rotation a₁ a₂) * a₁ = (frobenius_rotation a₁ a₂) * a₂`.
+/-- For nonzero `a₁` and `a₂`, `frobeniusRotation a₁ a₂` is a Witt vector that satisfies the
+equation `frobenius (frobeniusRotation a₁ a₂) * a₁ = (frobeniusRotation a₁ a₂) * a₂`.
 -/
 def frobeniusRotation {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha₂ : a₂.coeff 0 ≠ 0) : 𝕎 k :=
   WittVector.mk p (frobeniusRotationCoeff p ha₁ ha₂)

cead9313

chore: tidy various files (#10362)

1c8a8a8e

Diff

@@ -272,8 +272,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
 #align witt_vector.exists_frobenius_solution_fraction_ring_aux WittVector.exists_frobenius_solution_fractionRing_aux
 
 theorem exists_frobenius_solution_fractionRing {a : FractionRing (𝕎 k)} (ha : a ≠ 0) :
-    ∃ (b : FractionRing (𝕎 k)) (_ : b ≠ 0) (m : ℤ),
-      φ b * a = (p : FractionRing (𝕎 k)) ^ m * b := by
+    ∃ᵉ (b ≠ 0) (m : ℤ), φ b * a = (p : FractionRing (𝕎 k)) ^ m * b := by
   revert ha
   refine' Localization.induction_on a _
   rintro ⟨r, q, hq⟩ hrq

cead9313

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

@@ -169,7 +169,7 @@ theorem solution_nonzero {a₁ a₂ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (ha
   · simpa [ha₁, ha₂] using _root_.div_eq_zero_iff.mp this.symm
   · -- Porting note: was
     -- linarith [hp.out.one_lt, le_of_lt hp.out.one_lt]
-    exact tsub_pos_of_lt hp.out.one_lt
+    exact Nat.sub_ne_zero_of_lt hp.out.one_lt
 #align witt_vector.recursion_base.solution_nonzero WittVector.RecursionBase.solution_nonzero
 
 theorem solution_spec' {a₁ : 𝕎 k} (ha₁ : a₁.coeff 0 ≠ 0) (a₂ : 𝕎 k) :

cead9313

chore: replace exact_mod_cast tactic with mod_cast elaborator where possible (#8404)

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

693fd795

Diff

@@ -87,12 +87,12 @@ theorem succNthDefiningPoly_degree [IsDomain k] (n : ℕ) (a₁ a₂ : 𝕎 k) (
       (p : WithBot ℕ) := by
     rw [degree_sub_eq_left_of_degree_lt, this]
     rw [this, degree_mul, degree_C, degree_X, add_zero]
-    · exact_mod_cast hp.out.one_lt
+    · exact mod_cast hp.out.one_lt
     · exact pow_ne_zero _ ha₂
   rw [succNthDefiningPoly, degree_add_eq_left_of_degree_lt, this]
   apply lt_of_le_of_lt degree_C_le
   rw [this]
-  exact_mod_cast hp.out.pos
+  exact mod_cast hp.out.pos
 #align witt_vector.recursion_main.succ_nth_defining_poly_degree WittVector.RecursionMain.succNthDefiningPoly_degree
 
 end CommRing

cead9313

perf(FunLike.Basic): beta reduce CoeFun.coe (#7905)

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

e194c756

Diff

@@ -272,7 +272,7 @@ theorem exists_frobenius_solution_fractionRing_aux (m n : ℕ) (r' q' : 𝕎 k)
 #align witt_vector.exists_frobenius_solution_fraction_ring_aux WittVector.exists_frobenius_solution_fractionRing_aux
 
 theorem exists_frobenius_solution_fractionRing {a : FractionRing (𝕎 k)} (ha : a ≠ 0) :
-    ∃ (b : FractionRing (𝕎 k)) (hb : b ≠ 0) (m : ℤ),
+    ∃ (b : FractionRing (𝕎 k)) (_ : b ≠ 0) (m : ℤ),
       φ b * a = (p : FractionRing (𝕎 k)) ^ m * b := by
   revert ha
   refine' Localization.induction_on a _

cead9313

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

@@ -62,7 +62,7 @@ whose variable represents the `n`th coefficient of `x` in `x * a`.
 
