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.LaurentSeries | {
"line": 435,
"column": 82
} | {
"line": 435,
"column": 84
} | {
"line": 436,
"column": 4
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nP : K[X]\nhP : ¬P = 0\nspan_ne_zero : Ideal.span {P} ≠ 0 ∧ Ideal.span {Polynomial.X} ≠ 0\n⊢ Ideal.span {↑P} ≠ 0 ∧ (idealX K).asIdeal ≠ 0",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"False",
"MvPowerSeries.instZero",
"Semiring.to... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 444,
"column": 55
} | {
"line": 444,
"column": 57
} | {
"line": 444,
"column": 58
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nP : K[X]\nhP : ¬P = 0\nspan_ne_zero : Ideal.span {P} ≠ 0 ∧ Ideal.span {Polynomial.X} ≠ 0\nspan_ne_zero' : Ideal.span {↑P} ≠ 0 ∧ (idealX K).asIdeal ≠ 0\n⊢ ↑P ≠ 0",
"ppTerm": "?m.254",
"assigned": true,
"usedConstants": [
"False",
"MvPowerSeries.inst... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 425,
"column": 81
} | {
"line": 425,
"column": 83
} | {
"line": 426,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nP : K[X]\n⊢ (Polynomial.idealX K).intValuation P = (idealX K).intValuation ↑P",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Polynomial.instNormalizationMonoid",
"UniqueFactorizationMonoid.normalizedFactors",
"Iff.mpr",
"Eq.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 449,
"column": 69
} | {
"line": 449,
"column": 71
} | {
"line": 450,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\n⊢ (idealX K).intValuation X = exp (-1)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"Polynomial.idealX_span",
"Powe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 472,
"column": 48
} | {
"line": 472,
"column": 50
} | {
"line": 472,
"column": 51
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nP : K⟮X⟯\nf g : K[X]\nh : g ≠ 0\n⊢ ↑g ≠ 0",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"False",
"MvPowerSeries.instZero",
"eq_false",
"congrArg",
"CommSemiring.toSemiring",
"MvPowerSeries.instCommRing",
"F... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 466,
"column": 74
} | {
"line": 466,
"column": 76
} | {
"line": 467,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nP : K⟮X⟯\n⊢ (polynomialValuationX K) P = (valuation K⸨X⸩ (PowerSeries.idealX K)) ((algebraMap K⟮X⟯ K⸨X⸩) P)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"RatFunc.instFaithfulSMulPolynomialLaurentSeries",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 488,
"column": 40
} | {
"line": 488,
"column": 42
} | {
"line": 489,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nf : K⟮X⟯\n⊢ Valued.v ((algebraMap K⟮X⟯ K⸨X⸩) f) = Valued.v f",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"RatFunc.instFaithfulSMulPolynomialLaurentSeries",
"Int.instAddCommMonoid",
"LinearOrderedCom... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 492,
"column": 59
} | {
"line": 492,
"column": 61
} | {
"line": 493,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\ns : ℕ\n⊢ Valued.v ((ofPowerSeries ℤ K) PowerSeries.X ^ s) = exp (-↑s)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Algebra.cast",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Int.instAddCommMono... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 497,
"column": 70
} | {
"line": 497,
"column": 72
} | {
"line": 498,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\ns : ℤ\n⊢ Valued.v ((single s) 1) = exp (-s)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Multiplicative.group",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Int.instAddCommMonoid",
"Linear... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 507,
"column": 29
} | {
"line": 507,
"column": 31
} | {
"line": 508,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nn d : ℕ\nf : K⟦X⟧\nH : Valued.v ((ofPowerSeries ℤ K) f) ≤ exp (-↑d)\n⊢ n < d → (PowerSeries.coeff n) f = 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Algebra.cast",
"Int.instAddCommMonoid",
"Linea... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 507,
"column": 29
} | {
"line": 512,
"column": 83
} | {
"line": 514,
