ring_theory.witt_vector.identities | 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

07980376

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

9240e8be

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -62,7 +62,7 @@ theorem coeff_p_pow [CharP R p] (i : ℕ) : (p ^ i : 𝕎 R).coeff i = 1 :=
   induction' i with i h
   · simp only [one_coeff_zero, Ne.def, pow_zero]
   ·
-    rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_char_p, verschiebung_coeff_succ, h,
+    rw [pow_succ, ← frobenius_verschiebung, coeff_frobenius_char_p, verschiebung_coeff_succ, h,
       one_pow]
 #align witt_vector.coeff_p_pow WittVector.coeff_p_pow
 -/
@@ -73,7 +73,7 @@ theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : (p ^ i : 
   induction' i with i hi generalizing j
   · rw [pow_zero, one_coeff_eq_of_pos]
     exact Nat.pos_of_ne_zero hj
-  · rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_char_p]
+  · rw [pow_succ, ← frobenius_verschiebung, coeff_frobenius_char_p]
     cases j
     · rw [verschiebung_coeff_zero, zero_pow]
       exact Nat.Prime.pos hp.out

9240e8be

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) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
 -/
-import Mathbin.RingTheory.WittVector.Frobenius
-import Mathbin.RingTheory.WittVector.Verschiebung
-import Mathbin.RingTheory.WittVector.MulP
+import RingTheory.WittVector.Frobenius
+import RingTheory.WittVector.Verschiebung
+import RingTheory.WittVector.MulP
 
 #align_import ring_theory.witt_vector.identities from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"

9240e8be

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) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.identities
-! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.WittVector.Frobenius
 import Mathbin.RingTheory.WittVector.Verschiebung
 import Mathbin.RingTheory.WittVector.MulP
 
+#align_import ring_theory.witt_vector.identities from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
 /-!
 ## Identities between operations on the ring of Witt vectors

9240e8be

bump to nightly-2023-06-30-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

397a8f48

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 ring_theory.witt_vector.identities
-! leanprover-community/mathlib commit 0798037604b2d91748f9b43925fb7570a5f3256c
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
 ! 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.MulP
 /-!
 ## Identities between operations on the ring of Witt vectors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we derive common identities between the Frobenius and Verschiebung operators.
 
 ## Main declarations

07980376

bump to nightly-2023-06-28-01

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

c13c40e8

Diff

@@ -40,18 +40,23 @@ local notation "𝕎" => WittVector p
 -- type as `\bbW`
 noncomputable section
 
+#print WittVector.frobenius_verschiebung /-
 /-- The composition of Frobenius and Verschiebung is multiplication by `p`. -/
 theorem frobenius_verschiebung (x : 𝕎 R) : frobenius (verschiebung x) = x * p := by ghost_calc x;
   ghost_simp [mul_comm]
 #align witt_vector.frobenius_verschiebung WittVector.frobenius_verschiebung
+-/
 
+#print WittVector.verschiebung_zmod /-
 /-- Verschiebung is the same as multiplication by `p` on the ring of Witt vectors of `zmod p`. -/
-theorem verschiebung_zMod (x : 𝕎 (ZMod p)) : verschiebung x = x * p := by
+theorem verschiebung_zmod (x : 𝕎 (ZMod p)) : verschiebung x = x * p := by
   rw [← frobenius_verschiebung, frobenius_zmodp]
-#align witt_vector.verschiebung_zmod WittVector.verschiebung_zMod
+#align witt_vector.verschiebung_zmod WittVector.verschiebung_zmod
+-/
 
 variable (p R)
 
+#print WittVector.coeff_p_pow /-
 theorem coeff_p_pow [CharP R p] (i : ℕ) : (p ^ i : 𝕎 R).coeff i = 1 :=
   by
   induction' i with i h
@@ -60,7 +65,9 @@ theorem coeff_p_pow [CharP R p] (i : ℕ) : (p ^ i : 𝕎 R).coeff i = 1 :=
     rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_char_p, verschiebung_coeff_succ, h,
       one_pow]
 #align witt_vector.coeff_p_pow WittVector.coeff_p_pow
+-/
 
