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values | kind stringclasses 379
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Mathlib.RingTheory.WittVector.Basic | {
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Mathlib.RingTheory.WittVector.Basic | {
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Mathlib.RingTheory.WittVector.Basic | {
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} | {
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} | {
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{
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Mathlib.RingTheory.WittVector.WittPolynomial | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Basic | {
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} | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Basic | {
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{
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Mathlib.RingTheory.WittVector.Basic | {
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} | {
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} | {
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{
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"usedConstants": [
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Mathlib.RingTheory.WittVector.Basic | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Basic | {
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} | {
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} | {
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} | [
{
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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} | {
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{
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Mathlib.RingTheory.WittVector.IsPoly | {
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} | {
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} | {
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"column": 2
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{
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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} | {
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} | {
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Mathlib.RingTheory.WittVector.IsPoly | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Perfection | {
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} | {
"line": 92,
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} | {
"line": 93,
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} | [
{
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Mathlib.RingTheory.WittVector.IsPoly | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Perfection | {
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} | {
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} | {
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} | [
{
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Mathlib.RingTheory.Perfection | {
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} | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Frobenius | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Perfection | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Perfection | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Frobenius | {
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} | {
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} | {
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{
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Mathlib.RingTheory.WittVector.Frobenius | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Perfection | {
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} | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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} | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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} | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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} | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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{
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.Frobenius | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.IsPoly | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.WittVector.StructurePolynomial | {
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Mathlib.RingTheory.Perfection | {
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Mathlib.RingTheory.WittVector.IsPoly | {
