module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 220,
"column": 4
} | {
"line": 220,
"column": 31
} | {
"line": 220,
"column": 32
} | [
{
"pp": "case mp\nι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : DecidableEq (ι → ℕ)\ns : Finset ι\nn : ℕ\nhn : n ≠ 0\nf : ι → ℕ\nhf : ∀ (i : ι), f i ≠ 0 → i ∈ s\n⊢ s.sum (n • f) = n * s.sum f ∧ (∀ (i : ι), (n • f) i ≠ 0 → i ∈ s) ∧ ∀ i ∈ s, n ∣ (n • f) i",
"ppTerm": "?mp",
"assigned": true,
"usedCons... | [
"case mp\nι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : DecidableEq (ι → ℕ)\ns : Finset ι\nn : ℕ\nhn : n ≠ 0\nf : ι → ℕ\nhf : ∀ (i : ι), f i ≠ 0 → i ∈ s\n⊢ ∀ (i : ι), ¬f i = 0 → i ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 411,
"column": 61
} | {
"line": 411,
"column": 81
} | {
"line": 411,
"column": 81
} | [
{
"pp": "n : ℕ\nc : Composition n\ni : Fin c.length\nj : Fin (c.blocksFun i)\n⊢ c.sizeUpTo ↑i + ↑j - c.sizeUpTo ↑i = ↑j",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Nat.instOrderedSub",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"C... | [] | add_tsub_cancel_left | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 13
} | {
"line": 239,
"column": 14
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm n : ℕ\nhn : n ≠ 0\n⊢ SMul.smul n (univ.piAntidiag m) = {f ∈ univ.piAntidiag (n * m) | ∀ (i : ι), n ∣ f i}",
"ppTerm": "?m.54",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm n : ℕ\nhn : n ≠ 0\n⊢ SMul.smul n (univ.piAntidiag m) = {f ∈ univ.piAntidiag (n * m) | ∀ (i : ι), n ∣ f i}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 245,
"column": 2
} | {
"line": 245,
"column": 13
} | {
"line": 245,
"column": 14
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm n : ℕ\nhn : n ≠ 0\n⊢ map { toFun := fun x ↦ n • x, inj' := ⋯ } (univ.piAntidiag m) = {f ∈ univ.piAntidiag (n * m) | ∀ (i : ι), n ∣ f i}",
"ppTerm": "?m.82",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals... | [
"ι : Type u_1\ninst✝¹ : DecidableEq ι\ninst✝ : Fintype ι\nm n : ℕ\nhn : n ≠ 0\n⊢ map { toFun := fun x ↦ n • x, inj' := ⋯ } (univ.piAntidiag m) = {f ∈ univ.piAntidiag (n * m) | ∀ (i : ι), n ∣ f i}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 434,
"column": 2
} | {
"line": 434,
"column": 19
} | {
"line": 436,
"column": 0
} | [
{
"pp": "case refl.refl\nn₁ : ℕ\nc₁ : Composition n₁\ni₁ i₂ : Fin c₁.length\nhi : ↑i₁ = ↑i₂\n⊢ i₁ = i₂",
"ppTerm": "?refl.refl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.ext_iff",
"Composition.length",
"congrArg",
"id",
"Fin.val",
"Nat",
"pr... | [] | rwa [Fin.ext_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 484,
"column": 2
} | {
"line": 484,
"column": 13
} | {
"line": 484,
"column": 14
} | [
{
"pp": "n : ℕ\ni : Fin (ones n).length\nh : 0 < (ones n).blocksFun i\n⊢ ↑(((ones n).embedding i) ⟨0, h⟩) = ↑⟨↑i, ⋯⟩",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDistribLatticeNat",
"Composition.length",
"congrArg",
"AddMonoid.toAddZeroClass"... | [
"n : ℕ\ni : Fin (ones n).length\nh : 0 < (ones n).blocksFun i\n⊢ ↑i ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Antidiag.Pi | {
"line": 261,
"column": 6
} | {
"line": 261,
"column": 97
} | {
"line": 261,
"column": 98
} | [
{
"pp": "case mpr.refine_2\nι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nf : ι → ℕ\nhf : ∀ (i : ι), ¬f i = 0 → i ∈ s\n⊢ (∑ a ∈ s, f a • {a}).card = s.sum f ∧ ∀ (x : ι), Multiset.count x (∑ a ∈ s, f a • {a}) = f x",
"ppTerm": "?mpr.refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [
"case mpr.refine_2\nι : Type u_1\ninst✝ : DecidableEq ι\ns : Finset ι\nf : ι → ℕ\nhf : ∀ (i : ι), ¬f i = 0 → i ∈ s\n⊢ ∀ x ∉ s, f x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 496,
"column": 4
} | {
"line": 496,
"column": 29
} | {
"line": 498,
"column": 0
} | [
{
