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.GroupTheory.FreeGroup.CyclicallyReduced | {
"line": 142,
"column": 19
} | {
"line": 142,
"column": 30
} | [
{
"pp": "α : Type u\nL : List (α × Bool)\ninst✝ : DecidableEq α\na : α × Bool\nl : List (α × Bool)\nb : α × Bool\nih : IsReduced l → IsCyclicallyReduced (reduceCyclically l)\nh : IsReduced (a :: (l ++ [b]))\nh' : ¬(b.1 = a.1 ∧ (!b.2) = a.2)\n⊢ b.1 = a.1 → b.2 = a.2",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.CyclicallyReduced | {
"line": 232,
"column": 6
} | {
"line": 232,
"column": 78
} | [
{
"pp": "α : Type u\nL L₁ L₂ L₃ : List (α × Bool)\nn : ℕ\nhn : n ≠ 0\nx y : FreeGroup α\nheq : (fun a ↦ a ^ n) x = (fun a ↦ a ^ n) y\nf : FreeGroup α → ℕ → ℕ :=\n fun a n ↦ (conjugator a.toWord).length + (n * (reduceCyclically a.toWord).length + (conjugator a.toWord).length)\ng : FreeGroup α → ℕ → List (α × Bo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.CyclicallyReduced | {
"line": 234,
"column": 6
} | {
"line": 234,
"column": 78
} | [
{
"pp": "α : Type u\nL L₁ L₂ L₃ : List (α × Bool)\nn : ℕ\nhn : n ≠ 0\nx y : FreeGroup α\nf : FreeGroup α → ℕ → ℕ :=\n fun a n ↦ (conjugator a.toWord).length + (n * (reduceCyclically a.toWord).length + (conjugator a.toWord).length)\ng : FreeGroup α → ℕ → List (α × Bool) :=\n fun a k ↦ conjugator a.toWord ++ ((... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.CyclicallyReduced | {
"line": 235,
"column": 35
} | {
"line": 235,
"column": 50
} | [
{
"pp": "α : Type u\nL L₁ L₂ L₃ : List (α × Bool)\nn : ℕ\nhn : n ≠ 0\nx y : FreeGroup α\nf : FreeGroup α → ℕ → ℕ :=\n fun a n ↦ (conjugator a.toWord).length + (n * (reduceCyclically a.toWord).length + (conjugator a.toWord).length)\ng : FreeGroup α → ℕ → List (α × Bool) :=\n fun a k ↦ conjugator a.toWord ++ ((... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.CyclicallyReduced | {
"line": 236,
"column": 48
} | {
"line": 236,
"column": 63
} | [
{
"pp": "α : Type u\nL L₁ L₂ L₃ : List (α × Bool)\nn : ℕ\nhn : n ≠ 0\nx y : FreeGroup α\nf : FreeGroup α → ℕ → ℕ :=\n fun a n ↦ (conjugator a.toWord).length + (n * (reduceCyclically a.toWord).length + (conjugator a.toWord).length)\ng : FreeGroup α → ℕ → List (α × Bool) :=\n fun a k ↦ conjugator a.toWord ++ ((... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.Orbit | {
"line": 46,
"column": 2
} | {
"line": 46,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na b : α × Bool\nh : ∀ (x : FreeGroup α), x.toWord[0]? = some a ↔ x.toWord[0]? = some b\n⊢ a = b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.Orbit | {
"line": 84,
"column": 38
} | {
"line": 84,
"column": 68
} | [
{
"pp": "α : Type u_1\nX : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : MulAction (FreeGroup α) X\nx : X\nw : α × Bool\ng : FreeGroup α\nhg : g ∈ startsWith w\nl : List (α × Bool) := g.toWord\nh : ⟨g, hg⟩ = ⟨mk g.toWord, ⋯⟩\na : α × Bool\nhl : [a] = g.toWord\n⊢ a = w",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.Orbit | {
"line": 88,
"column": 28
} | {
"line": 88,
"column": 58
} | [
{
"pp": "α : Type u_1\nX : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : MulAction (FreeGroup α) X\nx : X\nw : α × Bool\ng : FreeGroup α\nhg : g ∈ startsWith w\nl✝ : List (α × Bool) := g.toWord\nh : ⟨g, hg⟩ = ⟨mk g.toWord, ⋯⟩\na b : α × Bool\nl : List (α × Bool)\nhl : a :: b :: l = g.toWord\n⊢ a = w",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 33
} | [
{
"pp": "G : Type u\ninst✝² : Groupoid G\ninst✝¹ : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\na : G\np : Path (root (WideSubquiver.toType (Symmetrify (Generators G)) T)) a\n⊢ treeHom T a = homOfPath T p",
"usedC... | rw [treeHom, Unique.default_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 33
} | [
{
"pp": "G : Type u\ninst✝² : Groupoid G\ninst✝¹ : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\na : G\np : Path (root (WideSubquiver.toType (Symmetrify (Generators G)) T)) a\n⊢ treeHom T a = homOfPath T p",
"usedC... | rw [treeHom, Unique.default_eq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 33
} | [
{
"pp": "G : Type u\ninst✝² : Groupoid G\ninst✝¹ : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\na : G\np : Path (root (WideSubquiver.toType (Symmetrify (Generators G)) T)) a\n⊢ treeHom T a = homOfPath T p",
"usedC... | rw [treeHom, Unique.default_eq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Nilpotent | {
"line": 223,
"column": 12
} | {
"line": 223,
"column": 50
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nH : Type u_2\ninst✝ : Group H\ne : H ≃* G\n⊢ comap (↑e) (upperCentralSeries G 0) = upperCentralSeries H 0",
"usedConstants": [
"Eq.mpr",
"MulEquiv.instEquivLike",
"_private.Mathlib.GroupTheory.Nilpotent.0.Subgroup.comap_upperCentralSeries._simp_1_3"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 244,
"column": 8
} | {
"line": 244,
"column": 17
} | [
{
"pp": "case refine_1\nG : Type u\ninst✝³ : Groupoid G\ninst✝² : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝¹ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\nX : Type u\ninst✝ : Group X\nf : ↑(wideSubquiverEquivSetTotal (wideSubquiverSymmetrify T))ᶜ → X\nf' : Lab... | intro a p | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.GroupTheory.FreeGroup.NielsenSchreier | {
"line": 257,
"column": 10
} | {
"line": 258,
"column": 53
} | [
{
