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.RepresentationTheory.Coinvariants | {
"line": 217,
"column": 40
} | {
"line": 217,
"column": 42
} | {
"line": 218,
"column": 2
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nρ : Representation k G V\nα : Type u_9\nx : α\na : V\n⊢ (ρ.coinvariantsToFinsupp α) ((Coinvariants.mk (ρ.finsupp α)) (single x a)) = single x ((Coinvariants.mk ρ) a)",
"ppTe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 232,
"column": 46
} | {
"line": 232,
"column": 48
} | {
"line": 232,
"column": 49
} | [
{
"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\nh : H\n⊢ ↑(coindVEquiv φ A) ∘ₗ (Representation.coind φ A.ρ) h = (Representation.coind' φ A) h ∘ₗ ↑(coindVEquiv φ A)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 226,
"column": 80
} | {
"line": 226,
"column": 82
} | {
"line": 226,
"column": 83
} | [
{
"pp": "k✝ : Type u_1\nG✝ : Type u_2\nV✝ : Type u_3\nW : Type u_4\nX : Type u_5\ninst✝¹¹ : CommRing k✝\ninst✝¹⁰ : Monoid G✝\ninst✝⁹ : AddCommGroup V✝\ninst✝⁸ : Module k✝ V✝\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : Module k✝ W\ninst✝⁵ : AddCommGroup X\ninst✝⁴ : Module k✝ X\nρ✝ : Representation k✝ G✝ V✝\nτ : Represent... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 231,
"column": 40
} | {
"line": 231,
"column": 42
} | {
"line": 232,
"column": 2
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nρ : Representation k G V\nα : Type u_9\na : α\nx : V\n⊢ (ρ.finsuppToCoinvariants α) (single a ((Coinvariants.mk ρ) x)) = (Coinvariants.mk (ρ.finsupp α)) (single a x)",
"ppTe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 241,
"column": 5
} | {
"line": 241,
"column": 7
} | {
"line": 241,
"column": 8
} | [
{
"pp": "k✝ : Type u_1\nG✝ : Type u_2\nV✝ : Type u_3\nW : Type u_4\nX : Type u_5\ninst✝¹¹ : CommRing k✝\ninst✝¹⁰ : Monoid G✝\ninst✝⁹ : AddCommGroup V✝\ninst✝⁸ : Module k✝ V✝\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : Module k✝ W\ninst✝⁵ : AddCommGroup X\ninst✝⁴ : Module k✝ X\nρ✝ : Representation k✝ G✝ V✝\nτ : Represent... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 241,
"column": 31
} | {
"line": 241,
"column": 33
} | {
"line": 241,
"column": 34
} | [
{
"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\nX✝ Y✝ : Rep k G\nx✝² : X✝ ⟶ Y✝\nx✝¹ : ↑((coindFunctor k φ).obj X✝)\nx✝ : H\n⊢ (Hom.hom ((Hom.hom ((coindFunctor k φ).map x✝² ≫ (coindIso φ Y✝).hom)).toLinearMap x✝¹)).toLinearMap\n ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 241,
"column": 20
} | {
"line": 241,
"column": 22
} | {
"line": 241,
"column": 23
} | [
{
"pp": "k✝ : Type u_1\nG✝ : Type u_2\nV✝ : Type u_3\nW : Type u_4\nX : Type u_5\ninst✝¹¹ : CommRing k✝\ninst✝¹⁰ : Monoid G✝\ninst✝⁹ : AddCommGroup V✝\ninst✝⁸ : Module k✝ V✝\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : Module k✝ W\ninst✝⁵ : AddCommGroup X\ninst✝⁴ : Module k✝ X\nρ✝ : Representation k✝ G✝ V✝\nτ : Represent... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 245,
"column": 69
} | {
"line": 245,
"column": 71
} | {
"line": 245,
"column": 72
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nρ : Representation k G V\nα : Type u_9\nx : (ρ.finsupp α).Coinvariants\n⊢ (ρ.coinvariantsFinsuppLEquiv α) x = (ρ.coinvariantsToFinsupp α) x",
"ppTerm": "?m.56",
"assigne... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 239,
"column": 44
} | {
"line": 239,
"column": 46
} | {
"line": 240,
"column": 4
} | [
{
"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\nX✝ Y✝ : Rep k G\nx✝ : X✝ ⟶ Y✝\n⊢ (coindFunctor k φ).map x✝ ≫ (coindIso φ Y✝).hom = (coindIso φ X✝).hom ≫ (coindFunctor' k φ).map x✝",
"ppTerm": "?m.33",
"assigned": true,
"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 261,
"column": 60
} | {
"line": 261,
"column": 62
} | {
"line": 261,
"column": 63
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\nW : Type u_9\ninst✝⁵ : CommRing k\ninst✝⁴ : Group G\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AddCommGroup W\ninst✝ : Module k W\nρ : Representation k G V\nτ : Representation k G W\nx : V\ny : W\ng : G\n⊢ ((ρ.tprod τ) g⁻¹) (x ⊗ₜ[k] (τ g) y) - x ⊗ₜ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 266,
"column": 60
} | {
"line": 266,
"column": 62
} | {
"line": 266,
"column": 63
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\nW : Type u_9\ninst✝⁵ : CommRing k\ninst✝⁴ : Group G\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AddCommGroup W\ninst✝ : Module k W\nρ : Representation k G V\nτ : Representation k G W\nx : V\ny : W\ng : G\n⊢ ((ρ.tprod τ) g⁻¹) ((ρ g) x ⊗ₜ[k] y) - (ρ g... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 253,
"column": 42
} | {
