module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Probability.StrongLaw | {
"line": 265,
"column": 13
} | {
"line": 265,
"column": 67
} | [
{
"pp": "Ω : Type u_1\ninst✝¹ : MeasureSpace Ω\ninst✝ : IsProbabilityMeasure ℙ\nX : Ω → ℝ\nhint : Integrable X ℙ\nhnonneg : 0 ≤ X\nK N : ℕ\nhKN : K ≤ N\nρ : Measure ℝ := Measure.map X ℙ\nthis : IsProbabilityMeasure ρ\n⊢ (∫ (a : Ω), truncation X (↑N) a) + ∫ (x : ℝ) in 0..↑N, 1 ∂ρ ≤ (∫ (a : Ω), X a) + ∫ (x : ℝ) i... | integral_truncation_le_integral_of_nonneg hint hnonneg | Mathlib.Tactic.evalGRewriteSeq | null |
Mathlib.RepresentationTheory.Equiv | {
"line": 169,
"column": 24
} | {
"line": 169,
"column": 49
} | [
{
"pp": "case h.h.h\nk✝ : Type u\ninst✝¹¹ : Semiring k✝\nG : Type v\ninst✝¹⁰ : Monoid G\nV : Type v'\ninst✝⁹ : AddCommMonoid V\ninst✝⁸ : Module k✝ V\nW : Type w'\ninst✝⁷ : AddCommMonoid W\ninst✝⁶ : Module k✝ W\nH : Type w\ninst✝⁵ : Subsingleton H\ninst✝⁴ : MulOneClass H\ninst✝³ : MulAction G H\nk : Type u\ninst... | simp [← x.isIntertwining] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Probability.Moments.SubGaussian | {
"line": 792,
"column": 2
} | {
"line": 792,
"column": 27
} | [
{
"pp": "Ω : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\nX : ℕ → Ω → ℝ\nh_indep : iIndepFun X μ\nc : ℝ≥0\nn : ℕ\nh_subG : ∀ i < n, HasSubgaussianMGF (X i) c μ\nε : ℝ\nhε : 0 ≤ ε\nh : μ.real {ω | ε ≤ ∑ i ∈ Finset.range n, X i ω} ≤ rexp (-ε ^ 2 / (2 * ↑(∑ i ∈ Finset.range n, c)))\n⊢ μ.real {ω | ε ≤ ∑ i ∈ Fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Probability.Moments.SubGaussian | {
"line": 865,
"column": 44
} | {
"line": 865,
"column": 55
} | [
{
"pp": "Ω : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\nX : Ω → ℝ\ninst✝ : IsProbabilityMeasure μ\na b : ℝ\nhm : AEMeasurable X μ\nhb : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b\nω : Ω\nhab : X ω ∈ Set.Icc a b\n⊢ X ω - ∫ (x : Ω), X x ∂μ ∈ Set.Icc (a - ∫ (x : Ω), X x ∂μ) (b - ∫ (x : Ω), X x ∂μ)",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Intertwining | {
"line": 55,
"column": 2
} | {
"line": 55,
"column": 13
} | [
{
"pp": "case mk.mk\nA : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁵ : Semiring A\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module A V\ninst✝ : Module A W\nρ : Representation A G V\nσ : Representation A G W\ntoLinearMap✝¹ : V →ₗ[A] W\nisIntertwining'✝¹ : ∀ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Intertwining | {
"line": 264,
"column": 35
} | {
"line": 264,
"column": 72
} | [
{
"pp": "case mk'.mk'\nA : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁵ : Semiring A\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module A V\ninst✝ : Module A W\nρ : Representation A G V\nσ : Representation A G W\ntoIntertwiningMap✝¹ : σ.IntertwiningMap ρ\ninvFu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Intertwining | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 13
} | [
{
"pp": "case mk'.mk'\nA : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁵ : Semiring A\ninst✝⁴ : Monoid G\ninst✝³ : AddCommMonoid V\ninst✝² : AddCommMonoid W\ninst✝¹ : Module A V\ninst✝ : Module A W\nρ : Representation A G V\nσ : Representation A G W\ntoIntertwiningMap✝¹ : ρ.IntertwiningMap σ\ninvFu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Intertwining | {
"line": 426,
"column": 37
} | {
"line": 426,
"column": 48
} | [
{
"pp": "case h\nA : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝⁷ : CommSemiring A\ninst✝⁶ : Monoid G\ninst✝⁵ : AddCommMonoid V\ninst✝⁴ : AddCommMonoid W\ninst✝³ : AddCommMonoid U\ninst✝² : Module A V\ninst✝¹ : Module A W\ninst✝ : Module A U\nρ : Representation A G V\nσ : Representat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Res | {
"line": 31,
"column": 38
} | {
"line": 31,
"column": 49
} | [
{
"pp": "k : Type u\ninst✝² : Semiring k\nG : Type v1\nH : Type v2\ninst✝¹ : Monoid G\ninst✝ : Monoid H\nf : H →* G\nX✝ Y✝ : Rep k G\nf' : X✝ ⟶ Y✝\nh : H\n⊢ ↑(Hom.hom f') ∘ₗ (MonoidHom.comp X✝.ρ f) h = (MonoidHom.comp Y✝.ρ f) h ∘ₗ ↑(Hom.hom f')",
"usedConstants": [
"Rep.V",
"Representation.Inter... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Res | {
"line": 53,
"column": 4
} | {
"line": 53,
"column": 15
} | [
{
"pp": "case hf.h\nk : Type u\ninst✝² : Semiring k\nG : Type v1\nH : Type v2\ninst✝¹ : Monoid G\ninst✝ : Monoid H\nf : H →* G\nM : Rep k G\nX✝ Y✝ : Rep k G\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : (Hom.hom ((resFunctor f).map a₁✝)).toLinearMap = (Hom.hom ((resFunctor f).map a₂✝)).toLinearMap\n⊢ (Hom.hom a₁✝).toLinearMap = (Hom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Res | {
"line": 58,
"column": 76
} | {
"line": 58,
"column": 87
} | [
{
