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.MvPolynomial.IrreducibleQuadratic | {
"line": 140,
"column": 18
} | {
"line": 140,
"column": 20
} | {
"line": 141,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\nH : IsUnit p\n⊢ False",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 111,
"column": 4
} | {
"line": 111,
"column": 13
} | {
"line": 112,
"column": 4
} | [
{
"pp": "case refine_1\nn m : ℕ\nhmn : m ≤ n\ns : Fin m → ℕ\nhs : Antitone s\nx✝¹ : Fin m\ni✝ : ℕ\nthis : i✝ ≤ m - 1\ni : ℕ\nhi : i + 1 < m\nx✝ : i✝ ≤ i\nih : ∀ (hi : i + 1 < m), (accumulate n m) (invAccumulate n m s) ⟨i + 1, hi⟩ = s ⟨i + 1, hi⟩\nhim : i < m\n⊢ s ⟨↑⟨i, ⋯⟩, him⟩ - s ⟨↑⟨i, ⋯⟩ + 1, hi⟩ + s ⟨i + 1,... | [
"case refine_1\nn m : ℕ\nhmn : m ≤ n\ns : Fin m → ℕ\nhs : Antitone s\nx✝¹ : Fin m\ni✝ : ℕ\nthis : i✝ ≤ m - 1\ni : ℕ\nhi : i + 1 < m\nx✝ : i✝ ≤ i\nih : ∀ (hi : i + 1 < m), (accumulate n m) (invAccumulate n m s) ⟨i + 1, hi⟩ = s ⟨i + 1, hi⟩\nhim : i < m\n⊢ s ⟨i, him⟩ - s ⟨i + 1, hi⟩ + s ⟨i + 1, hi⟩ = s ⟨i, him⟩"
] | simp only | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.LaurentSeries | {
"line": 793,
"column": 29
} | {
"line": 793,
"column": 31
} | {
"line": 793,
"column": 32
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nU : Set K⸨X⸩\nhU : U ∈ 𝓝 (limit hℱ)\nγ : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ\nhU₁ : {y | Valued.v.restrict (y - limit hℱ) < ↑γ} ⊆ U\nD : ℤ := -((embedding ↑γ).log - 1)\nhD₀ : D = -((embedding ↑γ).log - 1)\n⊢ embedding ↑γ ≠ 0"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 144,
"column": 23
} | {
"line": 144,
"column": 25
} | {
"line": 144,
"column": 26
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\na b : MvPolynomial n R\nhab : p = a * b\nthis : ∀ (a b : MvPolynomial n R), p = a * b → a.totalDegree ≤ b.totalDegree → IsUnit ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 144,
"column": 47
} | {
"line": 144,
"column": 49
} | {
"line": 144,
"column": 50
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\na b : MvPolynomial n R\nhab : p = a * b\nthis : ∀ (a b : MvPolynomial n R), p = a * b → a.totalDegree ≤ b.totalDegree → IsUnit ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 792,
"column": 40
} | {
"line": 792,
"column": 42
} | {
"line": 793,
"column": 4
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nU : Set K⸨X⸩\nhU : U ∈ 𝓝 (limit hℱ)\nγ : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ\nhU₁ : {y | Valued.v.restrict (y - limit hℱ) < ↑γ} ⊆ U\nD : ℤ := -((embedding ↑γ).log - 1)\nhD₀ : D = -((embedding ↑γ).log - 1)\n⊢ exp (-D) < embedd... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 105,
"column": 72
} | {
"line": 105,
"column": 74
} | {
"line": 106,
"column": 2
} | [
{
"pp": "n m : ℕ\nhmn : m ≤ n\ns : Fin m → ℕ\nhs : Antitone s\nx✝ : Fin m\ni : ℕ\nhi : i < m\n⊢ (accumulate n m) (invAccumulate n m s) ⟨i, hi⟩ = s ⟨i, hi⟩",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.not_gt",
"Eq.mpr",
"Preorder.toLT",
"Nat.succ_eq_add_one",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 147,
"column": 48
} | {
"line": 147,
"column": 50
} | {
"line": 148,
"column": 6
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\na b : MvPolynomial n R\nhab : p = a * b\nhle : a.totalDegree ≤ b.totalDegree\nha₀ : a ≠ 0\nhb₀ : b ≠ 0\n⊢ a.totalDegree + b.tot... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 143,
"column": 91
} | {
"line": 143,
"column": 93
} | {
"line": 144,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_3\nn : ℕ\ninst✝² : CommSemiring R\ninst✝¹ : Fintype σ\ninst✝ : Fintype τ\ne : σ ≃ τ\n⊢ (↑(renameSymmetricSubalgebra e)).comp (esymmAlgHom σ R n) = esymmAlgHom τ R n",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 149,
"column": 86
} | {
"line": 149,
"column": 88
} | {
"line": 149,
"column": 89