"line": 253,
"column": 44
} | {
"line": 253,
"column": 45
} | [
{
"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 ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 274,
"column": 60
} | {
"line": 274,
"column": 62
} | {
"line": 274,
"column": 63
} | [
{
"pp": "k✝ : Type u_1\nG✝ : Type u_2\nV✝ : Type u_3\nW✝ : Type u_4\nX : Type u_5\ninst✝¹³ : CommRing k✝\ninst✝¹² : Monoid G✝\ninst✝¹¹ : AddCommGroup V✝\ninst✝¹⁰ : Module k✝ V✝\ninst✝⁹ : AddCommGroup W✝\ninst✝⁸ : Module k✝ W✝\ninst✝⁷ : AddCommGroup X\ninst✝⁶ : Module k✝ X\nρ✝ : Representation k✝ G✝ V✝\nτ✝ : Rep... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 771,
"column": 63
} | {
"line": 771,
"column": 65
} | {
"line": 772,
"column": 6
} | [
{
"pp": "Ω : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\ninst✝⁵ : IsProbabilityMeasure μ\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\nh' : StronglyMeasurable (X 0... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 288,
"column": 5
} | {
"line": 288,
"column": 7
} | {
"line": 288,
"column": 8
} | [
{
"pp": "k✝ : Type u_1\nG✝ : Type u_2\nV✝ : Type u_3\nW✝ : Type u_4\nX : Type u_5\ninst✝¹³ : CommRing k✝\ninst✝¹² : Monoid G✝\ninst✝¹¹ : AddCommGroup V✝\ninst✝¹⁰ : Module k✝ V✝\ninst✝⁹ : AddCommGroup W✝\ninst✝⁸ : Module k✝ W✝\ninst✝⁷ : AddCommGroup X\ninst✝⁶ : Module k✝ X\nρ✝ : Representation k✝ G✝ V✝\nτ✝ : Rep... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 253,
"column": 87
} | {
"line": 253,
"column": 89
} | {
"line": 254,
"column": 4
} | [
{
"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\ng : H\n⊢ LinearMap.codRestrict (Representation.coindV φ A.ρ) (LinearMap.pi fun h ↦ (Hom.hom f).toLinearMap ∘ₗ B.ρ h) ⋯ ∘ₗ\n B.ρ g =\n ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 288,
"column": 20
} | {
"line": 288,
"column": 22
} | {
"line": 288,
"column": 23
} | [
{
"pp": "k✝ : Type u_1\nG✝ : Type u_2\nV✝ : Type u_3\nW✝ : Type u_4\nX : Type u_5\ninst✝¹³ : CommRing k✝\ninst✝¹² : Monoid G✝\ninst✝¹¹ : AddCommGroup V✝\ninst✝¹⁰ : Module k✝ V✝\ninst✝⁹ : AddCommGroup W✝\ninst✝⁸ : Module k✝ W✝\ninst✝⁷ : AddCommGroup X\ninst✝⁶ : Module k✝ X\nρ✝ : Representation k✝ G✝ V✝\nτ✝ : Rep... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 292,
"column": 83
} | {
"line": 292,
"column": 85
} | {
"line": 293,
"column": 2
} | [
{
"pp": "k : Type u_6\nG : Type u_7\nV : Type u_8\ninst✝³ : CommRing k\ninst✝² : Group G\ninst✝¹ : AddCommGroup V\ninst✝ : Module k V\nρ : Representation k G V\nx : (ρ.tprod (leftRegular k G)).Coinvariants\n⊢ ρ.coinvariantsTprodLeftRegularLEquiv x = ρ.ofCoinvariantsTprodLeftRegular x",
"ppTerm": "?m.67",
... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 779,
"column": 6
} | {
"line": 779,
"column": 17
} | {
"line": 780,
"column": 2
} | [
{
"pp": "case h₁\nΩ : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\ninst✝⁵ : IsProbabilityMeasure μ\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\nh' : StronglyMeasur... | [] | exact hn.le | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 333,
"column": 43
} | {
"line": 333,
"column": 45
} | {
"line": 333,
"column": 46
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\ng : G\n⊢ (Coinvariants.ker (MonoidHom.comp A.ρ S.subtype)).subtype ∘ₗ (A.ρ.toCoinvariantsKer S) g =\n A.ρ g ∘ₗ (Coinvariants.ker (MonoidHom.comp A.ρ S.subtype)).subtype",
"ppTerm": "?m.6... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 289,
"column": 13
} | {
"line": 289,
"column": 15
} | {
"line": 290,
"column": 6
} | [
{
"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.{?u.16, u, v} k G\nB : Rep.{max w t, u, w} k H\nA : Rep.{max w t, u, v} k G\nf : B ⟶ coind.{u, v, w, max t w} φ A\ng : G\n⊢ (LinearMap.proj 1 ∘ₗ (Representation.coindV φ A.ρ).subtype ∘ₗ (H... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 335,
"column": 10
} | {
"line": 335,
"column": 12
} | {
"line": 335,
"column": 13
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nS : Subgroup G\ninst✝ : S.Normal\n⊢ ofHom { toLinearMap := (Coinvariants.ker (MonoidHom.comp A.ρ S.subtype)).subtype, isIntertwining' := ⋯ } ≫\n A.toCoinvariantsMkQ S =\n 0",
"ppTerm": "?m.79",
"assigned": true,... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 354,
"column": 14
} | {
"line": 354,
"column": 16
} | {
"line": 354,
"column": 17
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : CommRing k\ninst✝ : Monoid G\nA B x✝ : Rep k G\n⊢ ModuleCat.ofHom (Coinvariants.map x✝.ρ x✝.ρ (Hom.hom (𝟙 x✝))) = 𝟙 (ModuleCat.of k x✝.ρ.Coinvariants)",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"Rep.V",
"Cat... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 294,
"column": 16
} | {