+#print WittVector.coeff_p_pow_eq_zero /-
 theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : (p ^ i : 𝕎 R).coeff j = 0 :=
   by
   induction' i with i hi generalizing j
@@ -74,61 +81,82 @@ theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : (p ^ i : 
       · exact Nat.Prime.pos hp.out
       · exact ne_of_apply_ne (fun j : ℕ => j.succ) hj
 #align witt_vector.coeff_p_pow_eq_zero WittVector.coeff_p_pow_eq_zero
+-/
 
+#print WittVector.coeff_p /-
 theorem coeff_p [CharP R p] (i : ℕ) : (p : 𝕎 R).coeff i = if i = 1 then 1 else 0 :=
   by
   split_ifs with hi
   · simpa only [hi, pow_one] using coeff_p_pow p R 1
   · simpa only [pow_one] using coeff_p_pow_eq_zero p R hi
 #align witt_vector.coeff_p WittVector.coeff_p
+-/
 
+#print WittVector.coeff_p_zero /-
 @[simp]
 theorem coeff_p_zero [CharP R p] : (p : 𝕎 R).coeff 0 = 0 := by rw [coeff_p, if_neg];
   exact zero_ne_one
 #align witt_vector.coeff_p_zero WittVector.coeff_p_zero
+-/
 
+#print WittVector.coeff_p_one /-
 @[simp]
 theorem coeff_p_one [CharP R p] : (p : 𝕎 R).coeff 1 = 1 := by rw [coeff_p, if_pos rfl]
 #align witt_vector.coeff_p_one WittVector.coeff_p_one
+-/
 
+#print WittVector.p_nonzero /-
 theorem p_nonzero [Nontrivial R] [CharP R p] : (p : 𝕎 R) ≠ 0 := by intro h;
   simpa only [h, zero_coeff, zero_ne_one] using coeff_p_one p R
 #align witt_vector.p_nonzero WittVector.p_nonzero
+-/
 
+#print WittVector.FractionRing.p_nonzero /-
 theorem FractionRing.p_nonzero [Nontrivial R] [CharP R p] : (p : FractionRing (𝕎 R)) ≠ 0 := by
   simpa using (IsFractionRing.injective (𝕎 R) (FractionRing (𝕎 R))).Ne (p_nonzero _ _)
 #align witt_vector.fraction_ring.p_nonzero WittVector.FractionRing.p_nonzero
+-/
 
 variable {p R}
 
+#print WittVector.verschiebung_mul_frobenius /-
 /-- The “projection formula” for Frobenius and Verschiebung. -/
 theorem verschiebung_mul_frobenius (x y : 𝕎 R) :
     verschiebung (x * frobenius y) = verschiebung x * y := by ghost_calc x y;
   rintro ⟨⟩ <;> ghost_simp [mul_assoc]
 #align witt_vector.verschiebung_mul_frobenius WittVector.verschiebung_mul_frobenius
+-/
 
+#print WittVector.mul_charP_coeff_zero /-
 theorem mul_charP_coeff_zero [CharP R p] (x : 𝕎 R) : (x * p).coeff 0 = 0 :=
   by
   rw [← frobenius_verschiebung, coeff_frobenius_char_p, verschiebung_coeff_zero, zero_pow]
   exact Nat.Prime.pos hp.out
 #align witt_vector.mul_char_p_coeff_zero WittVector.mul_charP_coeff_zero
+-/
 
+#print WittVector.mul_charP_coeff_succ /-
 theorem mul_charP_coeff_succ [CharP R p] (x : 𝕎 R) (i : ℕ) :
     (x * p).coeff (i + 1) = x.coeff i ^ p := by
   rw [← frobenius_verschiebung, coeff_frobenius_char_p, verschiebung_coeff_succ]
 #align witt_vector.mul_char_p_coeff_succ WittVector.mul_charP_coeff_succ
+-/
 
