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
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
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Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
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Mathlib.RepresentationTheory.Tannaka | {
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Mathlib.RepresentationTheory.Tannaka | {
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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{
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Mathlib.RepresentationTheory.Tannaka | {
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} | {
"line": 211,
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} | {
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{
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Mathlib.RepresentationTheory.Tannaka | {
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} | {
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} | {
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{
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
"line": 83,
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{
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Mathlib.RepresentationTheory.Tannaka | {
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} | {
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} | {
"line": 204,
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} | [
{
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Mathlib.RepresentationTheory.Tannaka | {
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} | {
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} | {
"line": 220,
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} | [
{
"pp": "k G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Finite G\ninst✝ : IsDomain k\n⊢ Function.Surjective ⇑(equivHom k G)",
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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{
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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{
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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} | [
{
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\n⊢ idealOfVars σ R ^ n = Ideal.span ((fun x ↦ (monomial x) 1) '' ⇑degree ⁻¹' {n})",
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\np : MvPolynomial σ R\n⊢ p ∈ idealOfVars σ R ^ n ↔ ∀ x ∈ p.support, n ≤ degree x",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Ideal | {
"line": 112,
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} | {
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} | {
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{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\np : MvPolynomial σ R\n⊢ p ∈ idealOfVars σ R ^ n ↔ ∀ (x : σ →₀ ℕ), degree x < n → coeff x p = 0",
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"_private.Mathlib.RingTheory.MvPolynomial.Ideal.0.MvPolynomial.mem_pow_id... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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} | [
{
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Mathlib.RingTheory.MvPolynomial.Ideal | {
"line": 120,
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} | {
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} | {
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} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nr : R\n⊢ C r ∈ idealOfVars σ R ^ n ↔ r = 0 ∨ n = 0",
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Mathlib.RingTheory.MvPolynomial.Ideal | {
"line": 132,
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} | {
"line": 132,
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} | {
"line": 133,
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} | [
{
"pp": "A : Type u_3\nσ : Type u_4\ninst✝ : CommRing A\nI : Ideal (MvPolynomial σ A)\n⊢ Ideal.Quotient.mkₐ A I = aeval fun d ↦ (Ideal.Quotient.mk I) (X d)",
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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{
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPolynomial.Ideal | {
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Mathlib.RingTheory.MvPolynomial.Ideal | {
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} | {