"line": 294,
"column": 18
} | {
"line": 294,
"column": 19
} | [
{
"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.{?u.16, u, v} k G\nB : Rep.{max w t, u, w} k H\nA : Rep.{max w t, u, v} k G\nx : res φ B ⟶ A\n⊢ (fun f ↦\n ofHom\n { toLinearMap := LinearMap.proj 1 ∘ₗ (Representation.coin... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 355,
"column": 18
} | {
"line": 355,
"column": 20
} | {
"line": 355,
"column": 21
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : CommRing k\ninst✝ : Monoid G\nA B X✝ Y✝ Z✝ : Rep k G\nx✝¹ : X✝ ⟶ Y✝\nx✝ : Y✝ ⟶ Z✝\n⊢ ModuleCat.ofHom (Coinvariants.map X✝.ρ Z✝.ρ (Hom.hom (x✝¹ ≫ x✝))) =\n ModuleCat.ofHom (Coinvariants.map X✝.ρ Y✝.ρ (Hom.hom x✝¹)) ≫\n ModuleCat.ofHom (Coinvariants.map Y✝.ρ Z✝.ρ ... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 777,
"column": 19
} | {
"line": 777,
"column": 21
} | {
"line": 778,
"column": 6
} | [
{
"pp": "Ω : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\ninst✝⁵ : IsProbabilityMeasure μ\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\nh' : StronglyMeasurable (X 0... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 377,
"column": 77
} | {
"line": 377,
"column": 79
} | {
"line": 377,
"column": 80
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Monoid G\nA B : Rep k G\ninst✝ : B.ρ.IsTrivial\nf : A ⟶ B\n⊢ ∀ (x : G), (Hom.hom f).toLinearMap ∘ₗ A.ρ x = (Hom.hom f).toLinearMap",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"LinearMap.id",
"Rep.V",
"Repr... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 295,
"column": 17
} | {
"line": 295,
"column": 19
} | {
"line": 295,
"column": 20
} | [
{
"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.{?u.16, u, v} k G\nB : Rep.{max w t, u, w} k H\nA : Rep.{max w t, u, v} k G\nz : B ⟶ coind.{u, v, w, max t w} φ A\n⊢ (fun f ↦ resCoindToHom φ B A f)\n ((fun f ↦\n ofHom\n ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 389,
"column": 74
} | {
"line": 389,
"column": 76
} | {
"line": 389,
"column": 77
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : CommRing k\ninst✝ : Monoid G\nA B X : Rep k G\ng : G\n⊢ ModuleCat.Hom.hom ((coinvariantsMk k G).app X) ∘ₗ X.ρ g =\n (Representation.trivial k G ↑((coinvariantsFunctor k G).obj X)) g ∘ₗ ModuleCat.Hom.hom ((coinvariantsMk k G).app X)",
"ppTerm": "?m.90",
"assig... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 396,
"column": 44
} | {
"line": 396,
"column": 46
} | {
"line": 397,
"column": 2
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : CommRing k\ninst✝ : Monoid G\nX : Rep k G\nY : ModuleCat k\nf : (coinvariantsFunctor k G).obj X ⟶ Y\n⊢ (Hom.hom (((coinvariantsAdjunction k G).homEquiv X Y) f)).toLinearMap =\n ModuleCat.Hom.hom ((coinvariantsMk k G).app X ≫ f)",
"ppTerm": "?m.61",
"assigned"... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 699,
"column": 90
} | {
"line": 699,
"column": 92
} | {
"line": 706,
"column": 2
} | [
{
"pp": "Ω : Type u_1\nmΩ : MeasurableSpace Ω\nμ : Measure Ω\ninst✝⁵ : IsProbabilityMeasure μ\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\nh' : StronglyMeasurable (X 0... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 403,
"column": 67
} | {
"line": 403,
"column": 69
} | {
"line": 404,
"column": 2
} | [
{
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"LinearMap.id",
"Rep.coinvaria... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
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} | {
"line": 449,
"column": 51
} | {
"line": 449,
"column": 52
} | [
{
"pp": "k✝ : Type u\nG✝ : Type v\ninst✝⁴ : CommRing k✝\ninst✝³ : Monoid G✝\nA B : Rep k✝ G✝\nk : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Group G\nS : Subgroup G\ninst✝ : S.Normal\nX Y : Rep k G\nf : X ⟶ Y\ng✝ : G ⧸ S\ng : G\n⊢ ModuleCat.Hom.hom ((coinvariantsFunctor k ↥S).map ((resFunctor S.subtype).... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 306,
"column": 37
} | {
"line": 306,
"column": 39
} | {
"line": 306,
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} | [
{
"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.{?u.16, u, v} k G\n⊢ ∀ {X' X : Rep.{max w t, u, w} k H} {Y : Rep.{max w t, u, v} k G} (f : X' ⟶ X) (g : X ⟶ (coindFunctor k φ).obj Y),\n (resCoindHomEquiv.{?u.42, u, v, w} φ X' Y).toEqui... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
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"column": 14
} | {
"line": 450,
"column": 16
} | {
"line": 450,
"column": 17
} | [
{
"pp": "k✝ : Type u\nG✝ : Type v\ninst✝⁴ : CommRing k✝\ninst✝³ : Monoid G✝\nA B : Rep k✝ G✝\nk : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Group G\nS : Subgroup G\ninst✝ : S.Normal\nX : Rep k G\n⊢ ofHom\n { toLinearMap := ModuleCat.Hom.hom ((coinvariantsFunctor k ↥S).map ((resFunctor S.subtype).ma... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 793,