"column": 0
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nn d : ℕ\nf : K⟦X⟧\nH : Valued.v ((ofPowerSeries ℤ K) f) ≤ exp (-↑d)\n⊢ n < d → (PowerSeries.coeff n) f = 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Algebra.cast",
"Int.instAddCommMonoid",
"Linea... | [] | by
intro hnd
apply (PowerSeries.X_pow_dvd_iff).mp _ n hnd
rwa [← LaurentSeries.coe_algebraMap, valuation_def, valuation_of_algebraMap,
intValuation_le_pow_iff_dvd (PowerSeries.idealX K) f d, PowerSeries.idealX,
Ideal.span_singleton_pow, Ideal.span_singleton_dvd_span_singleton_iff_dvd] at H | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.LaurentSeries | {
"line": 517,
"column": 40
} | {
"line": 517,
"column": 42
} | {
"line": 518,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nd : ℕ\nf : K⟦X⟧\n⊢ Valued.v ((ofPowerSeries ℤ K) f) ≤ exp (-↑d) ↔ ∀ n < d, (PowerSeries.coeff n) f = 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Algebra.cast",
"Iff.mpr",
"Eq.mpr",
"Int.ins... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 534,
"column": 60
} | {
"line": 534,
"column": 62
} | {
"line": 534,
"column": 63
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nn D : ℤ\nf : K⸨X⸩\nH : Valued.v f ≤ exp (-D)\nhnd : n < D\nh_n_ord : HahnSeries.order f ≤ n\nF : K⟦X⟧ := f.powerSeriesPart\nhF : F = f.powerSeriesPart\nord_nonpos : HahnSeries.order f ≤ 0\ns : ℕ\nhs : HahnSeries.order f = -↑s\nm : ℕ\nhm : n + ↑s = ↑m\n⊢ 0 ≤ D + ↑s",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LocalRing.Pullback | {
"line": 68,
"column": 67
} | {
"line": 68,
"column": 69
} | {
"line": 69,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Semiring T\nf : R →+* T\ng : S →+* T\na : R × S\na_in : a ∈ f.pullback g\n⊢ IsUnit ⟨a, a_in⟩ ↔ IsUnit a.1 ∧ IsUnit a.2",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Subring... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LocalRing.Pullback | {
"line": 83,
"column": 10
} | {
"line": 83,
"column": 12
} | {
"line": 83,
"column": 13
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Semiring T\nf : R →+* T\ng : S →+* T\nh : Function.Surjective ⇑g\nr : R\n⊢ ∃ a, (f.pullbackFst g) a = r",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Subring.instSetLike",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LocalRing.Pullback | {
"line": 87,
"column": 10
} | {
"line": 87,
"column": 12
} | {
"line": 87,
"column": 13
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Semiring T\nf : R →+* T\ng : S →+* T\nh : Function.Surjective ⇑f\ns : S\n⊢ ∃ a, (f.pullbackSnd g) a = s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"RingHom.pullbackSnd",
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 536,
"column": 61
} | {
"line": 536,
"column": 63
} | {
"line": 536,
"column": 64
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nn D : ℤ\nf : K⸨X⸩\nH : Valued.v f ≤ exp (-D)\nhnd : n < D\nh_n_ord : HahnSeries.order f ≤ n\nF : K⟦X⟧ := f.powerSeriesPart\nhF : F = f.powerSeriesPart\nord_nonpos : HahnSeries.order f ≤ 0\ns : ℕ\nhs : HahnSeries.order f = -↑s\nm : ℕ\nhm : n + ↑s = ↑m\nd : ℕ\nhd : D + ↑s =... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LocalRing.Pullback | {
"line": 96,
"column": 64
} | {
"line": 96,
"column": 66
} | {
"line": 96,
"column": 67
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Semiring T\nf : R →+* T\ng : S →+* T\ns : S\nhs : s ∈ ker g\n⊢ (0, s) ∈ f.pullback g",
"ppTerm": "?m.115",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"RingHom.instRingHomClass",
"Subrin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LocalRing.Pullback | {
"line": 97,
"column": 44
} | {
"line": 97,
"column": 46
} | {
"line": 97,
"column": 47
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Semiring T\nf : R →+* T\ng : S →+* T\ns : S\nhs : s ∈ ker g\n⊢ ⟨(0, s), ⋯⟩ ∈ ker (f.pullbackFst g)",
"ppTerm": "?m.116",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"RingHom.instRingHomClass",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LocalRing.Pullback | {
"line": 90,
"column": 83
} | {
"line": 90,
"column": 85
} | {
