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.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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} | {
"line": 268,
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"line": 268,
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
"line": 226,
"column": 41
} | {
"line": 227,
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{
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"usedConstants": [
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"con... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
"line": 233,
"column": 57
} | {
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"column": 0
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{
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"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Representation.IntertwiningMap.comp_add",
"Rep.V",
"Ca... | [] | simp [add_hom, Representation.IntertwiningMap.comp_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
"line": 231,
"column": 41
} | {
"line": 232,
"column": 2
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B C : Rep k G\nf : A ⟶ B\ng₁ g₂ : B ⟶ C\n⊢ f ≫ (g₁ + g₂) = f ≫ g₁ + f ≫ g₂",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Representation.IntertwiningMap.comp_add",
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"CategoryTheory.Categor... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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} | {
"line": 317,
"column": 16
} | {
"line": 317,
"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 | {
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"column": 30
} | {
"line": 328,
"column": 32
} | {
"line": 328,
"column": 33
} | [
{
"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.Rep.Basic | {
"line": 277,
"column": 47
} | {
"line": 277,
"column": 49
} | {
"line": 278,
"column": 2
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B : Rep k G\nι : Type u'\nf : ι → (A ⟶ B)\ns : Finset ι\n⊢ Hom.hom (∑ i ∈ s, f i) = ∑ i ∈ s, Hom.hom (f i)",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Rep.V",
"Representation.IntertwiningMap.instAddC... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 277,
"column": 47
} | {
"line": 280,
"column": 62
} | {
"line": 282,
"column": 0
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA B : Rep k G\nι : Type u'\nf : ι → (A ⟶ B)\ns : Finset ι\n⊢ Hom.hom (∑ i ∈ s, f i) = ∑ i ∈ s, Hom.hom (f i)",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Rep.V",
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classical induction s using Finset.induction with
| empty => simp
| insert a s ha h => simp [Finset.sum_insert ha, add_hom, h] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 285,
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} | {
"line": 285,
"column": 53
} | {
"line": 286,
"column": 2
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝⁵ : Semiring k\ninst✝⁴ : Monoid G\nι : Type u'\nM N : Type v'\ninst✝³ : AddCommGroup M\ninst✝² : AddCommGroup N\ninst✝¹ : Module k M\ninst✝ : Module k N\nσ : Representation k G M\nρ : Representation k G N\nf : ι → σ.IntertwiningMap ρ\ns : Finset ι\n⊢ ofHom (∑ i ∈ s, f i) = ... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 304,
"column": 62
} | {
"line": 304,
"column": 64
} | {
"line": 304,
"column": 65
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Semiring k\ninst✝ : Monoid G\nA : Rep k G\ng1 g2 : G\n⊢ A.ρ (g1 * g2) = A.ρ g1 ∘ₗ A.ρ g2",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Rep.V",
"MonoidHom.instMonoidHomClass",
"Representation",
"MonoidHom.instFunLike",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 313,
"column": 52
} | {
"line": 313,
"column": 54
} | {
"line": 313,
"column": 55
} | [
{
"pp": "k : Type u\nG✝ : Type v\ninst✝⁸ : Semiring k\ninst✝⁷ : Monoid G✝\nX Y : Type w\ninst✝⁶ : AddCommGroup X\ninst✝⁵ : AddCommGroup Y\ninst✝⁴ : Module k X\ninst✝³ : Module k Y\nρ : Representation k G✝ X\nσ : Representation k G✝ Y\nA✝ B C : Rep k G✝\nZ : Type w\ninst✝² : AddCommGroup Z\ninst✝¹ : Module k Z\n... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 320,
"column": 47
} | {
"line": 320,
"column": 49
} | {
"line": 321,
"column": 2
} | [
{
"pp": "k : Type u\ninst✝¹ : Semiring k\nG : Type v\ninst✝ : CommMonoid G\nA B : Rep k G\nf : A ⟶ B\ng : G\n⊢ A.applyAsHom g ≫ f = f ≫ B.applyAsHom g",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Rep.V",
"Representation",
"MonoidHom.instFunLike",
"Monoid.toMulOn... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 407,
"column": 12
} | {
"line": 407,
"column": 14
} | {
"line": 407,
"column": 15