"column": 40
} | {
"line": 793,
"column": 42
} | {
"line": 794,
"column": 6
} | [
{
"pp": "Ω : 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)\nhident : ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Coinvariants | {
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"column": 18
} | {
"line": 451,
"column": 20
} | {
"line": 451,
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} | [
{
"pp": "k✝ : Type u\nG✝ : Type v\ninst✝⁴ : CommRing k✝\ninst✝³ : Monoid G✝\nA B : Rep k✝ G✝\nk : Type u\nG : Type v\ninst✝² : CommRing k\ninst✝¹ : Group G\nS : Subgroup G\ninst✝ : S.Normal\nX✝ Y✝ Z✝ : Rep k G\nf : X✝ ⟶ Y✝\ng : Y✝ ⟶ Z✝\n⊢ ofHom\n { toLinearMap := ModuleCat.Hom.hom ((coinvariantsFunctor k ↥... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
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"column": 34
} | {
"line": 475,
"column": 36
} | {
"line": 476,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nα : Type u\ninst✝ : DecidableEq α\nx : ↑A\ni : α\ng : G\nr : k\n⊢ (A.coinvariantsTensorFreeToFinsupp α)\n ((Coinvariants.mk (A.ρ.tprod (Representation.free k G α))) (x ⊗ₜ[k] single i (MonoidAlgebra.single g r))) =\n single i (r •... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
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"column": 69
} | {
"line": 494,
"column": 71
} | {
"line": 495,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nα : Type u\ninst✝ : DecidableEq α\ni : α\nx : ↑A\n⊢ (A.finsuppToCoinvariantsTensorFree α) (single i x) =\n (Coinvariants.mk (A.ρ.tprod (Representation.free k G α))) (x ⊗ₜ[k] single i (MonoidAlgebra.single 1 1))",
"ppTerm": "?m.85"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 506,
"column": 25
} | {
"line": 506,
"column": 27
} | {
"line": 507,
"column": 6
} | [
{
"pp": "k✝¹ : Type u\nG✝¹ : Type v\ninst✝⁶ : CommRing k✝¹\ninst✝⁵ : Monoid G✝¹\nA✝ B : Rep k✝¹ G✝¹\nk✝ : Type u\nG✝ : Type v\ninst✝⁴ : CommRing k✝\ninst✝³ : Group G✝\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nα : Type u\ninst✝ : DecidableEq α\ni : α\nx : ↑A\n⊢ (A.coinvariantsTensorFreeT... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinduced | {
"line": 307,
"column": 33
} | {
"line": 307,
"column": 35
} | {
"line": 307,
"column": 36
} | [
{
"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.{?u.16, u, v} k G\n⊢ ∀ {X : Rep.{max w t, u, w} k H} {Y Y' : Rep.{max w t, u, v} k G} (f : (resFunctor φ).obj X ⟶ Y) (g : Y ⟶ Y'),\n (resCoindHomEquiv.{t, u, v, w} φ X Y').toEquiv (f ≫ g... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 510,
"column": 62
} | {
"line": 510,
"column": 64
} | {
"line": 511,
"column": 8
} | [
{
"pp": "k✝¹ : Type u\nG✝¹ : Type v\ninst✝⁶ : CommRing k✝¹\ninst✝⁵ : Monoid G✝¹\nA✝ B : Rep k✝¹ G✝¹\nk✝ : Type u\nG✝ : Type v\ninst✝⁴ : CommRing k✝\ninst✝³ : Group G✝\nk G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nα : Type u\ninst✝ : DecidableEq α\na : ↑A\ni : α\ng : G\nr : k\n⊢ ((((TensorPr... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Coinvariants | {
"line": 517,
"column": 89
} | {
"line": 517,
"column": 91
} | {
"line": 518,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝² : CommRing k\ninst✝¹ : Group G\nA : Rep k G\nα : Type u\ninst✝ : DecidableEq α\nx : (A ⊗ free k G α).ρ.Coinvariants\n⊢ (A.coinvariantsTensorFreeToFinsupp α) x = (A.coinvariantsTensorFreeToFinsupp α) x",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"Mono... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 809,
"column": 83
} | {
"line": 809,
"column": 85
} | {
"line": 810,
"column": 4
} | [
{
"pp": "Ω : 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)\nhident : ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 68,
"column": 29
} | {
"line": 68,
"column": 31
} | {
"line": 68,
"column": 32
} | [
{
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"ppTerm": "?m.4... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 71,
"column": 29
} | {
"line": 71,
"column": 31
} | {
"line": 71,
"column": 32
} | [
{
"pp": "k : Type u\nG : Type v\nX : Type w\ninst✝⁷ : TopologicalSpace k\ninst✝⁶ : Ring k\ninst✝⁵ : Monoid G\ninst✝⁴ : AddCommGroup X\ninst✝³ : Module k X\ninst✝² : TopologicalSpace X\ninst✝¹ : IsTopologicalAddGroup X\ninst✝ : ContinuousSMul k X\nρ : ContRepresentation k G X\n⊢ (of ρ).ρ = ρ",
"ppTerm": "?m.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 132,
"column": 88
} | {
"line": 132,
"column": 90
} | {
"line": 133,
"column": 2
} | [
{