+#print WittVector.verschiebung_frobenius /-
 theorem verschiebung_frobenius [CharP R p] (x : 𝕎 R) : verschiebung (frobenius x) = x * p :=
   by
   ext ⟨i⟩
   · rw [mul_char_p_coeff_zero, verschiebung_coeff_zero]
   · rw [mul_char_p_coeff_succ, verschiebung_coeff_succ, coeff_frobenius_char_p]
 #align witt_vector.verschiebung_frobenius WittVector.verschiebung_frobenius
+-/
 
+#print WittVector.verschiebung_frobenius_comm /-
 theorem verschiebung_frobenius_comm [CharP R p] :
     Function.Commute (verschiebung : 𝕎 R → 𝕎 R) frobenius := fun x => by
   rw [verschiebung_frobenius, frobenius_verschiebung]
 #align witt_vector.verschiebung_frobenius_comm WittVector.verschiebung_frobenius_comm
+-/
 
 /-!
 ## Iteration lemmas
@@ -137,6 +165,7 @@ theorem verschiebung_frobenius_comm [CharP R p] :
 
 open Function
 
+#print WittVector.iterate_verschiebung_coeff /-
 theorem iterate_verschiebung_coeff (x : 𝕎 R) (n k : ℕ) :
     ((verschiebung^[n]) x).coeff (k + n) = x.coeff k :=
   by
@@ -145,7 +174,9 @@ theorem iterate_verschiebung_coeff (x : 𝕎 R) (n k : ℕ) :
   · rw [iterate_succ_apply', Nat.add_succ, verschiebung_coeff_succ]
     exact ih
 #align witt_vector.iterate_verschiebung_coeff WittVector.iterate_verschiebung_coeff
+-/
 
+#print WittVector.iterate_verschiebung_mul_left /-
 theorem iterate_verschiebung_mul_left (x y : 𝕎 R) (i : ℕ) :
     (verschiebung^[i]) x * y = (verschiebung^[i]) (x * (frobenius^[i]) y) :=
   by
@@ -153,11 +184,13 @@ theorem iterate_verschiebung_mul_left (x y : 𝕎 R) (i : ℕ) :
   · simp
   · rw [iterate_succ_apply', ← verschiebung_mul_frobenius, ih, iterate_succ_apply']; rfl
 #align witt_vector.iterate_verschiebung_mul_left WittVector.iterate_verschiebung_mul_left
+-/
 
 section CharP
 
 variable [CharP R p]
 
+#print WittVector.iterate_verschiebung_mul /-
 theorem iterate_verschiebung_mul (x y : 𝕎 R) (i j : ℕ) :
     (verschiebung^[i]) x * (verschiebung^[j]) y =
       (verschiebung^[i + j]) ((frobenius^[j]) x * (frobenius^[i]) y) :=
@@ -176,7 +209,9 @@ theorem iterate_verschiebung_mul (x y : 𝕎 R) (i j : ℕ) :
   · rw [iterate_add_apply]
   · rw [mul_comm]
 #align witt_vector.iterate_verschiebung_mul WittVector.iterate_verschiebung_mul
+-/
 
+#print WittVector.iterate_frobenius_coeff /-
 theorem iterate_frobenius_coeff (x : 𝕎 R) (i k : ℕ) :
     ((frobenius^[i]) x).coeff k = x.coeff k ^ p ^ i :=
   by
@@ -185,7 +220,9 @@ theorem iterate_frobenius_coeff (x : 𝕎 R) (i k : ℕ) :
   · rw [iterate_succ_apply', coeff_frobenius_char_p, ih]
     ring
 #align witt_vector.iterate_frobenius_coeff WittVector.iterate_frobenius_coeff
+-/
 