"line": 91,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝² : Ring R\ninst✝¹ : Ring S\ninst✝ : Semiring T\nf : R →+* T\ng : S →+* T\n⊢ Ideal.map (f.pullbackSnd g) (ker (f.pullbackFst g)) = ker g",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"RingHom.pullbackSnd",
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Pi | {
"line": 47,
"column": 4
} | {
"line": 47,
"column": 51
} | {
"line": 48,
"column": 4
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_2\nS : ι → Type u_3\ninst✝³ : (i : ι) → CommSemiring (R i)\ninst✝² : (i : ι) → CommSemiring (S i)\ninst✝¹ : (i : ι) → Algebra (R i) (S i)\nM : (i : ι) → Submonoid (R i)\ninst✝ : ∀ (i : ι), IsLocalization (M i) (S i)\nz : (i : ι) → S i\n⊢ ∃ x, z * (algebraMap ((i : ι) → R i)... | [
"ι : Type u_1\nR : ι → Type u_2\nS : ι → Type u_3\ninst✝³ : (i : ι) → CommSemiring (R i)\ninst✝² : (i : ι) → CommSemiring (S i)\ninst✝¹ : (i : ι) → Algebra (R i) (S i)\nM : (i : ι) → Submonoid (R i)\ninst✝ : ∀ (i : ι), IsLocalization (M i) (S i)\nz : (i : ι) → S i\nrm : (i : ι) → R i × ↥(M i)\nh : ∀ (i : ι), z i * ... | choose rm h using fun i ↦ surj (M := M i) (z i) | Mathlib.Tactic.Choose._aux_Mathlib_Tactic_Choose___elabRules_Mathlib_Tactic_Choose_choose_1 | Mathlib.Tactic.Choose.choose |
Mathlib.RingTheory.Localization.Pi | {
"line": 46,
"column": 12
} | {
"line": 46,
"column": 14
} | {
"line": 47,
"column": 4
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_2\nS : ι → Type u_3\ninst✝³ : (i : ι) → CommSemiring (R i)\ninst✝² : (i : ι) → CommSemiring (S i)\ninst✝¹ : (i : ι) → Algebra (R i) (S i)\nM : (i : ι) → Submonoid (R i)\ninst✝ : ∀ (i : ι), IsLocalization (M i) (S i)\nz : (i : ι) → S i\n⊢ ∃ x, z * (algebraMap ((i : ι) → R i)... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Pi | {
"line": 49,
"column": 27
} | {
"line": 49,
"column": 29
} | {
"line": 50,
"column": 4
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_2\nS : ι → Type u_3\ninst✝³ : (i : ι) → CommSemiring (R i)\ninst✝² : (i : ι) → CommSemiring (S i)\ninst✝¹ : (i : ι) → Algebra (R i) (S i)\nM : (i : ι) → Submonoid (R i)\ninst✝ : ∀ (i : ι), IsLocalization (M i) (S i)\nx y : (i : ι) → R i\neq : (algebraMap ((i : ι) → R i) ((i... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Pi | {
"line": 57,
"column": 71
} | {
"line": 57,
"column": 73
} | {
"line": 58,
"column": 4
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_2\ninst✝³ : (i : ι) → CommSemiring (R i)\nS' : Type u_4\ninst✝² : CommSemiring S'\ninst✝¹ : Algebra ((i : ι) → R i) S'\nM : Submonoid ((i : ι) → R i)\ninst✝ : Finite ι\nn : (i : ι) → R i\nhn : n ∈ Submonoid.pi Set.univ fun i ↦ Submonoid.map (Pi.evalRingHom R i) M\n⊢ ∃ m ∈ M... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Pi | {
"line": 95,
"column": 39
} | {
"line": 95,
"column": 41
} | {
"line": 95,
"column": 42
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_2\nS : ι → Type u_3\ninst✝⁵ : (i : ι) → CommSemiring (R i)\ninst✝⁴ : (i : ι) → CommSemiring (S i)\ninst✝³ : (i : ι) → Algebra (R i) (S i)\nM : Submonoid ((i : ι) → R i)\ninst✝² : ∀ (i : ι), IsLocalization (Submonoid.map (Pi.evalRingHom R i) M) (S i)\ninst✝¹ : ∀ (i : ι), Rin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Pi | {
"line": 90,
"column": 92
} | {
"line": 90,
"column": 94
} | {
"line": 91,
"column": 2
} | [
{
"pp": "ι : Type u_1\nR : ι → Type u_2\nS : ι → Type u_3\ninst✝⁵ : (i : ι) → CommSemiring (R i)\ninst✝⁴ : (i : ι) → CommSemiring (S i)\ninst✝³ : (i : ι) → Algebra (R i) (S i)\nM : Submonoid ((i : ι) → R i)\ninst✝² : ∀ (i : ι), IsLocalization (Submonoid.map (Pi.evalRingHom R i) M) (S i)\ninst✝¹ : ∀ (i : ι), Rin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 541,
"column": 60
} | {
"line": 541,
"column": 62
} | {
"line": 541,
"column": 63
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nn D : ℤ\nf : K⸨X⸩\nH : Valued.v f ≤ exp (-D)\nhnd : n < D\nh_n_ord : HahnSeries.order f ≤ n\nF : K⟦X⟧ := f.powerSeriesPart\nhF : F = f.powerSeriesPart\nord_nonpos : 0 < HahnSeries.order f\ns : ℕ\nhs : -HahnSeries.order f = -↑s\n⊢ 0 ≤ n - ↑s",
