module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.WittVector.WittPolynomial | {
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} | {
"line": 149,
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{
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Mathlib.RingTheory.WittVector.WittPolynomial | {
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} | {
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} | {
"line": 164,
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{
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Mathlib.RingTheory.NoetherNormalization | {
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{
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Mathlib.RingTheory.WittVector.WittPolynomial | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.WittPolynomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.WittVector.WittPolynomial | {
"line": 200,
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} | {
"line": 200,
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} | {
"line": 201,
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{
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"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Teichmuller | {
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} | {
"line": 41,
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} | {
"line": 42,
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{
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Mathlib.RingTheory.NoetherNormalization | {
"line": 161,
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} | {
"line": 161,
"column": 27
} | {
"line": 161,
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} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nf : MvPolynomial (Fin (n + 1)) k\nfne : f ≠ 0\nv : Fin (n + 1) →₀ ℕ\nvin : v ∈ f.support\nh : (Fin (n + 1) →₀ ℕ) → MvPolynomial (Fin (n + 1)) k := fun w ↦ (MvPolynomial.monomial w) (MvPolynomial.coeff w f)\nvs :\n ∀ x ∈ f.support \\ {v},\n ((MvPolynomial.finSuc... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Teichmuller | {
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} | {
"line": 36,
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} | {
"line": 37,
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{
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"ppTerm": "?m.35",
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Mathlib.RingTheory.Teichmuller | {
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} | {
"line": 47,
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"line": 47,
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{
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"ppTerm": "?m.25",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
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} | {
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} | {
"line": 163,
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{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nf : MvPolynomial (Fin (n + 1)) k\nfne : f ≠ 0\nv : Fin (n + 1) →₀ ℕ\nvin : v ∈ f.support\nh : (Fin (n + 1) →₀ ℕ) → MvPolynomial (Fin (n + 1)) k := fun w ↦ (MvPolynomial.monomial w) (MvPolynomial.coeff w f)\nvs :\n ∀ x ∈ f.support \\ {v},\n ((MvPolynomial.finSuc... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Teichmuller | {
"line": 69,
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} | {
"line": 69,
"column": 94
} | {
"line": 70,
"column": 4
} | [
{
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Mathlib.RingTheory.Teichmuller | {
"line": 66,
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} | {
"line": 66,
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} | {
"line": 67,
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{
"pp": "p : ℕ\ninst✝³ : Fact (Nat.Prime p)\nR : Type u_1\ninst✝² : CommRing R\nI : Ideal R\ninst✝¹ : CharP (R ⧸ I) p\ninst✝ : IsPrecomplete I R\nx : Perfection (R ⧸ I) p\ny : R\nn : ℕ\nh : (Ideal.Quotient.mk I) y = (coeff (R ⧸ I) p n) x\n⊢ x.teichmullerFun ≡ y ^ p ^ n [SMOD I ^ (n + 1)]",
"ppTerm": "?m.52"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
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} | {
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} | {
"line": 158,