+#print WittVector.iterate_verschiebung_mul_coeff /-
 /-- This is a slightly specialized form of [Hazewinkel, *Witt Vectors*][Haze09] 6.2 equation 5. -/
 theorem iterate_verschiebung_mul_coeff (x y : 𝕎 R) (i j : ℕ) :
     ((verschiebung^[i]) x * (verschiebung^[j]) y).coeff (i + j) =
@@ -202,6 +239,7 @@ theorem iterate_verschiebung_mul_coeff (x y : 𝕎 R) (i j : ℕ) :
   · apply mul_coeff_zero
   · simp only [iterate_frobenius_coeff]
 #align witt_vector.iterate_verschiebung_mul_coeff WittVector.iterate_verschiebung_mul_coeff
+-/
 
 end CharP

07980376

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -35,12 +35,9 @@ namespace WittVector
 
 variable {p : ℕ} {R : Type _} [hp : Fact p.Prime] [CommRing R]
 
--- mathport name: expr𝕎
 local notation "𝕎" => WittVector p
 
 -- type as `\bbW`
-include hp
-
 noncomputable section
 
 /-- The composition of Frobenius and Verschiebung is multiplication by `p`. -/

07980376

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -172,7 +172,6 @@ theorem iterate_verschiebung_mul (x y : 𝕎 R) (i j : ℕ) :
     _ = (verschiebung^[i]) ((verschiebung^[j]) ((frobenius^[i]) y * (frobenius^[j]) x)) := _
     _ = (verschiebung^[i + j]) ((frobenius^[i]) y * (frobenius^[j]) x) := _
     _ = _ := _
-    
   · apply iterate_verschiebung_mul_left
   · rw [verschiebung_frobenius_comm.iterate_iterate] <;> infer_instance
   · rw [mul_comm]
@@ -200,7 +199,6 @@ theorem iterate_verschiebung_mul_coeff (x y : 𝕎 R) (i j : ℕ) :
     _ = ((frobenius^[j]) x * (frobenius^[i]) y).coeff 0 := _
     _ = ((frobenius^[j]) x).coeff 0 * ((frobenius^[i]) y).coeff 0 := _
     _ = _ := _
-    
   · rw [iterate_verschiebung_mul]
   · convert iterate_verschiebung_coeff _ _ _ using 2
     rw [zero_add]

07980376

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -44,9 +44,7 @@ include hp
 noncomputable section
 
 /-- The composition of Frobenius and Verschiebung is multiplication by `p`. -/
-theorem frobenius_verschiebung (x : 𝕎 R) : frobenius (verschiebung x) = x * p :=
-  by
-  ghost_calc x
+theorem frobenius_verschiebung (x : 𝕎 R) : frobenius (verschiebung x) = x * p := by ghost_calc x;
   ghost_simp [mul_comm]
 #align witt_vector.frobenius_verschiebung WittVector.frobenius_verschiebung
 
@@ -88,9 +86,7 @@ theorem coeff_p [CharP R p] (i : ℕ) : (p : 𝕎 R).coeff i = if i = 1 then 1 e
 #align witt_vector.coeff_p WittVector.coeff_p
 
 @[simp]
-theorem coeff_p_zero [CharP R p] : (p : 𝕎 R).coeff 0 = 0 :=
-  by
-  rw [coeff_p, if_neg]
+theorem coeff_p_zero [CharP R p] : (p : 𝕎 R).coeff 0 = 0 := by rw [coeff_p, if_neg];
   exact zero_ne_one
 #align witt_vector.coeff_p_zero WittVector.coeff_p_zero
 
@@ -98,9 +94,7 @@ theorem coeff_p_zero [CharP R p] : (p : 𝕎 R).coeff 0 = 0 :=
 theorem coeff_p_one [CharP R p] : (p : 𝕎 R).coeff 1 = 1 := by rw [coeff_p, if_pos rfl]
 #align witt_vector.coeff_p_one WittVector.coeff_p_one
 