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Mathlib.RingTheory.WittVector.Verschiebung | {
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Mathlib.RingTheory.WittVector.Verschiebung | {
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{
"pp": "p : ℕ\nR : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\nx : 𝕎 R\nn : ℕ\n⊢ (ghostComponent (n + 1)) x.verschiebungFun = ↑p * (ghostComponent n) x",
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"assigned": true,
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"Eq.mpr",
"Finset.mul_sum",
"Nat.instCanonicallyOrderedAdd"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 318,
"column": 42
} | {
"line": 318,
"column": 44
} | {
"line": 318,
"column": 45
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommSemiring R\np : ℕ\nhp : Fact (Nat.Prime p)\ninst✝ : CharP R p\nh : Function.Surjective ⇑(frobenius R p)\nn : ℕ\nx : R\nm : ℕ\nh1 : ¬n ≤ m + 1\nh1' : ¬n ≤ m\n⊢ n - m = n - (m + 1) + 1",
"ppTerm": "?m.159",
"assigned": true,
"usedConstants": [
"_private.Mathli... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 81,
"column": 72
} | {
"line": 81,
"column": 74
} | {
"line": 82,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝ : CommRing R\nx : 𝕎 R\nn : ℕ\n⊢ (aeval x.coeff) (verschiebungPoly n) = x.verschiebungFun.coeff n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 91,
"column": 86
} | {
"line": 91,
"column": 88
} | {
"line": 92,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\n⊢ IsPoly p fun R _Rcr ↦ verschiebungFun",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"WittVector.aeval_verschiebung_poly'",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"C... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 112,
"column": 15
} | {
"line": 112,
"column": 17
} | {
"line": 113,
"column": 4
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nhp : Fact (Nat.Prime p)\n⊢ verschiebungFun 0 = 0",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableTrue",
"congrArg",
"WittVector.instCommRing",
"CommSem... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 115,
"column": 14
} | {
"line": 115,
"column": 16
} | {
"line": 116,
"column": 4
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nhp : Fact (Nat.Prime p)\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 301,
"column": 52
} | {
"line": 301,
"column": 54
} | {
"line": 302,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommSemiring R\np : ℕ\nhp : Fact (Nat.Prime p)\ninst✝ : CharP R p\nh : Function.Surjective ⇑(frobenius R p)\nn : ℕ\n⊢ Function.Surjective ⇑(coeff R p n)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
"NonAsso... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 127,
"column": 55
} | {
"line": 127,
"column": 57
} | {
"line": 128,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nS : Type u_2\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nhp : Fact (Nat.Prime p)\nf : R →+* S\nx : 𝕎 R\n⊢ (map f) (verschiebung x) = verschiebung ((map f) x)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"WittVector.instCommRing",
"CommSemiring.to... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 331,
"column": 17
} | {
"line": 331,
"column": 19
} | {
"line": 331,
"column": 20
} | [
{
"pp": "R✝ : Type u_1\ninst✝⁶ : CommSemiring R✝\np : ℕ\nhp : Fact (Nat.Prime p)\ninst✝⁵ : CharP R✝ p\nR : Type u₁\ninst✝⁴ : CommSemiring R\ninst✝³ : CharP R p\ninst✝² : PerfectRing R p\nS : Type u₂\ninst✝¹ : CommSemiring S\ninst✝ : CharP S p\nf : R →+* S\nr : R\nn : ℕ\n⊢ (fun n ↦ f ((⇑↑(frobeniusEquiv R p).sym... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 155,
"column": 82
} | {
"line": 155,
"column": 84
} | {
"line": 156,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝ : CommRing R\nhp : Fact (Nat.Prime p)\n⊢ Function.Injective ⇑verschiebung",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"AddMonoidHom.instAddMonoidHomClass",
"WittVector.verschiebung_coef... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 434,
"column": 61
} | {
"line": 434,
"column": 63
} | {
"line": 435,
"column": 12
} | [
{
"pp": "p : ℕ\ninst✝³ : Fact (Nat.Prime p)\nR : Type u₁\ninst✝² : CommSemiring R\ninst✝¹ : CharP R p\ninst✝ : PerfectRing R p\nf : ℕ → R\nhf : ∀ (n : ℕ), f (n + 1) ^ p = f n\nn✝ n : ℕ\nih : (⇑(frobeniusEquiv R p).symm)^[n] (f 0) = f n\n⊢ (⇑(frobeniusEquiv R p).symm)^[n.succ] (f 0) ^ p = f n.succ ^ p",
"ppT... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 226,
"column": 49
} | {
"line": 226,
"column": 51
} | {
"line": 227,
