ring_theory.witt_vector.teichmullerMathlib.RingTheory.WittVector.Teichmuller

This file has been ported!

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,7 +3,7 @@ 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 RingTheory.WittVector.Basic
 
 #align_import ring_theory.witt_vector.teichmuller from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
 
Diff
@@ -2,14 +2,11 @@
 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.teichmuller
-! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.RingTheory.WittVector.Basic
 
+#align_import ring_theory.witt_vector.teichmuller from "leanprover-community/mathlib"@"6b31d1eebd64eab86d5bd9936bfaada6ca8b5842"
+
 /-!
 # Teichmüller lifts
 
Diff
@@ -40,7 +40,6 @@ open MvPolynomial
 
 variable (p : ℕ) {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
 
--- mathport name: expr𝕎
 local notation "𝕎" => WittVector p
 
 #print WittVector.teichmullerFun /-
@@ -68,8 +67,6 @@ satisfy the ring axioms.
 -/
 
 
-include hp
-
 private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
     ghostComponent n (teichmullerFun p r) = r ^ p ^ n :=
   by
@@ -102,6 +99,7 @@ private theorem teichmuller_mul_aux₂ (x y : MvPolynomial R ℤ) :
       (MvPolynomial.map_injective _ Int.cast_injective) _
   simp only [teichmuller_mul_aux₁, map_teichmuller_fun, RingHom.map_mul]
 
+#print WittVector.teichmuller /-
 /-- The Teichmüller lift of an element of `R` to `𝕎 R`.
 The `0`-th coefficient of `teichmuller p r` is `r`, and all others are `0`.
 This is a monoid homomorphism. -/
@@ -117,33 +115,44 @@ def teichmuller : R →* 𝕎 R where
     rcases counit_surjective R y with ⟨y, rfl⟩
     simp only [← map_teichmuller_fun, ← RingHom.map_mul, teichmuller_mul_aux₂]
 #align witt_vector.teichmuller WittVector.teichmuller
+-/
 
+#print WittVector.teichmuller_coeff_zero /-
 @[simp]
 theorem teichmuller_coeff_zero (r : R) : (teichmuller p r).coeff 0 = r :=
   rfl
 #align witt_vector.teichmuller_coeff_zero WittVector.teichmuller_coeff_zero
+-/
 
+#print WittVector.teichmuller_coeff_pos /-
 @[simp]
 theorem teichmuller_coeff_pos (r : R) : ∀ (n : ℕ) (hn : 0 < n), (teichmuller p r).coeff n = 0
   | n + 1, _ => rfl
 #align witt_vector.teichmuller_coeff_pos WittVector.teichmuller_coeff_pos
+-/
 
+#print WittVector.teichmuller_zero /-
 @[simp]
 theorem teichmuller_zero : teichmuller p (0 : R) = 0 := by ext ⟨⟩ <;> · rw [zero_coeff]; rfl
 #align witt_vector.teichmuller_zero WittVector.teichmuller_zero
+-/
 
+#print WittVector.map_teichmuller /-
 /-- `teichmuller` is a natural transformation. -/
 @[simp]
 theorem map_teichmuller (f : R →+* S) (r : R) : map f (teichmuller p r) = teichmuller p (f r) :=
   map_teichmullerFun _ _ _
 #align witt_vector.map_teichmuller WittVector.map_teichmuller
+-/
 
+#print WittVector.ghostComponent_teichmuller /-
 /-- The `n`-th ghost component of `teichmuller p r` is `r ^ p ^ n`. -/
 @[simp]
 theorem ghostComponent_teichmuller (r : R) (n : ℕ) :
     ghostComponent n (teichmuller p r) = r ^ p ^ n :=
   ghostComponent_teichmullerFun _ _ _
 #align witt_vector.ghost_component_teichmuller WittVector.ghostComponent_teichmuller
+-/
 
 end WittVector
 
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.teichmuller
-! leanprover-community/mathlib commit c0a51cf2de54089d69301befc4c73bbc2f5c7342
+! leanprover-community/mathlib commit 6b31d1eebd64eab86d5bd9936bfaada6ca8b5842
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.RingTheory.WittVector.Basic
 /-!
 # Teichmüller lifts
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines `witt_vector.teichmuller`, a monoid hom `R →* 𝕎 R`, which embeds `r : R` as the
 `0`-th component of a Witt vector whose other coefficients are `0`.
 