"pp": "case mpr\nn : ℕ\nc : Composition n\nH : ∀ i ∈ c.blocks, i = 1\nA : c.blocks = replicate c.blocks.length 1\nthis : c.blocks.length = n\n⊢ c.blocks = (ones n).blocks",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"congrArg",
"Compo... | [] | rw [A, this, ones_blocks] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 560,
"column": 4
} | {
"line": 560,
"column": 31
} | {
"line": 560,
"column": 32
} | [
{
"pp": "case mpr\nn : ℕ\nh : 0 < n\nc : Composition n\nH : c.length = 1\nA : c.blocks.length = 1\nB : [c.blocks.get ⟨0, ⋯⟩].sum = n\n⊢ [c.blocks.get ⟨0, ⋯⟩] = (single n h).blocks",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"and_true",
"congrArg",
"List... | [
"case mpr\nn : ℕ\nh : 0 < n\nc : Composition n\nH : c.length = 1\nA : c.blocks.length = 1\nB : [c.blocks.get ⟨0, ⋯⟩].sum = n\n⊢ c.blocks[0] = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 579,
"column": 4
} | {
"line": 579,
"column": 15
} | {
"line": 579,
"column": 16
} | [
{
"pp": "case mpr\nn : ℕ\nhn : 0 < n\nc : Composition n\ni : Fin c.length\nhi : n ≤ c.blocksFun i\nthis : ∀ (j : Fin c.length), j = i\n⊢ c.length = 1",
"ppTerm": "?mpr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mpr\nn : ℕ\nhn : 0 < n\nc : Composition n\ni : Fin c.length\nhi : n ≤ c.blocksFun i\nthis : ∀ (j : Fin c.length), j = i\n⊢ c.length = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Inv | {
"line": 135,
"column": 30
} | {
"line": 135,
"column": 59
} | {
"line": 135,
"column": 60
} | [
{
"pp": "α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : Fintype α✝\np✝ : α✝ → Prop\ninst✝² : DecidablePred p✝\nα : Type u_4\np : α → Prop\ninst✝¹ : Fintype { a // p a }\ninst✝ : DecidableEq α\nx y : { a // p a }\nhy : (fun a ↦ ↑a = ↑x) y\n⊢ y = x",
"ppTerm": "?m.24",
"assigned": true,
"usedCons... | [
"α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : Fintype α✝\np✝ : α✝ → Prop\ninst✝² : DecidablePred p✝\nα : Type u_4\np : α → Prop\ninst✝¹ : Fintype { a // p a }\ninst✝ : DecidableEq α\nx y : { a // p a }\nhy : (fun a ↦ ↑a = ↑x) y\n⊢ ↑y = ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 786,
"column": 28
} | {
"line": 786,
"column": 48
} | {
"line": 786,
"column": 48
} | [
{
"pp": "case cons\nα : Type u_1\nn : ℕ\nns : List ℕ\nIH : ∀ {l : List α}, ns.sum = l.length → (l.splitWrtCompositionAux ns).flatten = l\nl : List α\nh : n + ns.sum = l.length\n⊢ ns.sum = n + ns.sum - n",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroC... | [
"case cons\nα : Type u_1\nn : ℕ\nns : List ℕ\nIH : ∀ {l : List α}, ns.sum = l.length → (l.splitWrtCompositionAux ns).flatten = l\nl : List α\nh : n + ns.sum = l.length\n⊢ ns.sum = ns.sum"
] | add_tsub_cancel_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.Support | {
"line": 386,
"column": 9
} | {
"line": 386,
"column": 19
} | {
"line": 386,
"column": 20
} | [
{
"pp": "case succ.a\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : ∀ x ∈ f.support ∩ g.support, f x = g x\nk : ℕ\nhk : ∀ x ∈ f.support ∩ g.support, (f ^ k) x = (g ^ k) x\nx : α\nhx : x ∈ f.support ∩ g.support\n⊢ g x ∈ f.support ∩ g.support",
"ppTerm": "?succ.a",
"assigned":... | [
"case succ.a\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : ∀ x ∈ f.support ∩ g.support, f x = g x\nk : ℕ\nhk : ∀ x ∈ f.support ∩ g.support, (f ^ k) x = (g ^ k) x\nx : α\nhx : x ∈ f.support ∩ g.support\n⊢ g x ∈ f.support ∧ g x ∈ g.support"
] | mem_inter, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 944,
"column": 2
} | {
"line": 944,
"column": 82
} | {
"line": 945,
"column": 2
} | [
{
"pp": "n : ℕ\nc : CompositionAsSet n\n⊢ c.blocks.sum = n",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"instReflLe",
"congrArg",
"List.length_ofFn",
"Std.le_refl._simp_1",
"List.take_of_length_le",
"LE.le",
"instLENat",
"List",
"Comp... | [
"n : ℕ\nc : CompositionAsSet n\nthis : take c.length c.blocks = c.blocks\n⊢ c.blocks.sum = n"