-theorem p_nonzero [Nontrivial R] [CharP R p] : (p : 𝕎 R) ≠ 0 :=
-  by
-  intro h
+theorem p_nonzero [Nontrivial R] [CharP R p] : (p : 𝕎 R) ≠ 0 := by intro h;
   simpa only [h, zero_coeff, zero_ne_one] using coeff_p_one p R
 #align witt_vector.p_nonzero WittVector.p_nonzero
 
@@ -112,9 +106,7 @@ variable {p R}
 
 /-- The “projection formula” for Frobenius and Verschiebung. -/
 theorem verschiebung_mul_frobenius (x y : 𝕎 R) :
-    verschiebung (x * frobenius y) = verschiebung x * y :=
-  by
-  ghost_calc x y
+    verschiebung (x * frobenius y) = verschiebung x * y := by ghost_calc x y;
   rintro ⟨⟩ <;> ghost_simp [mul_assoc]
 #align witt_vector.verschiebung_mul_frobenius WittVector.verschiebung_mul_frobenius
 
@@ -162,8 +154,7 @@ theorem iterate_verschiebung_mul_left (x y : 𝕎 R) (i : ℕ) :
   by
   induction' i with i ih generalizing y
   · simp
-  · rw [iterate_succ_apply', ← verschiebung_mul_frobenius, ih, iterate_succ_apply']
-    rfl
+  · rw [iterate_succ_apply', ← verschiebung_mul_frobenius, ih, iterate_succ_apply']; rfl
 #align witt_vector.iterate_verschiebung_mul_left WittVector.iterate_verschiebung_mul_left
 
 section CharP

07980376

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

07980376

chore: backports from #11997, adaptations for nightly-2024-04-07 (#12176)

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

02293f49

Diff

@@ -56,7 +56,7 @@ variable (p R)
 
 theorem coeff_p_pow [CharP R p] (i : ℕ) : ((p : 𝕎 R) ^ i).coeff i = 1 := by
   induction' i with i h
-  · simp only [Nat.zero_eq, one_coeff_zero, Ne.def, pow_zero]
+  · simp only [Nat.zero_eq, one_coeff_zero, Ne, pow_zero]
   · rw [pow_succ, ← frobenius_verschiebung, coeff_frobenius_charP,
       verschiebung_coeff_succ, h, one_pow]
 #align witt_vector.coeff_p_pow WittVector.coeff_p_pow

07980376

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -57,7 +57,7 @@ variable (p R)
 theorem coeff_p_pow [CharP R p] (i : ℕ) : ((p : 𝕎 R) ^ i).coeff i = 1 := by
   induction' i with i h
   · simp only [Nat.zero_eq, one_coeff_zero, Ne.def, pow_zero]
-  · rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_charP,
+  · rw [pow_succ, ← frobenius_verschiebung, coeff_frobenius_charP,
       verschiebung_coeff_succ, h, one_pow]
 #align witt_vector.coeff_p_pow WittVector.coeff_p_pow
 
@@ -65,7 +65,7 @@ theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : ((p : 𝕎
   induction' i with i hi generalizing j
   · rw [Nat.zero_eq, pow_zero, one_coeff_eq_of_pos]
     exact Nat.pos_of_ne_zero hj
-  · rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_charP]
+  · rw [pow_succ, ← frobenius_verschiebung, coeff_frobenius_charP]
     cases j
     · rw [verschiebung_coeff_zero, zero_pow hp.out.ne_zero]
     · rw [verschiebung_coeff_succ, hi (ne_of_apply_ne _ hj), zero_pow hp.out.ne_zero]