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} | {
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{
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Mathlib.RingTheory.Noetherian.OfPrime | {
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{
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Mathlib.RingTheory.Noetherian.OfPrime | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
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Mathlib.RingTheory.MvPowerSeries.Rename | {
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{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\n⊢ Function.Injective ⇑(rename ⇑e)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 186,
"column": 45
} | {
"line": 186,
"column": 47
} | {
"line": 187,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\ng h : G\na : ↑A\n⊢ (ConcreteCategory.hom (d₂₁ A)) (single (g⁻¹, g * h) ((A.ρ g⁻¹) a) + single (g, h) a) =\n single g⁻¹ ((A.ρ g⁻¹) a) + single g a",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 180,
"column": 47
} | {
"line": 180,
"column": 49
} | {
"line": 181,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\nS : Type u_5\nf : σ → τ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\nφ : R →+* S\np : MvPowerSeries σ R\n⊢ (rename f) ((map φ) p) = (map φ) ((rename f) p)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 202,
"column": 63
} | {
"line": 202,
"column": 65
} | {
"line": 203,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\ng : G × G × G\na : ↑A\n⊢ (ConcreteCategory.hom (d₃₂ A)) (single g a) =\n single (g.2.1, g.2.2) ((A.ρ g.1⁻¹) a) - single (g.1 * g.2.1, g.2.2) a + single (g.1, g.2.1 * g.2.2) a -\n single (g.1, g.2.1) a",
"ppTerm": "?m.97",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Noetherian.OfPrime | {
"line": 36,
"column": 27
} | {
"line": 36,
"column": 29
} | {
"line": 37,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\na : R\nhsup : (I ⊔ span {a}).FG\nhcolon : (Submodule.colon I ↑(span {a})).FG\n⊢ I.FG",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"NonUnitalNonAssocCommRing.toN... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 183,
"column": 93
} | {
"line": 183,
"column": 95
} | {
"line": 184,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\nf : σ → τ\ninst✝¹ : TendstoCofinite f\ninst✝ : CommSemiring R\np : MvPolynomial σ R\n⊢ (rename f) ↑p = ↑((MvPolynomial.rename f) p)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"MvPolynomial.coe_C",
"Finsupp.instAddZeroClass... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 206,
"column": 74
} | {
"line": 206,
"column": 76
} | {
"line": 207,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\ng h : G\na : ↑A\n⊢ (ConcreteCategory.hom (d₃₂ A)) (single (1, g, h) a) = single (1, g * h) a - single (1, g) a",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"groupHomology.d₃₂",
"Finsupp.instAddZeroClas... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 196,
"column": 16
} | {
"line": 196,
"column": 18
} | {
"line": 196,
"column": 19
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nγ : Type u_3\nR : Type u_4\nS : Type u_5\nf : σ → τ\ng : τ → γ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\ne : σ ≃ τ\nx✝ : MvPowerSeries σ R\n⊢ (rename ⇑e.symm) ((↑↑(rename ⇑e).toRingHom).toFun x✝) = x✝",
"ppTerm": "?m.39",
"assigned... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 197,
"column": 17
} | {
"line": 197,
"column": 19
} | {
"line": 197,
"column": 20
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nγ : Type u_3\nR : Type u_4\nS : Type u_5\nf : σ → τ\ng : τ → γ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\ne : σ ≃ τ\nx✝ : MvPowerSeries τ R\n⊢ (↑↑(rename ⇑e).toRingHom).toFun ((rename ⇑e.symm) x✝) = x✝",
"ppTerm": "?m.40",
"assigned... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 200,
"column": 89
} | {
"line": 200,
"column": 91
} | {
"line": 200,
"column": 92
} | [
{
"pp": "σ : Type u_1\nR : Type u_4\ninst✝ : CommSemiring R\n⊢ ∀ (a : MvPowerSeries σ R), (renameEquiv R (Equiv.refl σ)) a = AlgEquiv.refl a",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Equiv.instEquivLike",
"MonoidHom",
"congrArg",
"CommSe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 210,
"column": 80
} | {
"line": 210,
"column": 82
} | {