"pp": "k : Type u\ninst✝² : Semiring k\nG : Type v1\nH : Type v2\ninst✝¹ : Monoid G\ninst✝ : Monoid H\nf : H →* G\nM : Rep k G\nX Y : Rep k G\nhf : Function.Surjective ⇑f\nf' : res f X ⟶ res f Y\nh : H\n⊢ (Hom.hom f').toLinearMap ∘ₗ X.ρ (f h) = Y.ρ (f h) ∘ₗ (Hom.hom f').toLinearMap",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Probability.StrongLaw | {
"line": 465,
"column": 8
} | {
"line": 465,
"column": 34
} | [
{
"pp": "case h.hbc\nΩ : Type u_1\ninst✝¹ : MeasureSpace Ω\ninst✝ : IsProbabilityMeasure ℙ\nX : ℕ → Ω → ℝ\nhint : Integrable (X 0) ℙ\nhindep : Pairwise ((fun f g ↦ f ⟂ᵢ g) on X)\nhident : ∀ (i : ℕ), IdentDistrib (X i) (X 0) ℙ ℙ\nhnonneg : ∀ (i : ℕ) (ω : Ω), 0 ≤ X i ω\nc : ℝ\nc_one : 1 < c\nε : ℝ\nεpos : 0 < ε\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Invariants | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 50
} | [
{
"pp": "case pred\nk : Type u_1\nG : Type u_2\nV : Type u_3\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nρ : Representation k G V\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nx : V\nhx : (ρ g) x = x\ni : ℕ\nh : (ρ ((fun x ↦ g ^ x) (-↑i))) x = x\n⊢ (ρ ((fun x ↦ g ^ x) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Invariants | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 15
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝⁴ : CommRing k\ninst✝³ : Group G\nV : Type u_5\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nρ : Representation k G V\nS : Subgroup G\ninst✝ : S.Normal\ng : G\nx : V\nhx : x ∈ invariants (MonoidHom.comp ρ S.subtype)\nx✝ : ↥S\ns : G\nhs : s ∈ S\n⊢ ((MonoidHom.comp ρ S.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Invariants | {
"line": 164,
"column": 58
} | {
"line": 164,
"column": 69
} | [
{
"pp": "k : Type u_1\nG : Type u_2\nV✝ : Type u_3\nW : Type u_4\ninst✝⁸ : CommRing k\ninst✝⁷ : Group G\ninst✝⁶ : AddCommGroup V✝\ninst✝⁵ : Module k V✝\ninst✝⁴ : AddCommGroup W\ninst✝³ : Module k W\nρ✝ : Representation k G V✝\nσ : Representation k G W\nV : Type u_5\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Character | {
"line": 213,
"column": 41
} | {
"line": 215,
"column": 52
} | [
{
"pp": "G : Type u_1\nk : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁹ : Group G\ninst✝⁸ : Field k\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : Module k V\ninst✝⁵ : FiniteDimensional k V\ninst✝⁴ : AddCommGroup W\ninst✝³ : Module k W\ninst✝² : FiniteDimensional k W\nρ : Representation k G V\nσ : Representation k G W\nins... | by
simp_rw [mul_comm, ← char_linHom, card_inv_mul_sum_char_eq_finrank,
(invariantsEquivIntertwiningMap ρ σ).finrank_eq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Probability.StrongLaw | {
"line": 541,
"column": 8
} | {
"line": 541,
"column": 58
} | [
{
"pp": "Ω : Type u_1\ninst✝¹ : MeasureSpace Ω\ninst✝ : IsProbabilityMeasure ℙ\nX : ℕ → Ω → ℝ\nhint : Integrable (X 0) ℙ\nhident : ∀ (i : ℕ), IdentDistrib (X i) (X 0) ℙ ℙ\nhnonneg : ∀ (i : ℕ) (ω : Ω), 0 ≤ X i ω\nA : ∑' (j : ℕ), ℙ {ω | X j ω ∈ Set.Ioi ↑j} < ∞\nω : Ω\nhω : ∀ᶠ (n : ℕ) in atTop, X n ω ∉ Set.Ioi ↑n\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Probability.StrongLaw | {
"line": 611,
"column": 4
} | {
"line": 611,
"column": 20
} | [
{
"pp": "case h\nΩ : Type u_2\nm : MeasurableSpace Ω\nμ : Measure Ω\nX : ℕ → Ω → ℝ\nhint : Integrable (X 0) μ\nhindep : Pairwise ((fun x1 x2 ↦ x1 ⟂ᵢ[μ] x2) on X)\nhident : ∀ (i : ℕ), IdentDistrib (X i) (X 0) μ μ\nmΩ : MeasureSpace Ω := { toMeasurableSpace := m, volume := μ }\nh : ∀ᵐ (ω : Ω), X 0 ω = 0\nI : ∀ᵐ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Probability.StrongLaw | {
"line": 799,
"column": 4
} | {
"line": 799,
"column": 20
} | [
{
"pp": "case h\nΩ : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : CompleteSpace E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nX : ℕ → Ω → E\nhint : Integrable (X 0) μ\nhindep : Pairwise ((fun x1 x2 ↦ x1 ⟂ᵢ[μ] x2) on X)\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinduced | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 27
} | [
{
"pp": "k : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁶ : Semiring k\ninst✝⁵ : Monoid G\ninst✝⁴ : Monoid H\nφ : G →* H\nA : Type u_4\nB : Type u_5\ninst✝³ : AddCommMonoid A\ninst✝² : Module k A\ninst✝¹ : AddCommMonoid B\ninst✝ : Module k B\nσ : Representation k G A\nρ : Representation k G B\nh : H\nx : H → B\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinduced | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 19
} | [
{
"pp": "k : Type u_1\nG : Type u_2\nH : Type u_3\ninst✝⁶ : Semiring k\ninst✝⁵ : Monoid G\ninst✝⁴ : Monoid H\nφ : G →* H\nA : Type u_4\nB : Type u_5\ninst✝³ : AddCommMonoid A\ninst✝² : Module k A\ninst✝¹ : AddCommMonoid B\ninst✝ : Module k B\nσ : Representation k G A\nρ : Representation k G B\nf : σ.Intertwinin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 162,
"column": 35
} | {
"line": 162,
"column": 76
} | [
{