] | have : c.blocks.take c.length = c.blocks := take_of_length_le (by simp [blocks]) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Combinatorics.Enumerative.Composition | {
"line": 986,
"column": 4
} | {
"line": 987,
"column": 45
} | {
"line": 987,
"column": 46
} | [
{
"pp": "n : ℕ\nc : Composition n\nd : CompositionAsSet n := c.toCompositionAsSet\nlength_eq : d.blocks.length = c.blocks.length\ni : ℕ\nhi : i ≤ d.blocks.length\n⊢ i < d.boundaries.card",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"CompositionAsSet.card_boundaries_eq_succ_length"... | [
"n : ℕ\nc : Composition n\nd : CompositionAsSet n := c.toCompositionAsSet\nlength_eq : d.blocks.length = c.blocks.length\ni : ℕ\nhi : i ≤ d.blocks.length\n⊢ i < d.length + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 75,
"column": 69
} | {
"line": 75,
"column": 84
} | {
"line": 75,
"column": 85
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nb : α\nl' : List α\nx : α\nhx : (zipWith swap (a :: l) (b :: l')).prod x ≠ x\nh : (zipWith swap l l').prod x = x\n⊢ (swap a b) x ≠ x",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Equiv.sw... | [
"α : Type u_1\ninst✝ : DecidableEq α\na : α\nl : List α\nb : α\nl' : List α\nx : α\nhx : (zipWith swap (a :: l) (b :: l')).prod x ≠ x\nh : (zipWith swap l l').prod x = x\n⊢ ¬(swap a b) x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 13
} | {
"line": 82,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nx✝ : α\nh : x✝ ∈ {x | (zipWith swap l l').prod x ≠ x}\n⊢ x✝ ∈ ↑(l.toFinset ⊔ l'.toFinset)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Finset.instUnion",
"congrArg... | [
"α : Type u_1\ninst✝ : DecidableEq α\nl l' : List α\nx✝ : α\nh : x✝ ∈ {x | (zipWith swap l l').prod x ≠ x}\n⊢ x✝ ∈ l ∨ x✝ ∈ l'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 87,
"column": 62
} | {
"line": 87,
"column": 73
} | {
"line": 87,
"column": 74
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nl l' : List α\nx : α\nhx : x ∈ (zipWith swap l l').prod.support\n⊢ x ∈ {x | (zipWith swap l l').prod x ≠ x}",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"List.zipWith",
"Equiv.instEquivLike",
"Equiv.Perm... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nl l' : List α\nx : α\nhx : x ∈ (zipWith swap l l').prod.support\n⊢ ¬(zipWith swap l l').prod x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 13
} | {
"line": 88,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nl l' : List α\nx : α\nhx : x ∈ (zipWith swap l l').prod.support\nhx' : x ∈ {x | (zipWith swap l l').prod x ≠ x}\n⊢ x ∈ l.toFinset ⊔ l'.toFinset",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.t... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nl l' : List α\nx : α\nhx : x ∈ (zipWith swap l l').prod.support\nhx' : x ∈ {x | (zipWith swap l l').prod x ≠ x}\n⊢ x ∈ l ∨ x ∈ l'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 96,
"column": 48
} | {
"line": 96,
"column": 59
} | {
"line": 96,
"column": 60
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nl : List α\ninst✝ : Fintype α\nx : α\nhx : x ∈ l.formPerm.support\n⊢ x ∈ {x | l.formPerm x ≠ x}",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"setOf",
"Membership.mem",
"id",
"Ne",
"... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\nl : List α\ninst✝ : Fintype α\nx : α\nhx : x ∈ l.formPerm.support\n⊢ ¬l.formPerm x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 13
} | {
"line": 97,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nl : List α\ninst✝ : Fintype α\nx : α\nhx : x ∈ l.formPerm.support\nhx' : x ∈ {x | l.formPerm x ≠ x}\n⊢ x ∈ l.toFinset",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset",
"Membership.mem",
"id",
"Li... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\nl : List α\ninst✝ : Fintype α\nx : α\nhx : x ∈ l.formPerm.support\nhx' : x ∈ {x | l.formPerm x ≠ x}\n⊢ x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Support | {
"line": 515,