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"ppTerm": "?m.70",
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"instFunL... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 147,
"column": 75
} | {
"line": 147,
"column": 77
} | {
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} | [
{
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"ppTerm": "?m.66",
"assigned": true,
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"TopRep.hom_ext",
"CategoryTheory.CategoryStruct.toQuiver",... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 150,
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} | {
"line": 150,
"column": 77
} | {
"line": 151,
"column": 2
} | [
{
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"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"TopRep.hom_ext",
"CategoryTheory.CategoryStruct.toQuiver",... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
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"column": 80
} | {
"line": 173,
"column": 82
} | {
"line": 174,
"column": 2
} | [
{
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"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"ContinuousLinearMap.comp",
"TopRep.hV5",
"ContI... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 177,
"column": 80
} | {
"line": 177,
"column": 82
} | {
"line": 178,
"column": 2
} | [
{
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"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"ContinuousLinearMap.comp",
"TopRep.hV5",
"ContI... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 194,
"column": 42
} | {
"line": 194,
"column": 44
} | {
"line": 194,
"column": 45
} | [
{
"pp": "k : Type u\nG : Type v\nX Y : Type w\ninst✝¹² : TopologicalSpace k\ninst✝¹¹ : Ring k\ninst✝¹⁰ : Monoid G\ninst✝⁹ : AddCommGroup X\ninst✝⁸ : Module k X\ninst✝⁷ : TopologicalSpace X\ninst✝⁶ : IsTopologicalAddGroup X\ninst✝⁵ : ContinuousSMul k X\ninst✝⁴ : AddCommGroup Y\ninst✝³ : Module k Y\ninst✝² : Topo... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.TopRep | {
"line": 200,
"column": 43
} | {
"line": 200,
"column": 45
} | {
"line": 201,
"column": 4
} | [
{
"pp": "k : Type u\nG : Type v\nX✝ Y✝ : Type w\ninst✝¹² : TopologicalSpace k\ninst✝¹¹ : Ring k\ninst✝¹⁰ : Monoid G\ninst✝⁹ : AddCommGroup X✝\ninst✝⁸ : Module k X✝\ninst✝⁷ : TopologicalSpace X✝\ninst✝⁶ : IsTopologicalAddGroup X✝\ninst✝⁵ : ContinuousSMul k X✝\ninst✝⁴ : AddCommGroup Y✝\ninst✝³ : Module k Y✝\ninst... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
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"column": 90
} | {
"line": 790,
"column": 92
} | {
"line": 792,
"column": 2
} | [
{
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Mathlib.RepresentationTheory.Semisimple | {
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"column": 73
} | {
"line": 38,
"column": 75
} | {
"line": 39,
"column": 2
} | [
{
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"usedConstants": [
"OrderIso... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Semisimple | {
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"column": 93
} | {
"line": 45,
"column": 95
} | {
"line": 46,
"column": 2
} | [
{
"pp": "k : Type u_1\nG : Type u_2\ninst✝³ : Monoid G\ninst✝² : Field k\nM : Type u_4\ninst✝¹ : AddCommGroup M\ninst✝ : Module k[G] M\n⊢ IsSemisimpleModule k[G] M ↔ (ofModule M).IsSemisimpleRepresentation",
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"OrderIso.complementedLattice_... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Maschke | {
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} | {
"line": 80,
"column": 43
} | {
"line": 81,
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} | [
{
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Mathlib.RepresentationTheory.Maschke | {
"line": 101,
"column": 75
} | {
"line": 101,
"column": 77
} | {
"line": 102,
"column": 4
} | [
{
"pp": "k : Type u_1\ninst✝¹⁰ : CommRing k\nG : Type u_2\ninst✝⁹ : Group G\nV : Type u_3\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : Module k[G] V\ninst✝⁵ : IsScalarTower k k[G] V\nW : Type u_4\ninst✝⁴ : AddCommGroup W\ninst✝³ : Module k W\ninst✝² : Module k[G] W\ninst✝¹ : IsScalarTower k k[G] W\nπ... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 838,
"column": 40
} | {
"line": 838,
"column": 42
} | {
"line": 839,
"column": 6
} | [
{
"pp": "Ω : 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\np : ℝ≥0∞\nhp : 1 ≤ p\nhp' : p ≠ ∞\nX : ℕ → Ω → E\nhℒp : MemLp (X 0) p μ\nhindep : Pairwise ((fun x1 x2 ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Maschke | {
"line": 119,
"column": 84
} | {
"line": 119,
"column": 86
} | {