"pp": "G : Type u\ninst✝³ : Groupoid G\ninst✝² : IsFreeGroupoid G\nT : WideSubquiver (Symmetrify (Generators G))\ninst✝¹ : Arborescence (WideSubquiver.toType (Symmetrify (Generators G)) T)\nX : Type u\ninst✝ : Group X\nf : ↑(wideSubquiverEquivSetTotal (wideSubquiverSymmetrify T))ᶜ → X\nf' : Labelling (Generat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Nilpotent | {
"line": 603,
"column": 4
} | {
"line": 603,
"column": 60
} | [
{
"pp": "case succ.h'\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\nd : ℕ\nhd : map H.subtype (lowerCentralSeries (↥H) d) ≤ lowerCentralSeries G d\nx3 : ↥H\nhx3 : x3 ∈ lowerCentralSeries (↥H) d\nx4 : ↥H\n_hx4 : x4 ∈ ⊤\n⊢ H.subtype ⁅x3, x4⁆ ∈ {x | ∃ p ∈ lowerCentralSeries G d, ∃ q ∈ ⊤, ⁅p, q⁆ = x}",
"usedC... | exact ⟨x3, hd (mem_map.mpr ⟨x3, hx3, rfl⟩), x4, by simp⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.GroupTheory.Nilpotent | {
"line": 640,
"column": 4
} | {
"line": 640,
"column": 15
} | [
{
"pp": "case succ\nG : Type u_1\ninst✝¹ : Group G\nH : Type u_2\ninst✝ : Group H\nf : G →* H\nh : Function.Surjective ⇑f\nd : ℕ\nhd : Subgroup.map f (upperCentralSeries G d) ≤ upperCentralSeries H d\nx : G\nhx : x ∈ upperCentralSeries G d.succ\ny : G\n⊢ ⁅f x, f y⁆ ∈ (upperCentralSeriesAux H d).fst",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Nilpotent | {
"line": 701,
"column": 4
} | {
"line": 704,
"column": 62
} | [] | ⊤ = f.range := symm (f.range_eq_top_of_surjective hf)
_ = Subgroup.map f ⊤ := MonoidHom.range_eq_map _
_ = Subgroup.map f (upperCentralSeries G n) := by rw [hn]
_ ≤ upperCentralSeries G' n := upperCentralSeries.map hf n | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcSteps |
Mathlib.GroupTheory.Nilpotent | {
"line": 719,
"column": 4
} | {
"line": 722,
"column": 62
} | [] | ⊤ = f.range := symm (f.range_eq_top_of_surjective hf)
_ = Subgroup.map f ⊤ := MonoidHom.range_eq_map _
_ = Subgroup.map f (upperCentralSeries G n) := by rw [hn]
_ ≤ upperCentralSeries G' n := upperCentralSeries.map hf n | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcSteps |
Mathlib.GroupTheory.Nilpotent | {
"line": 1086,
"column": 46
} | {
"line": 1086,
"column": 57
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : IsNilpotent G\nih : ∀ (H : Subgroup (G ⧸ center G)), normalizer ↑H = H → H = ⊤\nH : Subgroup G\nhH : normalizer ↑H = H\nhch : center G ≤ H\n⊢ (mk' (center G)).ker ≤ H",
"usedConstants": [
"Eq.mpr",
"Monoid.toMulOneClass",
"congrArg",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Goursat | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 44
} | [
{
"pp": "case mp\nG : Type u_1\nH : Type u_2\ninst✝¹ : Group G\ninst✝ : Group H\nI : Subgroup (G × H)\nhI₁ : Surjective (Prod.fst ∘ ⇑I.subtype)\nhI₂ : Surjective (Prod.snd ∘ ⇑I.subtype)\nx y : G × H\nhx : x ∈ I\nhy : y ∈ I\nthis✝ : I.goursatFst.Normal\nthis : I.goursatSnd.Normal\nh : (y.1 / x.1, 1) ∈ I\n⊢ (1, x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Goursat | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 44
} | [
{
"pp": "case mpr\nG : Type u_1\nH : Type u_2\ninst✝¹ : Group G\ninst✝ : Group H\nI : Subgroup (G × H)\nhI₁ : Surjective (Prod.fst ∘ ⇑I.subtype)\nhI₂ : Surjective (Prod.snd ∘ ⇑I.subtype)\nx y : G × H\nhx : x ∈ I\nhy : y ∈ I\nthis✝ : I.goursatFst.Normal\nthis : I.goursatSnd.Normal\nh : (1, x.2 / y.2) ∈ I\n⊢ (y.1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Goursat | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 13
} | [
{
"pp": "G : Type u_1\nH : Type u_2\ninst✝¹ : Group G\ninst✝ : Group H\nI : Subgroup (G × H)\ng : G\nh : H\nhg : (g, h).1 ∈ ↑I.goursatFst.toSubmonoid\nhh : (g, h).2 ∈ ↑I.goursatSnd.toSubmonoid\n⊢ (g, h) ∈ I",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Goursat | {
"line": 159,
"column": 6
} | {
"line": 163,
"column": 13
} | [
{
"pp": "case h.mp\nG : Type u_1\nH : Type u_2\ninst✝¹ : Group G\ninst✝ : Group H\nI : Subgroup (G × H)\nG' : Subgroup G := map (MonoidHom.fst G H) I\nH' : Subgroup H := map (MonoidHom.snd G H) I\nP : ↥I →* ↥G' := (MonoidHom.fst G H).subgroupMap I\nQ : ↥I →* ↥H' := (MonoidHom.snd G H).subgroupMap I\nI' : Subgro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Blocks | {
"line": 193,
"column": 27
} | {
"line": 193,
"column": 38
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝ : SMul G X\nB : Set X\ng₁ g₂ : G\nhB : IsBlock G B\nhg : g₁ • B ⊆ g₂ • B\nhg' : g₁ • B ≠ g₂ • B\n⊢ B = ∅",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Blocks | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 13
} | [
{
"pp": "M : Type u_1\nX : Type u_2\ninst✝¹ : Monoid M\ninst✝ : MulAction M X\nB : Set X\ns : Set M\nhB : IsBlock M B\nhs : ¬B ⊆ s • B\n⊢ Disjoint B (s • B)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Blocks | {
"line": 246,
"column": 53
} | {
"line": 246,
"column": 64
} | [
{
"pp": "M : Type u_1\nX : Type u_2\ninst✝¹ : Monoid M\ninst✝ : MulAction M X\nB : Set X\ns : Set M\nhB : IsBlock M B\nhs : ¬B ⊆ s • B\n⊢ ¬1 • B ⊆ s • B",
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
"Set.smul",
"id",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Blocks | {
"line": 261,
"column": 24
} | {
"line": 261,
"column": 35
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nX : Type u_2\ninst✝ : MulAction G X\nB : Set X\nhB : IsBlock G B\ng : G\n⊢ g • B ≠ B → Disjoint (g • B) B",
"usedConstants": [