"column": 6
} | {
"line": 515,
"column": 17
} | {
"line": 515,
"column": 18
} | [
{
"pp": "case cons.inr\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf hd : Perm α\ntl : List (Perm α)\nIH : f ∈ tl → List.Pairwise Disjoint tl → ∀ x ∈ f.support, f x = tl.prod x\nhl : (∀ a' ∈ tl, hd.Disjoint a') ∧ List.Pairwise Disjoint tl\nx : α\nhx : x ∈ f.support\nh : f ∈ tl\n⊢ f x ∈ f.support",... | [
"case cons.inr\nα : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf hd : Perm α\ntl : List (Perm α)\nIH : f ∈ tl → List.Pairwise Disjoint tl → ∀ x ∈ f.support, f x = tl.prod x\nhl : (∀ a' ∈ tl, hd.Disjoint a') ∧ List.Pairwise Disjoint tl\nx : α\nhx : x ∈ f.support\nh : f ∈ tl\n⊢ ¬f x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 50
} | {
"line": 102,
"column": 51
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh : l.formPerm x ≠ x\n⊢ x ∈ l",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nh : l.formPerm x ≠ x\n⊢ x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 111,
"column": 11
} | {
"line": 111,
"column": 22
} | {
"line": 111,
"column": 23
} | [
{
"pp": "case cons.nil\nα : Type u_1\ninst✝ : DecidableEq α\nx y : α\nh : x ∈ [y]\n⊢ [y].formPerm x ∈ [y]",
"ppTerm": "?cons.nil",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Equiv.instEquivLike",
"congrArg",
"Membership.mem",
"id",
"List.not_me... | [
"case cons.nil\nα : Type u_1\ninst✝ : DecidableEq α\nx y : α\nh : x ∈ [y]\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Support | {
"line": 593,
"column": 66
} | {
"line": 593,
"column": 73
} | {
"line": 593,
"column": 74
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\nh : #f.support = 2\nx y : α\nhmem : ¬x = y\nhins : {x, y} = f.support\nht : #{y} = 1\na b : α\n⊢ b ∈ f.support ↔ ?m.105 b",
"ppTerm": "?m.116",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.support... | [
"α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf : Perm α\nh : #f.support = 2\nx y : α\nhmem : ¬x = y\nhins : {x, y} = f.support\nht : #{y} = 1\na b : α\n⊢ b ∈ {x, y} ↔ ?m.105 b"
] | ← hins, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.GroupTheory.Perm.Finite | {
"line": 62,
"column": 2
} | {
"line": 62,
"column": 13
} | {
"line": 62,
"column": 14
} | [
{
"pp": "α : Type u\ns : Finset α\nf : Perm α\nh : ∀ x ∈ s, f x ∈ s\nh0 : ∀ y ∈ s, ∃ x, ∃ (hx : x ∈ s), y = (fun i x ↦ f i) x hx\ny2 : α\nhy2 : y2 ∈ s\nhy : (fun i x ↦ f i) y2 hy2 ∈ s\n⊢ (Equiv.symm f) ((fun i x ↦ f i) y2 hy2) ∈ s",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"α : Type u\ns : Finset α\nf : Perm α\nh : ∀ x ∈ s, f x ∈ s\nh0 : ∀ y ∈ s, ∃ x, ∃ (hx : x ∈ s), y = (fun i x ↦ f i) x hx\ny2 : α\nhy2 : y2 ∈ s\nhy : (fun i x ↦ f i) y2 hy2 ∈ s\n⊢ y2 ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Finite | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 13
} | {
"line": 89,
"column": 14
} | [
{
"pp": "α : Type u\nf : Perm α\np : α → Prop\ninst✝ : Finite { x // p x }\nh : ∀ (x : α), p x → p (f x)\nx : α\nhx : p x\nthis : Finite ↑{x | p x}\n⊢ p ((Equiv.symm f) x)",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nf : Perm α\np : α → Prop\ninst✝ : Finite { x // p x }\nh : ∀ (x : α), p x → p (f x)\nx : α\nhx : p x\nthis : Finite ↑{x | p x}\n⊢ p ((Equiv.symm f) x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 166,
"column": 12
} | {
"line": 166,
"column": 23
} | {
"line": 166,
"column": 24
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝ : DecidableEq α\nxs : List α\nh : xs.Nodup\nhn : 0 + 1 < xs.length\n⊢ xs.formPerm xs[0] = xs[0 + 1]",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"List.formPerm_apply_lt_getElem._proof_2",
"Eq.mpr",
"Equiv.instEquivLike",
"c... | [
"case zero\nα : Type u_1\ninst✝ : DecidableEq α\nxs : List α\nh : xs.Nodup\nhn : 0 + 1 < xs.length\n⊢ xs.formPerm xs[0] = xs[1]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 172,
"column": 8
