ring_theory.witt_vector.verschiebung
β·
Mathlib.RingTheory.WittVector.Verschiebung
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
@@ -84,7 +84,7 @@ theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
rw [Finset.sum_range_succ', verschiebung_fun_coeff, if_pos rfl, zero_pow (pow_pos hp.1.Pos _),
MulZeroClass.mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
rintro i -
- simp only [pow_succ, mul_assoc, verschiebung_fun_coeff, if_neg (Nat.succ_ne_zero i),
+ simp only [pow_succ', mul_assoc, verschiebung_fun_coeff, if_neg (Nat.succ_ne_zero i),
Nat.succ_sub_succ, tsub_zero]
#align witt_vector.ghost_component_verschiebung_fun WittVector.ghostComponent_verschiebungFun
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ 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.Basic
-import Mathbin.RingTheory.WittVector.IsPoly
+import RingTheory.WittVector.Basic
+import RingTheory.WittVector.IsPoly
#align_import ring_theory.witt_vector.verschiebung from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
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.verschiebung
-! 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.verschiebung from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
/-!
## The Verschiebung operator
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
! This file was ported from Lean 3 source module ring_theory.witt_vector.verschiebung
-! leanprover-community/mathlib commit 32b08ef840dd25ca2e47e035c5da03ce16d2dc3c
+! leanprover-community/mathlib commit 9240e8be927a0955b9a82c6c85ef499ee3a626b8
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.WittVector.IsPoly
/-!
## The Verschiebung operator
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
## References
* [Hazewinkel, *Witt Vectors*][Haze09]
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -33,6 +33,7 @@ local notation "π" => WittVector p
-- type as `\bbW`
noncomputable section
+#print WittVector.verschiebungFun /-
/-- `verschiebung_fun x` shifts the coefficients of `x` up by one,
by inserting 0 as the 0th coefficient.
`x.coeff i` then becomes `(verchiebung_fun x).coeff (i + 1)`.
@@ -42,29 +43,39 @@ by inserting 0 as the 0th coefficient.
def verschiebungFun (x : π R) : π R :=
mk' p fun n => if n = 0 then 0 else x.coeff (n - 1)
#align witt_vector.verschiebung_fun WittVector.verschiebungFun
+-/
+#print WittVector.verschiebungFun_coeff /-
theorem verschiebungFun_coeff (x : π R) (n : β) :
(verschiebungFun x).coeff n = if n = 0 then 0 else x.coeff (n - 1) := by
rw [verschiebung_fun, coeff_mk]
#align witt_vector.verschiebung_fun_coeff WittVector.verschiebungFun_coeff
+-/
+#print WittVector.verschiebungFun_coeff_zero /-
theorem verschiebungFun_coeff_zero (x : π R) : (verschiebungFun x).coeff 0 = 0 := by
rw [verschiebung_fun_coeff, if_pos rfl]
#align witt_vector.verschiebung_fun_coeff_zero WittVector.verschiebungFun_coeff_zero
+-/
+#print WittVector.verschiebungFun_coeff_succ /-
@[simp]
theorem verschiebungFun_coeff_succ (x : π R) (n : β) :
(verschiebungFun x).coeff n.succ = x.coeff n :=
rfl
#align witt_vector.verschiebung_fun_coeff_succ WittVector.verschiebungFun_coeff_succ
+-/
+#print WittVector.ghostComponent_zero_verschiebungFun /-
@[ghost_simps]
theorem ghostComponent_zero_verschiebungFun (x : π R) : ghostComponent 0 (verschiebungFun x) = 0 :=
by
rw [ghost_component_apply, aeval_wittPolynomial, Finset.range_one, Finset.sum_singleton,
verschiebung_fun_coeff_zero, pow_zero, pow_zero, pow_one, one_mul]
#align witt_vector.ghost_component_zero_verschiebung_fun WittVector.ghostComponent_zero_verschiebungFun
+-/
+#print WittVector.ghostComponent_verschiebungFun /-
@[ghost_simps]
theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
ghostComponent (n + 1) (verschiebungFun x) = p * ghostComponent n x :=
@@ -76,19 +87,25 @@ theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
simp only [pow_succ, mul_assoc, verschiebung_fun_coeff, if_neg (Nat.succ_ne_zero i),
Nat.succ_sub_succ, tsub_zero]
#align witt_vector.ghost_component_verschiebung_fun WittVector.ghostComponent_verschiebungFun
+-/
+#print WittVector.verschiebungPoly /-
/-- The 0th Verschiebung polynomial is 0. For `n > 0`, the `n`th Verschiebung polynomial is the
variable `X (n-1)`.