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{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nf : MvPolynomial (Fin (n + 1)) k\nfne : f ≠ 0\nv : Fin (n + 1) →₀ ℕ\nvin : v ∈ f.support\nh : (Fin (n + 1) →₀ ℕ) → MvPolynomial (Fin (n + 1)) k := fun w ↦ (MvPolynomial.monomial w) (MvPolynomial.coeff w f)\nvs :\n ∀ x ∈ f.support \\ {v},\n ((MvPolynomial.finSuc... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Teichmuller | {
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} | {
"line": 85,
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{
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Mathlib.RingTheory.WittVector.WittPolynomial | {
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} | {
"line": 205,
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} | {
"line": 206,
"column": 2
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{
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Mathlib.RingTheory.Teichmuller | {
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{
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Mathlib.RingTheory.WittVector.WittPolynomial | {
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} | {
"line": 216,
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} | {
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{
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Mathlib.RingTheory.Teichmuller | {
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} | {
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} | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Teichmuller | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Teichmuller | {
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{
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Mathlib.RingTheory.NoetherNormalization | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
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Mathlib.RingTheory.Teichmuller | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
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Mathlib.RingTheory.Teichmuller | {
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} | {
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{
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Mathlib.RingTheory.NoetherNormalization | {
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Mathlib.RingTheory.NoetherNormalization | {
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Mathlib.RingTheory.Teichmuller | {
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{
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Mathlib.RingTheory.NoetherNormalization | {
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Mathlib.RingTheory.Teichmuller | {
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Mathlib.RingTheory.NoetherNormalization | {
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} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nf : MvPolynomial (Fin (n + 1)) k\nv w : Fin (n + 1) →₀ ℕ\nI : Ideal (MvPolynomial (Fin (n + 1)) k)\n⊢ Ideal.map ((T f).symm.toRingEquiv.toRingHom.comp ↑(T f)) I = Ideal.map (↑(T f).symm) (Ideal.map (T f) I)",
"ppTerm": "?m.140",
"assigned": true,
"usedC... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 209,
"column": 59
} | {
"line": 209,
"column": 61
} | {
"line": 210,
"column": 2
} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nf : MvPolynomial (Fin (n + 1)) k\nv w : Fin (n + 1) →₀ ℕ\nI : Ideal (MvPolynomial (Fin (n + 1)) k)\n⊢ I = Ideal.map (↑(T f).symm) (Ideal.map (T f) I)",
"ppTerm": "?m.91",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.m... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Teichmuller | {
"line": 201,
"column": 43
} | {
"line": 201,
"column": 45
} | {
"line": 201,
"column": 46
} | [
{
"pp": "p✝ : ℕ\ninst✝⁷ : Fact (Nat.Prime p✝)\nR✝ : Type u_1\ninst✝⁶ : CommRing R✝\nI✝ : Ideal R✝\ninst✝⁵ : CharP (R✝ ⧸ I✝) p✝\ninst✝⁴ : IsAdicComplete I✝ R✝\np : ℕ\ninst✝³ : Fact (Nat.Prime p)\nR : Type u_2\ninst✝² : CommRing R\nI : Ideal R\ninst✝¹ : CharP (R ⧸ I) p\ninst✝ : IsAdicComplete I R\n⊢ (liftMonoidHo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Teichmuller | {
"line": 202,
"column": 43
} | {
"line": 202,
"column": 45
} | {
"line": 202,
"column": 46
} | [
{
"pp": "p✝ : ℕ\ninst✝⁷ : Fact (Nat.Prime p✝)\nR✝ : Type u_1\ninst✝⁶ : CommRing R✝\nI✝ : Ideal R✝\ninst✝⁵ : CharP (R✝ ⧸ I✝) p✝\ninst✝⁴ : IsAdicComplete I✝ R✝\np : ℕ\ninst✝³ : Fact (Nat.Prime p)\nR : Type u_2\ninst✝² : CommRing R\nI : Ideal R\ninst✝¹ : CharP (R ⧸ I) p\ninst✝ : IsAdicComplete I R\n⊢ (liftMonoidHo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Teichmuller | {