"ppTerm": "?m.244",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Rat | {
"line": 22,
"column": 61
} | {
"line": 22,
"column": 63
} | {
"line": 23,
"column": 2
} | [
{
"pp": "q : ℚ\n⊢ IsLocalization.IsInteger ℤ q ↔ q ∈ Set.range Int.cast",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"IsLocalization.IsInteger",
"Int.cast",
"RingHom.instRingHomClass",
"Subsemiring.instSetLike",
"Ring.toNonAssocRing",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Rat | {
"line": 27,
"column": 35
} | {
"line": 27,
"column": 37
} | {
"line": 27,
"column": 38
} | [
{
"pp": "q : ℚ\n⊢ ↑q.den ∈ nonZeroDivisors ℤ",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"False",
"Int.instIsStrictOrderedRing",
"congrArg",
"CommSemiring.toSemiring",
"Int.instLinearOrder",
"Rat.den_ne_zero._simp_1",
"PartialOrder.toPreorder",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Rat | {
"line": 28,
"column": 5
} | {
"line": 28,
"column": 7
} | {
"line": 28,
"column": 8
} | [
{
"pp": "q : ℚ\n⊢ IsRelPrime q.num ↑⟨↑q.den, ⋯⟩",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.Coprime",
"Rat.reduced",
"False",
"Int.instIsStrictOrderedRing",
"Rat.num",
"congrArg",
"CommSemiring.toSemiring",
"Int.instL... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 542,
"column": 60
} | {
"line": 542,
"column": 62
} | {
"line": 542,
"column": 63
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nn D : ℤ\nf : K⸨X⸩\nH : Valued.v f ≤ exp (-D)\nhnd : n < D\nh_n_ord : HahnSeries.order f ≤ n\nF : K⟦X⟧ := f.powerSeriesPart\nhF : F = f.powerSeriesPart\nord_nonpos : 0 < HahnSeries.order f\ns : ℕ\nhs : -HahnSeries.order f = -↑s\nm : ℕ\nhm : n - ↑s = ↑m\n⊢ 0 ≤ D - ↑s",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Rat | {
"line": 29,
"column": 5
} | {
"line": 29,
"column": 7
} | {
"line": 29,
"column": 8
} | [
{
"pp": "q : ℚ\n⊢ IsLocalization.mk' ℚ q.num ⟨↑q.den, ⋯⟩ = q",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Rat.num_div_den",
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"False",
"Int.instIsStrictOrderedRing",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.Rat | {
"line": 31,
"column": 83
} | {
"line": 31,
"column": 85
} | {
"line": 32,
"column": 2
} | [
{
"pp": "q : ℚ\n⊢ (↑(IsFractionRing.den ℤ q)).natAbs = q.den",
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Mathlib.RingTheory.Localization.Pi | {
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Mathlib.RingTheory.LaurentSeries | {
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{
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Mathlib.RingTheory.LaurentSeries | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹⁵ : CommRing R\ninst✝¹⁴ : CommRing S\ninst✝¹³ : Algebra R S\np : Ideal R\ninst✝¹² : p.IsPrime\nRₚ : Type u_3\ninst✝¹¹ : CommRing Rₚ\ninst✝¹⁰ : Algebra R Rₚ\ninst✝⁹ : IsLocalization.AtPrime Rₚ p\ninst✝⁸ : IsLocalRing Rₚ\nSₚ : Type u_4\ninst✝⁷ : CommRing Sₚ\ninst✝⁶ : Alg... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
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"line": 93,
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{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\np : Ideal R\ninst✝⁴ : p.IsPrime\nSₚ : Type u_4\ninst✝³ : CommRing Sₚ\ninst✝² : Algebra S Sₚ\ninst✝¹ : IsLocalization (algebraMapSubmonoid S p.primeCompl) Sₚ\nP : Ideal S\nhPp : P.LiesOver p\ninst✝ : P.IsMaximal\... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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"line": 129,
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{
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Mathlib.RingTheory.LaurentSeries | {
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} | {
"line": 552,
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} | {
"line": 553,
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{
"pp": "K : Type u_2\ninst✝ : Field K\nD : ℤ\nf : K⸨X⸩\n⊢ Valued.v f ≤ exp (-D) ↔ ∀ n < D, f.coeff n = 0",
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"Int.instAddCommGroup",
"Algebra.cast",
"WithZero.instNontrivial",
"WithZero.exp_add",