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\na b : MvPolynomial n R\nhab : p = a * b\nhle : a.totalDegree ≤ b.totalDegree\nha₀ : a ≠ 0\nhb₀ : b ≠ 0\nthis : a.totalDegree + ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 150,
"column": 24
} | {
"line": 150,
"column": 26
} | {
"line": 150,
"column": 27
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\nb : MvPolynomial n R\nhb₀ : b ≠ 0\nr : R\nhab : p = C r * b\nhle : (C r).totalDegree ≤ b.totalDegree\nha₀ : C r ≠ 0\nthis : (C ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 142,
"column": 30
} | {
"line": 142,
"column": 32
} | {
"line": 143,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\np : MvPolynomial n R\nhp : p.totalDegree = 1\nhp' : ∀ (x : R), (∀ (i : n →₀ ℕ), x ∣ coeff i p) → IsUnit x\na b : MvPolynomial n R\nhab : p = a * b\n⊢ IsUnit a ∨ IsUnit b",
"ppTerm": "?m.31",
"assigned": true,
"usedConstant... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 159,
"column": 82
} | {
"line": 159,
"column": 84
} | {
"line": 160,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\nn k : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : Fintype σ\ni : Fin n\nr : R\n⊢ esymmAlgHomMonomial σ (fun₀ | i => k) r = C r * esymm σ R (↑i + 1) ^ k",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
"Finsupp.instAddZeroCla... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 168,
"column": 32
} | {
"line": 168,
"column": 34
} | {
"line": 168,
"column": 35
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nc : n →₀ R\ni : n\n⊢ i ∉ c.support → coeff (Finsupp.single i 1) (c i • X i) = 0",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoidAlgebra.ins... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 165,
"column": 76
} | {
"line": 165,
"column": 78
} | {
"line": 166,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\nn k : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : Fintype σ\ni : Fin n\n⊢ esymmAlgHomMonomial σ (fun₀ | i => k) 1 = esymm σ R (↑i + 1) ^ k",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 169,
"column": 95
} | {
"line": 169,
"column": 97
} | {
"line": 170,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\nn : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : Fintype σ\nr : R\nt s : Fin n →₀ ℕ\n⊢ esymmAlgHomMonomial σ (t + s) r = esymmAlgHomMonomial σ t r * esymmAlgHomMonomial σ s 1",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 172,
"column": 75
} | {
"line": 172,
"column": 77
} | {
"line": 173,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\nn : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : Fintype σ\nr : R\n⊢ esymmAlgHomMonomial σ 0 r = C r",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"MvPolynomial.esymmAlgHom... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 165,
"column": 53
} | {
"line": 165,
"column": 55
} | {
"line": 166,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝ : CommRing R\nc : n →₀ R\ni : n\n⊢ coeff (Finsupp.single i 1) (sumSMulX c) = c i",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoidAlgebra.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 786,
"column": 72
} | {
"line": 786,
"column": 74
} | {
"line": 787,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nU : Set K⸨X⸩\nhU : U ∈ 𝓝 (limit hℱ)\n⊢ ∀ᶠ (f : K⸨X⸩) in ℱ, f ∈ U",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"WithZero.instNontrivial",
"Filter.instMembership",
"Mul... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 824,
"column": 47
} | {
"line": 824,
"column": 49
} | {
"line": 825,
"column": 6
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nF : K⟦X⟧\nη : (WithZero (Multiplicative ℤ))ˣ\nh_neg : Multiplicative.toAdd (unzero ⋯) ≤ 0\nd : ℕ\nhd : Multiplicative.toAdd (unzero ⋯) = -↑d\n⊢ Valued.v ((ofPowerSeries ℤ K) (F - ↑((trunc (d + 1)) F))) ≤ ↑(Multiplicative.ofAdd (-(↑d + 1)))",
"ppTerm": "?m.170",
"a... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 190,
"column": 41
} | {
"line": 190,
"column": 43
} | {
"line": 191,
"column": 8