"line": 208,
"column": 82
} | {
"line": 208,
"column": 84
} | {
"line": 209,
"column": 2
} | [
{
"pp": "p : ℕ\ninst✝³ : Fact (Nat.Prime p)\nR : Type u_1\ninst✝² : CommRing R\nI : Ideal R\ninst✝¹ : CharP (R ⧸ I) p\ninst✝ : IsAdicComplete I R\nx : Perfection (R ⧸ I) p\n⊢ (coeffMonoidHom R p 0) ((quotientMulEquiv p I).symm x) = (teichmuller₀ p I) x",
"ppTerm": "?m.33",
"assigned": true,
"usedCon... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 148,
"column": 48
} | {
"line": 148,
"column": 50
} | {
"line": 149,
"column": 6
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ (bind₁ (wittStructureRat p Φ)) (W_ ℚ n) =\n (bind₁ fun k ↦ (bind₁ fun i ↦ (rename (Prod.mk i)) (W_ ℚ k)) Φ) ((bind₁ (xInTermsOfW p ℚ)) (W_ ℚ n))",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 150,
"column": 58
} | {
"line": 150,
"column": 60
} | {
"line": 151,
"column": 6
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ (bind₁ fun k ↦ (bind₁ fun i ↦ (rename (Prod.mk i)) (W_ ℚ k)) Φ) ((bind₁ (xInTermsOfW p ℚ)) (W_ ℚ n)) =\n (bind₁ fun i ↦ (rename (Prod.mk i)) (W_ ℚ n)) Φ",
"ppTerm": "?m.90",
"assigned": true,
"usedConstants"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.WittPolynomial | {
"line": 231,
"column": 4
} | {
"line": 231,
"column": 29
} | {
"line": 232,
"column": 4
} | [
{
"pp": "case ind\np : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nih : ∀ m < n, m ∈ (xInTermsOfW p ℚ m).vars ∧ (xInTermsOfW p ℚ m).vars ⊆ range (m + 1)\ni : ℕ\n⊢ i ∈ {n} ∪ (∑ i ∈ range n, C (↑p ^ i) * xInTermsOfW p ℚ i ^ p ^ (n - i)).vars → i ∈ {n} ∪ range n",
"ppTerm": "?ind",
"assigned": true,
"usedConsta... | [
"case ind\np : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nih : ∀ m < n, m ∈ (xInTermsOfW p ℚ m).vars ∧ (xInTermsOfW p ℚ m).vars ⊆ range (m + 1)\ni : ℕ\n⊢ i ∈ {n} ∨ i ∈ (∑ i ∈ range n, C (↑p ^ i) * xInTermsOfW p ℚ i ^ p ^ (n - i)).vars → i ∈ {n} ∨ i ∈ range n"
] | rw [mem_union, mem_union] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.NoetherNormalization | {
"line": 249,
"column": 34
} | {
"line": 249,
"column": 36
} | {
"line": 250,
"column": 6
} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nI : Ideal (MvPolynomial (Fin 0) k)\nhi : I ≠ ⊤\na b : MvPolynomial (Fin 0) k\nhab : a - b ∈ I\nne✝ : ¬a = b\neq : a - b = MvPolynomial.C (MvPolynomial.coeff 0 (a - b))\nne : MvPolynomial.coeff 0 (a - b) ≠ 0\nc : k\nleft✝ : MvPolynomial.coeff 0 (a - b) * c = 1\neqr ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 155,
"column": 84
} | {
"line": 155,
"column": 86
} | {
"line": 156,
"column": 2
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\n⊢ ∃! φ, ∀ (n : ℕ), (bind₁ φ) (W_ ℚ n) = (bind₁ fun i ↦ (rename (Prod.mk i)) (W_ ℚ n)) Φ",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"RingHom.instRingHomClass",
"wittPolynomial",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 262,
"column": 27
} | {
"line": 262,
"column": 29
} | {
"line": 263,
"column": 10
} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn d : ℕ\nhd : ∀ (I : Ideal (MvPolynomial (Fin d) k)), I ≠ ⊤ → ∃ s ≤ d, ∃ g, Function.Injective ⇑g ∧ g.IsIntegral\nI : Ideal (MvPolynomial (Fin (d + 1)) k)\nhi : I ≠ ⊤\neqi : ¬I = 0\nf : MvPolynomial (Fin (d + 1)) k\nfi : f ∈ I\nfne : f ≠ 0\nϕ : MvPolynomial (Fin d) k ⧸ ke... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 264,
"column": 16
} | {
"line": 264,
"column": 18
} | {
"line": 264,
"column": 19
} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn d : ℕ\nhd : ∀ (I : Ideal (MvPolynomial (Fin d) k)), I ≠ ⊤ → ∃ s ≤ d, ∃ g, Function.Injective ⇑g ∧ g.IsIntegral\nI : Ideal (MvPolynomial (Fin (d + 1)) k)\nhi : I ≠ ⊤\neqi : ¬I = 0\nf : MvPolynomial (Fin (d + 1)) k\nfi : f ∈ I\nfne : f ≠ 0\nϕ : MvPolynomial (Fin d) k ⧸ ke... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 239,
"column": 43
} | {
"line": 239,
"column": 45
} | {
"line": 240,
"column": 2
} | [
{
"pp": "k : Type u_1\ninst✝ : Field k\nn : ℕ\nI : Ideal (MvPolynomial (Fin n) k)\nhi : I ≠ ⊤\n⊢ ∃ s ≤ n, ∃ g, Function.Injective ⇑g ∧ g.IsIntegral",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Nontrivial",
"Iff.mpr",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 168,
"column": 81
} | {
"line": 168,
"column": 83
} | {
"line": 169,
"column": 2
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ wittStructureRat p Φ n * C (↑p ^ n) =\n (bind₁ fun b ↦ (rename fun i ↦ (b, i)) (W_ ℚ n)) Φ -\n ∑ i ∈ Finset.range n, C (↑p ^ i) * wittStructureRat p Φ i ^ p ^ (n - i)",