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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} | {
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{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\np : Ideal R\ninst✝⁴ : p.IsPrime\nSₚ : Type u_4\ninst✝³ : CommRing Sₚ\ninst✝² : Algebra S Sₚ\ninst✝¹ : IsLocalization (algebraMapSubmonoid S p.primeCompl) Sₚ\nP : Ideal S\nhPp : P.LiesOver p\ninst✝ : P.IsMaximal\... | [] | rw [RingEquiv.symm_apply_eq, ← mul_left_inj' h₂, map_mul, mul_assoc, ← map_mul,
inv_mul_cancel₀ h₁, map_one, mul_one, equivQuotientMapOfIsMaximal_apply_mk,
← map_mul, mk'_spec, Quotient.mk_algebraMap, equivQuotientMapOfIsMaximal_apply_mk,
Quotient.mk_algebraMap] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
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Mathlib.RingTheory.MvPolynomial.EulerIdentity | {
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{
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"usedCon... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
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} | {
"line": 588,
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{
"pp": "K : Type u_2\ninst✝ : Field K\nD : WithZero (Multiplicative ℤ)\nhD : D ≠ 0\nf : K⸨X⸩\n⊢ Valued.v f ≤ D ↔ ∀ n < -D.log, f.coeff n = 0",
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"LinearOrderedCommGroupWithZero.toLinearOrdered... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
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} | {
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{
"pp": "K : Type u_2\ninst✝ : Field K\nd n : ℤ\nf g : K⸨X⸩\nH : Valued.v (g - f) ≤ exp (-d)\ntriv : g = f\nx✝ : n < d\n⊢ g.coeff n = f.coeff n",
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"congrArg",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.MvPolynomial.EulerIdentity | {
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"column": 44
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{
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Mathlib.RingTheory.LaurentSeries | {
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{
"pp": "K : Type u_2\ninst✝ : Field K\nd n : ℤ\nf g : K⸨X⸩\nH : Valued.v (g - f) ≤ exp (-d)\n⊢ n < d → g.coeff n = f.coeff n",
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"H... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.LaurentSeries | {
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{
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Mathlib.RingTheory.LaurentSeries | {
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Mathlib.RingTheory.LaurentSeries | {
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"usedConstant... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.EulerIdentity | {
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{
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Mathlib.RingTheory.MvPolynomial.EulerIdentity | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.MvPolynomial.Expand | {
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{
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"ppTerm": "?m.28",
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Mathlib.RingTheory.MvPolynomial.Expand | {
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Mathlib.RingTheory.MvPolynomial.Expand | {
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{
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Mathlib.RingTheory.Localization.AtPrime.Extension | {
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{
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Mathlib.RingTheory.LaurentSeries | {
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} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nuK : UniformSpace K\nd : ℤ\n⊢ UniformContinuous fun f ↦ f.coeff d",
"ppTerm": "?m.10",
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"usedConstants": [
"WithZero.instNontrivial",
"Filter.instMembership",
"Multiplicative.group",
"Iff.mpr",
"UniformContinuous"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 691,
"column": 66
} | {
"line": 691,