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc_gcd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nh : ∀ m ∈ (sumSMulX c).support, ∀ (x : n), m x = 0\ni : n\nhi : c i ≠ 0\n⊢ Finsupp.single i 1 ∈ (sumSMulX c).support",
"ppTerm": "?m.90",
"assigned": true,
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 185,
"column": 47
} | {
"line": 185,
"column": 49
} | {
"line": 186,
"column": 4
} | [
{
"pp": "R : Type u_3\nm : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\ni : ℕ\nhim : i < m\nt : Finset (Fin m)\nht : t ∈ powersetCard (i + 1) univ\nhne : t ≠ Iic ⟨i, him⟩\n⊢ #t = #(Iic ⟨i, him⟩)",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.univ",
... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 178,
"column": 32
} | {
"line": 178,
"column": 34
} | {
"line": 179,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc_nonempty : c.support.Nonempty\nhc_gcd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\n⊢ Irreducible (sumSMulX c)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 213,
"column": 15
} | {
"line": 213,
"column": 17
} | {
"line": 213,
"column": 18
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\ni j : n\n⊢ (fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1) i =\n (fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.sin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 815,
"column": 67
} | {
"line": 815,
"column": 69
} | {
"line": 816,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nF : K⟦X⟧\nη : (WithZero (Multiplicative ℤ))ˣ\n⊢ ∃ P, (PowerSeries.idealX K).intValuation (F - ↑P) < ↑η",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Algebra.cast",
"WithZero.instNontrivial",
"MvPower... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 214,
"column": 59
} | {
"line": 214,
"column": 61
} | {
"line": 215,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nι : n ↪ n ⊕ n →₀ ℕ := { toFun := fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1, inj' := ⋯ }\n⊢ sumSMulXSMulY c = AddMonoi... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 219,
"column": 63
} | {
"line": 219,
"column": 65
} | {
"line": 220,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nι : n ↪ n ⊕ n →₀ ℕ := { toFun := fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1, inj' := ⋯ }\naux : sumSMulXSMulY c = AddM... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 221,
"column": 62
} | {
"line": 221,
"column": 64
} | {
"line": 222,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nι : n ↪ n ⊕ n →₀ ℕ := { toFun := fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1, inj' := ⋯ }\naux : sumSMulXSMulY c = AddM... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 852,
"column": 45
} | {
"line": 852,
"column": 47
} | {
"line": 852,
"column": 48
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nf : K⸨X⸩\nγ : (WithZero (Multiplicative ℤ))ˣ\nF : K⟦X⟧ := f.powerSeriesPart\nhF : F = f.powerSeriesPart\nord_nonpos : HahnSeries.order f < 0\nη : (WithZero (Multiplicative ℤ))ˣ := Units.mk0 (exp (HahnSeries.order f)) ⋯\nhη : η = Units.mk0 (exp (HahnSeries.order f)) ⋯\nP :... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 178,
"column": 45
} | {
"line": 178,
"column": 47
} | {
"line": 179,
"column": 2
} | [
{
"pp": "R : Type u_3\nm : ℕ\ninst✝¹ : CommSemiring R\ninst✝ : Nontrivial R\ni : ℕ\nhim : i < m\n⊢ supDegree (⇑toLex) (esymm (Fin m) R (i + 1)) = toLex (Finsupp.indicator (Iic ⟨i, him⟩) fun x x_1 ↦ 1) ∧\n Monic (⇑toLex) (esymm (Fin m) R (i + 1))",
"ppTerm": "?m.53",
"assigned": true,
"usedConstan... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 226,
"column": 39
} | {
"line": 226,
"column": 46
} | {
"line": 226,
"column": 47
} | [
{
"pp": "case hd\nn : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nι : n ↪ n ⊕ n →₀ ℕ := { toFun := fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1, inj' := ⋯ }\naux : sumSMulXSMulY... | [