"instHSMul",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Primitive | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 67
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝¹ : Group G\ninst✝ : MulAction G X\nHnt : fixedPoints G X ≠ ⊤\nH : ∀ {B : Set X}, IsBlock G B → IsTrivialBlock B\n⊢ IsPreprimitive G X",
"usedConstants": [
"Membership.mem",
"Exists",
"Eq.mp",
"DivInvMonoid.toMonoid",
"Ne",
"Group... | simp only [Set.top_eq_univ, Set.ne_univ_iff_exists_notMem] at Hnt | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.GroupTheory.IndexNormal | {
"line": 51,
"column": 2
} | {
"line": 52,
"column": 36
} | [
{
"pp": "case pos\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\nhHp : H.index = (Nat.card G).minFac\nhG0 : ¬Nat.card G = 0\nhG1 : Nat.card G = 1\n⊢ H.Normal",
"usedConstants": [
"congrArg",
"Subgroup.normal_of_index_eq_one",
"Nat.minFac_one",
"Eq.mp",
"Nat.minFac",
"Nat... | · rw [hG1, minFac_one] at hHp
exact normal_of_index_eq_one hHp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.GroupAction.Primitive | {
"line": 333,
"column": 30
} | {
"line": 333,
"column": 59
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁶ : Group G\ninst✝⁵ : MulAction G X\nH : Type u_3\nY : Type u_4\ninst✝⁴ : Group H\ninst✝³ : MulAction H Y\nφ : G → H\nf : X →ₑ[φ] Y\ninst✝² : Finite Y\ninst✝¹ : IsPretransitive H Y\ninst✝ : IsPreprimitive G X\nhf' : Nat.card Y < 2 * (Set.range ⇑f).ncard\nB : Set Y\nhB :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Blocks | {
"line": 445,
"column": 4
} | {
"line": 445,
"column": 44
} | [
{
"pp": "case nonempty\nG : Type u_1\ninst✝¹ : Group G\nX : Type u_2\ninst✝ : MulAction G X\nB : Set X\nhGX : IsPretransitive G X\nhB : IsBlock G B\nhBe : B.Nonempty\ng : G\nhg : g • B = ∅\n⊢ B = ∅",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Primitive | {
"line": 379,
"column": 4
} | {
"line": 379,
"column": 62
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝² : Group G\ninst✝¹ : MulAction G X\ninst✝ : IsPreprimitive G X\nA : Set X\nhfA : A.Finite\nhA : A.Nonempty\nhA' : A ≠ Set.univ\na b : X\nh : a ≠ b\nB : Set X := ⋂ g, ⋂ (_ : a ∈ g • A), g • A\nthis : ¬∀ (i : G), b ∈ ⋂ (_ : a ∈ i • A), i • A\n⊢ ∃ g, a ∈ g • A ∧ b ∉ g • A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.SpecificGroups.Alternating | {
"line": 177,
"column": 4
} | {
"line": 177,
"column": 69
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nhσ✝ : σ ∈ alternatingGroup α\nhσ : (↑⟨σ, hσ✝⟩).support.card + 2 ≤ card α\nτ : Perm α\nhτ : τ ∈ alternatingGroup α\nhc : IsConj ↑⟨σ, hσ✝⟩ ↑⟨τ, hτ⟩\nπ : Perm α\nhπ : π * σ * π⁻¹ = τ\nh : sign π = 1\n⊢ ↑(⟨π, ⋯⟩ * ⟨σ, hσ✝⟩ * ⟨π,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | {
"line": 112,
"column": 46
} | {
"line": 112,
"column": 62
} | [
{
"pp": "G✝ : Type u_1\ninst✝³ : Group G✝\nα✝ : Type u_2\ninst✝² : MulAction G✝ α✝\nG : Type u_3\ninst✝¹ : AddGroup G\nα : Type u_4\ninst✝ : AddAction G α\ng : G\na b : α\nhg : b = g +ᵥ a\nx : ↥(SubAddAction.ofStabilizer G a)\nhy : g +ᵥ ↑x ∈ {b}\n⊢ ↑x ∈ {a}",
"usedConstants": [
"Eq.mpr",
"AddMon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | {
"line": 122,
"column": 45
} | {
"line": 122,
"column": 61
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\nα : Type u_2\ninst✝ : MulAction G α\ng : G\na b : α\nhg : b = g • a\nx : ↥(ofStabilizer G a)\nhy : g • ↑x ∈ {b}\n⊢ ↑x ∈ {a}",
"usedConstants": [
"SubMulAction.instSetLike",
"Eq.mpr",
"Membership.mem",
"Subgroup.instMulAction",
"Set.instS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 13
} | [
{
"pp": "case a.a\nG : Type u_1\ninst✝¹ : Group G\nα : Type u_2\ninst✝ : MulAction G α\ng h k : G\na b c : α\nhg : b = g • a\nhh : c = h • b\nhk : c = k • a\nH : k = h * g\nx : ↥(ofStabilizer G a)\n⊢ ↑(((conjMap hh).comp (conjMap hg)) x) = ↑((conjMap hk) x)",
"usedConstants": [
"SubMulAction.instSetLi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | {
"line": 218,
"column": 4
} | {
"line": 218,
"column": 35
} | [
{
"pp": "case h.h.inl\nG : Type u_1\ninst✝² : Group G\nα : Type u_2\ninst✝¹ : MulAction G α\ninst✝ : IsPretransitive G α\nn : ℕ\na : α\nx : Fin n.succ ↪ α\ng : G\nhgx : g • x (Fin.last n) = a\nH : ∀ (i : Fin n), (Fin.Embedding.init (g • x)) i ∈ ofStabilizer G a\ni : Fin n\n⊢ (g • x) i.castSucc = (ofStabilizer.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Embedding | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 38
} | [
{
"pp": "case h\nα : Type u_1\nn : ℕ\ns : Set α\ninst✝ : Finite ↑s\nhs : ↑s.ncard + ↑n ≤ ENat.card α\ny : Fin n ↪ ↑sᶜ\ni : Fin n\n⊢ (y.trans (subtype fun x ↦ x ∈ sᶜ)) i ∉ s",
"usedConstants": [
"Eq.mpr",
"Compl.compl",
"Membership.mem",
"Set.Elem",
"id",
"Set.instCompl",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.SpecificGroups.Alternating | {
"line": 306,
"column": 2
} | {
"line": 306,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh2 : Nat.card α ≤ 2\na✝ : Nontrivial α\n⊢ 2 ≤ Nat.card α",
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Fintype.card",
"id",
"Nat.card",
"instOfNatNat",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.SpecificGroups.Alternating | {
"line": 395,
"column": 2
} | {
"line": 395,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nH : IsMulCommutative ↥(alternatingGroup α)\nh : 3 < Nat.card α\n⊢ Subsingleton ↥(alternatingGroup α)",
"usedConstants": [
"Eq.mpr",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.MultipleTransitivity | {