"pp": "case mk''.mk''\nR : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁹ : Monoid G\ninst✝⁸ : Ring R\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : TopologicalSpace V\ninst✝⁵ : IsTopologicalAddGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddCommGroup W\ninst✝² : TopologicalSpace W\ninst✝¹ : IsTopologicalAddGroup W... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 13
} | [
{
"pp": "case mk''.mk''\nR : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\ninst✝⁹ : Monoid G\ninst✝⁸ : Ring R\ninst✝⁷ : AddCommGroup V\ninst✝⁶ : TopologicalSpace V\ninst✝⁵ : IsTopologicalAddGroup V\ninst✝⁴ : Module R V\ninst✝³ : AddCommGroup W\ninst✝² : TopologicalSpace W\ninst✝¹ : IsTopologicalAddGroup W... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinduced | {
"line": 189,
"column": 40
} | {
"line": 189,
"column": 51
} | [
{
"pp": "case h.h.h\nk : Type u\nG : Type v\nH : Type w\ninst✝² : CommRing k\ninst✝¹ : Monoid G\ninst✝ : Monoid H\nφ : G →* H\nA : Rep k G\nf g : ↑(coind' φ A)\nhfg : ∀ (h : H), (Hom.hom f).toLinearMap (single h 1) = (Hom.hom g).toLinearMap (single h 1)\nh : H\n⊢ ((Hom.hom f).toLinearMap ∘ₗ lsingle h) 1 = ((Hom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinduced | {
"line": 220,
"column": 15
} | {
"line": 220,
"column": 26
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type w\ninst✝² : CommRing k\ninst✝¹ : Monoid G\ninst✝ : Monoid H\nφ : G →* H\nA : Rep k G\nf : res φ (leftRegular k H) ⟶ A\ng : G\nh : H\n⊢ ?m.201",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinduced | {
"line": 249,
"column": 45
} | {
"line": 249,
"column": 56
} | [
{
"pp": "k : Type u\nG : Type v\nH : Type w\ninst✝² : CommRing k\ninst✝¹ : Monoid G\ninst✝ : Monoid H\nφ : G →* H\nA✝ : Rep k G\nB : Rep k H\nA : Rep k G\nf : res φ B ⟶ A\nx✝² : ↑B\nx✝¹ : G\nx✝ : H\n⊢ (LinearMap.pi fun h ↦ (Hom.hom f).toLinearMap ∘ₗ B.ρ h) x✝² (φ x✝¹ * x✝) =\n (A.ρ x✝¹) ((LinearMap.pi fun h ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 313,
"column": 6
} | {
"line": 313,
"column": 17
} | [
{
"pp": "R : Type u_1\nG✝ : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝²³ : Monoid G✝\ninst✝²² : Ring R\ninst✝²¹ : AddCommGroup V\ninst✝²⁰ : TopologicalSpace V\ninst✝¹⁹ : IsTopologicalAddGroup V\ninst✝¹⁸ : Module R V\ninst✝¹⁷ : AddCommGroup W\ninst✝¹⁶ : TopologicalSpace W\ninst✝¹⁵ : IsTopologicalA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FinGroupCharZero | {
"line": 114,
"column": 6
} | {
"line": 114,
"column": 22
} | [
{
"pp": "case refine_2\nk : Type u\ninst✝⁴ : Field k\nG : Type u\ninst✝³ : Finite G\ninst✝² : Group G\ninst✝¹ : IsAlgClosed k\ninst✝ : NeZero ↑(Nat.card G)\nV : FDRep k G\nh : Module.finrank k (V ⟶ V) = 1\nW : FDRep k G\nf : W ⟶ V\nx✝ : Mono f\nι : Abelian.image f ⟶ V := Abelian.image.ι f\nhf : Abelian.factorTh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FinGroupCharZero | {
"line": 131,
"column": 6
} | {
"line": 132,
"column": 11
} | [
{
"pp": "k : Type u\ninst✝⁴ : Field k\nG : Type u\ninst✝³ : Group G\ninst✝² : IsAlgClosed k\ninst✝¹ : CharZero k\ninst✝ : Fintype G\nV : FDRep k G\nh : Simple V\nthis✝¹ : NeZero ↑(Nat.card G)\nthis✝ : Invertible ↑(Nat.card G)\nthis : Invertible ↑(Fintype.card G)\n⊢ ⅟↑(Nat.card G) • ∑ g, V.character g * V.charac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 108,
"column": 4
} | {
"line": 109,
"column": 32
} | [
{
"pp": "k : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nX : Type u_5\ninst✝⁷ : CommRing k\ninst✝⁶ : Monoid G\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module k V\ninst✝³ : AddCommGroup W\ninst✝² : Module k W\ninst✝¹ : AddCommGroup X\ninst✝ : Module k X\nρ : Representation k G V\nτ : Representation k G W\nυ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 129,
"column": 34
} | {
"line": 129,
"column": 45
} | [
{
"pp": "k : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nX : Type u_5\ninst✝⁷ : CommRing k\ninst✝⁶ : Monoid G\ninst✝⁵ : AddCommGroup V\ninst✝⁴ : Module k V\ninst✝³ : AddCommGroup W\ninst✝² : Module k W\ninst✝¹ : AddCommGroup X\ninst✝ : Module k X\nρ : Representation k G V\nτ : Representation k G W\nυ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 159,
"column": 4
} | {
"line": 159,
"column": 22
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\ninst✝⁴ : CommRing k\ninst✝³ : Group G\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nρ : Representation k G V\nS : Subgroup G\ninst✝ : S.Normal\ng : G\nx✝¹ : V\nx✝ : x✝¹ ∈ Set.range fun gv ↦ ((MonoidHom.comp ρ S.subtype) gv.1) gv.2 - gv.2\ns : ↥S\nx : V\nhs : (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 15
} | [
{
"pp": "case h\nk : Type u_1\nG : Type u_2\ninst✝⁴ : CommRing k\ninst✝³ : Group G\nV : Type u_4\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nρ : Representation k G V\ng : G\ninst✝ : Finite G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nα : V\nn : ℕ\na✝ : (fun gv ↦ (ρ gv.1) gv.2 - gv.2) ((fun x ↦ g ^ x) n, α) ∈ ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 63,
