ring_theory.witt_vector.init_tail
β·
Mathlib.RingTheory.WittVector.InitTail
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.
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(last sync)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -137,7 +137,7 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
(bindβ (select_poly fun i => Β¬P i)) (wittPolynomial p β€ n) =
wittPolynomial p β€ n
by
- apply_fun aeval x.coeff at this
+ apply_fun aeval x.coeff at this
simpa only [AlgHom.map_add, aeval_bindβ, β coeff_select]
simp only [wittPolynomial_eq_sum_C_mul_X_pow, select_poly, AlgHom.map_sum, AlgHom.map_pow,
AlgHom.map_mul, bindβ_X_right, bindβ_C_right, β Finset.sum_add_distrib, β mul_add]
@@ -169,7 +169,7 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
_ = x.coeff n + y.coeff n := _
dsimp [z]
split_ifs with hn
- Β· dsimp [P] at hn ; rw [hn, add_zero]
+ Β· dsimp [P] at hn; rw [hn, add_zero]
Β· rw [(h n).resolve_right hn, zero_add]
#align witt_vector.coeff_add_of_disjoint WittVector.coeff_add_of_disjoint
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-/
-import Mathbin.RingTheory.WittVector.Basic
-import Mathbin.RingTheory.WittVector.IsPoly
+import RingTheory.WittVector.Basic
+import RingTheory.WittVector.IsPoly
#align_import ring_theory.witt_vector.init_tail from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
@@ -49,9 +49,9 @@ namespace Tactic
namespace Interactive
/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Core.lean:38:34: unsupported: setup_tactic_parser -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
-- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
-- failed to format: unknown constant 'term.pseudo.antiquot'
/--
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.init_tail
-! 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.Basic
import Mathbin.RingTheory.WittVector.IsPoly
+#align_import ring_theory.witt_vector.init_tail from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
/-!
# `init` and `tail`
mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
! This file was ported from Lean 3 source module ring_theory.witt_vector.init_tail
-! 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.IsPoly
# `init` and `tail`
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Given a Witt vector `x`, we are sometimes interested
in its components before and after an index `n`.
This file defines those operations, proves that `init` is polynomial,
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -139,7 +139,7 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
by
apply_fun aeval x.coeff at this
simpa only [AlgHom.map_add, aeval_bindβ, β coeff_select]
- simp only [wittPolynomial_eq_sum_c_mul_x_pow, select_poly, AlgHom.map_sum, AlgHom.map_pow,
+ simp only [wittPolynomial_eq_sum_C_mul_X_pow, select_poly, AlgHom.map_sum, AlgHom.map_pow,
AlgHom.map_mul, bindβ_X_right, bindβ_C_right, β Finset.sum_add_distrib, β mul_add]
apply Finset.sum_congr rfl
refine' fun m hm => mul_eq_mul_left_iff.mpr (Or.inl _)
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -84,23 +84,28 @@ noncomputable section
section
+#print WittVector.select /-
/-- `witt_vector.select P x`, for a predicate `P : β β Prop` is the Witt vector
whose `n`-th coefficient is `x.coeff n` if `P n` is true, and `0` otherwise.
-/
def select (P : β β Prop) (x : π R) : π R :=
mk' p fun n => if P n then x.coeff n else 0
#align witt_vector.select WittVector.select
+-/
section Select
variable (P : β β Prop)
+#print WittVector.selectPoly /-
/-- The polynomial that witnesses that `witt_vector.select` is a polynomial function.