07980376

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

@@ -67,11 +67,8 @@ theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : ((p : 𝕎
     exact Nat.pos_of_ne_zero hj
   · rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_charP]
     cases j
-    · rw [verschiebung_coeff_zero, zero_pow]
-      exact Nat.Prime.pos hp.out
-    · rw [verschiebung_coeff_succ, hi, zero_pow]
-      · exact Nat.Prime.pos hp.out
-      · exact ne_of_apply_ne (fun j : ℕ => j.succ) hj
+    · rw [verschiebung_coeff_zero, zero_pow hp.out.ne_zero]
+    · rw [verschiebung_coeff_succ, hi (ne_of_apply_ne _ hj), zero_pow hp.out.ne_zero]
 #align witt_vector.coeff_p_pow_eq_zero WittVector.coeff_p_pow_eq_zero
 
 theorem coeff_p [CharP R p] (i : ℕ) : (p : 𝕎 R).coeff i = if i = 1 then 1 else 0 := by
@@ -115,8 +112,8 @@ theorem verschiebung_mul_frobenius (x y : 𝕎 R) :
 #align witt_vector.verschiebung_mul_frobenius WittVector.verschiebung_mul_frobenius
 
 theorem mul_charP_coeff_zero [CharP R p] (x : 𝕎 R) : (x * p).coeff 0 = 0 := by
-  rw [← frobenius_verschiebung, coeff_frobenius_charP, verschiebung_coeff_zero, zero_pow]
-  exact Nat.Prime.pos hp.out
+  rw [← frobenius_verschiebung, coeff_frobenius_charP, verschiebung_coeff_zero,
+    zero_pow hp.out.ne_zero]
 #align witt_vector.mul_char_p_coeff_zero WittVector.mul_charP_coeff_zero
 
 theorem mul_charP_coeff_succ [CharP R p] (x : 𝕎 R) (i : ℕ) :

07980376

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

@@ -40,7 +40,6 @@ noncomputable section
 -- Porting note: `ghost_calc` failure: `simp only []` and the manual instances had to be added.
 /-- The composition of Frobenius and Verschiebung is multiplication by `p`. -/
 theorem frobenius_verschiebung (x : 𝕎 R) : frobenius (verschiebung x) = x * p := by
-  simp only []
   have : IsPoly p fun {R} [CommRing R] x ↦ frobenius (verschiebung x) :=
     IsPoly.comp (hg := frobenius_isPoly p) (hf := verschiebung_isPoly)
   have : IsPoly p fun {R} [CommRing R] x ↦ x * p := mulN_isPoly p p
@@ -106,7 +105,6 @@ variable {p R}
 /-- The “projection formula” for Frobenius and Verschiebung. -/
 theorem verschiebung_mul_frobenius (x y : 𝕎 R) :
     verschiebung (x * frobenius y) = verschiebung x * y := by
-  simp only []
   have : IsPoly₂ p fun {R} [Rcr : CommRing R] x y ↦ verschiebung (x * frobenius y) :=
     IsPoly.comp₂ (hg := verschiebung_isPoly)
       (hf := IsPoly₂.comp (hh := mulIsPoly₂) (hf := idIsPolyI' p) (hg := frobenius_isPoly p))

07980376

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

@@ -30,7 +30,7 @@ In this file we derive common identities between the Frobenius and Verschiebung
 
 namespace WittVector
 
-variable {p : ℕ} {R : Type _} [hp : Fact p.Prime] [CommRing R]
+variable {p : ℕ} {R : Type*} [hp : Fact p.Prime] [CommRing R]
 
 -- type as `\bbW`
 local notation "𝕎" => WittVector p

07980376

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) 2020 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.identities
-! leanprover-community/mathlib commit 0798037604b2d91748f9b43925fb7570a5f3256c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.WittVector.Frobenius
 import Mathlib.RingTheory.WittVector.Verschiebung
 import Mathlib.RingTheory.WittVector.MulP
 
+#align_import ring_theory.witt_vector.identities from "leanprover-community/mathlib"@"0798037604b2d91748f9b43925fb7570a5f3256c"
+
 /-!
 ## Identities between operations on the ring of Witt vectors

07980376

chore: tidy various files (#5628)

3282e2f7

Diff

@@ -58,23 +58,18 @@ theorem verschiebung_zmod (x : 𝕎 (ZMod p)) : verschiebung x = x * p := by
 
 variable (p R)
 