"column": 4
} | {
"line": 63,
"column": 15
} | [
{
"pp": "case refine_2\nk : Type u_1\nG : Type u_2\ninst✝⁴ : CommRing k\ninst✝³ : Group G\nV : Type u_4\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\nρ : Representation k G V\ng : G\ninst✝ : Finite G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\ny : V\n⊢ (ρ g - LinearMap.id) y ∈ Coinvariants.ker ρ",
"usedConsta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 79,
"column": 4
} | {
"line": 80,
"column": 11
} | [
{
"pp": "case refine_1\nk : Type u_1\nG : Type u_2\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Finite G\nthis : Fintype G\ng : G\ny : G →₀ k\n⊢ (fun gv ↦ ((leftRegular k G) gv.1) gv.2 - gv.2) (g, y) ∈ ↑(linearCombination k fun x ↦ 1).ker",
"usedConstants": [
"Finsupp.instFunLike",
"LinearMap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 107,
"column": 10
} | {
"line": 107,
"column": 44
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nx : ↑(leftRegular k G)\nhx : x ∈ (Hom.hom ((leftRegular k G).applyAsHom g - 𝟙 (leftRegular k G))).ker\na✝ : G\n⊢ ((Representation.leftRegular k G) g) x = x",
"usedConstants": ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 211,
"column": 8
} | {
"line": 212,
"column": 81
} | [
{
"pp": "case zero.left.hS\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\n⊢ ({\n X₁ :=\n ((HomologicalComplex.shortComplexFunctor' (Rep k G) (ComplexShape.down ℕ) 1 0 0).obj\n ((chainComplexFunctor k ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 224,
"column": 8
} | {
"line": 226,
"column": 15
} | [
{
"pp": "case pos\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nm : ℕ\na✝ : QuasiIsoAt (resolution.π k g) m\nhm : Odd (m + 1)\n⊢ (ModuleCat.Hom.hom\n ((HomologicalComplex.sc' ((chainComplexFunctor k g).obj (leftRegular k G)) (m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.FiniteCyclic | {
"line": 227,
"column": 8
} | {
"line": 229,
"column": 13
} | [
{
"pp": "case neg\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nm : ℕ\na✝ : QuasiIsoAt (resolution.π k g) m\nhm : ¬Odd (m + 1)\n⊢ (ModuleCat.Hom.hom\n ((HomologicalComplex.sc' ((chainComplexFunctor k g).obj (leftRegular k G)) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 13
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B : Rep k G\nf : A ⟶ B\ng : G\na : ↑A\n⊢ (Hom.hom f) ((A.ρ g) a) = (B.ρ g) ((Hom.hom f) a)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 13
} | [
{
"pp": "case hfg\nk G : Type u\ninst✝¹ : CommRing k\ninst✝ : Monoid G\n⊢ (((forget₂ (Rep k G) (ModuleCat k)).mapHomologicalComplex (ComplexShape.down ℕ)).map (εToSingle₀ k G) ≫\n (HomologicalComplex.singleMapHomologicalComplex (forget₂ (Rep k G) (ModuleCat k)) (ComplexShape.down ℕ)\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 498,
"column": 40
} | {
"line": 498,
"column": 51
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA B C : Rep k G\nX✝ Y✝ : Action (ModuleCat k) G\nf : X✝ ⟶ Y✝\ng : G\n⊢ ModuleCat.Hom.hom f.hom ∘ₗ (X✝.V.endRingEquiv.toMonoidHom.comp X✝.ρ) g =\n (Y✝.V.endRingEquiv.toMonoidHom.comp Y✝.ρ) g ∘ₗ ModuleCat.Hom.hom f.hom",
"usedConstants": [... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 406,
"column": 63
} | {
"line": 406,
"column": 74
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn : ℕ\ninst✝ : Group G\nm : ℕ\nkey : (barComplex.d k G (m + 1) ≫ barComplex.d k G m) ≫ (diagonalSuccIsoFree k G m).inv = 0\n⊢ ((fun n ↦ barComplex.d k G n) (m + 1) ≫ (fun n ↦ barComplex.d k G n) m) ≫ (diagonalSuccIsoFree k G m).inv =\n 0 ≫ (diagonalSuccIsoFree k G ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.Resolution | {
"line": 418,
"column": 43
} | {
"line": 418,
"column": 76
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn : ℕ\ninst✝ : Group G\nj : ℕ\n⊢ (diagonalSuccIsoFree k G (j + 1)).inv ≫ (standardComplex k G).d (j + 1) j = d k G j ≫ (diagonalSuccIsoFree k G j).inv",
"usedConstants": [
"Eq.mpr",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"... | d_comp_diagonalSuccIsoFree_inv_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 19
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn✝ : ℕ\ninst✝ : Group G\nA : Rep k G\nn : ℕ\n⊢ d A n ≫ d A (n + 1) = 0",
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
"inhomogeneousCochains.d",
"Rep.V",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiv... | rw [d_eq, d_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Basic | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 35
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\nn : ℕ\ninst✝ : Group G\nA : Rep k G\n⊢ d A n ≫ d A (n + 1) = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 753,
"column": 15
} | {
"line": 753,
"column": 26
} | [
{