`select_poly n` is `X n` if `P n` holds, and `0` otherwise. -/
def selectPoly (n : β) : MvPolynomial β β€ :=
if P n then X n else 0
#align witt_vector.select_poly WittVector.selectPoly
+-/
+#print WittVector.coeff_select /-
theorem coeff_select (x : π R) (n : β) : (select P x).coeff n = aeval x.coeff (selectPoly P n) :=
by
dsimp [select, select_poly]
@@ -108,7 +113,9 @@ theorem coeff_select (x : π R) (n : β) : (select P x).coeff n = aeval x.coe
Β· rw [aeval_X]
Β· rw [AlgHom.map_zero]
#align witt_vector.coeff_select WittVector.coeff_select
+-/
+#print WittVector.select_isPoly /-
@[is_poly]
theorem select_isPoly (P : β β Prop) : IsPoly p fun R _Rcr x => select P x :=
by
@@ -117,7 +124,9 @@ theorem select_isPoly (P : β β Prop) : IsPoly p fun R _Rcr x => select P x :
funext i
apply coeff_select
#align witt_vector.select_is_poly WittVector.select_isPoly
+-/
+#print WittVector.select_add_select_not /-
theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬P i) x = x :=
by
ghost_calc _
@@ -140,7 +149,9 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
exact not_not.mpr Pm
Β· rwa [if_neg Pm, if_pos, zero_add]
#align witt_vector.select_add_select_not WittVector.select_add_select_not
+-/
+#print WittVector.coeff_add_of_disjoint /-
theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coeff n = 0) :
(x + y).coeff n = x.coeff n + y.coeff n :=
by
@@ -161,9 +172,11 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
Β· dsimp [P] at hn ; rw [hn, add_zero]
Β· rw [(h n).resolve_right hn, zero_add]
#align witt_vector.coeff_add_of_disjoint WittVector.coeff_add_of_disjoint
+-/
end Select
+#print WittVector.init /-
/-- `witt_vector.init n x` is the Witt vector of which the first `n` coefficients are those from `x`
and all other coefficients are `0`.
See `witt_vector.tail` for the complementary part.
@@ -171,61 +184,84 @@ See `witt_vector.tail` for the complementary part.
def init (n : β) : π R β π R :=
select fun i => i < n
#align witt_vector.init WittVector.init
+-/
+#print WittVector.tail /-
/-- `witt_vector.tail n x` is the Witt vector of which the first `n` coefficients are `0`
and all other coefficients are those from `x`.
See `witt_vector.init` for the complementary part. -/
def tail (n : β) : π R β π R :=
select fun i => n β€ i
#align witt_vector.tail WittVector.tail
+-/
+#print WittVector.init_add_tail /-
@[simp]
theorem init_add_tail (x : π R) (n : β) : init n x + tail n x = x := by
simp only [init, tail, β not_lt, select_add_select_not]
#align witt_vector.init_add_tail WittVector.init_add_tail
+-/
end
+#print WittVector.init_init /-
@[simp]
theorem init_init (x : π R) (n : β) : init n (init n x) = init n x := by init_ring
#align witt_vector.init_init WittVector.init_init
+-/
+#print WittVector.init_add /-
theorem init_add (x y : π R) (n : β) : init n (x + y) = init n (init n x + init n y) := by
init_ring using witt_add_vars
#align witt_vector.init_add WittVector.init_add
+-/
+#print WittVector.init_mul /-
theorem init_mul (x y : π R) (n : β) : init n (x * y) = init n (init n x * init n y) := by
init_ring using witt_mul_vars
#align witt_vector.init_mul WittVector.init_mul
+-/
+#print WittVector.init_neg /-
theorem init_neg (x : π R) (n : β) : init n (-x) = init n (-init n x) := by
init_ring using witt_neg_vars
#align witt_vector.init_neg WittVector.init_neg
+-/
+#print WittVector.init_sub /-
theorem init_sub (x y : π R) (n : β) : init n (x - y) = init n (init n x - init n y) := by
init_ring using witt_sub_vars
#align witt_vector.init_sub WittVector.init_sub
+-/
+#print WittVector.init_nsmul /-
theorem init_nsmul (m : β) (x : π R) (n : β) : init n (m β’ x) = init n (m β’ init n x) := by
init_ring using fun p [Fact (Nat.Prime p)] n => witt_nsmul_vars p m n
#align witt_vector.init_nsmul WittVector.init_nsmul
+-/
+#print WittVector.init_zsmul /-
theorem init_zsmul (m : β€) (x : π R) (n : β) : init n (m β’ x) = init n (m β’ init n x) := by
init_ring using fun p [Fact (Nat.Prime p)] n => witt_zsmul_vars p m n
#align witt_vector.init_zsmul WittVector.init_zsmul
+-/
+#print WittVector.init_pow /-
theorem init_pow (m : β) (x : π R) (n : β) : init n (x ^ m) = init n (init n x ^ m) := by
init_ring using fun p [Fact (Nat.Prime p)] n => witt_pow_vars p m n
#align witt_vector.init_pow WittVector.init_pow
+-/
section
variable (p)
+#print WittVector.init_isPoly /-
/-- `witt_vector.init n x` is polynomial in the coefficients of `x`. -/
theorem init_isPoly (n : β) : IsPoly p fun R _Rcr => init n :=
select_isPoly fun i => i < n
#align witt_vector.init_is_poly WittVector.init_isPoly
+-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -41,7 +41,6 @@ and shows how that polynomial interacts with `mv_polynomial.bindβ`.