} | {
"line": 172,
"column": 42
} | {
"line": 172,
"column": 43
} | [
{
"pp": "case succ.cons.cons\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℕ\nIH : ∀ (xs : List α), xs.Nodup → ∀ (hn : n + 1 < xs.length), xs.formPerm xs[n] = xs[n + 1]\nx y : α\nl : List α\nh : (x :: y :: l).Nodup\nhn : n + 1 + 1 < (x :: y :: l).length\n⊢ n + 1 < (y :: l).length",
"ppTerm": "?succ.cons.cons✝",... | [
"case succ.cons.cons\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℕ\nIH : ∀ (xs : List α), xs.Nodup → ∀ (hn : n + 1 < xs.length), xs.formPerm xs[n] = xs[n + 1]\nx y : α\nl : List α\nh : (x :: y :: l).Nodup\nhn : n + 1 + 1 < (x :: y :: l).length\n⊢ n < l.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 172,
"column": 8
} | {
"line": 172,
"column": 45
} | {
"line": 173,
"column": 6
} | [
{
"pp": "case succ.cons.cons\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℕ\nIH : ∀ (xs : List α), xs.Nodup → ∀ (hn : n + 1 < xs.length), xs.formPerm xs[n] = xs[n + 1]\nx y : α\nl : List α\nh : (x :: y :: l).Nodup\nhn : n + 1 + 1 < (x :: y :: l).length\n⊢ n + 1 < (y :: l).length",
"ppTerm": "?succ.cons.cons✝",... | [] | simpa [Nat.succ_lt_succ_iff] using hn | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.GroupTheory.Perm.List | {
"line": 172,
"column": 8
} | {
"line": 172,
"column": 45
} | {
"line": 173,
"column": 6
} | [
{
"pp": "case succ.cons.cons\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℕ\nIH : ∀ (xs : List α), xs.Nodup → ∀ (hn : n + 1 < xs.length), xs.formPerm xs[n] = xs[n + 1]\nx y : α\nl : List α\nh : (x :: y :: l).Nodup\nhn : n + 1 + 1 < (x :: y :: l).length\n⊢ n + 1 < (y :: l).length",
"ppTerm": "?succ.cons.cons✝",... | [] | simpa [Nat.succ_lt_succ_iff] using hn | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.List | {
"line": 172,
"column": 8
} | {
"line": 172,
"column": 45
} | {
"line": 173,
"column": 6
} | [
{
"pp": "case succ.cons.cons\nα : Type u_1\ninst✝ : DecidableEq α\nn : ℕ\nIH : ∀ (xs : List α), xs.Nodup → ∀ (hn : n + 1 < xs.length), xs.formPerm xs[n] = xs[n + 1]\nx y : α\nl : List α\nh : (x :: y :: l).Nodup\nhn : n + 1 + 1 < (x :: y :: l).length\n⊢ n + 1 < (y :: l).length",
"ppTerm": "?succ.cons.cons✝",... | [] | simpa [Nat.succ_lt_succ_iff] using hn | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Support | {
"line": 610,
"column": 4
} | {
"line": 610,
"column": 15
} | {
"line": 610,
"column": 16
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : f.Disjoint g\n⊢ _root_.Disjoint f.support g.support",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf g : Perm α\nh : f.Disjoint g\n⊢ _root_.Disjoint f.support g.support"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Perm | {
"line": 72,
"column": 23
} | {
"line": 72,
"column": 48
} | {
"line": 72,
"column": 49
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nf : Equiv.Perm α\nh : f ∈ permsOfList []\nheq_iff_eq : α\n⊢ f = 1",
"ppTerm": "?m.169",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\nf : Equiv.Perm α\nh : f ∈ permsOfList []\nheq_iff_eq : α\n⊢ f = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 187,
"column": 6
} | {
"line": 187,
"column": 17
} | {
"line": 187,
"column": 18
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ni : ℕ\nx : α\nxs : List α\nw : (x :: xs).Nodup\nh : i < (x :: xs).length\n⊢ i < xs.length.succ",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"id",
"Nat",
"LT.lt",
"instLTNat",
"Nat.succ",
"List.length"
... | [
"α : Type u_1\ninst✝ : DecidableEq α\ni : ℕ\nx : α\nxs : List α\nw : (x :: xs).Nodup\nh : i < (x :: xs).length\n⊢ i < xs.length + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 218,
"column": 37
} | {
"line": 218,
"column": 48
} | {
"line": 218,
"column": 49
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\n⊢ (l.rotate 1).Nodup",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"instOfNatNat",