"case hd\nn : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nι : n ↪ n ⊕ n →₀ ℕ := { toFun := fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1, inj' := ⋯ }\naux : sumSMulXSMulY c = AddMono... | hcoeff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 201,
"column": 96
} | {
"line": 201,
"column": 98
} | {
"line": 202,
"column": 2
} | [
{
"pp": "R : Type u_3\nn m : ℕ\ninst✝¹ : CommSemiring R\ni : Fin n\ninst✝ : Nontrivial R\nhim : ↑i < m\n⊢ ⇑(ofLex (supDegree (⇑toLex) (esymm (Fin m) R (↑i + 1)))) = (accumulate n m) ⇑fun₀ | i => 1",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Finsupp.i... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 207,
"column": 77
} | {
"line": 207,
"column": 79
} | {
"line": 208,
"column": 2
} | [
{
"pp": "R : Type u_3\nm : ℕ\ninst✝ : CommSemiring R\ni : ℕ\nhim : i ≤ m\n⊢ Monic (⇑toLex) (esymm (Fin m) R i)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Nontrivial",
"Finsupp.instAddZeroClass",
"Finsupp.indicator",
"Eq.mpr",
"Nat.instCanonicallyOrderedA... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 217,
"column": 64
} | {
"line": 217,
"column": 66
} | {
"line": 218,
"column": 2
} | [
{
"pp": "R : Type u_3\nn m : ℕ\ninst✝ : CommSemiring R\nr : R\nt : Fin n →₀ ℕ\nhnm : n ≤ m\n⊢ leadingCoeff (⇑toLex) (esymmAlgHomMonomial (Fin m) t r) = r",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Finsupp.instAddZeroC... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 229,
"column": 81
} | {
"line": 229,
"column": 83
} | {
"line": 230,
"column": 6
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\nι : n ↪ n ⊕ n →₀ ℕ := { toFun := fun i ↦ Finsupp.single (Sum.inl i) 1 + Finsupp.single (Sum.inr i) 1, inj' := ⋯ }\naux : sumSMulXSMulY c = AddM... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 209,
"column": 37
} | {
"line": 209,
"column": 39
} | {
"line": 210,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\nc : n →₀ R\ninst✝ : IsDomain R\nhc : c.support.Nontrivial\nh_dvd : ∀ (r : R), (∀ (i : n), r ∣ c i) → IsUnit r\n⊢ Irreducible (sumSMulXSMulY c)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Function.instEmbeddingLikeEmbeddin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 842,
"column": 40
} | {
"line": 842,
"column": 42
} | {
"line": 843,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nf : K⸨X⸩\nγ : (WithZero (Multiplicative ℤ))ˣ\n⊢ ∃ Q, Valued.v (f - (algebraMap K⟮X⟯ K⸨X⸩) Q) < ↑γ",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"RatFunc.instFaithfulSMulPolynomialLaurentSeries",
"Algebra.ca... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 228,
"column": 85
} | {
"line": 228,
"column": 87
} | {
"line": 229,
"column": 2
} | [
{
"pp": "R : Type u_3\nn m : ℕ\ninst✝ : CommSemiring R\nr : R\nhr : r ≠ 0\nt : Fin n →₀ ℕ\nhnm : n ≤ m\n⊢ ⇑(ofLex (supDegree (⇑toLex) (esymmAlgHomMonomial (Fin m) t r))) = (accumulate n m) ⇑t",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addR... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 873,
"column": 60
} | {
"line": 873,
"column": 62
} | {
"line": 874,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\n⊢ DenseRange ⇑(algebraMap K⟮X⟯ K⸨X⸩)",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"RatFunc.instFaithfulSMulPolynomialLaurentSeries",
"Filter.instMembership",
"Multiplicative.group",
"AddGroup.to... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 898,
"column": 78
} | {
"line": 898,
"column": 80
} | {
"line": 899,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nx : K⸨X⸩\n⊢ ∃ f, Valued.v f = Valued.v x",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Multiplicative.group",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCommGroupWithZero.toLinear... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 67,
"column": 70
} | {
"line": 67,
"column": 72
} | {