-/
def verschiebungPoly (n : β) : MvPolynomial β β€ :=
if n = 0 then 0 else X (n - 1)
#align witt_vector.verschiebung_poly WittVector.verschiebungPoly
+-/
+#print WittVector.verschiebungPoly_zero /-
@[simp]
theorem verschiebungPoly_zero : verschiebungPoly 0 = 0 :=
rfl
#align witt_vector.verschiebung_poly_zero WittVector.verschiebungPoly_zero
+-/
+#print WittVector.aeval_verschiebung_poly' /-
theorem aeval_verschiebung_poly' (x : π R) (n : β) :
aeval x.coeff (verschiebungPoly n) = (verschiebungFun x).coeff n :=
by
@@ -98,9 +115,11 @@ theorem aeval_verschiebung_poly' (x : π R) (n : β) :
rw [verschiebung_poly, verschiebung_fun_coeff_succ, if_neg n.succ_ne_zero, aeval_X,
Nat.succ_eq_add_one, add_tsub_cancel_right]
#align witt_vector.aeval_verschiebung_poly' WittVector.aeval_verschiebung_poly'
+-/
variable (p)
+#print WittVector.verschiebungFun_isPoly /-
/-- `witt_vector.verschiebung` has polynomial structure given by `witt_vector.verschiebung_poly`.
-/
@[is_poly]
@@ -109,9 +128,11 @@ theorem verschiebungFun_isPoly : IsPoly p fun R _Rcr => @verschiebungFun p R _Rc
use verschiebung_poly
simp only [aeval_verschiebung_poly', eq_self_iff_true, forallβ_true_iff]
#align witt_vector.verschiebung_fun_is_poly WittVector.verschiebungFun_isPoly
+-/
variable {p}
+#print WittVector.verschiebung /-
/--
`verschiebung x` shifts the coefficients of `x` up by one, by inserting 0 as the 0th coefficient.
`x.coeff i` then becomes `(verchiebung x).coeff (i + 1)`.
@@ -126,50 +147,68 @@ noncomputable def verschiebung : π R β+ π R
simp only [if_true, eq_self_iff_true, zero_coeff, if_t_t]
map_add' := by ghost_calc _ _; rintro β¨β© <;> ghost_simp
#align witt_vector.verschiebung WittVector.verschiebung
+-/
+#print WittVector.verschiebung_isPoly /-
/-- `witt_vector.verschiebung` is a polynomial function. -/
@[is_poly]
theorem verschiebung_isPoly : IsPoly p fun R _Rcr => @verschiebung p R hp _Rcr :=
verschiebungFun_isPoly p
#align witt_vector.verschiebung_is_poly WittVector.verschiebung_isPoly
+-/
+#print WittVector.map_verschiebung /-
/-- verschiebung is a natural transformation -/
@[simp]
theorem map_verschiebung (f : R β+* S) (x : π R) :
map f (verschiebung x) = verschiebung (map f x) := by ext β¨-, -β©; exact f.map_zero; rfl
#align witt_vector.map_verschiebung WittVector.map_verschiebung
+-/
+#print WittVector.ghostComponent_zero_verschiebung /-
@[ghost_simps]
theorem ghostComponent_zero_verschiebung (x : π R) : ghostComponent 0 (verschiebung x) = 0 :=
ghostComponent_zero_verschiebungFun _
#align witt_vector.ghost_component_zero_verschiebung WittVector.ghostComponent_zero_verschiebung
+-/
+#print WittVector.ghostComponent_verschiebung /-
@[ghost_simps]
theorem ghostComponent_verschiebung (x : π R) (n : β) :
ghostComponent (n + 1) (verschiebung x) = p * ghostComponent n x :=