"pp": "k : Type u\nG✝ : Type v\ninst✝² : CommRing k\ninst✝¹ : Monoid G✝\nG : Type v\ninst✝ : Group G\nA✝ B✝ C✝ : Rep k G\nA B C : Rep k G\nf : A ⊗ B ⟶ C\ng : G\nx : ↑B\ny : ↑A\n⊢ ?m.292",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 757,
"column": 4
} | {
"line": 757,
"column": 15
} | [
{
"pp": "k : Type u\nG✝ : Type v\ninst✝² : CommRing k\ninst✝¹ : Monoid G✝\nG : Type v\ninst✝ : Group G\nA✝ B✝ C✝ : Rep k G\nA B C : Rep k G\nf : B ⟶ A.ihom.obj C\ng : G\nx : ↑A\ny : ↑B\n⊢ ((TensorProduct.uncurry (RingHom.id k) ↑A ↑B ↑C) (Hom.hom f).flip ∘ₗ (A.ρ.tprod B.ρ) g) (x ⊗ₜ[k] y) =\n (C.ρ g ∘ₗ (Tensor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic | {
"line": 73,
"column": 62
} | {
"line": 74,
"column": 9
} | [
{
"pp": "case h\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g\nx✝ : ↑A\n⊢ x✝ ∈ A.ρ.invariants ↔ x✝ ∈ (Hom.hom (A.applyAsHom g - 𝟙 A)).ker",
"usedConstants": [
"LinearMap.id",
"Eq.mpr",
"Submodule",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FiniteIndex | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 13
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Group G\nS : Subgroup G\ninst✝ : DecidableRel ⇑(QuotientGroup.rightRel S)\nA : Rep.{w, u, v} k ↥S\ng₁ g₂ g₃ : G\na : ↑A\n⊢ (A.indToCoindAux (g₁ * g₂⁻¹)) a g₃ = (A.indToCoindAux g₁) a (g₃ * g₂)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FiniteIndex | {
"line": 124,
"column": 21
} | {
"line": 124,
"column": 83
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝³ : CommRing k\ninst✝² : Group G\nS : Subgroup G\ninst✝¹ : DecidableRel ⇑(QuotientGroup.rightRel S)\nA : Rep.{w, u, v} k ↥S\ninst✝ : S.FiniteIndex\nx✝¹ x✝ : ↑(coind.{u, v, v, w} S.subtype A)\n⊢ ∑ g, g.liftOn (fun g ↦ (IndV.mk S.subtype A.ρ g) (↑(x✝¹ + x✝) g)) ⋯ =\n ∑ g, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FiniteIndex | {
"line": 126,
"column": 22
} | {
"line": 126,
"column": 51
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝³ : CommRing k\ninst✝² : Group G\nS : Subgroup G\ninst✝¹ : DecidableRel ⇑(QuotientGroup.rightRel S)\nA : Rep.{w, u, v} k ↥S\ninst✝ : S.FiniteIndex\nx✝¹ : k\nx✝ : ↑(coind.{u, v, v, w} S.subtype A)\n⊢ ∑ g, g.liftOn (fun g ↦ (IndV.mk S.subtype A.ρ g) (↑(x✝¹ • x✝) g)) ⋯ =\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FiniteIndex | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 15
} | [
{
"pp": "case h.a.h.h₀.h\nk : Type u\nG : Type v\ninst✝³ : CommRing k\ninst✝² : Group G\nS : Subgroup G\ninst✝¹ : DecidableRel ⇑(QuotientGroup.rightRel S)\nA : Rep.{w, u, v} k ↥S\ninst✝ : S.FiniteIndex\ng : ↑(coind.{u, v, v, w} S.subtype A)\na b : G\na✝ : ⟦b⟧ ∈ Finset.univ\nhb : ⟦b⟧ ≠ ⟦a⟧\n⊢ ↑(A.indToCoind (⟦b⟧... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.FiniteIndex | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 15
} | [
{
"pp": "case H.a.h.h.h.hx\nk : Type u\nG : Type v\ninst✝³ : CommRing k\ninst✝² : Group G\nS : Subgroup G\ninst✝¹ : DecidableRel ⇑(QuotientGroup.rightRel S)\nA : Rep.{w, u, v} k ↥S\ninst✝ : S.FiniteIndex\ng : G\na : ↑A\nx : G\nhx : x ∉ MulAction.orbit (↥S) g\n⊢ x ∉\n Function.support\n ↑(A.indToCoind\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 72
} | [
{
"pp": "K L : Type\ninst✝¹⁶ : Field K\ninst✝¹⁵ : Field L\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : FiniteDimensional K L\ninst✝¹² : IsGalois K L\ninst✝¹¹ : IsCyclic Gal(L/K)\ng : Gal(L/K)\nA : Type u_1\nB : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : CommRing B\ninst✝⁸ : Algebra A B\ninst✝⁷ : Algebra A L\ninst✝⁶ : Algebr... | exact (algebraMap K L).injective.comp (IsFractionRing.injective A K) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 110,
"column": 21
} | {
"line": 110,
"column": 54
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\ny : (Fin i → G) → ↑X.X₂\nx : (Fin j → G) → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom ((inhomogeneousCochains X.X₂).d i j)) y\n⊢ (ConcreteCategory.hom (inhomogeneousCochains.d X.X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 112,
"column": 10
} | {
"line": 112,
"column": 21
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\ny : (Fin i → G) → ↑X.X₂\nx : (Fin j → G) → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom ((inhomogeneousCochains X.X₂).d i j)) y\n⊢ (ConcreteCategory.hom ((forget₂ (ModuleCat k) Ab).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 123,
"column": 58
} | {
"line": 123,
"column": 91
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni : ℕ\nz : (Fin i → G) → ↑X.X₃\ny : (Fin i → G) → ↑X.X₂\nhy : (ConcreteCategory.hom ((cochainsMap (MonoidHom.id G) X.g).f i)) y = z\nhz : (ConcreteCategory.hom ((inhomogeneousCochains X.X₃).d i (i + 1))) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 126,
"column": 8
} | {
"line": 126,
"column": 19