variable {p : β} [hp : Fact p.Prime] (n : β) {R : Type _} [CommRing R]
--- mathport name: exprπ
local notation "π" => WittVector p
-- type as `\bbW`
@@ -119,8 +118,6 @@ theorem select_isPoly (P : β β Prop) : IsPoly p fun R _Rcr x => select P x :
apply coeff_select
#align witt_vector.select_is_poly WittVector.select_isPoly
-include hp
-
theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬P i) x = x :=
by
ghost_calc _
@@ -182,8 +179,6 @@ def tail (n : β) : π R β π R :=
select fun i => n β€ i
#align witt_vector.tail WittVector.tail
-include hp
-
@[simp]
theorem init_add_tail (x : π R) (n : β) : init n x + tail n x = x := by
simp only [init, tail, β not_lt, select_add_select_not]
@@ -195,8 +190,6 @@ end
theorem init_init (x : π R) (n : β) : init n (init n x) = init n x := by init_ring
#align witt_vector.init_init WittVector.init_init
-include hp
-
theorem init_add (x y : π R) (n : β) : init n (x + y) = init n (init n x + init n y) := by
init_ring using witt_add_vars
#align witt_vector.init_add WittVector.init_add
@@ -229,8 +222,6 @@ section
variable (p)
-omit hp
-
/-- `witt_vector.init n x` is polynomial in the coefficients of `x`. -/
theorem init_isPoly (n : β) : IsPoly p fun R _Rcr => init n :=
select_isPoly fun i => i < n
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -50,9 +50,9 @@ namespace Tactic
namespace Interactive
/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Core.lean:38:34: unsupported: setup_tactic_parser -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
-- failed to format: unknown constant 'term.pseudo.antiquot'
/--
@@ -159,7 +159,6 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
calc
(x + y).coeff n = z.coeff n := by rw [β hx, β hy, select_add_select_not P z]
_ = x.coeff n + y.coeff n := _
-
dsimp [z]
split_ifs with hn
Β· dsimp [P] at hn ; rw [hn, add_zero]
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -53,6 +53,7 @@ namespace Interactive
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+-- PLEASE REPORT THIS TO MATHPORT DEVS, THIS SHOULD NOT HAPPEN.
-- failed to format: unknown constant 'term.pseudo.antiquot'
/--
`init_ring` is an auxiliary tactic that discharges goals factoring `init` over ring operations.
@@ -110,13 +111,13 @@ theorem coeff_select (x : π R) (n : β) : (select P x).coeff n = aeval x.coe
#align witt_vector.coeff_select WittVector.coeff_select
@[is_poly]
-theorem selectIsPoly (P : β β Prop) : IsPoly p fun R _Rcr x => select P x :=
+theorem select_isPoly (P : β β Prop) : IsPoly p fun R _Rcr x => select P x :=
by
use select_poly P
rintro R _Rcr x
funext i
apply coeff_select
-#align witt_vector.select_is_poly WittVector.selectIsPoly
+#align witt_vector.select_is_poly WittVector.select_isPoly
include hp
@@ -232,9 +233,9 @@ variable (p)
omit hp
/-- `witt_vector.init n x` is polynomial in the coefficients of `x`. -/
-theorem initIsPoly (n : β) : IsPoly p fun R _Rcr => init n :=
- selectIsPoly fun i => i < n
-#align witt_vector.init_is_poly WittVector.initIsPoly
+theorem init_isPoly (n : β) : IsPoly p fun R _Rcr => init n :=
+ select_isPoly fun i => i < n
+#align witt_vector.init_is_poly WittVector.init_isPoly
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725
@@ -88,7 +88,7 @@ section
whose `n`-th coefficient is `x.coeff n` if `P n` is true, and `0` otherwise.
