ring_theory.witt_vector.domain
β·
Mathlib.RingTheory.WittVector.Domain
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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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -104,7 +104,7 @@ theorem verschiebung_nonzero {x : π R} (hx : x β 0) :
β n : β, β x' : π R, x'.coeff 0 β 0 β§ x = (verschiebung^[n]) x' :=
by
have hex : β k : β, x.coeff k β 0 := by
- by_contra' hall
+ by_contra! hall
apply hx
ext i
simp only [hall, zero_coeff]
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ 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
-/
-import Mathbin.RingTheory.WittVector.Identities
+import RingTheory.WittVector.Identities
#align_import ring_theory.witt_vector.domain from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
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
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.domain
-! 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.Identities
+#align_import ring_theory.witt_vector.domain from "leanprover-community/mathlib"@"9240e8be927a0955b9a82c6c85ef499ee3a626b8"
+
/-!
# Witt vectors over a domain
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: Robert Y. Lewis
! This file was ported from Lean 3 source module ring_theory.witt_vector.domain
-! leanprover-community/mathlib commit b1d911acd60ab198808e853292106ee352b648ea
+! 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.Identities
# Witt vectors over a domain
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file builds to the proof `witt_vector.is_domain`,
an instance that says if `R` is an integral domain, then so is `π R`.
It depends on the API around iterated applications
mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9
@@ -54,6 +54,7 @@ local notation "π" => WittVector p
-/
+#print WittVector.shift /-
-- type as `\bbW`
/--
`witt_vector.verschiebung` translates the entries of a Witt vector upward, inserting 0s in the gaps.
@@ -63,13 +64,17 @@ This is mainly useful as an auxiliary construction for `witt_vector.verschiebung
def shift (x : π R) (n : β) : π R :=
mk' p fun i => x.coeff (n + i)
#align witt_vector.shift WittVector.shift
+-/
+#print WittVector.shift_coeff /-
theorem shift_coeff (x : π R) (n k : β) : (x.shift n).coeff k = x.coeff (n + k) :=
rfl
#align witt_vector.shift_coeff WittVector.shift_coeff
+-/
variable [hp : Fact p.Prime] [CommRing R]
+#print WittVector.verschiebung_shift /-
theorem verschiebung_shift (x : π R) (k : β) (h : β i < k + 1, x.coeff i = 0) :
verschiebung (x.shift k.succ) = x.shift k :=
by
@@ -80,7 +85,9 @@ theorem verschiebung_shift (x : π R) (k : β) (h : β i < k + 1, x.coeff i
congr 1
rw [Nat.add_succ, add_comm, Nat.add_succ, add_comm]
#align witt_vector.verschiebung_shift WittVector.verschiebung_shift
+-/
+#print WittVector.eq_iterate_verschiebung /-
theorem eq_iterate_verschiebung {x : π R} {n : β} (h : β i < n, x.coeff i = 0) :
x = (verschiebung^[n]) (x.shift n) :=
by
@@ -90,7 +97,9 @@ theorem eq_iterate_verschiebung {x : π R} {n : β} (h : β i < n, x.coeff i
Β· exact ih fun i hi => h _ (hi.trans (Nat.lt_succ_self _))
Β· exact h
#align witt_vector.eq_iterate_verschiebung WittVector.eq_iterate_verschiebung
+-/
+#print WittVector.verschiebung_nonzero /-
theorem verschiebung_nonzero {x : π R} (hx : x β 0) :
β n : β, β x' : π R, x'.coeff 0 β 0 β§ x = (verschiebung^[n]) x' :=
by
@@ -104,6 +113,7 @@ theorem verschiebung_nonzero {x : π R} (hx : x β 0) :
refine' β¨Nat.find_spec hex, eq_iterate_verschiebung fun i hi => not_not.mp _β©
exact Nat.find_min hex hi
#align witt_vector.verschiebung_nonzero WittVector.verschiebung_nonzero
+-/
/-!
## Witt vectors over a domain
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -47,7 +47,6 @@ open Function
variable {p : β} {R : Type _}
--- mathport name: exprπ
local notation "π" => WittVector p
/-!