"line": 357,
"column": 2
} | {
"line": 381,
"column": 18
} | [
{
"pp": "G : Type u_1\nα : Type u_2\ninst✝² : Group G\ninst✝¹ : MulAction G α\ninst✝ : IsPretransitive G α\nn : ℕ\na : α\n⊢ IsMultiplyPretransitive G α n.succ ↔ IsMultiplyPretransitive (↥(stabilizer G a)) (↥(ofStabilizer G a)) n",
"usedConstants": [
"SubMulAction.mulAction",
"SubMulAction.instSe... | refine ⟨fun hn ↦ ⟨fun x y ↦ ?_⟩, fun hn ↦ ⟨fun x y ↦ ?_⟩⟩
· obtain ⟨g, hgxy⟩ := exists_smul_eq G (ofStabilizer.snoc x) (ofStabilizer.snoc y)
have hg : g ∈ stabilizer G a := by
rw [DFunLike.ext_iff] at hgxy
convert! hgxy (last n)
simp [ofStabilizer.snoc_last]
use ⟨g, hg⟩
ext i
simp on... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.GroupAction.MultipleTransitivity | {
"line": 357,
"column": 2
} | {
"line": 381,
"column": 18
} | [
{
"pp": "G : Type u_1\nα : Type u_2\ninst✝² : Group G\ninst✝¹ : MulAction G α\ninst✝ : IsPretransitive G α\nn : ℕ\na : α\n⊢ IsMultiplyPretransitive G α n.succ ↔ IsMultiplyPretransitive (↥(stabilizer G a)) (↥(ofStabilizer G a)) n",
"usedConstants": [
"SubMulAction.mulAction",
"SubMulAction.instSe... | refine ⟨fun hn ↦ ⟨fun x y ↦ ?_⟩, fun hn ↦ ⟨fun x y ↦ ?_⟩⟩
· obtain ⟨g, hgxy⟩ := exists_smul_eq G (ofStabilizer.snoc x) (ofStabilizer.snoc y)
have hg : g ∈ stabilizer G a := by
rw [DFunLike.ext_iff] at hgxy
convert! hgxy (last n)
simp [ofStabilizer.snoc_last]
use ⟨g, hg⟩
ext i
simp on... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 136,
"column": 6
} | {
"line": 136,
"column": 17
} | [
{
"pp": "case mpr.right\nM : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\nh : IsPreprimitive M α\n⊢ ∀ {s : Set α}, s.encard + 1 = ↑1 → IsPreprimitive ↥(fixingSubgroup M s) ↥(ofFixingSubgroup M s)",
"usedConstants": [
"SubMulAction.instSetLike",
"Eq.mpr",
"IsAddRightRegu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 196,
"column": 12
} | {
"line": 196,
"column": 28
} | [
{
"pp": "case h.mpr.inr\nM : Type u_1\nα : Type u_2\ninst✝² : Group M\ninst✝¹ : MulAction M α\ninst✝ : IsPretransitive M α\nn : ℕ\nhn : 1 ≤ n\na : α\nH : IsMultiplyPreprimitive (↥(stabilizer M a)) (↥(ofStabilizer M a)) n\ns : Set α\nhs : s.encard + 1 = ↑n.succ\nb : α\nhb : b ∈ s\ng : M\nhg : g • b = a\ns' : Set... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.VectorBundle.Riemannian | {
"line": 393,
"column": 6
} | {
"line": 393,
"column": 17
} | [
{
"pp": "case inr\nB✝ : Type u_1\ninst✝¹⁸ : TopologicalSpace B✝\nF✝ : Type u_2\ninst✝¹⁷ : NormedAddCommGroup F✝\ninst✝¹⁶ : NormedSpace ℝ F✝\nE✝ : B✝ → Type u_3\ninst✝¹⁵ : TopologicalSpace (TotalSpace F✝ E✝)\ninst✝¹⁴ : (x : B✝) → NormedAddCommGroup (E✝ x)\ninst✝¹³ : (x : B✝) → InnerProductSpace ℝ (E✝ x)\ninst✝¹²... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 228,
"column": 28
} | {
"line": 228,
"column": 52
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝³ : Group M\ninst✝² : MulAction M α\nm n : ℕ\ninst✝¹ : IsMultiplyPreprimitive M α n\ns : Set α\ninst✝ : Finite ↑s\nhs : s.ncard + m = n\nt : Set ↥(ofFixingSubgroup M s)\nht : t.encard + 1 = ↑m\nt' : Set α := Subtype.val '' t\nhtt' : t = Subtype.val ⁻¹' t'\n⊢ s.encard + ... | Set.Finite.cast_ncard_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.GroupAction.MultipleTransitivity | {
"line": 502,
"column": 2
} | {
"line": 502,
"column": 56
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\nα : Type u_2\ninst✝¹ : MulAction G α\ninst✝ : Finite α\ns : Set α\nhMk : IsMultiplyPretransitive G α s.ncard\n⊢ (fixingSubgroup G s).index = (Nat.card α).choose s.ncard * s.ncard !",
"usedConstants": [
"Nat.choose",
"HMul.hMul",
"fixingSubgroup",
... | apply Nat.eq_of_mul_eq_mul_right (Nat.factorial_pos _) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 300,
"column": 8
} | {
"line": 300,
"column": 48
} | [
{
"pp": "case h\nM : Type u_1\nα : Type u_2\ninst✝³ : Group M\ninst✝² : MulAction M α\nN : Type u_3\nβ : Type u_4\ninst✝¹ : Group N\ninst✝ : MulAction N β\nφ : M → N\nf : α →ₑ[φ] β\nhf : Function.Bijective ⇑f\nn : ℕ\nh : IsMultiplyPreprimitive M α n\nt : Set β\nht : t.encard + 1 = ↑n\ns : Set α := ⋯\nhs' : ⇑f '... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 329,
"column": 6
} | {
"line": 329,
"column": 50
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝³ : Group M\ninst✝² : MulAction M α\nN : Type u_3\nβ : Type u_4\ninst✝¹ : Group N\ninst✝ : MulAction N β\nφ : M → N\nhφ : Function.Surjective φ\nf : α →ₑ[φ] β\nhf : Function.Bijective ⇑f\nn : ℕ\nH : IsMultiplyPreprimitive N β n\ns : Set α\nhs : s.encard + 1 = ↑n\nt : Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 350,
"column": 10
} | {
"line": 350,
"column": 62
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝³ : Group M\ninst✝² : MulAction M α\nN : Type u_3\nβ : Type u_4\ninst✝¹ : Group N\ninst✝ : MulAction N β\nφ : M → N\nhφ : Function.Surjective φ\nf : α →ₑ[φ] β\nhf : Function.Bijective ⇑f\nn : ℕ\nH : IsMultiplyPreprimitive N β n\ns : Set α\nhs : s.encard + 1 = ↑n\nt : Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.MultiplePrimitivity | {
"line": 351,
"column": 8
} | {
"line": 351,
"column": 47
} | [
{
"pp": "case right.hf.left\nM : Type u_1\nα : Type u_2\ninst✝³ : Group M\ninst✝² : MulAction M α\nN : Type u_3\nβ : Type u_4\ninst✝¹ : Group N\ninst✝ : MulAction N β\nφ : M → N\nhφ : Function.Surjective φ\nf : α →ₑ[φ] β\nhf : Function.Bijective ⇑f\nn : ℕ\nH : IsMultiplyPreprimitive N β n\ns : Set α\nhs : s.enc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 128,