-theorem coeff_p_pow [CharP R p] (i : ℕ) : (p ^ i : 𝕎 R).coeff i = 1 := by
+theorem coeff_p_pow [CharP R p] (i : ℕ) : ((p : 𝕎 R) ^ i).coeff i = 1 := by
   induction' i with i h
-  · -- Porting note: needed to move `pow_zero` out of `simp only` and into `rw` for it to fire, and
-    -- had to add the following for this goal. The original
-    -- `simp only [one_coeff_zero, Ne.def, pow_zero]` was no longer needed.
-    rw [pow_zero]
-    simp only [Nat.cast_one, Nat.zero_eq, one_coeff_zero]
-  · -- Porting note: needed to add manual `Nat.cast_mul`, `Nat.cast_pow` manipulations.
-    rw [pow_succ', Nat.cast_mul, Nat.cast_pow, ← frobenius_verschiebung, coeff_frobenius_charP,
-      verschiebung_coeff_succ, ← Nat.cast_pow, h, one_pow]
+  · simp only [Nat.zero_eq, one_coeff_zero, Ne.def, pow_zero]
+  · rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_charP,
+      verschiebung_coeff_succ, h, one_pow]
 #align witt_vector.coeff_p_pow WittVector.coeff_p_pow
 
-theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : (p ^ i : 𝕎 R).coeff j = 0 := by
+theorem coeff_p_pow_eq_zero [CharP R p] {i j : ℕ} (hj : j ≠ i) : ((p : 𝕎 R) ^ i).coeff j = 0 := by
   induction' i with i hi generalizing j
-  · rw [pow_zero, Nat.cast_one, one_coeff_eq_of_pos]
+  · rw [Nat.zero_eq, pow_zero, one_coeff_eq_of_pos]
     exact Nat.pos_of_ne_zero hj
-  · rw [pow_succ', Nat.cast_mul, ← frobenius_verschiebung, coeff_frobenius_charP]
+  · rw [pow_succ', ← frobenius_verschiebung, coeff_frobenius_charP]
     cases j
     · rw [verschiebung_coeff_zero, zero_pow]
       exact Nat.Prime.pos hp.out

07980376

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -153,7 +153,7 @@ theorem verschiebung_frobenius_comm [CharP R p] :
 open Function
 
 theorem iterate_verschiebung_coeff (x : 𝕎 R) (n k : ℕ) :
-    ((verschiebung^[n]) x).coeff (k + n) = x.coeff k := by
+    (verschiebung^[n] x).coeff (k + n) = x.coeff k := by
   induction' n with k ih
   · simp
   · rw [iterate_succ_apply', Nat.add_succ, verschiebung_coeff_succ]
@@ -161,7 +161,7 @@ theorem iterate_verschiebung_coeff (x : 𝕎 R) (n k : ℕ) :
 #align witt_vector.iterate_verschiebung_coeff WittVector.iterate_verschiebung_coeff
 
 theorem iterate_verschiebung_mul_left (x y : 𝕎 R) (i : ℕ) :
-    (verschiebung^[i]) x * y = (verschiebung^[i]) (x * (frobenius^[i]) y) := by
+    verschiebung^[i] x * y = verschiebung^[i] (x * frobenius^[i] y) := by
   induction' i with i ih generalizing y
   · simp
   · rw [iterate_succ_apply', ← verschiebung_mul_frobenius, ih, iterate_succ_apply']; rfl
@@ -172,14 +172,14 @@ section CharP
 variable [CharP R p]
 