"line": 68,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝ : DecidableEq σ\nt : Finset σ × σ\n⊢ pairMap σ t ≠ t",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"eq_false",
"Finset.cons",
"congrArg",
"Finset",
"False.elim",
"false_and",
"Membership.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 73,
"column": 48
} | {
"line": 73,
"column": 50
} | {
"line": 74,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝ : DecidableEq σ\nt : Finset σ × σ\nh : t.2 ∈ t.1\n⊢ pairMap σ t = (t.1.erase t.2, t.2)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Finset.cons",
"congrArg",
"Finset",
"Membership.mem",
"Prod.mk",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 77,
"column": 49
} | {
"line": 77,
"column": 51
} | {
"line": 78,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝ : DecidableEq σ\nt : Finset σ × σ\nh : t.2 ∉ t.1\n⊢ pairMap σ t = (cons t.2 t.1 h, t.2)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"of_eq_false",
"eq_false",
"Finset.cons",
"congrArg",
"Finset",
"Membership.mem",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 81,
"column": 63
} | {
"line": 81,
"column": 65
} | {
"line": 82,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝ : DecidableEq σ\n⊢ Function.Involutive (pairMap σ)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"dite_congr",
"eq_false",
"Finset.cons",
"congrArg",
"true_or",
"Finset",
"False.elim",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 97,
"column": 61
} | {
"line": 97,
"column": 63
} | {
"line": 98,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\nt : Finset σ × σ\n⊢ t ∈ pairs σ k ↔ #t.1 ≤ k ∧ (#t.1 = k → t.2 ∈ t.1)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Finset.fintype",
"Finset.mem_filter._simp_1",
"Finset.univ",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 245,
"column": 46
} | {
"line": 245,
"column": 48
} | {
"line": 246,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝¹ : CommSemiring R\ninst✝ : LinearOrder σ\np : MvPolynomial σ R\nhp : p.IsSymmetric\n⊢ Antitone ⇑(ofLex (supDegree (⇑toLex) p))",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Finsupp.Lex.isBotZeroClass",
"Mathlib.Tactic.Push.not_foral... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 277,
"column": 2
} | {
"line": 278,
"column": 67
} | {
"line": 279,
"column": 2
} | [
{
"pp": "R : Type u_3\nn m : ℕ\ninst✝ : CommRing R\nh : n ≤ m\np : MvPolynomial (Fin n) R\nhp : ¬p = 0\n⊢ ¬∑ i ∈ p.support, ↑((esymmAlgHom (Fin m) R n) ((monomial i) (coeff i p))) = 0",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
"Iff.mpr",
"Fi... | [
"case refine_1\nR : Type u_3\nn m : ℕ\ninst✝ : CommRing R\nh : n ≤ m\np : MvPolynomial (Fin n) R\nhp : ¬p = 0\nt : Fin n →₀ ℕ\nht : t ∈ p.support\n⊢ ↑((esymmAlgHom (Fin m) R n) ((monomial t) (coeff t p))) ≠ 0",
"case refine_2\nR : Type u_3\nn m : ℕ\ninst✝ : CommRing R\nh : n ≤ m\np : MvPolynomial (Fin n) R\nhp : ... | refine sum_ne_zero_of_injOn_supDegree (D := toLex) (support_nonempty.2 hp) (fun t ht ↦ ?_)
(fun t ht s hs he ↦ DFunLike.ext' <| accumulate_injective h ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.RingTheory.LaurentSeries | {
"line": 921,
"column": 43
} | {
"line": 921,
"column": 45
} | {
"line": 922,
"column": 8
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nS : Set (K⟮X⟯ × K⟮X⟯)\nT : Set (K⸨X⸩ × K⸨X⸩)\npre_T : (fun x ↦ ((algebraMap K⟮X⟯ K⸨X⸩) x.1, (algebraMap K⟮X⟯ K⸨X⸩) x.2)) ⁻¹' T ⊆ S\nR : Set K⸨X⸩\nhR : R ∈ nhds 0\npre_R : (fun x ↦ x.2 - x.1) ⁻¹' R ⊆ T\nd : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ\nhd : {y | Value... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 272,
"column": 52
} | {
"line": 272,
"column": 54
} | {
"line": 273,
"column": 2
} | [
{
"pp": "R : Type u_3\nn m : ℕ\ninst✝ : CommRing R\nh : n ≤ m\n⊢ Function.Injective ⇑(esymmAlgHom (Fin m) R n)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Finsupp.instAddZeroClass",
"Fins... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 104,
"column": 31