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : i + 1 = j\nz : (Fin i → G) → ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousCochains X.X₃).d i j)) z = 0\ny : (Fin i → G) → ↑X.X₂\nhy : (ConcreteCategory.hom ((cochainsMap (MonoidHom.id G... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 69
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥X.X₃.ρ.invariants\ny : ↑X.X₂\nhy : (Rep.Hom.hom X.g) y = ↑z\nx : G → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom (d₀₁ X.X₂)) y\n⊢ (ConcreteCategory.hom (δ hX 0 1 ⋯)) ((ConcreteCategory... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 152,
"column": 6
} | {
"line": 152,
"column": 24
} | [
{
"pp": "case h\nk G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥X.X₃.ρ.invariants\ny : ↑X.X₂\nhy : (Rep.Hom.hom X.g) y = ↑z\nx : G → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom (d₀₁ X.X₂)) y\ng : Fin (0 + 1) → G\n⊢ (⇑(Rep.Hom.hom X.f) ∘ (Co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 172,
"column": 2
} | {
"line": 172,
"column": 70
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cocycles₁ X.X₃)\ny : G → ↑X.X₂\nhy : ⇑(Rep.Hom.hom X.g) ∘ y = ⇑z\nx : G × G → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom (d₁₂ X.X₂)) y\n⊢ (ConcreteCategory.hom (δ hX 1 2 ⋯)) ((Concre... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence | {
"line": 179,
"column": 6
} | {
"line": 179,
"column": 24
} | [
{
"pp": "case h\nk G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cocycles₁ X.X₃)\ny : G → ↑X.X₂\nhy : ⇑(Rep.Hom.hom X.g) ∘ y = ⇑z\nx : G × G → ↑X.X₁\nhx : ⇑(Rep.Hom.hom X.f) ∘ x = (ConcreteCategory.hom (d₁₂ X.X₂)) y\ng : Fin (1 + 1) → G\n⊢ (⇑(Rep.Hom.hom ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.Basic | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 33
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nn : ℕ\n⊢ d A (n + 1) ≫ d A n = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 309,
"column": 2
} | {
"line": 309,
"column": 79
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nf : ↥(cocycles₁ A)\nthis : (A.ρ 1) (f 1) - f (1 * 1) + f 1 = 0\n⊢ f 1 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 504,
"column": 2
} | {
"line": 504,
"column": 51
} | [
{
"pp": "G : Type u_1\nA : Type u_2\ninst✝² : Monoid G\ninst✝¹ : AddCommGroup A\ninst✝ : MulAction G A\nf : G → A\nhf : IsCocycle₁ f\n⊢ f 1 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 508,
"column": 2
} | {
"line": 508,
"column": 62
} | [
{
"pp": "G : Type u_1\nA : Type u_2\ninst✝² : Monoid G\ninst✝¹ : AddCommGroup A\ninst✝ : MulAction G A\nf : G × G → A\nhf : IsCocycle₂ f\ng : G\n⊢ f (1, g) = f (1, 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 512,
"column": 2
} | {
"line": 512,
"column": 42
} | [
{
"pp": "G : Type u_1\nA : Type u_2\ninst✝² : Monoid G\ninst✝¹ : AddCommGroup A\ninst✝ : MulAction G A\nf : G × G → A\nhf : IsCocycle₂ f\ng : G\n⊢ f (g, 1) = g • f (1, 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 636,
"column": 2
} | {
"line": 636,
"column": 51
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝² : Monoid G\ninst✝¹ : CommGroup M\ninst✝ : MulAction G M\nf : G → M\nhf : IsMulCocycle₁ f\n⊢ f 1 = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 640,
"column": 2
} | {
"line": 640,
"column": 62
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝² : Monoid G\ninst✝¹ : CommGroup M\ninst✝ : MulAction G M\nf : G × G → M\nhf : IsMulCocycle₂ f\ng : G\n⊢ f (1, g) = f (1, 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 644,
"column": 2
} | {
"line": 644,
"column": 42
} | [
{
"pp": "G : Type u_1\nM : Type u_2\ninst✝² : Monoid G\ninst✝¹ : CommGroup M\ninst✝ : MulAction G M\nf : G × G → M\nhf : IsMulCocycle₂ f\ng : G\n⊢ f (g, 1) = g • f (1, 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 919,
"column": 2
} | {
"line": 919,
"column": 13
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H0 A) → Prop\nx : ↑(H0 A)\nh : ∀ (x : ↥A.ρ.invariants), C ((ConcreteCategory.hom (H0Iso A).inv) x)\n⊢ C x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 981,
"column": 45
} | {
"line": 981,
"column": 62
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H1 A) → Prop\nx : ↑(H1 A)\nh : ∀ (x : ↥(cocycles₁ A)), C ((ConcreteCategory.hom (H1π A)) x)\ny : ↑(cocycles A 1)\n⊢ C ((ConcreteCategory.hom (π A 1)) y)",
"usedConstants": [
"groupCohomology",
"groupCohomology.cocycl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 1055,
"column": 2
} | {
"line": 1056,
"column": 5
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx y : ↥(cocycles₂ A)\n⊢ (ConcreteCategory.hom (H2π A)) x = (ConcreteCategory.hom (H2π A)) y ↔ ⇑x - ⇑y ∈ coboundaries₂ A",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Pi.Function.module",
"Subm... | rw [← sub_eq_zero, ← map_sub, H2π_eq_zero_iff]
rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 1055,
"column": 2
} | {
"line": 1056,
"column": 5