"column": 68
} | {
"line": 691,
"column": 69
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nentourage : Set (K⸨X⸩ × K⸨X⸩) := {P | Valued.v.restrict (P.2 - P.1) < 1}\nζ : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ := Units.mk0 1 ⋯\n⊢ True",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"True.intr... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
"line": 180,
"column": 74
} | {
"line": 180,
"column": 76
} | {
"line": 181,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹⁵ : CommRing R\ninst✝¹⁴ : CommRing S\ninst✝¹³ : Algebra R S\np : Ideal R\ninst✝¹² : p.IsPrime\nRₚ : Type u_3\ninst✝¹¹ : CommRing Rₚ\ninst✝¹⁰ : Algebra R Rₚ\ninst✝⁹ : IsLocalization.AtPrime Rₚ p\ninst✝⁸ : IsLocalRing Rₚ\nSₚ : Type u_4\ninst✝⁷ : CommRing Sₚ\ninst✝⁶ : Alg... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
"line": 227,
"column": 16
} | {
"line": 227,
"column": 18
} | {
"line": 228,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹⁷ : CommRing R\ninst✝¹⁶ : CommRing S\ninst✝¹⁵ : Algebra R S\np : Ideal R\ninst✝¹⁴ : p.IsPrime\nRₚ : Type u_3\ninst✝¹³ : CommRing Rₚ\ninst✝¹² : Algebra R Rₚ\ninst✝¹¹ : IsLocalization.AtPrime Rₚ p\ninst✝¹⁰ : IsLocalRing Rₚ\nSₚ : Type u_4\ninst✝⁹ : CommRing Sₚ\ninst✝⁸ : A... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
"line": 220,
"column": 25
} | {
"line": 220,
"column": 27
} | {
"line": 221,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹⁷ : CommRing R\ninst✝¹⁶ : CommRing S\ninst✝¹⁵ : Algebra R S\np : Ideal R\ninst✝¹⁴ : p.IsPrime\nRₚ : Type u_3\ninst✝¹³ : CommRing Rₚ\ninst✝¹² : Algebra R Rₚ\ninst✝¹¹ : IsLocalization.AtPrime Rₚ p\ninst✝¹⁰ : IsLocalRing Rₚ\nSₚ : Type u_4\ninst✝⁹ : CommRing Sₚ\ninst✝⁸ : A... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 694,
"column": 53
} | {
"line": 694,
"column": 55
} | {
"line": 695,
"column": 4
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nentourage : Set (K⸨X⸩ × K⸨X⸩) := {P | Valued.v.restrict (P.2 - P.1) < 1}\nζ : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ := Units.mk0 1 ⋯\nS : Set K⸨X⸩\nhS : S ∈ ℱ\nT : Set K⸨X⸩\nhT : T ∈ ℱ\nH : S ×ˢ T ⊆ entourage\nf : K⸨X⸩\nhf : f ∈... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 708,
"column": 35
} | {
"line": 708,
"column": 37
} | {
"line": 708,
"column": 38
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nentourage : Set (K⸨X⸩ × K⸨X⸩) := {P | Valued.v.restrict (P.2 - P.1) < 1}\nζ : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ := Units.mk0 1 ⋯\nS : Set K⸨X⸩\nhS : S ∈ ℱ\nT : Set K⸨X⸩\nhT : T ∈ ℱ\nH : S ×ˢ T ⊆ entourage\nf : K⸨X⸩\nhf : f ∈... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Localization.AtPrime.Extension | {
"line": 243,
"column": 29
} | {
"line": 243,
"column": 31
} | {
"line": 244,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹⁸ : CommRing R\ninst✝¹⁷ : CommRing S\ninst✝¹⁶ : Algebra R S\np : Ideal R\ninst✝¹⁵ : p.IsPrime\nRₚ : Type u_3\ninst✝¹⁴ : CommRing Rₚ\ninst✝¹³ : Algebra R Rₚ\ninst✝¹² : IsLocalization.AtPrime Rₚ p\ninst✝¹¹ : IsLocalRing Rₚ\nSₚ : Type u_4\ninst✝¹⁰ : CommRing Sₚ\ninst✝⁹ : ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 686,
"column": 59
} | {
"line": 686,
"column": 61
} | {
"line": 687,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\n⊢ ∃ N, ∀ᶠ (f : K⸨X⸩) in ℱ, ∀ n < N, f.coeff n = 0",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"HahnSeries.support",
"WithZero.instNontrivial",
"Filter.instMembership",
"Iff.mpr",
"Int.... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 714,
"column": 40
} | {
"line": 714,
"column": 42
} | {
"line": 715,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\n⊢ ∃ N, ∀ n < N, coeff hℱ n = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Filter.instMembership",
"UniformSpace",
"Eq.mpr",
"Int.instAddCommMonoid",
"LaurentSeries... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 724,
"column": 35
} | {
"line": 724,
"column": 37
} | {
"line": 725,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\n⊢ BddBelow (Function.support (coeff hℱ))",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"not_le",