"column": 2
} | {
"line": 128,
"column": 32
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns : Set α\nx : α\nhx : x ∈ ofFixingSubgroup M s\ny : α\nhy : y ∈ ofFixingSubgroup M s\nhxy : (ofFixingSubgroup_equivariantMap M s) ⟨x, hx⟩ = (ofFixingSubgroup_equivariantMap M s) ⟨y, hy⟩\n⊢ ⟨x, hx⟩ = ⟨y, hy⟩",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Period | {
"line": 124,
"column": 2
} | {
"line": 124,
"column": 27
} | [
{
"pp": "case h\nα : Type v\nM : Type u\ninst✝¹ : Monoid M\ninst✝ : MulAction M α\nexp_pos : 0 < Monoid.exponent M\nm : M\n⊢ Monoid.exponent M ∈ upperBounds (Set.range fun a ↦ period m a)",
"usedConstants": [
"Eq.mpr",
"congrArg",
"setOf",
"Membership.mem",
"Exists",
"id"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 206,
"column": 4
} | {
"line": 206,
"column": 75
} | [
{
"pp": "case left\nM : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\na : α\ns : Set ↥(ofStabilizer M a)\nx : α\nhx : x ∈ ofFixingSubgroup M (insert a (Subtype.val '' s))\ny : α\nhy : y ∈ ofFixingSubgroup M (insert a (Subtype.val '' s))\nh : (ofFixingSubgroup_insert_map a s) ⟨x, hx⟩ = (ofFixi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 226,
"column": 2
} | {
"line": 231,
"column": 10
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns t : Set α\ng : M\nhg : g • t = s\nk : M\nhk : k ∈ fixingSubgroup M t\n⊢ (MulAut.conj g) k ∈ fixingSubgroup M s",
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"instHSMul",
"M... | simp only [mem_fixingSubgroup_iff] at hk ⊢
intro y hy
rw [MulAut.conj_apply, eq_comm, mul_smul, mul_smul, ← inv_smul_eq_iff, eq_comm]
apply hk
rw [← Set.mem_smul_set_iff_inv_smul_mem, hg]
exact hy | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 226,
"column": 2
} | {
"line": 231,
"column": 10
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns t : Set α\ng : M\nhg : g • t = s\nk : M\nhk : k ∈ fixingSubgroup M t\n⊢ (MulAut.conj g) k ∈ fixingSubgroup M s",
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"instHSMul",
"M... | simp only [mem_fixingSubgroup_iff] at hk ⊢
intro y hy
rw [MulAut.conj_apply, eq_comm, mul_smul, mul_smul, ← inv_smul_eq_iff, eq_comm]
apply hk
rw [← Set.mem_smul_set_iff_inv_smul_mem, hg]
exact hy | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.GroupAction.Jordan | {
"line": 189,
"column": 10
} | {
"line": 189,
"column": 49
} | [
{
"pp": "n : ℕ\nhrec :\n ∀ m < n,\n ∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α],\n IsPreprimitive G α →\n ∀ {s : Set α},\n s.ncard = m + 1 →\n m + 2 < Nat.card α →\n (IsPretransitive ↥(fixingSubgroup G s) ↥(ofFixingSubgroup G s) → Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 297,
"column": 4
} | {
"line": 297,
"column": 38
} | [
{
"pp": "case left\nM : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns t : Set α\ng : M\nhst : g • s = t\nx y : ↥(ofFixingSubgroup M s)\nhxy : (conjMap_ofFixingSubgroup hst) x = (conjMap_ofFixingSubgroup hst) y\n⊢ x = y",
"usedConstants": [
"SubMulAction.instSetLike",
"Eq.mpr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 353,
"column": 10
} | {
"line": 353,
"column": 61
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns✝ s t : Set α\nx : ↥(ofFixingSubgroup M (s ∪ t))\nhx : ⟨↑x, ⋯⟩ ∈ Subtype.val ⁻¹' t\n⊢ ↑x ∈ t",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 368,
"column": 4
} | {
"line": 368,
"column": 43
} | [
{
"pp": "case left\nM : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns t : Set α\na b : ↥(ofFixingSubgroup M (s ∪ t))\nh : (map_ofFixingSubgroupUnion M s t) a = (map_ofFixingSubgroupUnion M s t) b\n⊢ a = b",
"usedConstants": [
"SubMulAction.instSetLike",
"Eq.mpr",
"fixi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 433,
"column": 20
} | {
"line": 433,
"column": 54
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns t : Set α\nhst : s = t\nx✝¹ x✝ : ↥(ofFixingSubgroup M s)\nhxy : (ofFixingSubgroup_of_eq M hst) x✝¹ = (ofFixingSubgroup_of_eq M hst) x✝\n⊢ x✝¹ = x✝",
"usedConstants": [
"SubMulAction.instSetLike",
"Eq.mpr",
"fix... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Jordan | {
"line": 207,
"column": 8
} | {
"line": 207,
"column": 80
} | [
{
"pp": "n : ℕ\nhrec :\n ∀ m < n,\n ∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α],\n IsPreprimitive G α →\n ∀ {s : Set α},\n s.ncard = m + 1 →\n m + 2 < Nat.card α →\n (IsPretransitive ↥(fixingSubgroup G s) ↥(ofFixingSubgroup G s) → Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.MaximalSubgroups | {
"line": 245,
"column": 4
} | {
"line": 247,
"column": 28
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns B : Set α\nhB_ss_sc : B ⊂ s\nhB : IsBlock M B\nhG : Function.Surjective toPerm\nthis : IsPreprimitive ↥(stabilizer M s) ↑s\nφ' : ↥(stabilizer M s) → M := Subtype.val\n⊢ IsBlock (↥(stabilizer M s)) (Subtype.val ⁻¹' B)",
"usedCons... | let f' : (s : Set α) →ₑ[φ'] α := {
toFun := Subtype.val
map_smul' _ _ := rfl } | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 17
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝² : Group M\ninst✝¹ : MulAction M α\ns : Set α\nn : ℕ\ninst✝ : Finite ↑s\nx : Fin n ↪ ↥(ofFixingSubgroup M s)\nthis : Nonempty (Fin s.ncard ≃ ↑s)\ny : Fin s.ncard ↪ ↑s := ⋯\nj : Fin s.ncard\ni : Fin n\nH : ↑(y j) = ↑(x i)\n⊢ ↑(x i) ∈ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Jordan | {