ghostComponent_verschiebungFun _ _
#align witt_vector.ghost_component_verschiebung WittVector.ghostComponent_verschiebung
+-/
+#print WittVector.verschiebung_coeff_zero /-
@[simp]
theorem verschiebung_coeff_zero (x : π R) : (verschiebung x).coeff 0 = 0 :=
rfl
#align witt_vector.verschiebung_coeff_zero WittVector.verschiebung_coeff_zero
+-/
+#print WittVector.verschiebung_coeff_add_one /-
-- simp_nf complains if this is simp
theorem verschiebung_coeff_add_one (x : π R) (n : β) : (verschiebung x).coeff (n + 1) = x.coeff n :=
rfl
#align witt_vector.verschiebung_coeff_add_one WittVector.verschiebung_coeff_add_one
+-/
+#print WittVector.verschiebung_coeff_succ /-
@[simp]
theorem verschiebung_coeff_succ (x : π R) (n : β) : (verschiebung x).coeff n.succ = x.coeff n :=
rfl
#align witt_vector.verschiebung_coeff_succ WittVector.verschiebung_coeff_succ
+-/
+#print WittVector.aeval_verschiebungPoly /-
theorem aeval_verschiebungPoly (x : π R) (n : β) :
aeval x.coeff (verschiebungPoly n) = (verschiebung x).coeff n :=
aeval_verschiebung_poly' x n
#align witt_vector.aeval_verschiebung_poly WittVector.aeval_verschiebungPoly
+-/
+#print WittVector.bindβ_verschiebungPoly_wittPolynomial /-
@[simp]
theorem bindβ_verschiebungPoly_wittPolynomial (n : β) :
bindβ verschiebungPoly (wittPolynomial p β€ n) =
@@ -190,6 +229,7 @@ theorem bindβ_verschiebungPoly_wittPolynomial (n : β) :
exact evalβ_hom_congr (RingHom.ext_int _ _) rfl rfl
Β· rw [ghost_component_verschiebung]; rfl
#align witt_vector.bindβ_verschiebung_poly_witt_polynomial WittVector.bindβ_verschiebungPoly_wittPolynomial
+-/
end WittVector
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -28,7 +28,6 @@ open MvPolynomial
variable {p : β} {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
--- mathport name: exprπ
local notation "π" => WittVector p
-- type as `\bbW`
@@ -59,8 +58,6 @@ theorem verschiebungFun_coeff_succ (x : π R) (n : β) :
rfl
#align witt_vector.verschiebung_fun_coeff_succ WittVector.verschiebungFun_coeff_succ
-include hp
-
@[ghost_simps]
theorem ghostComponent_zero_verschiebungFun (x : π R) : ghostComponent 0 (verschiebungFun x) = 0 :=
by
@@ -80,8 +77,6 @@ theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
Nat.succ_sub_succ, tsub_zero]
#align witt_vector.ghost_component_verschiebung_fun WittVector.ghostComponent_verschiebungFun
-omit hp
-
/-- The 0th Verschiebung polynomial is 0. For `n > 0`, the `n`th Verschiebung polynomial is the
variable `X (n-1)`.
-/
@@ -117,8 +112,6 @@ theorem verschiebungFun_isPoly : IsPoly p fun R _Rcr => @verschiebungFun p R _Rc
variable {p}
-include hp
-
/--
`verschiebung x` shifts the coefficients of `x` up by one, by inserting 0 as the 0th coefficient.
`x.coeff i` then becomes `(verchiebung x).coeff (i + 1)`.