-/
def select (P : β β Prop) (x : π R) : π R :=
- mk p fun n => if P n then x.coeff n else 0
+ mk' p fun n => if P n then x.coeff n else 0
#align witt_vector.select WittVector.select
section Select
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -130,7 +130,7 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
(bindβ (select_poly fun i => Β¬P i)) (wittPolynomial p β€ n) =
wittPolynomial p β€ n
by
- apply_fun aeval x.coeff at this
+ apply_fun aeval x.coeff at this
simpa only [AlgHom.map_add, aeval_bindβ, β coeff_select]
simp only [wittPolynomial_eq_sum_c_mul_x_pow, select_poly, AlgHom.map_sum, AlgHom.map_pow,
AlgHom.map_mul, bindβ_X_right, bindβ_C_right, β Finset.sum_add_distrib, β mul_add]
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -130,7 +130,7 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
(bindβ (select_poly fun i => Β¬P i)) (wittPolynomial p β€ n) =
wittPolynomial p β€ n
by
- apply_fun aeval x.coeff at this
+ apply_fun aeval x.coeff at this
simpa only [AlgHom.map_add, aeval_bindβ, β coeff_select]
simp only [wittPolynomial_eq_sum_c_mul_x_pow, select_poly, AlgHom.map_sum, AlgHom.map_pow,
AlgHom.map_mul, bindβ_X_right, bindβ_C_right, β Finset.sum_add_distrib, β mul_add]
@@ -161,7 +161,7 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
dsimp [z]
split_ifs with hn
- Β· dsimp [P] at hn; rw [hn, add_zero]
+ Β· dsimp [P] at hn ; rw [hn, add_zero]
Β· rw [(h n).resolve_right hn, zero_add]
#align witt_vector.coeff_add_of_disjoint WittVector.coeff_add_of_disjoint
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -78,7 +78,7 @@ namespace WittVector
open MvPolynomial
-open Classical
+open scoped Classical
noncomputable section
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -150,25 +150,18 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
haveI : DecidablePred P := Classical.decPred P
set z := mk p fun n => if P n then x.coeff n else y.coeff n with hz
have hx : select P z = x := by
- ext1 n
- rw [select, coeff_mk, coeff_mk]
- split_ifs with hn
- Β· rfl
- Β· rw [(h n).resolve_right hn]
+ ext1 n; rw [select, coeff_mk, coeff_mk]
+ split_ifs with hn; Β· rfl; Β· rw [(h n).resolve_right hn]
have hy : select (fun i => Β¬P i) z = y := by
- ext1 n
- rw [select, coeff_mk, coeff_mk]
- split_ifs with hn
- Β· exact hn.symm
- Β· rfl
+ ext1 n; rw [select, coeff_mk, coeff_mk]
+ split_ifs with hn; Β· exact hn.symm; Β· rfl
calc
(x + y).coeff n = z.coeff n := by rw [β hx, β hy, select_add_select_not P z]
_ = x.coeff n + y.coeff n := _
dsimp [z]
split_ifs with hn
- Β· dsimp [P] at hn
- rw [hn, add_zero]
+ Β· dsimp [P] at hn; rw [hn, add_zero]
Β· rw [(h n).resolve_right hn, zero_add]
#align witt_vector.coeff_add_of_disjoint WittVector.coeff_add_of_disjoint
mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd
@@ -98,7 +98,7 @@ variable (P : β β Prop)
/-- The polynomial that witnesses that `witt_vector.select` is a polynomial function.