"line": 120,
"column": 2
} | [
{
"pp": "k : Type u_1\ninst✝¹⁰ : CommRing k\nG : Type u_2\ninst✝⁹ : Group G\nV : Type u_3\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : Module k[G] V\ninst✝⁵ : IsScalarTower k k[G] V\nW : Type u_4\ninst✝⁴ : AddCommGroup W\ninst✝³ : Module k W\ninst✝² : Module k[G] W\ninst✝¹ : IsScalarTower k k[G] W\nπ... | [] | by | [anonymous] | by |
Mathlib.Probability.StrongLaw | {
"line": 842,
"column": 95
} | {
"line": 842,
"column": 97
} | {
"line": 843,
"column": 6
} | [
{
"pp": "Ω : 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\np : ℝ≥0∞\nhp : 1 ≤ p\nhp' : p ≠ ∞\nX : ℕ → Ω → E\nhℒp : MemLp (X 0) p μ\nhindep : Pairwise ((fun x1 x2 ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.Probability.StrongLaw | {
"line": 835,
"column": 21
} | {
"line": 835,
"column": 23
} | {
"line": 837,
"column": 2
} | [
{
"pp": "Ω : 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\np : ℝ≥0∞\nhp : 1 ≤ p\nhp' : p ≠ ∞\nX : ℕ → Ω → E\nhℒp : MemLp (X 0) p μ\nhindep : Pairwise ((fun x1 x2 ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Maschke | {
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"column": 82
} | {
"line": 124,
"column": 84
} | {
"line": 125,
"column": 2
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{
"pp": "k : Type u_1\ninst✝¹⁰ : CommRing k\nG : Type u_2\ninst✝⁹ : Group G\nV : Type u_3\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : Module k[G] V\ninst✝⁵ : IsScalarTower k k[G] V\nW : Type u_4\ninst✝⁴ : AddCommGroup W\ninst✝³ : Module k W\ninst✝² : Module k[G] W\ninst✝¹ : IsScalarTower k k[G] W\nπ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Maschke | {
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} | {
"line": 151,
"column": 40
} | {
"line": 152,
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} | [
{
"pp": "k : Type u_1\ninst✝⁷ : Field k\nG : Type u_2\ninst✝⁶ : Finite G\ninst✝⁵ : NeZero ↑(Nat.card G)\ninst✝⁴ : Group G\nV : Type u_3\ninst✝³ : AddCommGroup V\ninst✝² : Module k[G] V\nW : Type u_4\ninst✝¹ : AddCommGroup W\ninst✝ : Module k[G] W\nf : V →ₗ[k[G]] W\nhf : f.ker = ⊥\nA : Type (max u_1 u_2) := k[G]... | [
"k : Type u_1\ninst✝⁷ : Field k\nG : Type u_2\ninst✝⁶ : Finite G\ninst✝⁵ : NeZero ↑(Nat.card G)\ninst✝⁴ : Group G\nV : Type u_3\ninst✝³ : AddCommGroup V\ninst✝² : Module k[G] V\nW : Type u_4\ninst✝¹ : AddCommGroup W\ninst✝ : Module k[G] W\nf : V →ₗ[k[G]] W\nhf : f.ker = ⊥\nA : Type (max u_1 u_2) := k[G]\nthis✝² : M... | have := IsScalarTower.of_compHom k A V | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RepresentationTheory.Maschke | {
"line": 153,
"column": 38
} | {
"line": 153,
"column": 40
} | {
"line": 154,
"column": 4
} | [
{
"pp": "k : Type u_1\ninst✝⁷ : Field k\nG : Type u_2\ninst✝⁶ : Finite G\ninst✝⁵ : NeZero ↑(Nat.card G)\ninst✝⁴ : Group G\nV : Type u_3\ninst✝³ : AddCommGroup V\ninst✝² : Module k[G] V\nW : Type u_4\ninst✝¹ : AddCommGroup W\ninst✝ : Module k[G] W\nf : V →ₗ[k[G]] W\nhf : f.ker = ⊥\nA : Type (max u_1 u_2) := k[G]... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RepresentationTheory.Maschke | {
"line": 146,
"column": 42
} | {
"line": 146,
"column": 44
} | {
"line": 147,
"column": 2
} | [
{
"pp": "k : Type u_1\ninst✝⁷ : Field k\nG : Type u_2\ninst✝⁶ : Finite G\ninst✝⁵ : NeZero ↑(Nat.card G)\ninst✝⁴ : Group G\nV : Type u_3\ninst✝³ : AddCommGroup V\ninst✝² : Module k[G] V\nW : Type u_4\ninst✝¹ : AddCommGroup W\ninst✝ : Module k[G] W\nf : V →ₗ[k[G]] W\nhf : f.ker = ⊥\n⊢ ∃ g, g ∘ₗ f = LinearMap.id",... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Maschke | {
"line": 162,
"column": 87
} | {
"line": 162,
"column": 89
} | {
"line": 163,
"column": 2
} | [
{
"pp": "k : Type u_1\ninst✝⁵ : Field k\nG : Type u_2\ninst✝⁴ : Finite G\ninst✝³ : NeZero ↑(Nat.card G)\ninst✝² : Group G\nV : Type u_3\ninst✝¹ : AddCommGroup V\ninst✝ : Module k[G] V\np : Submodule k[G] V\n⊢ ∃ q, IsCompl p q",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"MonoidAlg... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Maschke | {
"line": 172,
"column": 54
} | {
"line": 172,
"column": 56
} | {
"line": 173,
"column": 4
} | [
{
"pp": "k : Type u_1\ninst✝⁸ : Field k\nG : Type u_2\ninst✝⁷ : Finite G\ninst✝⁶ : NeZero ↑(Nat.card G)\ninst✝⁵ : Group G\nV : Type u_3\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k[G] V\nW : Type u_4\ninst✝² : AddCommGroup W\ninst✝¹ : Module k[G] W\ninst✝ : AddGroup G\n⊢ NeZero ↑(Nat.card (Multiplicative G))",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Maschke | {
"line": 184,
"column": 43
} | {
"line": 184,
"column": 45
} | {
"line": 185,
"column": 2
} | [
{