"List.Nodup",
"Nat",
"OfNat.ofNat",
"Eq",
"List.nodup_rotate._simp_1",... | [
"α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\n⊢ l.Nodup"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 15
} | {
"line": 225,
"column": 16
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\nh' : (l.rotate 1).Nodup\nx : α\nhx : x ∉ l.rotate 1\n⊢ x ∉ l",
"ppTerm": "?neg✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case neg\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nh : l.Nodup\nh' : (l.rotate 1).Nodup\nx : α\nhx : x ∉ l.rotate 1\n⊢ x ∉ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 246,
"column": 4
} | {
"line": 246,
"column": 27
} | {
"line": 246,
"column": 28
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nx y : α\nl : List α\na b : α\n⊢ (x :: y :: l ++ [a, b]).formPerm = (x :: y :: l ++ [a]).formPerm * swap a b",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"HMul.hMul",
"congrArg",
"Can... | [
"α : Type u_1\ninst✝ : DecidableEq α\nx y : α\nl : List α\na b : α\n⊢ (y :: (l ++ [a, b])).formPerm = (y :: (l ++ [a])).formPerm * swap a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 251,
"column": 15
} | {
"line": 252,
"column": 69
} | {
"line": 254,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\na b : α\nl : List α\n⊢ (a :: b :: l).reverse.formPerm = (a :: b :: l).formPerm⁻¹",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"DivInvMonoid.toInv",
"HMul.hMul",
"Equiv.Perm.instInv",
"List.append_assoc",
"Monoid... | [] | by
simp [formPerm_append_pair, swap_comm, ← formPerm_reverse (b::l)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Perm.List | {
"line": 280,
"column": 4
} | {
"line": 280,
"column": 15
} | {
"line": 280,
"column": 16
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nx y x' y' : α\nl l' : List α\nhd : (x :: y :: l).Nodup\nhd' : (x' :: y' :: l').Nodup\nh : ∀ (x_1 : α), (x :: y :: l).formPerm x_1 = (x' :: y' :: l').formPerm x_1\nthis : x' ∈ {z | (x :: y :: l).formPerm z ≠ z}\n⊢ x' ∈ x :: y :: l",
"ppTerm": "?m.59",
"assign... | [
"α : Type u_1\ninst✝ : DecidableEq α\nx y x' y' : α\nl l' : List α\nhd : (x :: y :: l).Nodup\nhd' : (x' :: y' :: l').Nodup\nh : ∀ (x_1 : α), (x :: y :: l).formPerm x_1 = (x' :: y' :: l').formPerm x_1\nthis : x' ∈ {z | (x :: y :: l).formPerm z ≠ z}\n⊢ x' = x ∨ x' = y ∨ x' ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Perm | {
"line": 115,
"column": 72
} | {
"line": 115,
"column": 83
} | {
"line": 115,
"column": 84
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl' : l.Nodup\nhln' : (permsOfList l).Nodup\nf : Equiv.Perm α\nhf₁ : f ∈ permsOfList l\nx : α\nhx : x ∈ l\ng : Equiv.Perm α\nhl : ((Equiv.symm g) x :: l).Nodup\nhmeml : ∀ {f : Equiv.Perm α}, f ∈ permsOfList l → f ((Equiv.symm g) x) = (Equiv.symm g) x\nhf... | [
"α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl' : l.Nodup\nhln' : (permsOfList l).Nodup\nf : Equiv.Perm α\nhf₁ : f ∈ permsOfList l\nx : α\nhx : x ∈ l\ng : Equiv.Perm α\nhl : ((Equiv.symm g) x :: l).Nodup\nhmeml : ∀ {f : Equiv.Perm α}, f ∈ permsOfList l → f ((Equiv.symm g) x) = (Equiv.symm g) x\nhf₂ : f ∈ flat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 297,
"column": 6
} | {
"line": 297,
"column": 17
} | {
"line": 297,
"column": 18
} | [
{
"pp": "case h.h.zero.e_i\nα : Type u_1\ninst✝ : DecidableEq α\nx y x' y' : α\nl l' : List α\nhd : (x :: y :: l).Nodup\nhd' : (x' :: y' :: l').Nodup\nh : ∀ (x_1 : α), (x :: y :: l).formPerm x_1 = (x' :: y' :: l').formPerm x_1\nhx : x' ∈ x :: y :: l\nn : ℕ\nhn : n < (x :: y :: l).length\nhx' : (x :: y :: l).get... | [
"case h.h.zero.e_i\nα : Type u_1\ninst✝ : DecidableEq α\nx y x' y' : α\nl l' : List α\nhd : (x :: y :: l).Nodup\nhd' : (x' :: y' :: l').Nodup\nh : ∀ (x_1 : α), (x :: y :: l).formPerm x_1 = (x' :: y' :: l').formPerm x_1\nhx : x' ∈ x :: y :: l\nn : ℕ\nhn : n < (x :: y :: l).length\nhx' : (x :: y :: l).get ⟨n, hn⟩ = x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 315,