 theorem iterate_verschiebung_mul (x y : 𝕎 R) (i j : ℕ) :
-    (verschiebung^[i]) x * (verschiebung^[j]) y =
-      (verschiebung^[i + j]) ((frobenius^[j]) x * (frobenius^[i]) y) := by
+    verschiebung^[i] x * verschiebung^[j] y =
+      verschiebung^[i + j] (frobenius^[j] x * frobenius^[i] y) := by
   calc
-    _ = (verschiebung^[i]) (x * (frobenius^[i]) ((verschiebung^[j]) y)) := ?_
-    _ = (verschiebung^[i]) (x * (verschiebung^[j]) ((frobenius^[i]) y)) := ?_
-    _ = (verschiebung^[i]) ((verschiebung^[j]) ((frobenius^[i]) y) * x) := ?_
-    _ = (verschiebung^[i]) ((verschiebung^[j]) ((frobenius^[i]) y * (frobenius^[j]) x)) := ?_
-    _ = (verschiebung^[i + j]) ((frobenius^[i]) y * (frobenius^[j]) x) := ?_
+    _ = verschiebung^[i] (x * frobenius^[i] (verschiebung^[j] y)) := ?_
+    _ = verschiebung^[i] (x * verschiebung^[j] (frobenius^[i] y)) := ?_
+    _ = verschiebung^[i] (verschiebung^[j] (frobenius^[i] y) * x) := ?_
+    _ = verschiebung^[i] (verschiebung^[j] (frobenius^[i] y * frobenius^[j] x)) := ?_
+    _ = verschiebung^[i + j] (frobenius^[i] y * frobenius^[j] x) := ?_
     _ = _ := ?_
   · apply iterate_verschiebung_mul_left
   · rw [verschiebung_frobenius_comm.iterate_iterate]
@@ -191,7 +191,7 @@ theorem iterate_verschiebung_mul (x y : 𝕎 R) (i j : ℕ) :
 
 -- Porting note: `ring_nf` doesn't handle powers yet; needed to add `Nat.pow_succ` rewrite
 theorem iterate_frobenius_coeff (x : 𝕎 R) (i k : ℕ) :
-    ((frobenius^[i]) x).coeff k = x.coeff k ^ p ^ i := by
+    (frobenius^[i] x).coeff k = x.coeff k ^ p ^ i := by
   induction' i with i ih
   · simp
   · rw [iterate_succ_apply', coeff_frobenius_charP, ih, Nat.pow_succ]
@@ -200,12 +200,12 @@ theorem iterate_frobenius_coeff (x : 𝕎 R) (i k : ℕ) :
 
 /-- This is a slightly specialized form of [Hazewinkel, *Witt Vectors*][Haze09] 6.2 equation 5. -/
 theorem iterate_verschiebung_mul_coeff (x y : 𝕎 R) (i j : ℕ) :
-    ((verschiebung^[i]) x * (verschiebung^[j]) y).coeff (i + j) =
+    (verschiebung^[i] x * verschiebung^[j] y).coeff (i + j) =
       x.coeff 0 ^ p ^ j * y.coeff 0 ^ p ^ i := by
   calc
-    _ = ((verschiebung^[i + j]) ((frobenius^[j]) x * (frobenius^[i]) y)).coeff (i + j) := ?_
-    _ = ((frobenius^[j]) x * (frobenius^[i]) y).coeff 0 := ?_
-    _ = ((frobenius^[j]) x).coeff 0 * ((frobenius^[i]) y).coeff 0 := ?_
+    _ = (verschiebung^[i + j] (frobenius^[j] x * frobenius^[i] y)).coeff (i + j) := ?_
+    _ = (frobenius^[j] x * frobenius^[i] y).coeff 0 := ?_
+    _ = (frobenius^[j] x).coeff 0 * (frobenius^[i] y).coeff 0 := ?_
     _ = _ := ?_
   · rw [iterate_verschiebung_mul]
   · convert iterate_verschiebung_coeff (p := p) (R := R) _ _ _ using 2

07980376

feat: port RingTheory.WittVector.Identities (#5527)

Co-authored-by: Johan Commelin <johan@commelin.net>

0e596046

`ring_theory.witt_vector.identities` ⟷ `Mathlib.RingTheory.WittVector.Identities`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 680

ring_theory.witt_vector.identities ⟷ Mathlib.RingTheory.WittVector.Identities

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 680

`ring_theory.witt_vector.identities` ⟷ `Mathlib.RingTheory.WittVector.Identities`