@@ -71,8 +70,6 @@ theorem shift_coeff (x : π R) (n k : β) : (x.shift n).coeff k = x.coeff (n
variable [hp : Fact p.Prime] [CommRing R]
-include hp
-
theorem verschiebung_shift (x : π R) (k : β) (h : β i < k + 1, x.coeff i = 0) :
verschiebung (x.shift k.succ) = x.shift k :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725
@@ -62,7 +62,7 @@ local notation "π" => WittVector p
This is mainly useful as an auxiliary construction for `witt_vector.verschiebung_nonzero`.
-/
def shift (x : π R) (n : β) : π R :=
- mk p fun i => x.coeff (n + i)
+ mk' p fun i => x.coeff (n + i)
#align witt_vector.shift WittVector.shift
theorem shift_coeff (x : π R) (n k : β) : (x.shift n).coeff k = x.coeff (n + k) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -39,7 +39,7 @@ the 0th component of which must be nonzero.
noncomputable section
-open Classical
+open scoped Classical
namespace WittVector
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -89,8 +89,7 @@ theorem eq_iterate_verschiebung {x : π R} {n : β} (h : β i < n, x.coeff i
by
induction' n with k ih
Β· cases x <;> simp [shift]
- Β· dsimp
- rw [verschiebung_shift]
+ Β· dsimp; rw [verschiebung_shift]
Β· exact ih fun i hi => h _ (hi.trans (Nat.lt_succ_self _))
Β· exact h
#align witt_vector.eq_iterate_verschiebung WittVector.eq_iterate_verschiebung
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -88,7 +88,7 @@ theorem eq_iterate_verschiebung {x : π R} {n : β} (h : β i < n, x.coeff i
theorem verschiebung_nonzero {x : π R} (hx : x β 0) :
β n : β, β x' : π R, x'.coeff 0 β 0 β§ x = verschiebung^[n] x' := by
have hex : β k : β, x.coeff k β 0 := by
- by_contra' hall
+ by_contra! hall
apply hx
ext i
simp only [hall, zero_coeff]
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -42,7 +42,7 @@ namespace WittVector
open Function
-variable {p : β} {R : Type _}
+variable {p : β} {R : Type*}
local notation "π" => WittVector p -- type as `\bbW`
@@ -2,14 +2,11 @@
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
-
-! This file was ported from Lean 3 source module ring_theory.witt_vector.domain
-! leanprover-community/mathlib commit b1d911acd60ab198808e853292106ee352b648ea
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.RingTheory.WittVector.Identities
+#align_import ring_theory.witt_vector.domain from "leanprover-community/mathlib"@"b1d911acd60ab198808e853292106ee352b648ea"
+
/-!
# Witt vectors over a domain
@@ -80,7 +80,7 @@ theorem verschiebung_shift (x : π R) (k : β) (h : β i < k + 1, x.coeff i
#align witt_vector.verschiebung_shift WittVector.verschiebung_shift
theorem eq_iterate_verschiebung {x : π R} {n : β} (h : β i < n, x.coeff i = 0) :
- x = (verschiebung^[n]) (x.shift n) := by
+ x = verschiebung^[n] (x.shift n) := by
induction' n with k ih
Β· cases x; simp [shift]
Β· dsimp; rw [verschiebung_shift]
@@ -89,7 +89,7 @@ theorem eq_iterate_verschiebung {x : π R} {n : β} (h : β i < n, x.coeff i
#align witt_vector.eq_iterate_verschiebung WittVector.eq_iterate_verschiebung
theorem verschiebung_nonzero {x : π R} (hx : x β 0) :
- β n : β, β x' : π R, x'.coeff 0 β 0 β§ x = (verschiebung^[n]) x' := by
+ β n : β, β x' : π R, x'.coeff 0 β 0 β§ x = verschiebung^[n] x' := by
have hex : β k : β, x.coeff k β 0 := by
by_contra' hall
apply hx
The unported dependencies are