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA : Rep k G\nx : ↑A\ng : G\n⊢ (((Finsupp.lift (↑A) k G) fun g ↦ (A.ρ g) x) ∘ₗ ↑(MonoidAlgebra.coeffLinearEquiv k)) ∘ₗ\n (Representation.ofMulAction k G G) g =\n A.ρ g ∘ₗ ((Finsupp.lift (↑A) k G) fun g ↦ (A.ρ g) x) ∘ₗ ↑(MonoidAlgebra.coe... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 410,
"column": 60
} | {
"line": 410,
"column": 62
} | {
"line": 411,
"column": 2
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA : Rep k G\ng : G\nx : ↑A\nr : k\n⊢ (Hom.hom (A.leftRegularHom x)) (MonoidAlgebra.single g r) = r • (A.ρ g) x",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Rep.V",
"instHSMul",
"Representation",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
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"column": 59
} | {
"line": 489,
"column": 61
} | {
"line": 490,
"column": 4
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA B C X✝ Y✝ : Rep k G\nf : X✝ ⟶ Y✝\ng : G\n⊢ ModuleCat.Hom.hom\n ({ V := ModuleCat.of k ↑X✝, ρ := (ModuleCat.of k ↑X✝).endRingEquiv.symm.toMonoidHom.comp X✝.ρ }.ρ g ≫\n Hom.toModuleCatHom f) =\n ModuleCat.Hom.hom\n (Hom.toMo... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
"line": 341,
"column": 61
} | {
"line": 341,
"column": 63
} | {
"line": 342,
"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 | {
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"column": 61
} | {
"line": 347,
"column": 63
} | {
"line": 347,
"column": 64
} | [
{
"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.Rep.Basic | {
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"column": 37
} | {
"line": 499,
"column": 39
} | {
"line": 499,
"column": 40
} | [
{
"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",
"ppTerm": "?m.88",... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 504,
"column": 23
} | {
"line": 504,
"column": 25
} | {
"line": 504,
"column": 26
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA✝ B C : Rep k G\nA : Action (ModuleCat k) G\ng : G\n⊢ ((RepToAction k G).obj ((ActionToRep k G).obj A)).ρ g ≫ 𝟙 ((RepToAction k G).obj ((ActionToRep k G).obj A)).V =\n 𝟙 ((RepToAction k G).obj ((ActionToRep k G).obj A)).V ≫ A.ρ g",
"p... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
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"column": 23
} | {
"line": 505,
"column": 25
} | {
"line": 505,
"column": 26
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA✝ B C : Rep k G\nA : Action (ModuleCat k) G\ng : G\n⊢ A.ρ g ≫ 𝟙 A.V = 𝟙 A.V ≫ ((RepToAction k G).obj ((ActionToRep k G).obj A)).ρ g",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"MonoidHom.instFunLike",
"C... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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"column": 69
} | {
"line": 372,
"column": 71
} | {
"line": 373,
"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.Rep.Basic | {
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"column": 23
} | {
"line": 527,
"column": 25
} | {
"line": 527,
"column": 26
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA B C X Y : Rep k G\nf g : X ⟶ Y\n⊢ (forget₂ (Rep k G) (ModuleCat k)).map (f + g) =\n (forget₂ (Rep k G) (ModuleCat k)).map f + (forget₂ (Rep k G) (ModuleCat k)).map g",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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"column": 73
} | {
"line": 395,
"column": 75
} | {
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"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.Rep.Basic | {
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"column": 62
} | {
"line": 545,
"column": 64
} | {
"line": 545,
"column": 65
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA✝ B✝ C A B : Rep k G\n⊢ ofHom (Representation.IntertwiningMap.inl k A.ρ B.ρ) ≫ ofHom (Representation.IntertwiningMap.fst k A.ρ B.ρ) = 𝟙 A",
"ppTerm": "?m.174",
"assigned": true,
"usedConstants": [
"Rep.V",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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"column": 63
} | {
"line": 418,
"column": 65
} | {
"line": 418,
"column": 66
} | [
{
"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.Rep.Basic | {
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"column": 6
} | {
"line": 546,
"column": 8
} | {
"line": 546,
"column": 9
} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA✝ B✝ C A B : Rep k G\n⊢ ofHom (Representation.IntertwiningMap.inl k A.ρ B.ρ) ≫ ofHom (Representation.IntertwiningMap.snd k A.ρ B.ρ) = 0",
"ppTerm": "?m.175",
"assigned": true,
"usedConstants": [
"Rep.V",
"CategoryTheory... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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} | {