`select_poly n` is `X n` if `P n` holds, and `0` otherwise. -/
def selectPoly (n : β) : MvPolynomial β β€ :=
- if P n then x n else 0
+ if P n then X n else 0
#align witt_vector.select_poly WittVector.selectPoly
theorem coeff_select (x : π R) (n : β) : (select P x).coeff n = aeval x.coeff (selectPoly P n) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -50,9 +50,9 @@ namespace Tactic
namespace Interactive
/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Core.lean:38:34: unsupported: setup_tactic_parser -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-- failed to format: unknown constant 'term.pseudo.antiquot'
/--
`init_ring` is an auxiliary tactic that discharges goals factoring `init` over ring operations.
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -127,7 +127,7 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
calc
(x + y).coeff n = z.coeff n := by rw [β hx, β hy, select_add_select_not P z]
_ = x.coeff n + y.coeff n := by
- simp only [mk._eq_1]
+ simp only [z, mk._eq_1]
split_ifs with y0
Β· rw [y0, add_zero]
Β· rw [h n |>.resolve_right y0, zero_add]
f ^ n
(#9617)
This involves moving lemmas from Algebra.GroupPower.Ring
to Algebra.GroupWithZero.Basic
and changing some 0 < n
assumptions to n β 0
.
From LeanAPAP
@@ -103,11 +103,9 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
AlgHom.map_mul, bindβ_X_right, bindβ_C_right, β Finset.sum_add_distrib, β mul_add]
apply Finset.sum_congr rfl
refine' fun m _ => mul_eq_mul_left_iff.mpr (Or.inl _)
- rw [ite_pow, zero_pow (pow_pos hp.out.pos _)]
+ rw [ite_pow, zero_pow (pow_ne_zero _ hp.out.ne_zero)]
by_cases Pm : P m
- Β· rw [if_pos Pm, if_neg _, zero_pow, add_zero]
- Β· exact Fin.size_positive'
- Β· exact not_not_intro Pm
+ Β· rw [if_pos Pm, if_neg $ not_not_intro Pm, zero_pow Fin.size_pos'.ne', add_zero]
Β· rwa [if_neg Pm, if_pos, zero_add]
#align witt_vector.select_add_select_not WittVector.select_add_select_not
Removes nonterminal simps on lines looking like simp [...]
@@ -129,7 +129,7 @@ theorem coeff_add_of_disjoint (x y : π R) (h : β n, x.coeff n = 0 β¨ y.coe
calc
(x + y).coeff n = z.coeff n := by rw [β hx, β hy, select_add_select_not P z]
_ = x.coeff n + y.coeff n := by
- simp [mk]
+ simp only [mk._eq_1]
split_ifs with y0
Β· rw [y0, add_zero]
Β· rw [h n |>.resolve_right y0, zero_add]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -36,7 +36,7 @@ and shows how that polynomial interacts with `MvPolynomial.bindβ`.
-/
-variable {p : β} [hp : Fact p.Prime] (n : β) {R : Type _} [CommRing R]
+variable {p : β} [hp : Fact p.Prime] (n : β) {R : Type*} [CommRing R]
-- type as `\bbW`
local notation "π" => WittVector p
@@ -2,15 +2,12 @@
Copyright (c) 2020 Johan Commelin, Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Robert Y. Lewis
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.init_tail
-! 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.Basic
import Mathlib.RingTheory.WittVector.IsPoly
+#align_import ring_theory.witt_vector.init_tail from "leanprover-community/mathlib"@"0798037604b2d91748f9b43925fb7570a5f3256c"
+
/-!
# `init` and `tail`
@@ -102,7 +102,7 @@ theorem select_add_select_not : β x : π R, select P x + select (fun i => Β¬
wittPolynomial p β€ n by
apply_fun aeval x.coeff at this
simpa only [AlgHom.map_add, aeval_bindβ, β coeff_select]
- simp only [wittPolynomial_eq_sum_c_mul_x_pow, selectPoly, AlgHom.map_sum, AlgHom.map_pow,
+ simp only [wittPolynomial_eq_sum_C_mul_X_pow, selectPoly, AlgHom.map_sum, AlgHom.map_pow,
AlgHom.map_mul, bindβ_X_right, bindβ_C_right, β Finset.sum_add_distrib, β mul_add]
apply Finset.sum_congr rfl
refine' fun m _ => mul_eq_mul_left_iff.mpr (Or.inl _)
The unported dependencies are