"ppTerm": "?m.80",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 277,
"column": 43
} | {
"line": 277,
"column": 45
} | {
"line": 278,
"column": 2
} | [
{
"pp": "k : Type u_2\nR : Type u_3\ninst✝² : Field k\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\na : Algebra k R\nfin : Algebra.FiniteType k R\n⊢ ∃ s g, Function.Injective ⇑g ∧ g.IsIntegral",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AlgEquiv.instEquivLike",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 186,
"column": 13
} | {
"line": 186,
"column": 15
} | {
"line": 186,
"column": 16
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ C (1 / ↑p ^ n) * (wittStructureRat p Φ n * C (↑p ^ n)) =\n C (1 / ↑p ^ n) *\n ((bind₁ fun b ↦ (rename fun i ↦ (b, i)) (W_ ℚ n)) Φ -\n ∑ i ∈ Finset.range n, C (↑p ^ i) * wittStructureRat p Φ i ^ p ^ (n - i))"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 292,
"column": 88
} | {
"line": 292,
"column": 90
} | {
"line": 293,
"column": 4
} | [
{
"pp": "k : Type u_2\nR : Type u_3\ninst✝² : Field k\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\na : Algebra k R\nfin : Algebra.FiniteType k R\ns : ℕ\ng : MvPolynomial (Fin s) k →ₐ[k] R\ninj : Function.Injective ⇑g\nint : g.IsIntegral\n⊢ algebraMap k R = g.comp (algebraMap k (MvPolynomial (Fin s) k))",
"pp... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.NoetherNormalization | {
"line": 290,
"column": 39
} | {
"line": 290,
"column": 41
} | {
"line": 291,
"column": 2
} | [
{
"pp": "k : Type u_2\nR : Type u_3\ninst✝² : Field k\ninst✝¹ : CommRing R\ninst✝ : Nontrivial R\na : Algebra k R\nfin : Algebra.FiniteType k R\n⊢ ∃ s g, Function.Injective ⇑g ∧ g.Finite",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"RingHom.finiteType_algebraMap",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 77,
"column": 68
} | {
"line": 77,
"column": 70
} | {
"line": 78,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\nx y : 𝕎 R\nh : ∀ (n : ℕ), x.coeff n = y.coeff n\n⊢ x = y",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"congrArg",
"WittVector.mk'.injEq",
"WittVector.casesOn",
"_private.Mathlib.RingTheory.WittVector.Defs.0.WittVector.ext._simp_1_1",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 210,
"column": 55
} | {
"line": 210,
"column": 57
} | {
"line": 211,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ wittZero p n = 0",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"AlgHom.algHo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 216,
"column": 49
} | {
"line": 216,
"column": 51
} | {
"line": 217,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ wittOne p 0 = 1",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"AlgHom.algHomClass",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 183,
"column": 84
} | {
"line": 183,
"column": 86
} | {
"line": 184,
"column": 2
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℚ\nn : ℕ\n⊢ wittStructureRat p Φ n =\n C (1 / ↑p ^ n) *\n ((bind₁ fun b ↦ (rename fun i ↦ (b, i)) (W_ ℚ n)) Φ -\n ∑ i ∈ Finset.range n, C (↑p ^ i) * wittStructureRat p Φ i ^ p ^ (n - i))",
"ppTerm": "?m.86",
"as... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.WittPolynomial | {
"line": 224,
"column": 79
} | {
"line": 224,
"column": 81
} | {
"line": 225,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ n ∈ (xInTermsOfW p ℚ n).vars ∧ (xInTermsOfW p ℚ n).vars ⊆ range (n + 1)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"MvPolynomial.vars_X",
"Finsupp.instAddZeroClass",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommS... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.WittPolynomial | {
"line": 257,
"column": 80
} | {
"line": 257,
"column": 82
} | {
"line": 258,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Invertible ↑p\nn : ℕ\n⊢ xInTermsOfW p R n * C (↑p ^ n) = X n - ∑ i ∈ range n, C (↑p ^ i) * xInTermsOfW p R i ^ p ^ (n - i)",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"one_pow",
"Finsupp.instAddZeroClass",
"Eq... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 222,
"column": 70
} | {
"line": 222,
"column": 72
} | {
"line": 223,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nhn : 0 < n\n⊢ wittOne p n = 0",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"one_pow",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"RingHom.instRingHomClass",
"MulOne.toOne",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.StructurePolynomial | {