Diff
@@ -40,6 +40,7 @@ variable (p : ℕ) {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
 -- mathport name: expr𝕎
 local notation "𝕎" => WittVector p
 
+#print WittVector.teichmullerFun /-
 -- type as `\bbW`
 /-- The underlying function of the monoid hom `witt_vector.teichmuller`.
 The `0`-th coefficient of `teichmuller_fun p r` is `r`, and all others are `0`.
@@ -47,6 +48,7 @@ The `0`-th coefficient of `teichmuller_fun p r` is `r`, and all others are `0`.
 def teichmullerFun (r : R) : 𝕎 R :=
   ⟨p, fun n => if n = 0 then r else 0⟩
 #align witt_vector.teichmuller_fun WittVector.teichmullerFun
+-/
 
 /-!
 ## `teichmuller` is a monoid homomorphism
Diff
@@ -72,22 +72,13 @@ private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
     tsub_zero]
   · rfl
   · intro i hi h0
-    convert MulZeroClass.mul_zero _
-    convert zero_pow _
-    · cases i
-      · contradiction
-      · rfl
+    convert MulZeroClass.mul_zero _; convert zero_pow _
+    · cases i; · contradiction; · rfl
     · exact pow_pos hp.1.Pos _
-  · rw [Finset.mem_range]
-    intro h
-    exact (h (Nat.succ_pos n)).elim
+  · rw [Finset.mem_range]; intro h; exact (h (Nat.succ_pos n)).elim
 
 private theorem map_teichmuller_fun (f : R →+* S) (r : R) :
-    map f (teichmullerFun p r) = teichmullerFun p (f r) :=
-  by
-  ext n
-  cases n
-  · rfl
+    map f (teichmullerFun p r) = teichmullerFun p (f r) := by ext n; cases n; · rfl;
   · exact f.map_zero
 
 private theorem teichmuller_mul_aux₁ (x y : MvPolynomial R ℚ) :
@@ -113,10 +104,8 @@ def teichmuller : R →* 𝕎 R where
   toFun := teichmullerFun p
   map_one' := by
     ext ⟨⟩
-    · rw [one_coeff_zero]
-      rfl
-    · rw [one_coeff_eq_of_pos _ _ _ (Nat.succ_pos n)]
-      rfl
+    · rw [one_coeff_zero]; rfl
+    · rw [one_coeff_eq_of_pos _ _ _ (Nat.succ_pos n)]; rfl
   map_mul' := by
     intro x y
     rcases counit_surjective R x with ⟨x, rfl⟩
@@ -135,10 +124,7 @@ theorem teichmuller_coeff_pos (r : R) : ∀ (n : ℕ) (hn : 0 < n), (teichmuller
 #align witt_vector.teichmuller_coeff_pos WittVector.teichmuller_coeff_pos
 
 @[simp]
-theorem teichmuller_zero : teichmuller p (0 : R) = 0 := by
-  ext ⟨⟩ <;>
-    · rw [zero_coeff]
-      rfl
+theorem teichmuller_zero : teichmuller p (0 : R) = 0 := by ext ⟨⟩ <;> · rw [zero_coeff]; rfl
 #align witt_vector.teichmuller_zero WittVector.teichmuller_zero
 