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx y : ↥(cocycles₂ A)\n⊢ (ConcreteCategory.hom (H2π A)) x = (ConcreteCategory.hom (H2π A)) y ↔ ⇑x - ⇑y ∈ coboundaries₂ A",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Pi.Function.module",
"Subm... | rw [← sub_eq_zero, ← map_sub, H2π_eq_zero_iff]
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 1061,
"column": 45
} | {
"line": 1061,
"column": 62
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H2 A) → Prop\nx : ↑(H2 A)\nh : ∀ (x : ↥(cocycles₂ A)), C ((ConcreteCategory.hom (H2π A)) x)\ny : ↑(cocycles A 2)\n⊢ C ((ConcreteCategory.hom (π A 2)) y)",
"usedConstants": [
"groupCohomology",
"groupCohomology.cocycl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 1061,
"column": 45
} | {
"line": 1061,
"column": 89
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H2 A) → Prop\nx : ↑(H2 A)\nh : ∀ (x : ↥(cocycles₂ A)), C ((ConcreteCategory.hom (H2π A)) x)\ny : ↑(cocycles A 2)\n⊢ C ((ConcreteCategory.hom (π A 2)) y)",
"usedConstants": [
"Pi.Function.module",
"Submodule",
"... | simpa [H2π] using h ((isoCocycles₂ A).hom y) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 1061,
"column": 45
} | {
"line": 1061,
"column": 89
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H2 A) → Prop\nx : ↑(H2 A)\nh : ∀ (x : ↥(cocycles₂ A)), C ((ConcreteCategory.hom (H2π A)) x)\ny : ↑(cocycles A 2)\n⊢ C ((ConcreteCategory.hom (π A 2)) y)",
"usedConstants": [
"Pi.Function.module",
"Submodule",
"... | simpa [H2π] using h ((isoCocycles₂ A).hom y) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | {
"line": 1061,
"column": 45
} | {
"line": 1061,
"column": 89
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H2 A) → Prop\nx : ↑(H2 A)\nh : ∀ (x : ↥(cocycles₂ A)), C ((ConcreteCategory.hom (H2π A)) x)\ny : ↑(cocycles A 2)\n⊢ C ((ConcreteCategory.hom (π A 2)) y)",
"usedConstants": [
"Pi.Function.module",
"Submodule",
"... | simpa [H2π] using h ((isoCocycles₂ A).hom y) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 59,
"column": 4
} | {
"line": 60,
"column": 11
} | [
{
"pp": "case hf.h.h\nk G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn i : ℕ\nx✝ : ↑((inhomogeneousCochains A).X i)\ng✝ : Fin (i + 1) → G\n⊢ (ModuleCat.Hom.hom\n (ModuleCat.ofHom ((Hom.hom φ).compLeft (Fin i → G) ∘ₗ LinearMap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 44
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nhf : Function.Surjective ⇑f\ninst✝ : Mono φ\ni : ℕ\n⊢ Mono ((cochainsMap f φ).f i)",
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
"Rep.V",
"C... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 44
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nhf : Function.Injective ⇑f\ninst✝ : Epi φ\ni : ℕ\n⊢ Epi ((cochainsMap f φ).f i)",
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
"Rep.V",
"Cate... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 261,
"column": 4
} | {
"line": 261,
"column": 51
} | [
{
"pp": "case hf.h.h\nk G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\nx : ↑(shortComplexH1 A).X₁\ng : G\n⊢ (ModuleCat.Hom.hom (Hom.toModuleCatHom φ ≫ (shortComplexH1 B).f)) x g =\n (ModuleCat.Hom.hom ((shortComplexH1 A).f ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 265,
"column": 4
} | {
"line": 265,
"column": 65
} | [
{
"pp": "case hf.h.h\nk G H : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nA : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A ⟶ B\nn : ℕ\nx : ↑(shortComplexH1 A).X₂\ng : G × G\n⊢ (ModuleCat.Hom.hom (cochainsMap₁ f φ ≫ (shortComplexH1 B).g)) x g =\n (ModuleCat.Hom.hom ((shortComplexH1 A).g ≫... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 360,
"column": 31
} | {
"line": 360,
"column": 64
} | [
{
"pp": "k G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA✝ : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A✝ ⟶ B\nn : ℕ\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cocycles₁ (A.quotientToInvariants S))\nhx :\n (ConcreteCategory.hom (H1π (of A.ρ)))\n ((ConcreteCategory.ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 92
} | [
{
"pp": "case h\nk G H : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Group H\nA✝ : Rep k H\nB : Rep k G\nf : G →* H\nφ : res f A✝ ⟶ B\nn : ℕ\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\nx : ↥(cocycles₁ (A.quotientToInvariants S))\nhx :\n (ConcreteCategory.hom (H1π (of A.ρ)))\n ((ConcreteCat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Induced | {
"line": 152,
"column": 4
} | {
"line": 152,
"column": 15
} | [
{
"pp": "case hf.h.H.a.h.h.h\nk : Type u\nG : Type v\nH : Type v'\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA✝ : Rep k G\nB✝ : Rep k H\nA : Rep k G\nB : Rep k H\nf : ind φ A ⟶ B\nh : H\na : ↑A\n⊢ ((TensorProduct.AlgebraTensorModule.curry\n ((Hom.hom\n ((fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Induced | {
"line": 193,
"column": 22
} | {
"line": 194,
"column": 13
} | [
{