"line": 211,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\ng h : G\na : ↑A\n⊢ (ConcreteCategory.hom (d₃₂ A)) (single (g, 1, h) a) = single (1, h) ((A.ρ g⁻¹) a) - single (g, 1) a",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"groupHomology.d₃₂",
"Pi.Function.mod... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Noetherian.OfPrime | {
"line": 70,
"column": 64
} | {
"line": 70,
"column": 66
} | {
"line": 71,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nH : ∀ (I : Ideal R), I.IsPrime → I.FG\nC : Set (Ideal R)\nhC₁ : C ⊆ {I | ¬I.FG}\nhC₂ : IsChain (fun x1 x2 ↦ x1 ≤ x2) C\nI : Ideal R\nhI : I ∈ C\nG : Finset R\nhG : span ↑G = sSup C\n⊢ ∃ J ∈ C, ↑G ⊆ ↑J",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 219,
"column": 66
} | {
"line": 219,
"column": 68
} | {
"line": 220,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\nx : σ →₀ ℕ\nr : R\n⊢ killComplFun e ((monomial (embDomain e x)) r) = (monomial x) r",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"Semiring.toModule",
"congrArg... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 214,
"column": 84
} | {
"line": 214,
"column": 86
} | {
"line": 215,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\ng h : G\na : ↑A\n⊢ (ConcreteCategory.hom (d₃₂ A)) (single (g, h, 1) a) = single (h, 1) ((A.ρ g⁻¹) a) - single (g * h, 1) a",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"groupHomology.d₃₂",
"Pi.Function... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Noetherian.OfPrime | {
"line": 67,
"column": 26
} | {
"line": 67,
"column": 28
} | {
"line": 68,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nH : ∀ (I : Ideal R), I.IsPrime → I.FG\n⊢ IsNoetherianRing R",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Ideal.span_le",
"Iff.mpr",
"Eq.mpr",
"Ideal.subset_span",
"Submodule",
"Semiring.toModule",
"_pri... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 234,
"column": 43
} | {
"line": 234,
"column": 45
} | {
"line": 235,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx✝¹ : Fin 1 → G\nx✝ : ↑A\n⊢ (ModuleCat.Hom.hom ((chainsIso₁ A).hom ≫ d₁₀ A)) (single x✝¹ x✝) =\n (ModuleCat.Hom.hom ((inhomogeneousChains A).d 1 0 ≫ (chainsIso₀ A).hom)) (single x✝¹ x✝)",
"ppTerm": "?m.69",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 224,
"column": 77
} | {
"line": 224,
"column": 79
} | {
"line": 225,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\nx : τ →₀ ℕ\nr : R\nh : x ∉ Set.range (embDomain e)\n⊢ killComplFun e ((monomial x) r) = 0",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"MvPowerSeries... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 230,
"column": 68
} | {
"line": 230,
"column": 70
} | {
"line": 231,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\np q : MvPowerSeries τ R\n⊢ killComplFun e (p * q) = killComplFun e p * killComplFun e q",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Finsupp.instHasAntidiagonal",
"Iff.mpr",
"Nat.ins... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 243,
"column": 14
} | {
"line": 243,
"column": 16
} | {
"line": 243,
"column": 17
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nγ : Type u_3\nR : Type u_4\nS : Type u_5\nf : σ → τ\ng : τ → γ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\ne✝ e : σ ↪ τ\n⊢ killComplFun e 1 = 1",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toA... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 259,
"column": 43
} | {
"line": 259,
"column": 45
} | {
"line": 260,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx✝¹ : Fin 2 → G\nx✝ : ↑A\n⊢ (ModuleCat.Hom.hom ((chainsIso₂ A).hom ≫ d₂₁ A)) (single x✝¹ x✝) =\n (ModuleCat.Hom.hom ((inhomogeneousChains A).d 2 1 ≫ (chainsIso₁ A).hom)) (single x✝¹ x✝)",
"ppTerm": "?m.69",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 245,
"column": 15
} | {
"line": 245,
"column": 17
} | {
"line": 245,
"column": 18
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nγ : Type u_3\nR : Type u_4\nS : Type u_5\nf : σ → τ\ng : τ → γ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\ne✝ e : σ ↪ τ\n⊢ killComplFun e 0 = 0",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toA... | [] | by | [anonymous] | by |
Mathlib.RingTheory.UniqueFactorizationDomain.Kaplansky | {
"line": 45,
"column": 14
} | {
"line": 45,
"column": 16
} | {
"line": 45,
"column": 17