"column": 6
} | {
"line": 315,
"column": 81
} | {
"line": 316,
"column": 8
} | [
{
"pp": "case succ.inr\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nk : ℕ\nhk✝ : k < l.length\nhx : l[k] ∈ l\nn✝ : ℕ\nhk : k < n✝ + 1\nhn : l.length = n✝ + 1\nhk' : k < n✝\n⊢ (k + 1) % (n✝ + 1) = k ↔ n✝ + 1 ≤ 1",
"ppTerm": "?succ.inr",
"assigned": true,
"usedConstants": [
"E... | [
"case succ.inr\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nk : ℕ\nhk✝ : k < l.length\nhx : l[k] ∈ l\nn✝ : ℕ\nhk : k < n✝ + 1\nhn : l.length = n✝ + 1\nhk' : k < n✝\n⊢ ¬n✝ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Sign | {
"line": 194,
"column": 2
} | {
"line": 194,
"column": 16
} | {
"line": 194,
"column": 17
} | [
{
"pp": "n : ℕ\nf : Perm (Fin n)\na₁ a₂ : Fin n\nha : ⟨a₁, a₂⟩.snd < ⟨a₁, a₂⟩.fst\nb₁ b₂ : Fin n\nhb : ⟨b₁, b₂⟩.snd < ⟨b₁, b₂⟩.fst\nh : (if f a₂ < f a₁ then ⟨f a₁, f a₂⟩ else ⟨f a₂, f a₁⟩) = if f b₂ < f b₁ then ⟨f b₁, f b₂⟩ else ⟨f b₂, f b₁⟩\nthis : ¬b₁ < b₂\n⊢ ⟨a₁, a₂⟩ = ⟨b₁, b₂⟩",
"ppTerm": "?m.81",
"... | [
"case pos\nn : ℕ\nf : Perm (Fin n)\na₁ a₂ : Fin n\nha : ⟨a₁, a₂⟩.snd < ⟨a₁, a₂⟩.fst\nb₁ b₂ : Fin n\nhb : ⟨b₁, b₂⟩.snd < ⟨b₁, b₂⟩.fst\nthis : ¬b₁ < b₂\nh✝¹ : f a₂ < f a₁\nh✝ : f b₂ < f b₁\nh : ⟨f a₁, f a₂⟩ = ⟨f b₁, f b₂⟩\n⊢ ⟨a₁, a₂⟩ = ⟨b₁, b₂⟩",
"case neg\nn : ℕ\nf : Perm (Fin n)\na₁ a₂ : Fin n\nha : ⟨a₁, a₂⟩.snd ... | split_ifs at h | Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1 | Mathlib.Tactic.splitIfs |
Mathlib.GroupTheory.Perm.List | {
"line": 357,
"column": 4
} | {
"line": 357,
"column": 19
} | {
"line": 357,
"column": 20
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nhx : x ∈ l\nn : ℤ\nh : (l.formPerm ^ n) x = x\n⊢ (l.formPerm ^ n) x ∈ l",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"congrArg",
"DivInvMonoid.toZPow",
... | [
"case pos\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nhx : x ∈ l\nn : ℤ\nh : (l.formPerm ^ n) x = x\n⊢ x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 361,
"column": 4
} | {
"line": 361,
"column": 15
} | {
"line": 361,
"column": 16
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nhx : x ∈ l\nn : ℤ\nh✝ : ¬(l.formPerm ^ n) x = x\nh : (l.formPerm ^ n) x ∈ {x | l.formPerm x ≠ x}\n⊢ (l.formPerm ^ n) x ∈ l",
"ppTerm": "?neg✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"case neg\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nx : α\nhx : x ∈ l\nn : ℤ\nh✝ : ¬(l.formPerm ^ n) x = x\nh : (l.formPerm ^ n) x ∈ {x | l.formPerm x ≠ x}\n⊢ (l.formPerm ^ n) x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 372,
"column": 6
} | {
"line": 372,
"column": 17
} | {
"line": 372,
"column": 18
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nx : α\nhx : x ∉ l\nH : x ∈ {x | l.formPerm x ≠ x}\n⊢ x ∈ l",
"ppTerm": "?m.87",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nx : α\nhx : x ∉ l\nH : x ∈ {x | l.formPerm x ≠ x}\n⊢ x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.List | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 15
} | {
"line": 373,
"column": 16
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nx : α\nhx : x ∉ l\nthis : x ∉ {x | (l.formPerm ^ l.length) x ≠ x}\n⊢ (l.formPerm ^ l.length) x = 1 x",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
... | [
"case neg\nα : Type u_1\ninst✝ : DecidableEq α\nl : List α\nhl : l.Nodup\nx : α\nhx : x ∉ l\nthis : x ∉ {x | (l.formPerm ^ l.length) x ≠ x}\n⊢ (l.formPerm ^ l.length) x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 13
} | {
"line": 262,
"column": 14
} | [
{
"pp": "α : Type u_2\nf g : Perm α\nx : α\nhx : f x ≠ x\nh : ∀ ⦃y : α⦄, f y ≠ y → f.SameCycle x y\ny : α\nhy : (g * f * g⁻¹) y ≠ y\n⊢ (g * f * g⁻¹).SameCycle (g x) y",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"HMul.hMul",
"Equi... | [