"pp": "k✝ : Type u_1\ninst✝¹³ : Field k✝\nG✝ : Type u_2\ninst✝¹² : Finite G✝\ninst✝¹¹ : NeZero ↑(Nat.card G✝)\ninst✝¹⁰ : Group G✝\nV✝ : Type u_3\ninst✝⁹ : AddCommGroup V✝\ninst✝⁸ : Module k✝[G✝] V✝\nW : Type u_4\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : Module k✝[G✝] W\nG : Type u_5\nk : Type u_6\nV : Type u_7\ninst... | [] | by | [anonymous] | by |
Mathlib.RingTheory.SimpleModule.InjectiveProjective | {
"line": 26,
"column": 16
} | {
"line": 26,
"column": 18
} | {
"line": 26,
"column": 19
} | [
{
"pp": "R : Type u_1\ninst✝³ : Ring R\ninst✝² : IsSemisimpleRing R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nX Y : Type u_2\nx✝⁴ : AddCommGroup X\nx✝³ : AddCommGroup Y\nx✝² : Module R X\nx✝¹ : Module R Y\nf : X →ₗ[R] Y\nhf : Function.Injective ⇑f\ng : X →ₗ[R] M\nh : Y →ₗ[R] M\ncomp : h ∘ₗ f =... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 60,
"column": 27
} | {
"line": 60,
"column": 29
} | {
"line": 60,
"column": 30
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 102,
"column": 23
} | {
"line": 102,
"column": 25
} | {
"line": 102,
"column": 26
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 110,
"column": 89
} | {
"line": 110,
"column": 91
} | {
"line": 111,
"column": 2
} | [
{
"pp": "R : 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\ninst✝ : Module... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 121,
"column": 14
} | {
"line": 121,
"column": 16
} | {
"line": 121,
"column": 17
} | [
{
"pp": "R : 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\ninst✝ : Module... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 124,
"column": 66
} | {
"line": 124,
"column": 68
} | {
"line": 125,
"column": 2
} | [
{
"pp": "R : 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\ninst✝ : Module... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 152,
"column": 23
} | {
"line": 152,
"column": 25
} | {
"line": 152,
"column": 26
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 160,
"column": 65
} | {
"line": 160,
"column": 67
} | {
"line": 160,
"column": 68
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 169,
"column": 44
} | {
"line": 169,
"column": 46
} | {
"line": 169,
"column": 47
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 172,
"column": 44
} | {
"line": 172,
"column": 46
} | {
"line": 172,
"column": 47
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 183,
"column": 46
} | {
"line": 183,
"column": 48
} | {
"line": 183,
"column": 49
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 199,
"column": 38
} | {
"line": 199,
"column": 40
} | {
"line": 199,
"column": 41
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 208,
"column": 65
} | {
"line": 208,
"column": 67
} | {
"line": 208,
"column": 68
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 217,
"column": 44
} | {
"line": 217,
"column": 46
} | {
"line": 218,
"column": 2
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 221,
"column": 44
} | {
"line": 221,
"column": 46
} | {
"line": 222,
"column": 2
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹³ : Monoid G\ninst✝¹² : Ring R\ninst✝¹¹ : AddCommGroup V\ninst✝¹⁰ : TopologicalSpace V\ninst✝⁹ : IsTopologicalAddGroup V\ninst✝⁸ : Module R V\ninst✝⁷ : AddCommGroup W\ninst✝⁶ : TopologicalSpace W\ninst✝⁵ : IsTopologicalAddGroup... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 227,
"column": 52
} | {
"line": 227,
"column": 54
} | {
"line": 228,
"column": 4
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹⁸ : Monoid G\ninst✝¹⁷ : Ring R\ninst✝¹⁶ : AddCommGroup V\ninst✝¹⁵ : TopologicalSpace V\ninst✝¹⁴ : IsTopologicalAddGroup V\ninst✝¹³ : Module R V\ninst✝¹² : AddCommGroup W\ninst✝¹¹ : TopologicalSpace W\ninst✝¹⁰ : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 243,
"column": 81
} | {
"line": 243,
"column": 83
} | {
"line": 244,
"column": 2
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹⁸ : Monoid G\ninst✝¹⁷ : Ring R\ninst✝¹⁶ : AddCommGroup V\ninst✝¹⁵ : TopologicalSpace V\ninst✝¹⁴ : IsTopologicalAddGroup V\ninst✝¹³ : Module R V\ninst✝¹² : AddCommGroup W\ninst✝¹¹ : TopologicalSpace W\ninst✝¹⁰ : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 250,
"column": 81
} | {
"line": 250,
"column": 83
} | {
"line": 251,
"column": 2
} | [
{
"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 : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 260,
"column": 20
} | {
"line": 260,
"column": 22
} | {
"line": 260,
"column": 23
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹⁸ : Monoid G\ninst✝¹⁷ : Ring R\ninst✝¹⁶ : AddCommGroup V\ninst✝¹⁵ : TopologicalSpace V\ninst✝¹⁴ : IsTopologicalAddGroup V\ninst✝¹³ : Module R V\ninst✝¹² : AddCommGroup W\ninst✝¹¹ : TopologicalSpace W\ninst✝¹⁰ : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 65,