@@ -134,16 +127,12 @@ noncomputable def verschiebung : π R β+ π R
map_add' := by ghost_calc _ _; rintro β¨β© <;> ghost_simp
#align witt_vector.verschiebung WittVector.verschiebung
-omit hp
-
/-- `witt_vector.verschiebung` is a polynomial function. -/
@[is_poly]
theorem verschiebung_isPoly : IsPoly p fun R _Rcr => @verschiebung p R hp _Rcr :=
verschiebungFun_isPoly p
#align witt_vector.verschiebung_is_poly WittVector.verschiebung_isPoly
-include hp
-
/-- verschiebung is a natural transformation -/
@[simp]
theorem map_verschiebung (f : R β+* S) (x : π R) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -195,7 +195,6 @@ theorem bindβ_verschiebungPoly_wittPolynomial (n : β) :
calc
_ = ghost_component (n + 1) (verschiebung <| mk p x) := _
_ = _ := _
-
Β· apply evalβ_hom_congr (RingHom.ext_int _ _) _ rfl
simp only [β aeval_verschiebung_poly, coeff_mk]
funext k
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -109,11 +109,11 @@ variable (p)
/-- `witt_vector.verschiebung` has polynomial structure given by `witt_vector.verschiebung_poly`.
-/
@[is_poly]
-theorem verschiebungFunIsPoly : IsPoly p fun R _Rcr => @verschiebungFun p R _Rcr :=
+theorem verschiebungFun_isPoly : IsPoly p fun R _Rcr => @verschiebungFun p R _Rcr :=
by
use verschiebung_poly
simp only [aeval_verschiebung_poly', eq_self_iff_true, forallβ_true_iff]
-#align witt_vector.verschiebung_fun_is_poly WittVector.verschiebungFunIsPoly
+#align witt_vector.verschiebung_fun_is_poly WittVector.verschiebungFun_isPoly
variable {p}
@@ -138,9 +138,9 @@ omit hp
/-- `witt_vector.verschiebung` is a polynomial function. -/
@[is_poly]
-theorem verschiebungIsPoly : IsPoly p fun R _Rcr => @verschiebung p R hp _Rcr :=
- verschiebungFunIsPoly p
-#align witt_vector.verschiebung_is_poly WittVector.verschiebungIsPoly
+theorem verschiebung_isPoly : IsPoly p fun R _Rcr => @verschiebung p R hp _Rcr :=
+ verschiebungFun_isPoly p
+#align witt_vector.verschiebung_is_poly WittVector.verschiebung_isPoly
include hp
mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725
@@ -41,7 +41,7 @@ by inserting 0 as the 0th coefficient.
`verschiebung_fun` is the underlying function of the additive monoid hom `witt_vector.verschiebung`.
-/
def verschiebungFun (x : π R) : π R :=
- mk p fun n => if n = 0 then 0 else x.coeff (n - 1)
+ mk' p fun n => if n = 0 then 0 else x.coeff (n - 1)
#align witt_vector.verschiebung_fun WittVector.verschiebungFun
theorem verschiebungFun_coeff (x : π R) (n : β) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -131,9 +131,7 @@ noncomputable def verschiebung : π R β+ π R
map_zero' := by
ext β¨β© <;> rw [verschiebung_fun_coeff] <;>
simp only [if_true, eq_self_iff_true, zero_coeff, if_t_t]
- map_add' := by
- ghost_calc _ _
- rintro β¨β© <;> ghost_simp
+ map_add' := by ghost_calc _ _; rintro β¨β© <;> ghost_simp
#align witt_vector.verschiebung WittVector.verschiebung
omit hp
@@ -149,11 +147,7 @@ include hp
/-- verschiebung is a natural transformation -/
@[simp]
theorem map_verschiebung (f : R β+* S) (x : π R) :
- map f (verschiebung x) = verschiebung (map f x) :=
- by
- ext β¨-, -β©
- exact f.map_zero
- rfl
+ map f (verschiebung x) = verschiebung (map f x) := by ext β¨-, -β©; exact f.map_zero; rfl
#align witt_vector.map_verschiebung WittVector.map_verschiebung
@[ghost_simps]
@@ -206,8 +200,7 @@ theorem bindβ_verschiebungPoly_wittPolynomial (n : β) :
simp only [β aeval_verschiebung_poly, coeff_mk]
funext k
exact evalβ_hom_congr (RingHom.ext_int _ _) rfl rfl
- Β· rw [ghost_component_verschiebung]
- rfl
+ Β· rw [ghost_component_verschiebung]; rfl
#align witt_vector.bindβ_verschiebung_poly_witt_polynomial WittVector.bindβ_verschiebungPoly_wittPolynomial
end WittVector
mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd
@@ -86,7 +86,7 @@ omit hp
variable `X (n-1)`.