"Exists.choose_spec",
"LaurentSeries.Cauchy.coeff",
"Preorder.toLT",
"lowerBounds",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 740,
"column": 62
} | {
"line": 740,
"column": 64
} | {
"line": 741,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\n⊢ ∃ N, ∀ᶠ (f : K⸨X⸩) in ℱ, ∀ d < N, coeff hℱ d = f.coeff d",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LaurentSeries.Cauchy.coeff",
"congrArg",
"Int.instLinearOrder",
"Set.o... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 78,
"column": 68
} | {
"line": 78,
"column": 70
} | {
"line": 78,
"column": 71
} | [
{
"pp": "n : Type u_3\nR : Type u_4\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf g : MvPolynomial n R\ni : n\nhf0 : f ≠ 0\nhif : i ∉ f.vars\nhig : i ∉ g.vars\nh : IsRelPrime f g\nS : Type (max u_4 u_3) := MvPolynomial { j // j ≠ i } R\ne : MvPolynomial n R ≃ₐ[R] S[X] :=\n (renameEquiv R (Equiv.optionSubtypeNe i... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 80,
"column": 74
} | {
"line": 80,
"column": 76
} | {
"line": 80,
"column": 77
} | [
{
"pp": "n : Type u_3\nR : Type u_4\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf g : MvPolynomial n R\ni : n\nhf0 : f ≠ 0\nhif : i ∉ f.vars\nhig : i ∉ g.vars\nh : IsRelPrime f g\nS : Type (max u_4 u_3) := MvPolynomial { j // j ≠ i } R\ne : MvPolynomial n R ≃ₐ[R] S[X] :=\n (renameEquiv R (Equiv.optionSubtypeNe i... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 752,
"column": 85
} | {
"line": 752,
"column": 87
} | {
"line": 753,
"column": 4
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nD : ℤ\nφ : ℤ → Set K⸨X⸩ := fun d ↦ {f | coeff hℱ d = f.coeff d}\n⊢ ⋂ n ∈ Set.Iio D, φ n ⊆ {x | ∀ d < D, coeff hℱ d = x.coeff d}",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Set.iInter",
"PartialOrder.to... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 82,
"column": 74
} | {
"line": 82,
"column": 76
} | {
"line": 82,
"column": 77
} | [
{
"pp": "n : Type u_3\nR : Type u_4\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\ng : MvPolynomial n R\ni : n\nhig : i ∉ g.vars\nS : Type (max u_4 u_3) := MvPolynomial { j // j ≠ i } R\ne : MvPolynomial n R ≃ₐ[R] S[X] :=\n (renameEquiv R (Equiv.optionSubtypeNe i).symm).trans (optionEquivLeft R { b // b ≠ i })\nhe ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 84,
"column": 59
} | {
"line": 84,
"column": 61
} | {
"line": 84,
"column": 62
} | [
{
"pp": "n : Type u_3\nR : Type u_4\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\ni : n\nS : Type (max u_4 u_3) := MvPolynomial { j // j ≠ i } R\ne : MvPolynomial n R ≃ₐ[R] S[X] :=\n (renameEquiv R (Equiv.optionSubtypeNe i).symm).trans (optionEquivLeft R { b // b ≠ i })\nhe : (↑e.symm).comp Polynomial.CAlgHom = re... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 73,
"column": 33
} | {
"line": 73,
"column": 35
} | {
"line": 74,
"column": 2
} | [
{
"pp": "n : Type u_3\nR : Type u_4\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf g : MvPolynomial n R\ni : n\nhf0 : f ≠ 0\nhif : i ∉ f.vars\nhig : i ∉ g.vars\nh : IsRelPrime f g\n⊢ Irreducible (f * X i + g)",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Subalgebra.instSetLike",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 98,
"column": 30
} | {
"line": 98,
"column": 32
} | {
"line": 98,
"column": 33
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 102,
"column": 31
} | {
"line": 102,
"column": 33
} | {
"line": 102,
"column": 34
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 103,
"column": 48
} | {
"line": 103,
"column": 50
} | {
"line": 104,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 105,
"column": 63
} | {
"line": 105,
"column": 65
} | {
"line": 106,
"column": 4
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 758,
"column": 95
} | {
"line": 758,
"column": 97
} | {
"line": 759,
"column": 4
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nD : ℤ\nφ : ℤ → Set K⸨X⸩ := fun d ↦ {f | coeff hℱ d = f.coeff d}\nintersec₁ : ⋂ n ∈ Set.Iio D, φ n ⊆ {x | ∀ d < D, coeff hℱ d = x.coeff d}\nℓ : ℤ := ⋯.choose\nN : ℤ := max ℓ D\n⊢ ⋂ n ∈ Set.Iio D, φ n ⊇ (⋂ n ∈ Set.Iio ℓ, φ n) ∩ ⋂ n ∈ Set.Icc ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 764,