} | {
"line": 104,
"column": 33
} | {
"line": 105,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\nt : Finset σ × σ\nh : t ∈ pairs σ k\n⊢ pairMap σ t ∈ pairs σ k",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"le_iff_eq_or_lt",
"Iff.mpr",
"Eq.mpr",
"instDecidableNot",
"False",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 288,
"column": 46
} | {
"line": 288,
"column": 48
} | {
"line": 289,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\nn : ℕ\ninst✝¹ : Fintype σ\ninst✝ : CommRing R\nhn : n ≤ Fintype.card σ\n⊢ Function.Injective ⇑(esymmAlgHom σ R n)",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
"Eq.mpr",
"Nat.instMulZeroClass",
"AddMono... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 124,
"column": 69
} | {
"line": 124,
"column": 71
} | {
"line": 125,
"column": 4
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\nt : Finset σ × σ\nh : #t.1 ≤ k ∧ (#t.1 = k → t.2 ∈ t.1)\nn : ℕ\n⊢ -(-1) ^ n = (-1) ^ (n + 1)",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUni... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 303,
"column": 95
} | {
"line": 303,
"column": 97
} | {
"line": 304,
"column": 4
} | [
{
"pp": "R : Type u_3\ninst✝ : CommRing R\nn : ℕ\np : MvPolynomial (Fin n) R\nhp : p ∈ symmetricSubalgebra (Fin n) R\nh0 : p ≠ 0\nih :\n ∀ y < supDegree (⇑toLex) p,\n ∀ (p : MvPolynomial (Fin n) R) (hp : p ∈ symmetricSubalgebra (Fin n) R),\n p ≠ 0 → supDegree (⇑toLex) p = y → ⟨p, hp⟩ ∈ (esymmAlgHom (Fi... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 936,
"column": 54
} | {
"line": 936,
"column": 56
} | {
"line": 937,
"column": 10
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nS : Set (K⟮X⟯ × K⟮X⟯)\nw✝ : Set K⟮X⟯\nhT : w✝ ∈ nhds 0\npre_T : (fun x ↦ x.2 - x.1) ⁻¹' w✝ ⊆ S\nd : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ\nhd : {y | Valued.v.restrict (y - 0) < ↑d} ⊆ w✝\nX : Set K⸨X⸩ := {f | Valued.v f < embedding ↑d}\nX_def : X = {f | Valued.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 121,
"column": 55
} | {
"line": 121,
"column": 57
} | {
"line": 122,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\nt : Finset σ × σ\nh : t ∈ pairs σ k\n⊢ weight σ R k t + weight σ R k (pairMap σ t) = 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"NonUnitalNonAssocCommRi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 151,
"column": 89
} | {
"line": 151,
"column": 91
} | {
"line": 152,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\nf : Finset σ × σ → MvPolynomial σ R\n⊢ ∑ t ∈ pairs σ k with #t.1 = k, f t = ∑ A ∈ powersetCard k univ, ∑ j ∈ A, f (A, j)",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 161,
"column": 23
} | {
"line": 161,
"column": 25
} | {
"line": 161,
"column": 26
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\na : ℕ × ℕ\nha : a ∈ {a ∈ antidiagonal k | a.1 < k}\nf : Finset σ × σ → MvPolynomial σ R\np : Finset σ × σ\nhp : #p.1 = a.1\n⊢ #p.1 ≤ k",
"ppTerm": "?m.84",
"assigned": true,
"usedConstants": [... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 157,
"column": 89
} | {
"line": 157,
"column": 91
} | {
"line": 158,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\na : ℕ × ℕ\nha : a ∈ {a ∈ antidiagonal k | a.1 < k}\nf : Finset σ × σ → MvPolynomial σ R\n⊢ ∑ t ∈ pairs σ k with #t.1 = a.1, f t = ∑ A ∈ powersetCard a.1 univ, ∑ j, f (A, j)",
"ppTerm": "?m.64",
"a... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 168,
"column": 19
} | {
"line": 168,
"column": 21
} | {
"line": 168,
"column": 22
} | [
{
"pp": "σ : Type u_1\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\n⊢ {x ∈ pairs σ k |\n match x with\n | (s, snd) => #s < k} =\n (range k).disjiUnion (fun x ↦ powersetCard x univ) ⋯ ×ˢ univ",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 174,
"column": 91
} | {
"line": 174,
"column": 93
} | {