"column": 2
} | [
{
"pp": "p : ℕ\nR S : Type u\nidx : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nh : ⦃R : Type u_2⦄ → [CommRing R] → 𝕎 R → 𝕎 R → 𝕎 R\nf g : ⦃R : Type u_2⦄ → [CommRing R] → 𝕎 R → 𝕎 R\nhh : IsPoly₂ p h\nhf : IsPoly p f\nhg : IsPoly p g\n⊢ IsPoly₂ p fun x _Rcr x_1 y ↦ h (f x_1) (g y)",
"ppTerm": "?m... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 475,
"column": 16
} | {
"line": 475,
"column": 18
} | {
"line": 476,
"column": 4
} | [
{
"pp": "p : ℕ\ninst✝¹¹ : Fact (Nat.Prime p)\nR : Type u₁\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CharP R p\nP✝ : Type u₃\ninst✝⁸ : CommSemiring P✝\ninst✝⁷ : CharP P✝ p\ninst✝⁶ : PerfectRing P✝ p\ninst✝⁵ : PerfectRing R p\nS : Type u₂\ninst✝⁴ : CommSemiring S\ninst✝³ : CharP S p\nP : Type u₃\ninst✝² : CommSemiring ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 481,
"column": 27
} | {
"line": 481,
"column": 29
} | {
"line": 481,
"column": 30
} | [
{
"pp": "p : ℕ\ninst✝¹¹ : Fact (Nat.Prime p)\nR : Type u₁\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CharP R p\nP✝ : Type u₃\ninst✝⁸ : CommSemiring P✝\ninst✝⁷ : CharP P✝ p\ninst✝⁶ : PerfectRing P✝ p\ninst✝⁵ : PerfectRing R p\nS : Type u₂\ninst✝⁴ : CommSemiring S\ninst✝³ : CharP S p\nP : Type u₃\ninst✝² : CommSemiring ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 183,
"column": 7
} | {
"line": 183,
"column": 57
} | {
"line": 184,
"column": 6
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℕ → ℤ\nn : ℕ\nhn : ¬n.succ = 0\nk : ℕ\n⊢ (MvPolynomial.eval x) (verschiebungPoly k) = (aeval (mk p x).coeff) (verschiebungPoly k)",
"ppTerm": "?m.154",
"assigned": true,
"usedConstants": [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
... | [] | exact eval₂Hom_congr (RingHom.ext_int _ _) rfl rfl | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.Perfection | {
"line": 478,
"column": 17
} | {
"line": 478,
"column": 19
} | {
"line": 479,
"column": 4
} | [
{
"pp": "p : ℕ\ninst✝¹¹ : Fact (Nat.Prime p)\nR : Type u₁\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CharP R p\nP✝ : Type u₃\ninst✝⁸ : CommSemiring P✝\ninst✝⁷ : CharP P✝ p\ninst✝⁶ : PerfectRing P✝ p\ninst✝⁵ : PerfectRing R p\nS : Type u₂\ninst✝⁴ : CommSemiring S\ninst✝³ : CharP S p\nP : Type u₃\ninst✝² : CommSemiring ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 179,
"column": 61
} | {
"line": 179,
"column": 63
} | {
"line": 180,
"column": 7
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℕ → ℤ\nn : ℕ\nhn : ¬n.succ = 0\n⊢ (eval₂Hom ((MvPolynomial.eval x).comp C) fun i ↦ (MvPolynomial.eval x) (verschiebungPoly i))\n (wittPolynomial p ℤ (n + 1)) =\n (ghostComponent (n + 1)) (verschiebung (mk p x))",
"ppTerm": "?m.121",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 509,
"column": 30
} | {
"line": 509,
"column": 32
} | {
"line": 509,
"column": 33
} | [
{
"pp": "p : ℕ\ninst✝⁴ : Fact (Nat.Prime p)\nR : Type u₁\ninst✝³ : CommSemiring R\ninst✝² : CharP R p\nS : Type u₂\ninst✝¹ : CommSemiring S\ninst✝ : CharP S p\nφ : R →+* S\nf : Perfection R p\n⊢ (Perfection.coeff S p 0) ((map p ⋯ ⋯ φ) f) = (Perfection.coeff S p 0) ((Perfection.map p φ) f)",
"ppTerm": "?m.60... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 184,
"column": 15
} | {
"line": 184,
"column": 17
} | {
"line": 184,
"column": 18
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx : ℕ → ℤ\nn : ℕ\nhn : ¬n.succ = 0\n⊢ (ghostComponent (n + 1)) (verschiebung (mk p x)) = ↑p * (MvPolynomial.eval x) (wittPolynomial p ℤ n)",
"ppTerm": "?m.127",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonA... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Verschiebung | {
"line": 169,
"column": 61
} | {
"line": 169,
"column": 63
} | {
"line": 170,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ (bind₁ verschiebungPoly) (wittPolynomial p ℤ n) = if n = 0 then 0 else ↑p * wittPolynomial p ℤ (n - 1)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoid... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 243,
"column": 45
} | {
"line": 243,
"column": 47
} | {
"line": 244,
"column": 2
} | [
{
"pp": "p : ℕ\nR S : Type u\nidx : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\ng : ⦃R : Type u_2⦄ → [CommRing R] → 𝕎 R → 𝕎 R\nf : ⦃R : Type u_2⦄ → [CommRing R] → 𝕎 R → 𝕎 R → 𝕎 R\nhg : IsPoly p g\nhf : IsPoly₂ p f\n⊢ IsPoly₂ p fun x _Rcr x_1 y ↦ g (f x_1 y)",
"ppTerm": "?m.11",
"assigned": t... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 559,
"column": 69
} | {
"line": 559,
"column": 71
} | {
"line": 560,
"column": 2
} | [
{