"line": 256,
"column": 12
} | {
"line": 256,
"column": 23
} | [
{
"pp": "case zero\nG : Type u_1\nα : Type u_2\ninst✝¹ : Group G\ninst✝ : MulAction G α\nhG : IsPreprimitive G α\ns : Set α\nhsn : s.ncard = 0 + 1\nhsn' : 0 + 2 < Nat.card α\nhprim : IsPreprimitive ↥(fixingSubgroup G s) ↥(ofFixingSubgroup G s)\nhα : Finite α\n⊢ IsMultiplyPreprimitive G α (0 + 2)",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | {
"line": 539,
"column": 2
} | {
"line": 539,
"column": 47
} | [
{
"pp": "case h\nG : Type u_1\ninst✝¹ : Group G\nα : Type u_2\ninst✝ : MulAction G α\ns : Set α\nk : G\nhk : k ∈ fixingSubgroup G s\n⊢ ∀ a ∈ s, k • a = id a",
"usedConstants": [
"instHSMul",
"Membership.mem",
"id",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"Monoid.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Jordan | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 33
} | [
{
"pp": "case h.a\nα : Type u_1\nK : Type u_2\ninst✝¹ : Group K\ninst✝ : MulAction K α\nhα : Nat.card α = 2\nhK : fixedPoints K α ≠ _root_.Set.univ\nn : ℕ\nthis✝ : Finite α\nthis : Fintype α\nφ : K →* Perm α := toPermHom K α\nf : α →ₑ[⇑φ] α := { toFun := id, map_smul' := ⋯ }\nhf : Function.Bijective ⇑f\nH : Sub... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Jordan | {
"line": 376,
"column": 4
} | {
"line": 376,
"column": 72
} | [
{
"pp": "α : Type u_1\nG : Subgroup (Perm α)\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng : Perm α\nhg : g ∈ G\na : α\nleft✝ : g a ≠ a\nhgc : ∀ ⦃y : α⦄, g y ≠ y → g.SameCycle a y\nhs : ∀ (x : α), g • x ≠ x ↔ x ∈ ofFixingSubgroup (↥G) (↑g.support)ᶜ\nx : α\nhx : x ∈ ofFixingSubgroup (↥G) (↑g.support)ᶜ\ny : α\nhy... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.Jordan | {
"line": 395,
"column": 4
} | {
"line": 395,
"column": 49
} | [
{
"pp": "case inl.h\nα : Type u_1\nG : Subgroup (Perm α)\ninst✝¹ : DecidableEq α\ninst✝ : Finite α\nhG : IsPreprimitive (↥G) α\ng : Perm α\nh2g : g.IsSwap\nhg : g ∈ G\nthis : Fintype α\nhα3 : Nat.card α ≤ 2\n⊢ Fintype.card ↥G = Fintype.card (Perm α)",
"usedConstants": [
"Fintype.card_subtype_le",
... | apply le_antisymm (Fintype.card_subtype_le _) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.GroupTheory.GroupExtension.Defs | {
"line": 282,
"column": 4
} | {
"line": 282,
"column": 16
} | [
{
"pp": "N : Type u_1\nE : Type u_2\nG : Type u_3\ninst✝² : Group N\ninst✝¹ : Group E\ninst✝ : Group G\nS : GroupExtension N E G\n⊢ Function.Injective fun s ↦ (↑s.toMonoidHom).toFun",
"usedConstants": [
"GroupExtension.Splitting"
]
}
] | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 72
} | [
{
"pp": "case h\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh4 : 4 < Nat.card α\nG : Subgroup ↥(alternatingGroup α)\nhG' : IsPreprimitive (↥G) α\ns : Set α\nhG : stabilizer (↥(alternatingGroup α)) s ≤ G\ng : Perm α\nhg : g ∈ stabilizer (Perm α) s\nhg3 : g.IsThreeCycle\n⊢ ⟨g, ⋯⟩ ∈ ↑G ∧ (alternating... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.SpecificGroups.Alternating.MaximalSubgroups | {
"line": 188,
"column": 4
} | {
"line": 189,
"column": 28
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nh4 : 4 < Nat.card α\nG : Subgroup ↥(alternatingGroup α)\nhG' : IsPreprimitive (↥G) α\ns : Set α\nhG : stabilizer (↥(alternatingGroup α)) s ≤ G\ng : Perm α\nhg : g ∈ stabilizer (Perm α) s\nhg3 : g.IsThreeCycle\nφ : ↥G →* ↥(Subgroup.map (alternatin... | rwa [← isPreprimitive_congr (f := f) ((alternatingGroup α).subtype.subgroupMap_surjective G)
Function.bijective_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.GroupTheory.GroupExtension.Basic | {
"line": 64,
"column": 12
} | {
"line": 64,
"column": 44
} | [
{
"pp": "N : Type u_1\nG : Type u_2\ninst✝² : Group N\ninst✝¹ : Group G\nE : Type u_3\ninst✝ : Group E\nS : GroupExtension N E G\nσ σ' : S.Section\ng : G\nn : N\nhn : S.inl n = σ g * (σ' g)⁻¹\n⊢ σ g = S.inl n * σ' g",
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"MonoidHom.instFunLik... | by rw [hn, inv_mul_cancel_right] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.GroupExtension.Basic | {
"line": 128,
"column": 6
} | {
"line": 128,
"column": 44
} | [
{
"pp": "N : Type u_1\nG : Type u_2\ninst✝³ : Group N\ninst✝² : Group G\nE : Type u_3\ninst✝¹ : Group E\nS : GroupExtension N E G\nE' : Type u_4\ninst✝ : Group E'\nS' : GroupExtension N E' G\nf : E →* E'\ncomp_inl : f.comp S.inl = S'.inl\nrightHom_comp : S'.rightHom.comp f = S.rightHom\ne : E\n⊢ (S.rightHom (Fu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupExtension.Basic | {
"line": 128,
"column": 6
} | {
"line": 128,
"column": 74
} | [
{
"pp": "N : Type u_1\nG : Type u_2\ninst✝³ : Group N\ninst✝² : Group G\nE : Type u_3\ninst✝¹ : Group E\nS : GroupExtension N E G\nE' : Type u_4\ninst✝ : Group E'\nS' : GroupExtension N E' G\nf : E →* E'\ncomp_inl : f.comp S.inl = S'.inl\nrightHom_comp : S'.rightHom.comp f = S.rightHom\ne : E\n⊢ (S.rightHom (Fu... | simpa only [Function.surjInv_eq] using inv_mul_cancel (S.rightHom e) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.GroupTheory.GroupExtension.Basic | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 42
} | [
{