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nS : Subsemigroup R\nhS : 0 ∉ S\nhC : ∅ ⊆ kaplanskySet S\nhC₂ : IsChain (fun x1 x2 ↦ x1 ≤ x2) ∅\n⊢ ⊥ ∈ kaplanskySet S ∧ ∀ J ∈ ∅, J ≤ ⊥",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"False",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 246,
"column": 18
} | {
"line": 246,
"column": 20
} | {
"line": 246,
"column": 21
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nγ : Type u_3\nR : Type u_4\nS : Type u_5\nf : σ → τ\ng : τ → γ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\ne✝ e : σ ↪ τ\nx✝¹ x✝ : MvPowerSeries τ R\n⊢ killComplFun e (x✝¹ + x✝) = killComplFun e x✝¹ + killComplFun e x✝",
"ppTerm": "?m.29"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.UniqueFactorizationDomain.Kaplansky | {
"line": 43,
"column": 74
} | {
"line": 43,
"column": 76
} | {
"line": 44,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nS : Subsemigroup R\nC : Set (Ideal R)\nhS : 0 ∉ S\nhC : C ⊆ kaplanskySet S\nhC₂ : IsChain (fun x1 x2 ↦ x1 ≤ x2) C\n⊢ ∃ P ∈ kaplanskySet S, ∀ J ∈ C, J ≤ P",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Set... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 247,
"column": 15
} | {
"line": 247,
"column": 17
} | {
"line": 247,
"column": 18
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nγ : Type u_3\nR : Type u_4\nS : Type u_5\nf : σ → τ\ng : τ → γ\ninst✝² : TendstoCofinite f\ninst✝¹ : CommSemiring R\ninst✝ : CommSemiring S\ne✝ e : σ ↪ τ\n⊢ ∀ (r : R), killComplFun e ((algebraMap R (MvPowerSeries τ R)) r) = (algebraMap R (MvPowerSeries σ R)) r",
"ppTerm"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 284,
"column": 43
} | {
"line": 284,
"column": 45
} | {
"line": 285,
"column": 4
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx✝¹ : Fin 3 → G\nx✝ : ↑A\n⊢ (ModuleCat.Hom.hom ((chainsIso₃ A).hom ≫ d₃₂ A)) (single x✝¹ x✝) =\n (ModuleCat.Hom.hom ((inhomogeneousChains A).d 3 2 ≫ (chainsIso₂ A).hom)) (single x✝¹ x✝)",
"ppTerm": "?m.69",
"assigned": true,
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 250,
"column": 57
} | {
"line": 250,
"column": 59
} | {
"line": 250,
"column": 60
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\np : MvPowerSeries τ R\nx : σ →₀ ℕ\n⊢ (coeff x) ((killCompl e) p) = (coeff (embDomain e x)) p",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"CommSemiring.toSemiring",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 261,
"column": 55
} | {
"line": 261,
"column": 57
} | {
"line": 262,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\nr : R\n⊢ (killCompl e) (C r) = C r",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"MvPowerSeries.killCompl_monomial_embDomain",
"Nat",
"Zero.toOfNat0",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.UniqueFactorizationDomain.Kaplansky | {
"line": 55,
"column": 65
} | {
"line": 55,
"column": 67
} | {
"line": 56,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nS : Subsemigroup R\nhS : 0 ∉ S\n⊢ ∃ P ∈ kaplanskySet S, ∀ I ∈ kaplanskySet S, P ≤ I → I = P",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 297,
"column": 44
} | {
"line": 297,
"column": 46
} | {
"line": 298,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\n⊢ d₂₁ A ≫ d₁₀ A = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Finsupp.instAddZeroClass",
"LinearMap.id",
"Pi.Function.module",
"Rep.V",
"Mono... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 302,
"column": 44
} | {
"line": 302,
"column": 46
} | {
"line": 303,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\n⊢ d₃₂ A ≫ d₂₁ A = 0",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"groupHomology.d₃₂",
"dite_cond_eq_true",
"CategoryTheory.Category.assoc",
"Rep.V",
"_private.Mathlib.RepresentationTh... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Rename | {
"line": 265,
"column": 70
} | {
"line": 265,
"column": 72
} | {
"line": 266,
"column": 2
} | [
{
"pp": "σ : Type u_1\nτ : Type u_2\nR : Type u_4\ninst✝ : CommSemiring R\ne : σ ↪ τ\ni : σ\n⊢ (killCompl e) (X (e i)) = X i",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Semiring.toModule",
"cong... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 338,
"column": 75
} | {
"line": 338,
"column": 77
} | {
"line": 339,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx : G →₀ ↑A\n⊢ x ∈ cycles₁ A ↔ (x.sum fun g a ↦ (A.ρ g⁻¹) a) = x.sum fun x a ↦ a",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"Rep.V",... | [] | by | [anonymous] | by |
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