"column": 65
} | {
"line": 764,
"column": 67
} | {
"line": 765,
"column": 4
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nD : ℤ\nφ : ℤ → Set K⸨X⸩ := fun d ↦ {f | coeff hℱ d = f.coeff d}\nintersec₁ : ⋂ n ∈ Set.Iio D, φ n ⊆ {x | ∀ d < D, coeff hℱ d = x.coeff d}\nℓ : ℤ := ⋯.choose\nN : ℤ := max ℓ D\nintersec₂ : ⋂ n ∈ Set.Iio D, φ n ⊇ (⋂ n ∈ Set.Iio ℓ, φ n) ∩ ⋂ n ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 111,
"column": 56
} | {
"line": 111,
"column": 58
} | {
"line": 112,
"column": 6
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 58
} | {
"line": 114,
"column": 59
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 76,
"column": 96
} | {
"line": 76,
"column": 98
} | {
"line": 77,
"column": 2
} | [
{
"pp": "i n m : ℕ\nhin : i < n\nhim : i + 1 < m\nt : Fin n → ℕ\n⊢ (accumulate n m) t ⟨i, ⋯⟩ = t ⟨i, hin⟩ + (accumulate n m) t ⟨i + 1, him⟩",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Finset.mem_univ",
"Eq.mpr",
"le_rfl",
"Finset.univ",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 87,
"column": 75
} | {
"line": 87,
"column": 77
} | {
"line": 88,
"column": 2
} | [
{
"pp": "i n m : ℕ\nhin : i < n\nhmi : m = i + 1\nt : Fin n → ℕ\nht : ∀ (j : Fin n), m ≤ ↑j → t j = 0\n⊢ (accumulate n m) t ⟨i, ⋯⟩ = t ⟨i, hin⟩",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Finset.mem_univ",
"Eq.mpr",
"Finset.sum_eq_single_of_mem",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 119,
"column": 35
} | {
"line": 119,
"column": 37
} | {
"line": 119,
"column": 38
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 99,
"column": 39
} | {
"line": 99,
"column": 59
} | {
"line": 99,
"column": 59
} | [
{
"pp": "case inl\nn m : ℕ\nhnm : n ≤ m\nt s : Fin n → ℕ\nhe : (accumulate n m) t = (accumulate n m) s\ni : Fin n\nh : ↑i + 1 < m\nthis : t ⟨↑i, ⋯⟩ + (accumulate n m) t ⟨↑i + 1, h⟩ = s ⟨↑i, ⋯⟩ + (accumulate n m) t ⟨↑i + 1, h⟩\n⊢ t i = s i",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
... | [
"case inl\nn m : ℕ\nhnm : n ≤ m\nt s : Fin n → ℕ\nhe : (accumulate n m) t = (accumulate n m) s\ni : Fin n\nh : ↑i + 1 < m\nthis : t ⟨↑i, ⋯⟩ = s ⟨↑i, ⋯⟩\n⊢ t i = s i"
] | add_right_cancel_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 118,
"column": 26
} | {
"line": 118,
"column": 28
} | {
"line": 119,
"column": 6
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 748,
"column": 61
} | {
"line": 748,
"column": 63
} | {
"line": 750,
"column": 2
} | [
{
"pp": "K : Type u_2\ninst✝ : Field K\nℱ : Filter K⸨X⸩\nhℱ : Cauchy ℱ\nD : ℤ\n⊢ ∀ᶠ (f : K⸨X⸩) in ℱ, ∀ d < D, coeff hℱ d = f.coeff d",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Filter.instMembership",
"Set.ext",
"Eq.mpr",
"Exists.choose_spec"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 124,
"column": 43
} | {
"line": 124,
"column": 45
} | {
"line": 124,
"column": 46
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Symmetric.FundamentalTheorem | {
"line": 95,
"column": 88
} | {
"line": 95,
"column": 90
} | {
"line": 96,
"column": 2
} | [
{
"pp": "n m : ℕ\nhnm : n ≤ m\n⊢ Function.Injective ⇑(accumulate n m)",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"congrArg",
"False.elim",
"Add... | [] | by | [anonymous] | by |
Mathlib.RingTheory.LaurentSeries | {
"line": 788,
"column": 79
} | {
"line": 788,
"column": 81
} | {
"line": 789,
"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\nthis : ∀ᶠ (f : K⸨X⸩) in ℱ, f ∈ {y | Valued.v (y - limit hℱ) < embedding ↑γ}\n⊢ ∀ᶠ (f : K⸨X⸩)... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic | {
"line": 96,
"column": 21
} | {
"line": 96,
"column": 23
} | {
"line": 97,
"column": 2
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nf : MvPolynomial n R\nnontrivial : f.support.Nontrivial\nd : n →₀ ℕ\nhd : d ∈ f.support\ni : n\nhdi : d i = 1\ndisjoint : (↑f.support).PairwiseDisjoint Finsupp.support\nisPrimitive : ∀ (r : R), (∀ (d : n →₀ ℕ), r ∣ coeff d f) → IsUnit... | [] | by | [anonymous] | by |
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