"pp": "K : Type u₁\ninst✝² : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝¹ : CommRing O\ninst✝ : Algebra O K\nhv : v.Integers O\np : ℕ\nx : O\nhx : (Ideal.Quotient.mk (Ideal.span {↑p})) x ≠ 0\n⊢ preVal K v O p ((Ideal.Quotient.mk (Ideal.span {↑p})) x) = v ((algebraMap O K) x)",
"ppTerm": "?m.34",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 569,
"column": 26
} | {
"line": 569,
"column": 28
} | {
"line": 569,
"column": 29
} | [
{
"pp": "K : Type u₁\ninst✝² : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝¹ : CommRing O\ninst✝ : Algebra O K\nhv : v.Integers O\np : ℕ\nx y : ModP O p\nhxy0 : x * y ≠ 0\n⊢ x = 0 → x * y = 0",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule.Quotient.inst... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 570,
"column": 26
} | {
"line": 570,
"column": 28
} | {
"line": 570,
"column": 29
} | [
{
"pp": "K : Type u₁\ninst✝² : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝¹ : CommRing O\ninst✝ : Algebra O K\nhv : v.Integers O\np : ℕ\nx y : ModP O p\nhxy0 : x * y ≠ 0\nhx0 : x ≠ 0\n⊢ y = 0 → x * y = 0",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.MulP | {
"line": 49,
"column": 56
} | {
"line": 49,
"column": 58
} | {
"line": 50,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nn : ℕ\nx : 𝕎 R\nk : ℕ\n⊢ (x * ↑n).coeff k = (aeval x.coeff) (wittMulN p n k)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Distrib.leftDistribClass",
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.MulP | {
"line": 65,
"column": 34
} | {
"line": 65,
"column": 36
} | {
"line": 65,
"column": 37
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nR : Type u_2\n_Rcr : CommRing R\nx : 𝕎 R\n⊢ (x * ↑n).coeff = fun n_1 ↦ (aeval x.coeff) (wittMulN p n n_1)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"HMul.hMul",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 251,
"column": 81
} | {
"line": 251,
"column": 83
} | {
"line": 252,
"column": 2
} | [
{
"pp": "p : ℕ\nR S : Type u\nidx : Type u_1\ninst✝¹ : CommRing R\ninst✝ : CommRing S\nf : ⦃R : Type u_2⦄ → [CommRing R] → 𝕎 R → 𝕎 R → 𝕎 R\nhf : IsPoly₂ p f\n⊢ IsPoly p fun x _Rcr x_1 ↦ f x_1 x_1",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"WittVector.IsPoly₂.casesOn",
"E... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Perfection | {
"line": 568,
"column": 68
} | {
"line": 568,
"column": 70
} | {
"line": 569,
"column": 2
} | [
{
"pp": "K : Type u₁\ninst✝² : Field K\nv : Valuation K ℝ≥0\nO : Type u₂\ninst✝¹ : CommRing O\ninst✝ : Algebra O K\nhv : v.Integers O\np : ℕ\nx y : ModP O p\nhxy0 : x * y ≠ 0\n⊢ preVal K v O p (x * y) = preVal K v O p x * preVal K v O p y",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 262,
"column": 44
} | {
"line": 262,
"column": 46
} | {
"line": 263,
"column": 6
} | [
{
"pp": "p : ℕ\nR S : Type u\nidx : Type u_1\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\n⊢ ∀ ⦃R : Type u_2⦄ [inst : CommRing R] (x : 𝕎 R),\n (-x).coeff = fun n ↦ (aeval x.coeff) ((fun n ↦ (rename Prod.snd) (wittNeg p n)) n)",
"ppTerm": "?m.17",
"assigned": true,
"usedC... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 274,
"column": 7
} | {
"line": 274,
"column": 9
} | {
"line": 274,
"column": 10
} | [
{
"pp": "p : ℕ\nR S : Type u\nidx : Type u_1\ninst✝² : CommRing R\ninst✝¹ : CommRing S\ninst✝ : Fact (Nat.Prime p)\n⊢ ∀ ⦃R : Type u_2⦄ [inst : CommRing R] (x : 𝕎 R), coeff 0 = fun n ↦ (aeval x.coeff) (0 n)",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"WittVector.instZero",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.IsPoly | {
"line": 278,
"column": 67
} | {
"line": 278,
"column": 69
} | {
"line": 279,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nn : ℕ\n⊢ (bind₁ 0) (wittPolynomial p R n) = 0",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.MulP | {
"line": 69,
"column": 78
} | {
"line": 69,
"column": 80
} | {
"line": 70,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn k : ℕ\n⊢ (bind₁ (wittMulN p n)) (wittPolynomial p ℤ k) = ↑n * wittPolynomial p ℤ k",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"CharP.cast_eq_zero",
"add_mul",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Identities | {
"line": 44,
"column": 81
} | {
"line": 44,
"column": 83
} | {
"line": 45,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nhp : Fact (Nat.Prime p)\ninst✝ : CommRing R\nx : 𝕎 R\n⊢ frobenius (verschiebung x) = x * ↑p",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"NonAssocSemiring.toAddCommMonoidWithOne",
... | [] | by | [anonymous] | by |
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