"pp": "case a.h.h.h.h\nk : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ng : G\na✝ : H\nx✝¹ : ↑A\nx✝ : ↑B\n⊢ (((TensorProduct.AlgebraTensorModule... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Induced | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 62
} | [
{
"pp": "case a.h.h\nk : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\ns : G\nx : ↑A\ny : ↑B\n⊢ ((TensorProduct.AlgebraTensorModule.curry\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Induced | {
"line": 243,
"column": 4
} | {
"line": 244,
"column": 61
} | [
{
"pp": "case hfg.H.a.h.h.h.h\nk : Type u\nG✝ : Type v\nH✝ : Type v'\ninst✝⁴ : CommRing k\ninst✝³ : Group G✝\ninst✝² : Group H✝\nφ✝ : G✝ →* H✝\nA✝ : Rep k G✝\nG H : Type u\ninst✝¹ : Group G\ninst✝ : Group H\nφ : G →* H\nA : Rep k G\nB : Rep k H\nh : H\na : ↑A\nb : ↑B\n⊢ (((TensorProduct.AlgebraTensorModule.curr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic | {
"line": 63,
"column": 6
} | {
"line": 64,
"column": 83
} | [
{
"pp": "case pos\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : CommGroup G\ninst✝ : Fintype G\nA : Rep k G\ng✝ : G\nhg : ∀ (x : G), x ∈ Subgroup.zpowers g✝\nj : ℕ\na : ↑A\ng : G\nhj : Even (j + 1)\n⊢ (((A.coinvariantsTensorMk ((resolution k g✝⁻¹ ⋯).complex.X (j + 1))).compr₂\n (ModuleCat.Hom.hom\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 115,
"column": 4
} | {
"line": 115,
"column": 15
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\ny : (Fin i → G) →₀ ↑X.X₂\nx : (Fin j → G) →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom ((inhomogeneousChains X.X₂).d i j)) y\n⊢ (ConcreteCategory.ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 116,
"column": 10
} | {
"line": 116,
"column": 21
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\ny : (Fin i → G) →₀ ↑X.X₂\nx : (Fin j → G) →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom ((inhomogeneousChains X.X₂).d i j)) y\n⊢ (ConcreteCategory.ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 129,
"column": 67
} | {
"line": 129,
"column": 78
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : j + 1 = i\nz : (Fin i → G) →₀ ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousChains X.X₃).d i j)) z = 0\ny : (Fin i → G) →₀ ↑X.X₂\nhy : (ConcreteCategory.hom ((chainsMap (MonoidHom.id G) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 131,
"column": 74
} | {
"line": 131,
"column": 85
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\ni j : ℕ\nhij : j + 1 = i\nz : (Fin i → G) →₀ ↑X.X₃\nhz : (ConcreteCategory.hom ((inhomogeneousChains X.X₃).d i j)) z = 0\ny : (Fin i → G) →₀ ↑X.X₂\nhy : (ConcreteCategory.hom ((chainsMap (MonoidHom.id G) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 141,
"column": 2
} | {
"line": 143,
"column": 7
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₁ X.X₃)\ny : G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : ↑X.X₁\nhx : (Rep.Hom.hom X.f) x = (ConcreteCategory.hom (d₁₀ X.X₂)) y\n⊢ (ConcreteCategory.hom (δ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence | {
"line": 167,
"column": 2
} | {
"line": 169,
"column": 7
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nX : ShortComplex (Rep k G)\nhX : X.ShortExact\nz : ↥(cycles₂ X.X₃)\ny : G × G →₀ ↑X.X₂\nhy : (mapRange.linearMap (Rep.Hom.hom X.g).toLinearMap) y = ↑z\nx : G →₀ ↑X.X₁\nhx : (mapRange.linearMap (Rep.Hom.hom X.f).toLinearMap) x = (ConcreteCategory.hom (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Tannaka | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 24
} | [
{
"pp": "case h.h\nk G : Type u\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : Finite G\ninst✝ : Fintype G\nX : FDRep k G\nv : ↑X.V\nt : G\nf : ↑rightFDRep.V.obj\nφ_term : (X : FDRep k G) → (G → k) → ↑X.V → G → ↑X.V := fun X f v s ↦ f s • (X.ρ s⁻¹) v\nthis :\n ∑ x ∈ map (mulRightEmbedding t⁻¹) univ, φ_term X... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RepresentationTheory.Tannaka | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 13
} | [
{
"pp": "case h.h.w.h.h.h\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\ninst✝ : Finite G\nη₁ η₂ : Aut (forget k G)\nh : η₁.hom.hom.app rightFDRep = η₂.hom.hom.app rightFDRep\nthis : Fintype G\nX : FDRep k G\nv : ↑((forget k G).obj X).obj\nh1 : (forget k G).map (ofRightFDRep X v) ≫ η₁.hom.hom.app X = (fo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.MvPolynomial.Ideal | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 37
} | [
{
"pp": "case a\nσ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ni : σ\nc : σ →₀ ℕ\nhx : c + single i 1 ∈ ⇑degree ⁻¹' Set.Ici 1\nhi : i ∈ (c + single i 1).support\n⊢ c + single i 1 ∈ (fun x ↦ (monomial x) 1) ⁻¹' ↑(Submodule.restrictScalars R (idealOfVars σ R))",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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