"pp": "case h\nN : Type u_1\nG : Type u_2\ninst✝³ : Group N\ninst✝² : Group G\nE : Type u_3\ninst✝¹ : Group E\nS : GroupExtension N E G\nE' : Type u_4\ninst✝ : Group E'\nS' : GroupExtension N E' G\nf : E →* E'\ncomp_inl : f.comp S.inl = S'.inl\nrightHom_comp : S'.rightHom.comp f = S.rightHom\ne' : E'\n⊢ (S.ri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupExtension.Basic | {
"line": 168,
"column": 4
} | {
"line": 170,
"column": 97
} | [
{
"pp": "N : Type u_1\nG : Type u_2\ninst✝² : Group N\ninst✝¹ : Group G\nE : Type u_3\ninst✝ : Group E\nS : GroupExtension N E G\ns : S.Splitting\n⊢ ⇑{\n toFun := fun x ↦\n match x with\n | ⟨n, g⟩ => S.inl n * s g,\n invFun := fun e ↦ ⟨Function.invFun (⇑S.inl) (e * (s (S.... | ext n
simp only [SemidirectProduct.toGroupExtension, Function.comp_apply, MulEquiv.coe_mk,
Equiv.coe_fn_mk, SemidirectProduct.left_inl, SemidirectProduct.right_inl, map_one, mul_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.GroupExtension.Basic | {
"line": 168,
"column": 4
} | {
"line": 170,
"column": 97
} | [
{
"pp": "N : Type u_1\nG : Type u_2\ninst✝² : Group N\ninst✝¹ : Group G\nE : Type u_3\ninst✝ : Group E\nS : GroupExtension N E G\ns : S.Splitting\n⊢ ⇑{\n toFun := fun x ↦\n match x with\n | ⟨n, g⟩ => S.inl n * s g,\n invFun := fun e ↦ ⟨Function.invFun (⇑S.inl) (e * (s (S.... | ext n
simp only [SemidirectProduct.toGroupExtension, Function.comp_apply, MulEquiv.coe_mk,
Equiv.coe_fn_mk, SemidirectProduct.left_inl, SemidirectProduct.right_inl, map_one, mul_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.IsPerfect | {
"line": 51,
"column": 6
} | {
"line": 51,
"column": 26
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ IsPerfect ↥H ↔ ⁅H, H⁆ = H",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Group.isPerfect_def",
"Bracket.bracket",
"Membership.mem",
"id",
"Subtype",
"Subgroup",
"commutator",
"Iff",
"prop... | Group.isPerfect_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | {
"line": 84,
"column": 39
} | {
"line": 84,
"column": 66
} | [
{
"pp": "α : Type u_2\ninst✝² : DecidableEq α\nG : Type u_3\ninst✝¹ : AddGroup G\ninst✝ : AddAction G α\nn : ℕ\nhn : 1 ≤ n\nhα : ↑n < ENat.card α\ng : G\nh : ¬AddAction.toPerm g = 1\n⊢ ∃ a, g +ᵥ a ≠ a",
"usedConstants": [
"AddMonoid.toAddSemigroup",
"Exists",
"id",
"Ne",
"HVAdd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | {
"line": 112,
"column": 38
} | {
"line": 112,
"column": 65
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\nα : Type u_2\ninst✝¹ : MulAction G α\nn : ℕ\ninst✝ : DecidableEq α\nhn : 1 ≤ n\nhα : ↑n < ENat.card α\ng : G\nh : ¬toPerm g = 1\n⊢ ∃ a, g • a ≠ a",
"usedConstants": [
"instHSMul",
"Exists",
"id",
"DivInvMonoid.toMonoid",
"Ne",
"Gro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.IndexNSmul | {
"line": 42,
"column": 6
} | {
"line": 43,
"column": 13
} | [
{
"pp": "M : Type u_1\ninst✝² : AddCommGroup M\ninst✝¹ : Free ℤ M\ninst✝ : Module.Finite ℤ M\nn : ℕ\n⊢ (nsmulAddMonoidHom n).range.index = (nsmulAddMonoidHom n).range.index",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.IndexNSmul | {
"line": 56,
"column": 2
} | {
"line": 57,
"column": 9
} | [
{
"pp": "M : Type u_1\ninst✝² : AddCommGroup M\nn : ℕ\nS : AddSubgroup M\ninst✝¹ : Free ℤ ↥(toIntSubmodule S)\ninst✝ : Module.Finite ℤ ↥(toIntSubmodule S)\n⊢ (map (nsmulAddMonoidHom n) S).relIndex S = n ^ finrank ℤ ↥S",
"usedConstants": [
"Eq.mpr",
"congrArg",
"AddSubgroup.index",
"A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.IndexNSmul | {
"line": 82,
"column": 47
} | {
"line": 82,
"column": 58
} | [
{
"pp": "M : Type u_1\ninst✝³ : AddCommGroup M\ninst✝² : Module.Finite ℤ M\ninst✝¹ : IsTorsionFree ℤ M\nA : AddSubgroup M\ninst✝ : A.FiniteIndex\nthis : finrank ℤ ↥(DistribSMul.toLinearMap ℤ M A.index).range = finrank ℤ M\nm : M\nhm : m ∈ toIntSubmodule.symm (DistribSMul.toLinearMap ℤ M A.index).range\n⊢ ∃ x, A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | {
"line": 311,
"column": 73
} | {
"line": 311,
"column": 84
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nh_three_le : 3 ≤ n\nhn : n < Nat.card α\nhα : Nat.card α ≠ 2 * n\nthis : IsPretransitive ↥(alternatingGroup α) ↑(powersetCard α n)\n⊢ ↑n < ENat.card α",
"usedConstants": [
"Eq.mpr",
"instCompleteLinearOrderENat",
"ins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.IsSubnormal | {
"line": 138,
"column": 21
} | {
"line": 138,
"column": 36
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH✝ H K : Subgroup G\nHK : H ≤ K\nhS : K.IsSubnormal\nhN : (H.subgroupOf K).Normal\nK' : Subgroup G\nHK' : K < K'\nhS' : K'.IsSubnormal\nhN' : (K.subgroupOf K').Normal\nhH : H ≠ K\n⊢ H < K ∧ K.IsSubnormal ∧ (H.subgroupOf K).Normal",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.IsSubnormal | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 29
} | [
{
"pp": "case step\nG : Type u_1\ninst✝ : Group G\nH✝ H K : Subgroup G\nHK : H ≤ K\nhS : K.IsSubnormal\nhN : (H.subgroupOf K).Normal\nih : K = ⊤ ∨ ∃ K_1, K < K_1 ∧ K_1.IsSubnormal ∧ (K.subgroupOf K_1).Normal\n⊢ H = ⊤ ∨ ∃ K, H < K ∧ K.IsSubnormal ∧ (H.subgroupOf K).Normal",
"usedConstants": [
"Eq.mpr",... | | step H K HK hS hN ih => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | {
"line": 317,
"column": 4
} | {
"line": 317,
"column": 68
} | [
{
"pp": "case h1\nα : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nn : ℕ\nh_three_le : 3 ≤ n\nhn : n < Nat.card α\nhα : Nat.card α ≠ 2 * n\nthis✝ : IsPretransitive ↥(alternatingGroup α) ↑(powersetCard α n)\nthis : Nontrivial ↑(powersetCard α n)\ns : ↑(powersetCard α n)\n⊢ (↑s)ᶜ.Nonempty",