"line": 421,
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} | {
"line": 421,
"column": 66
} | [
{
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Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
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} | {
"line": 546,
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} | [
{
"pp": "k : Type u\nG : Type v\ninst✝¹ : Ring k\ninst✝ : Monoid G\nA✝ B✝ C A B : Rep k G\n⊢ ofHom (Representation.IntertwiningMap.inr k A.ρ B.ρ) ≫ ofHom (Representation.IntertwiningMap.fst k A.ρ B.ρ) = 0",
"ppTerm": "?m.176",
"assigned": true,
"usedConstants": [
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"Representation... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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} | {
"line": 449,
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} | {
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{
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Mathlib.RepresentationTheory.FinGroupCharZero | {
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} | {
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} | {
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} | [
{
"pp": "k : Type u\ninst✝³ : Field k\nG : Type u\ninst✝² : Finite G\ninst✝¹ : Group G\ninst✝ : NeZero ↑(Nat.card G)\nV : Rep k G\n⊢ Injective V",
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Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
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} | {
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{
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"ppTerm": "?m.177",
"assigned": true,
"usedConstants": [
"Rep.V",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.FinGroupCharZero | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.FinGroupCharZero | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.FinGroupCharZero | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Continuous.Basic | {
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} | {
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{
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Mathlib.RepresentationTheory.Continuous.Basic | {
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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Mathlib.RepresentationTheory.Continuous.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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Mathlib.RepresentationTheory.Rep.Basic | {
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"as... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
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} | {
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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"line": 788,
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{
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Mathlib.RepresentationTheory.Rep.Basic | {
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} | {
"line": 789,
"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 : A ⊗ B ⟶ C\ng : G\n⊢ (TensorProduct.curry (Hom.hom f).toLinearMap).flip ∘ₗ B.ρ g =\n (A.ρ.linHom C.ρ) g ∘ₗ (TensorProduct.curry (Hom.hom f).toLinearMap).flip",
"... | [] | ext x y
simp only [tensor_V, tensor_ρ, LinearMap.coe_comp, Function.comp_apply, LinearMap.flip_apply,
TensorProduct.curry_apply, Representation.IntertwiningMap.toLinearMap_apply,
Representation.linHom_apply]
have := by simpa using (hom_comm_apply f g (A.ρ g⁻¹ y ⊗ₜ[k] x)).symm
simp [this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 784,
"column": 4
} | {
"line": 789,
"column": 15
} | {
"line": 789,
"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 : A ⊗ B ⟶ C\ng : G\n⊢ (TensorProduct.curry (Hom.hom f).toLinearMap).flip ∘ₗ B.ρ g =\n (A.ρ.linHom C.ρ) g ∘ₗ (TensorProduct.curry (Hom.hom f).toLinearMap).flip",
"... | [] | ext x y
simp only [tensor_V, tensor_ρ, LinearMap.coe_comp, Function.comp_apply, LinearMap.flip_apply,
TensorProduct.curry_apply, Representation.IntertwiningMap.toLinearMap_apply,
Representation.linHom_apply]
have := by simpa using (hom_comm_apply f g (A.ρ g⁻¹ y ⊗ₜ[k] x)).symm
simp [this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RepresentationTheory.Rep.Basic | {
"line": 783,
"column": 78
} | {
"line": 783,
"column": 80
} | {
"line": 784,
"column": 4
} | [
{
"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\n⊢ (TensorProduct.curry (Hom.hom f).toLinearMap).flip ∘ₗ B.ρ g =\n (A.ρ.linHom C.ρ) g ∘ₗ (TensorProduct.curry (Hom.hom f).toLinearMap).flip",
"... | [] | by | [anonymous] | by |
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