"line": 175,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝² : CommRing R\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\nf : Finset σ × σ → MvPolynomial σ R\n⊢ ∑ t ∈ pairs σ k with #t.1 < k, f t = ∑ a ∈ antidiagonal k with a.1 < k, ∑ A ∈ powersetCard a.1 univ, ∑ j, f (A, j)",
"ppTerm": "?m.64",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 180,
"column": 70
} | {
"line": 180,
"column": 72
} | {
"line": 181,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\n⊢ Disjoint ({t ∈ pairs σ k | #t.1 < k}) ({t ∈ pairs σ k | #t.1 = k})",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"lt_irrefl",
"congrArg",
"Finset",
"D... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
"line": 186,
"column": 68
} | {
"line": 186,
"column": 70
} | {
"line": 187,
"column": 2
} | [
{
"pp": "σ : Type u_1\ninst✝¹ : DecidableEq σ\ninst✝ : Fintype σ\nk : ℕ\n⊢ {t ∈ pairs σ k | #t.1 < k}.disjUnion ({t ∈ pairs σ k | #t.1 = k}) ⋯ = pairs σ k",
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Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
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Mathlib.RingTheory.MvPolynomial.Symmetric.NewtonIdentities | {
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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} | {
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{
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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} | {
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} | {
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{
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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{
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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Mathlib.RingTheory.MvPowerSeries.Expand | {
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{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommRing R\np : ℕ\nhp : p ≠ 0\nφ : MvPowerSeries σ R\nm : σ →₀ ℕ\ni : σ\nh : ¬p ∣ m i\n⊢ (coeff m) ((expand p hp) φ) = 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"MvPowerSeries.expand",
"Mathlib.Tactic.Push.not_exists._simp_1"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Expand | {
"line": 141,
"column": 57
} | {
"line": 141,
"column": 59
} | {
"line": 142,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommRing R\np : ℕ\nhp : p ≠ 0\nφ : MvPowerSeries σ R\n⊢ Function.support ((expand p hp) φ) ⊆ (fun x ↦ p • x) '' Function.support φ",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"MvPowerSeries.expand",
"Finsupp.instFunLike",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Morita.Matrix | {
"line": 64,
"column": 66
} | {
"line": 64,
"column": 68
} | {
"line": 65,
"column": 10
} | [
{
"pp": "R : Type u\nι : Type v\ninst✝⁶ : Ring R\ninst✝⁵ : Fintype ι\ninst✝⁴ : DecidableEq ι\nM : Type u_1\ninst✝³ : AddCommGroup M\ninst✝² : Module (Matrix ι ι R) M\ninst✝¹ : Module R M\ninst✝ : IsScalarTower R (Matrix ι ι R) M\ni : ι\nr : R\nx : M\n⊢ Commute (diagonal fun x ↦ r) (single i i 1)",
"ppTerm":... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPowerSeries.Expand | {
"line": 152,
"column": 57
} | {
"line": 152,
"column": 59
} | {
"line": 153,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommRing R\np : ℕ\nhp : p ≠ 0\nφ : MvPowerSeries σ R\n⊢ Function.support ((expand p hp) φ) = (fun x ↦ p • x) '' Function.support φ",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"MvPowerSeries.expand",
"Eq.mpr",
"False",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Expand | {
"line": 165,
"column": 36
} | {
"line": 165,
"column": 38
} | {
"line": 165,
"column": 39
} | [
{
"pp": "σ : Type u_1\nR : Type u_3\ninst✝ : CommRing R\np : ℕ\nhp : p ≠ 0\nφ : MvPowerSeries σ R\nhφ : φ = 0\n⊢ ↑p ≠ 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instCharZeroENat",
"instAddMonoidWithOneENat... | [] | by | [anonymous] | by |
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