"line": 215,
"column": 69
} | {
"line": 215,
"column": 71
} | {
"line": 216,
"column": 2
} | [
{
"pp": "p : ℕ\nidx : Type u_2\nhp : Fact (Nat.Prime p)\nΦ : MvPolynomial idx ℤ\nn : ℕ\nIH :\n ∀ m < n + 1, (map (Int.castRingHom ℚ)) (wittStructureInt p Φ m) = wittStructureRat p ((map (Int.castRingHom ℚ)) Φ) m\n⊢ (bind₁ fun b ↦ (rename fun i ↦ (b, i)) ((expand p) (W_ ℤ n))) Φ =\n (bind₁ fun i ↦ (expand p)... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 239,
"column": 60
} | {
"line": 239,
"column": 62
} | {
"line": 240,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ wittAdd p 0 = X (0, 0) + X (1, 0)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.instMulZeroCl... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 245,
"column": 60
} | {
"line": 245,
"column": 62
} | {
"line": 246,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ wittSub p 0 = X (0, 0) - X (1, 0)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"M... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 251,
"column": 60
} | {
"line": 251,
"column": 62
} | {
"line": 252,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ wittMul p 0 = X (0, 0) * X (1, 0)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"A... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 257,
"column": 50
} | {
"line": 257,
"column": 52
} | {
"line": 258,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ wittNeg p 0 = -X (0, 0)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"NegZeroClass.toNeg",
"RingHom.instRingHomClass",
"wittPolynomial",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.s... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 263,
"column": 75
} | {
"line": 263,
"column": 77
} | {
"line": 264,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ constantCoeff (wittAdd p n) = 0",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Nat.instMulZeroClass",
"AddMono... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 268,
"column": 75
} | {
"line": 268,
"column": 77
} | {
"line": 269,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ constantCoeff (wittSub p n) = 0",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Finsupp.instAddZeroClass",
"RingHom.instRingHomClass",
"Nat.instMulZeroClass",
"RingHomClass.toAddMonoidHo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 273,
"column": 75
} | {
"line": 273,
"column": 77
} | {
"line": 274,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\n⊢ constantCoeff (wittMul p n) = 0",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"RingHom.instRingHomClass",
"Nat.instMulZeroClass",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Defs | {
"line": 278,
"column": 75
} | {
"line": 278,
"column": 77
} | {
"line": 279,
"column": 2
} | [
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.WittPolynomial | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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Mathlib.RingTheory.WittVector.Defs | {
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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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Mathlib.RingTheory.WittVector.Basic | {
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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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Mathlib.RingTheory.WittVector.Basic | {
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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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Mathlib.RingTheory.WittVector.Basic | {
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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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Mathlib.RingTheory.WittVector.Basic | {
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"Finsupp.instAddZeroClass",
"Int.cast",
"Eq.mpr",
"Fin.last_zero",
"instNeZeroNa... | [] | by | [anonymous] | by |
Mathlib.RingTheory.WittVector.Basic | {
"line": 203,
"column": 76
} | {
"line": 203,
"column": 78
} | {
"line": 204,
"column": 2
} | [
{
"pp": "p : ℕ\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Fact (Nat.Prime p)\nx : 𝕎 R\nm : ℕ\n⊢ (x ^ m).ghostFun = x.ghostFun ^ m",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"wittPolynomial",
"Nat.instMulZeroClass",
... | [] | by | [anonymous] | by |
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