 section CommRing
 
-variable {k : Type _} [CommRing k] [CharP k p]
+variable {k : Type*} [CommRing k] [CharP k p]
 
 open Polynomial
 
@@ -99,7 +99,7 @@ end CommRing
 
 section IsAlgClosed
 
-variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
+variable {k : Type*} [Field k] [CharP k p] [IsAlgClosed k]
 
 theorem root_exists (n : ℕ) (a₁ a₂ : 𝕎 k) (bs : Fin (n + 1) → k) (ha₁ : a₁.coeff 0 ≠ 0)
     (ha₂ : a₂.coeff 0 ≠ 0) : ∃ b : k, (succNthDefiningPoly p n a₁ a₂ bs).IsRoot b :=
@@ -143,7 +143,7 @@ end RecursionMain
 
 namespace RecursionBase
 
-variable {k : Type _} [Field k] [IsAlgClosed k]
+variable {k : Type*} [Field k] [IsAlgClosed k]
 
 theorem solution_pow (a₁ a₂ : 𝕎 k) : ∃ x : k, x ^ (p - 1) = a₂.coeff 0 / a₁.coeff 0 :=
   IsAlgClosed.exists_pow_nat_eq _ <|
@@ -194,7 +194,7 @@ section FrobeniusRotation
 
 section IsAlgClosed
 
-variable {k : Type _} [Field k] [CharP k p] [IsAlgClosed k]
+variable {k : Type*} [Field k] [CharP k p] [IsAlgClosed k]
 
 /-- Recursively defines the sequence of coefficients for `WittVector.frobeniusRotation`.
 -/

cead9313

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Robert Y. Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Y. Lewis, Heather Macbeth
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.frobenius_fraction_field
-! leanprover-community/mathlib commit cead93130da7100f8a9fe22ee210f7636a91168f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Nat.Cast.WithTop
 import Mathlib.FieldTheory.IsAlgClosed.Basic
 import Mathlib.RingTheory.WittVector.DiscreteValuationRing
 
+#align_import ring_theory.witt_vector.frobenius_fraction_field from "leanprover-community/mathlib"@"cead93130da7100f8a9fe22ee210f7636a91168f"
+
 /-!
 # Solving equations about the Frobenius map on the field of fractions of `𝕎 k`

cead9313

fix: filenames with typos in doc (#5836)

1657aebc

Diff

@@ -28,7 +28,7 @@ The construction proceeds by recursively defining a sequence of coefficients as
 polynomial equation in `k`. We must define these as generic polynomials using Witt vector API
 (`WittVector.wittMul`, `wittPolynomial`) to show that they satisfy the desired equation.
 
-Preliminary work is done in the dependency `ring_theory.witt_vector.mul_coeff`
+Preliminary work is done in the dependency `RingTheory.WittVector.MulCoeff`
 to isolate the `n+1`st coefficients of `x` and `y` in the `n+1`st coefficient of `x*y`.
 
 This construction is described in Dupuis, Lewis, and Macbeth,

cead9313

feat: port RingTheory.WittVector.FrobeniusFractionField (#5561)

cac608bc

`ring_theory.witt_vector.frobenius_fraction_field` ⟷ `Mathlib.RingTheory.WittVector.FrobeniusFractionField`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 713

ring_theory.witt_vector.frobenius_fraction_field ⟷ Mathlib.RingTheory.WittVector.FrobeniusFractionField

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 713

`ring_theory.witt_vector.frobenius_fraction_field` ⟷ `Mathlib.RingTheory.WittVector.FrobeniusFractionField`