-/
def verschiebungPoly (n : β) : MvPolynomial β β€ :=
- if n = 0 then 0 else x (n - 1)
+ if n = 0 then 0 else X (n - 1)
#align witt_vector.verschiebung_poly WittVector.verschiebungPoly
@[simp]
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -74,7 +74,7 @@ theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
by
simp only [ghost_component_apply, aeval_wittPolynomial]
rw [Finset.sum_range_succ', verschiebung_fun_coeff, if_pos rfl, zero_pow (pow_pos hp.1.Pos _),
- mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
+ MulZeroClass.mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
rintro i -
simp only [pow_succ, mul_assoc, verschiebung_fun_coeff, if_neg (Nat.succ_ne_zero i),
Nat.succ_sub_succ, tsub_zero]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
We change the following field in the definition of an additive commutative monoid:
nsmul_succ : β (n : β) (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 notnpowRec n x * x
in the definition to make sure that definitional unfolding ofnpowRec
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.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
.@@ -68,7 +68,7 @@ theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
rw [Finset.sum_range_succ', verschiebungFun_coeff, if_pos rfl,
zero_pow (pow_ne_zero _ hp.1.ne_zero), mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
rintro i -
- simp only [pow_succ, mul_assoc, verschiebungFun_coeff, if_neg (Nat.succ_ne_zero i),
+ simp only [pow_succ', mul_assoc, verschiebungFun_coeff, if_neg (Nat.succ_ne_zero i),
Nat.succ_sub_succ, tsub_zero]
#align witt_vector.ghost_component_verschiebung_fun WittVector.ghostComponent_verschiebungFun
Ξ»
by fun
(#11301)
Per the style guidelines, Ξ»
is disallowed in mathlib.
This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.
Notes
=>
to β¦
.Mathlib/Order/SupClosed
.Ξ» x,
, which I also replaced.@@ -106,7 +106,7 @@ instance verschiebungFun_isPoly : IsPoly p fun R _Rcr => @verschiebungFun p R _R
-- Porting note: we add this example as a verification that Lean 4's instance resolution
-- can handle what in Lean 3 we needed the `@[is_poly]` attribute to help with.
example (p : β) (f : β¦R : Type _β¦ β [CommRing R] β WittVector p R β WittVector p R) [IsPoly p f] :
- IsPoly p (Ξ» (R : Type*) (I : CommRing R) => verschiebungFun β (@f R I)) :=
+ IsPoly p (fun (R : Type*) (I : CommRing R) β¦ verschiebungFun β (@f R I)) :=
inferInstance
variable {p}
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
@@ -65,8 +65,8 @@ theorem ghostComponent_zero_verschiebungFun (x : π R) :
theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
ghostComponent (n + 1) (verschiebungFun x) = p * ghostComponent n x := by
simp only [ghostComponent_apply, aeval_wittPolynomial]
- rw [Finset.sum_range_succ', verschiebungFun_coeff, if_pos rfl, zero_pow (pow_pos hp.1.pos _),
- mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
+ rw [Finset.sum_range_succ', verschiebungFun_coeff, if_pos rfl,
+ zero_pow (pow_ne_zero _ hp.1.ne_zero), mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
rintro i -
simp only [pow_succ, mul_assoc, verschiebungFun_coeff, if_neg (Nat.succ_ne_zero i),
Nat.succ_sub_succ, tsub_zero]
@@ -56,7 +56,7 @@ theorem verschiebungFun_coeff_succ (x : π R) (n : β) :
@[ghost_simps]
theorem ghostComponent_zero_verschiebungFun (x : π R) :
- ghostComponent 0 (verschiebungFun x) = 0 := by
+ ghostComponent 0 (verschiebungFun x) = 0 := by
rw [ghostComponent_apply, aeval_wittPolynomial, Finset.range_one, Finset.sum_singleton,
verschiebungFun_coeff_zero, pow_zero, pow_zero, pow_one, one_mul]
#align witt_vector.ghost_component_zero_verschiebung_fun WittVector.ghostComponent_zero_verschiebungFun
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).