 /-- `teichmuller` is a natural transformation. -/
Diff
@@ -81,7 +81,6 @@ private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
   · rw [Finset.mem_range]
     intro h
     exact (h (Nat.succ_pos n)).elim
-#align witt_vector.ghost_component_teichmuller_fun witt_vector.ghost_component_teichmuller_fun
 
 private theorem map_teichmuller_fun (f : R →+* S) (r : R) :
     map f (teichmullerFun p r) = teichmullerFun p (f r) :=
@@ -90,7 +89,6 @@ private theorem map_teichmuller_fun (f : R →+* S) (r : R) :
   cases n
   · rfl
   · exact f.map_zero
-#align witt_vector.map_teichmuller_fun witt_vector.map_teichmuller_fun
 
 private theorem teichmuller_mul_aux₁ (x y : MvPolynomial R ℚ) :
     teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y :=
@@ -99,7 +97,6 @@ private theorem teichmuller_mul_aux₁ (x y : MvPolynomial R ℚ) :
   rw [RingHom.map_mul]
   ext1 n
   simp only [Pi.mul_apply, ghost_map_apply, ghost_component_teichmuller_fun, mul_pow]
-#align witt_vector.teichmuller_mul_aux₁ witt_vector.teichmuller_mul_aux₁
 
 private theorem teichmuller_mul_aux₂ (x y : MvPolynomial R ℤ) :
     teichmullerFun p (x * y) = teichmullerFun p x * teichmullerFun p y :=
@@ -108,7 +105,6 @@ private theorem teichmuller_mul_aux₂ (x y : MvPolynomial R ℤ) :
     map_injective (MvPolynomial.map (Int.castRingHom ℚ))
       (MvPolynomial.map_injective _ Int.cast_injective) _
   simp only [teichmuller_mul_aux₁, map_teichmuller_fun, RingHom.map_mul]
-#align witt_vector.teichmuller_mul_aux₂ witt_vector.teichmuller_mul_aux₂
 
 /-- The Teichmüller lift of an element of `R` to `𝕎 R`.
 The `0`-th coefficient of `teichmuller p r` is `r`, and all others are `0`.
Diff
@@ -72,7 +72,7 @@ private theorem ghost_component_teichmuller_fun (r : R) (n : ℕ) :
     tsub_zero]
   · rfl
   · intro i hi h0
-    convert mul_zero _
+    convert MulZeroClass.mul_zero _
     convert zero_pow _
     · cases i
       · contradiction

Changes in mathlib4

mathlib3
mathlib4
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

Diff
@@ -63,13 +63,8 @@ private theorem ghostComponent_teichmullerFun (r : R) (n : ℕ) :
   rw [ghostComponent_apply, aeval_wittPolynomial, Finset.sum_eq_single 0, pow_zero, one_mul,
     tsub_zero]
   · rfl
-  · intro i hi h0
-    convert mul_zero (M₀ := R) _
-    convert zero_pow (M := R) _
-    · cases i
-      · contradiction
-      · rfl
-    · exact pow_pos hp.1.pos _
+  · intro i _ h0
+    simp [teichmullerFun, h0, hp.1.ne_zero]
   · rw [Finset.mem_range]; intro h; exact (h (Nat.succ_pos n)).elim
 
 private theorem map_teichmullerFun (f : R →+* S) (r : R) :
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.

Diff
@@ -32,7 +32,7 @@ namespace WittVector
 
 open MvPolynomial
 
-variable (p : ℕ) {R S : Type _} [hp : Fact p.Prime] [CommRing R] [CommRing S]
+variable (p : ℕ) {R S : Type*} [hp : Fact p.Prime] [CommRing R] [CommRing S]
 
 local notation "𝕎" => WittVector p -- type as `\bbW`
 
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff
@@ -2,14 +2,11 @@
 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.teichmuller
-! leanprover-community/mathlib commit c0a51cf2de54089d69301befc4c73bbc2f5c7342
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.WittVector.Basic
 
+#align_import ring_theory.witt_vector.teichmuller from "leanprover-community/mathlib"@"c0a51cf2de54089d69301befc4c73bbc2f5c7342"
+
 /-!
 # Teichmüller lifts
 
feat: port RingTheory.WittVector.Teichmuller (#4845)

Dependencies 10 + 672

673 files ported (98.5%)
278052 lines ported (98.8%)
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The unported dependencies are