"usedConst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.IsSubnormal | {
"line": 184,
"column": 6
} | {
"line": 185,
"column": 50
} | [
{
"pp": "case top\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ ∃ n f, Monotone f ∧ (∀ (i : ℕ), ((f i).subgroupOf (f (i + 1))).Normal) ∧ f 0 = ⊤ ∧ f n = ⊤",
"usedConstants": [
"Subgroup.subgroupOf",
"Subgroup.subgroupOf_self",
"congrArg",
"PartialOrder.toPreorder",
"Monoton... | use 0, fun _ ↦ ⊤, ?_, (by simp)
exact monotone_nat_of_le_succ fun _ ↦ le_top | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.IsSubnormal | {
"line": 184,
"column": 6
} | {
"line": 185,
"column": 50
} | [
{
"pp": "case top\nG : Type u_1\ninst✝ : Group G\nH : Subgroup G\n⊢ ∃ n f, Monotone f ∧ (∀ (i : ℕ), ((f i).subgroupOf (f (i + 1))).Normal) ∧ f 0 = ⊤ ∧ f n = ⊤",
"usedConstants": [
"Subgroup.subgroupOf",
"Subgroup.subgroupOf_self",
"congrArg",
"PartialOrder.toPreorder",
"Monoton... | use 0, fun _ ↦ ⊤, ?_, (by simp)
exact monotone_nat_of_le_succ fun _ ↦ le_top | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.IsSubnormal | {
"line": 281,
"column": 2
} | {
"line": 281,
"column": 13
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nH K : Subgroup G\nhH : H.IsSubnormal\nhK : K.IsSubnormal\n⊢ (H ⊓ K).IsSubnormal",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.NoncommCoprod | {
"line": 54,
"column": 24
} | {
"line": 54,
"column": 35
} | [
{
"pp": "M : Type u_1\nN : Type u_2\nP : Type u_3\ninst✝² : Mul M\ninst✝¹ : Mul N\ninst✝ : Semigroup P\nf : M →ₙ* P\ng : N →ₙ* P\ncomm : ∀ (m : M) (n : N), Commute (f m) (g n)\nmn mn' : M × N\n⊢ f (mn * mn').1 * g (mn * mn').2 = f mn.1 * g mn.2 * (f mn'.1 * g mn'.2)",
"usedConstants": [
"MulHom",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.NoncommCoprod | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 15
} | [
{
"pp": "case refine_1\nM : Type u_4\nN : Type u_5\nP : Type u_6\ninst✝² : Group M\ninst✝¹ : Group N\ninst✝ : Group P\nf : M →* P\ng : N →* P\ncomm : ∀ (m : M) (n : N), Commute (f m) (g n)\nh : ∀ (a : M) (b : N), f a * g b = 1 → a = 1 ∧ b = 1\nx : M\n⊢ f x = 1 → x = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.NoncommCoprod | {
"line": 135,
"column": 4
} | {
"line": 135,
"column": 15
} | [
{
"pp": "case refine_2\nM : Type u_4\nN : Type u_5\nP : Type u_6\ninst✝² : Group M\ninst✝¹ : Group N\ninst✝ : Group P\nf : M →* P\ng : N →* P\ncomm : ∀ (m : M) (n : N), Commute (f m) (g n)\nh : ∀ (a : M) (b : N), f a * g b = 1 → a = 1 ∧ b = 1\nx : N\n⊢ g x = 1 → x = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.PossibleTypes | {
"line": 70,
"column": 6
} | {
"line": 70,
"column": 44
} | [
{
"pp": "case h.right.right.hS.hf\nα : Type u_2\ninst✝ : Fintype α\nc : List ℕ\nhc : c.sum ≤ Fintype.card α\nklift : (n : ℕ) → n < Fintype.card α → Fin (Fintype.card α) := fun n hn ↦ ⟨n, hn⟩\nklift' : (l : List ℕ) → (∀ a ∈ l, a < Fintype.card α) → List (Fin (Fintype.card α)) := fun l hl ↦ pmap klift l hl\nhc'_l... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.HNNExtension | {
"line": 128,
"column": 21
} | {
"line": 128,
"column": 32
} | [
{
"pp": "G : Type u_1\ninst✝ : Group G\nA B : Subgroup G\nφ : ↥A ≃* ↥B\nmotive : HNNExtension G A B φ → Prop\nx : HNNExtension G A B φ\nof : ∀ (g : G), motive (HNNExtension.of g)\nt : motive HNNExtension.t\nmul : ∀ (x y : HNNExtension G A B φ), motive x → motive y → motive (x * y)\ninv : ∀ (x : HNNExtension G A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.PossibleTypes | {
"line": 114,
"column": 6
} | {
"line": 114,
"column": 17
} | [
{
"pp": "case h.h1\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nm : Multiset ℕ\nhc : m.sum ≤ Fintype.card α\nh2c : ∀ a ∈ m, 2 ≤ a\nhc' : m.toList.sum ≤ Fintype.card α\np : List (List α)\nhp_length : List.map List.length p = m.toList\nhp_nodup : ∀ s ∈ p, s.Nodup\nhp_disj : List.Pairwise List.Disjoin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.ClosureSwap | {
"line": 94,
"column": 33
} | {
"line": 94,
"column": 56
} | [
{
"pp": "case refine_4.inl\nα : Type u_2\ninst✝ : DecidableEq α\nS : Set (Equiv.Perm α)\nhS : ∀ f ∈ S, f.IsSwap\nx y : α\nhf : x ∈ orbit (↥(closure S)) y\nh : swap x y ∉ closure S\na : α\nha : a ∈ {x | swap x y ∈ closure S}\nw : α\nhzw : a ≠ w\nhσ : swap a w ∈ S\nhσa : swap a w • a ∉ {x | swap x y ∈ closure S}\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.ClosureSwap | {
"line": 94,
"column": 33
} | {
"line": 94,
"column": 56
} | [
{
"pp": "case refine_4.inr\nα : Type u_2\ninst✝ : DecidableEq α\nS : Set (Equiv.Perm α)\nhS : ∀ f ∈ S, f.IsSwap\nx y : α\nhf : x ∈ orbit (↥(closure S)) y\nh : swap x y ∉ closure S\na : α\nha : a ∈ {x | swap x y ∈ closure S}\nz : α\nhzw : z ≠ a\nhσ : swap z a ∈ S\nhσa : swap z a • a ∉ {x | swap x y ∈ closure S}\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.ClosureSwap | {
"line": 95,
"column": 38
} | {
"line": 95,
"column": 52
} | [
{
"pp": "case refine_1\nα : Type u_2\ninst✝ : DecidableEq α\nS : Set (Equiv.Perm α)\nhS : ∀ f ∈ S, f.IsSwap\nx✝ y✝ : α\nhf✝ : x✝ ∈ orbit (↥(closure S)) y✝\nh : swap x✝ y✝ ∉ closure S\nx y : α\nhf : swap x y ∈ S\n⊢ (swap x y)⁻¹ ∈ S",
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.instInv",
"DivIn... | rwa [swap_inv] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
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