@@ -66,7 +66,7 @@ theorem ghostComponent_verschiebungFun (x : π R) (n : β) :
ghostComponent (n + 1) (verschiebungFun x) = p * ghostComponent n x := by
simp only [ghostComponent_apply, aeval_wittPolynomial]
rw [Finset.sum_range_succ', verschiebungFun_coeff, if_pos rfl, zero_pow (pow_pos hp.1.pos _),
- MulZeroClass.mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
+ mul_zero, add_zero, Finset.mul_sum, Finset.sum_congr rfl]
rintro i -
simp only [pow_succ, mul_assoc, verschiebungFun_coeff, if_neg (Nat.succ_ne_zero i),
Nat.succ_sub_succ, tsub_zero]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -23,7 +23,7 @@ namespace WittVector
open MvPolynomial
-variable {p : β} {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
+variable {p : β} {R S : Type*} [hp : Fact p.Prime] [CommRing R] [CommRing S]
local notation "π" => WittVector p -- type as `\bbW`
@@ -106,7 +106,7 @@ instance verschiebungFun_isPoly : IsPoly p fun R _Rcr => @verschiebungFun p R _R
-- Porting note: we add this example as a verification that Lean 4's instance resolution
-- can handle what in Lean 3 we needed the `@[is_poly]` attribute to help with.
example (p : β) (f : β¦R : Type _β¦ β [CommRing R] β WittVector p R β WittVector p R) [IsPoly p f] :
- IsPoly p (Ξ» (R : Type _) (I : CommRing R) => verschiebungFun β (@f R I)) :=
+ IsPoly p (Ξ» (R : Type*) (I : CommRing R) => verschiebungFun β (@f R I)) :=
inferInstance
variable {p}
@@ -2,15 +2,12 @@
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.verschiebung
-! leanprover-community/mathlib commit 32b08ef840dd25ca2e47e035c5da03ce16d2dc3c
-! 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.verschiebung from "leanprover-community/mathlib"@"32b08ef840dd25ca2e47e035c5da03ce16d2dc3c"
+
/-!
## The Verschiebung operator
register_simp_attr
s to 1 file (#5681)
There are slight differences between mathlib3
and mathlib4
(different set of attributes, different lemmas are in core/std), so I redid the same refactor instead of forward-porting changes.
mathlib3 PR: leanprover-community/mathlib#19223
@@ -114,9 +114,6 @@ example (p : β) (f : β¦R : Type _β¦ β [CommRing R] β WittVector p R β
variable {p}
--- Porting note: until we change the default induction principle on `Nat`:
-attribute [ghost_simps] Nat.zero_eq
-
/--
`verschiebung x` shifts the coefficients of `x` up by one, by inserting 0 as the 0th coefficient.
`x.coeff i` then becomes `(verchiebung x).coeff (i + 1)`.
@@ -121,7 +121,7 @@ attribute [ghost_simps] Nat.zero_eq
`verschiebung x` shifts the coefficients of `x` up by one, by inserting 0 as the 0th coefficient.
`x.coeff i` then becomes `(verchiebung x).coeff (i + 1)`.
-This is a additive monoid hom with underlying function `verschiebung_fun`.
+This is an additive monoid hom with underlying function `verschiebung_fun`.
-/
noncomputable def verschiebung : π R β+ π R where
toFun := verschiebungFun
The unported dependencies are