"column": 29
} | {
"line": 65,
"column": 31
} | {
"line": 65,
"column": 32
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝³ : Semiring k\ninst✝² : Monoid G\nX : Type w\ninst✝¹ : AddCommGroup X\ninst✝ : Module k X\nρ : Representation k G X\n⊢ ↑(of ρ) = X",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Rep.V",
"Rep.of",
"Eq.refl"
],
"usedFVars": [... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 259,
"column": 16
} | {
"line": 259,
"column": 18
} | {
"line": 259,
"column": 19
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹⁸ : Monoid G\ninst✝¹⁷ : Ring R\ninst✝¹⁶ : AddCommGroup V\ninst✝¹⁵ : TopologicalSpace V\ninst✝¹⁴ : IsTopologicalAddGroup V\ninst✝¹³ : Module R V\ninst✝¹² : AddCommGroup W\ninst✝¹¹ : TopologicalSpace W\ninst✝¹⁰ : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 68,
"column": 29
} | {
"line": 68,
"column": 31
} | {
"line": 68,
"column": 32
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝³ : Semiring k\ninst✝² : Monoid G\nX : Type w\ninst✝¹ : AddCommGroup X\ninst✝ : Module k X\nρ : Representation k G X\n⊢ (of ρ).ρ = ρ",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Rep.V",
"Representation",
"AddCommGroup.toAddCommMon... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 110,
"column": 48
} | {
"line": 110,
"column": 50
} | {
"line": 111,
"column": 2
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA : Rep k G\na : ↑A\n⊢ (ConcreteCategory.hom (𝟙 A)) a = a",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Rep.V",
"eq_self",
"of_eq_true",
"Eq"
],
"usedFVars": [
"k",
"G",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 261,
"column": 17
} | {
"line": 261,
"column": 19
} | {
"line": 261,
"column": 20
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹⁸ : Monoid G\ninst✝¹⁷ : Ring R\ninst✝¹⁶ : AddCommGroup V\ninst✝¹⁵ : TopologicalSpace V\ninst✝¹⁴ : IsTopologicalAddGroup V\ninst✝¹³ : Module R V\ninst✝¹² : AddCommGroup W\ninst✝¹¹ : TopologicalSpace W\ninst✝¹⁰ : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 117,
"column": 74
} | {
"line": 117,
"column": 76
} | {
"line": 117,
"column": 77
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B C : Rep k G\nf : A ⟶ B\ng : B ⟶ C\na : ↑A\n⊢ (ConcreteCategory.hom (f ≫ g)) a = (ConcreteCategory.hom g) ((ConcreteCategory.hom f) a)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Rep.V",
"AddCommGro... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 262,
"column": 20
} | {
"line": 262,
"column": 22
} | {
"line": 262,
"column": 23
} | [
{
"pp": "R : Type u_1\nG : Type u_2\nV : Type u_3\nW : Type u_4\nU : Type u_5\ninst✝¹⁸ : Monoid G\ninst✝¹⁷ : Ring R\ninst✝¹⁶ : AddCommGroup V\ninst✝¹⁵ : TopologicalSpace V\ninst✝¹⁴ : IsTopologicalAddGroup V\ninst✝¹³ : Module R V\ninst✝¹² : AddCommGroup W\ninst✝¹¹ : TopologicalSpace W\ninst✝¹⁰ : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 123,
"column": 88
} | {
"line": 123,
"column": 90
} | {
"line": 124,
"column": 2
} | [
{
"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)",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Rep.V",
"Representation",
"MonoidHom.instFunLike",
"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 139,
"column": 73
} | {
"line": 139,
"column": 75
} | {
"line": 139,
"column": 76
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B : Rep k G\ne : A ≅ B\nx : ↑A\n⊢ (Hom.hom e.inv) ((Hom.hom e.hom) x) = x",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"Rep.V",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 141,
"column": 73
} | {
"line": 141,
"column": 75
} | {
"line": 141,
"column": 76
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B : Rep k G\ne : A ≅ B\nx : ↑B\n⊢ (Hom.hom e.hom) ((Hom.hom e.inv) x) = x",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"Rep.V",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 267,
"column": 20
} | {
"line": 267,
"column": 22
} | {
"line": 267,
"column": 23
} | [
{
"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 : IsTopologicalAdd... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 184,
"column": 16
} | {
"line": 184,
"column": 18
} | {
"line": 184,
"column": 19
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝⁷ : Semiring k\ninst✝⁶ : Monoid G\nX Y : Type w\ninst✝⁵ : AddCommGroup X\ninst✝⁴ : AddCommGroup Y\ninst✝³ : Module k X\ninst✝² : Module k Y\nρ : Representation k G X\nσ : Representation k G Y\nA B C : Rep k G\nZ : Type w\ninst✝¹ : AddCommGroup Z\ninst✝ : Module k Z\nτ : Rep... | [] | by | [anonymous] | by |
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