"α : Type u_2\nf g : Perm α\nx : α\nhx : f x ≠ x\nh : ∀ ⦃y : α⦄, f y ≠ y → f.SameCycle x y\ny : α\nhy : (g * f * g⁻¹) y ≠ y\n⊢ f.SameCycle x ((Equiv.symm g) y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 380,
"column": 6
} | {
"line": 381,
"column": 13
} | {
"line": 381,
"column": 14
} | [
{
"pp": "α : Type u_4\ninst✝ : DecidableEq α\nn : ℕ\nhn : ∀ {b x : α} {f : Perm α}, (swap x (f x) * f) b ≠ b → (f ^ n) (f x) = b → ∃ i, ((swap x (f x) * f) ^ i) (f x) = b\nb x : α\nf : Perm α\nhb : (swap x (f x) * f) b ≠ b\nh : (f ^ (n + 1)) (f x) = b\nhfbx : f x ≠ b\nthis : f b ≠ b ∧ b ≠ x\n⊢ (swap x (f x) * f... | [
"α : Type u_4\ninst✝ : DecidableEq α\nn : ℕ\nhn : ∀ {b x : α} {f : Perm α}, (swap x (f x) * f) b ≠ b → (f ^ n) (f x) = b → ∃ i, ((swap x (f x) * f) ^ i) (f x) = b\nb x : α\nf : Perm α\nhb : (swap x (f x) * f) b ≠ b\nh : (f ^ (n + 1)) (f x) = b\nhfbx : f x ≠ b\nthis : f b ≠ b ∧ b ≠ x\n⊢ ¬f b = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 382,
"column": 50
} | {
"line": 382,
"column": 73
} | {
"line": 382,
"column": 74
} | [
{
"pp": "α : Type u_4\ninst✝ : DecidableEq α\nn : ℕ\nhn : ∀ {b x : α} {f : Perm α}, (swap x (f x) * f) b ≠ b → (f ^ n) (f x) = b → ∃ i, ((swap x (f x) * f) ^ i) (f x) = b\nb x : α\nf : Perm α\nhb : (swap x (f x) * f) b ≠ b\nh : (f ^ (n + 1)) (f x) = b\nhfbx : f x ≠ b\nthis : f b ≠ b ∧ b ≠ x\nhb' : (swap x (f x)... | [
"α : Type u_4\ninst✝ : DecidableEq α\nn : ℕ\nhn : ∀ {b x : α} {f : Perm α}, (swap x (f x) * f) b ≠ b → (f ^ n) (f x) = b → ∃ i, ((swap x (f x) * f) ^ i) (f x) = b\nb x : α\nf : Perm α\nhb : (swap x (f x) * f) b ≠ b\nh : (f ^ (n + 1)) (f x) = b\nhfbx : f x ≠ b\nthis : f b ≠ b ∧ b ≠ x\nhb' : (swap x (f x) * f) ((Equi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Iterate | {
"line": 34,
"column": 65
} | {
"line": 34,
"column": 76
} | {
"line": 34,
"column": 77
} | [
{
"pp": "α : Type u_1\nf : α → α\na : α\nn i : ℕ\nh : i + 1 < n + 1\n⊢ i < n",
"ppTerm": "?m.94",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nf : α → α\na : α\nn i : ℕ\nh : i + 1 < n + 1\n⊢ i < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.GCD.BigOperators | {
"line": 32,
"column": 42
} | {
"line": 32,
"column": 53
} | {
"line": 32,
"column": 54
} | [
{
"pp": "case h\nk : ℕ\na✝ : List ℕ\n⊢ (Multiset.prod ⟦a✝⟧).Coprime k ↔ ∀ n ∈ ⟦a✝⟧, n.Coprime k",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.Coprime",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Multiset.prod",
"Multiset.mem... | [
"case h\nk : ℕ\na✝ : List ℕ\n⊢ a✝.prod.Coprime k ↔ ∀ n ∈ a✝, n.Coprime k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.GCD.BigOperators | {
"line": 36,
"column": 42
} | {
"line": 36,
"column": 53
} | {
"line": 36,
"column": 54
} | [
{
"pp": "case h\nk : ℕ\na✝ : List ℕ\n⊢ k.Coprime (Multiset.prod ⟦a✝⟧) ↔ ∀ n ∈ ⟦a✝⟧, k.Coprime n",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.Coprime",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Multiset.prod",
"Multiset.mem... | [
"case h\nk : ℕ\na✝ : List ℕ\n⊢ k.Coprime a✝.prod ↔ ∀ n ∈ a✝, k.Coprime n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.GCD.BigOperators | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 13
} | {
"line": 40,
"column": 14
} | [
{
"pp": "ι : Type u_1\nt : Finset ι\ns : ι → ℕ\nx : ℕ\n⊢ (∏ i ∈ t, s i).Coprime x ↔ ∀ i ∈ t, (s i).Coprime x",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nt : Finset ι\ns : ι → ℕ\nx : ℕ\n⊢ (∏ i ∈ t, s i).Coprime x ↔ ∀ i ∈ t, (s i).Coprime x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.GCD.BigOperators | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 13
} | {
"line": 44,
"column": 14
} | [
{
"pp": "ι : Type u_1\nx : ℕ\nt : Finset ι\ns : ι → ℕ\n⊢ x.Coprime (∏ i ∈ t, s i) ↔ ∀ i ∈ t, x.Coprime (s i)",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nx : ℕ\nt : Finset ι\ns : ι → ℕ\n⊢ x.Coprime (∏ i ∈ t, s i) ↔ ∀ i ∈ t, x.Coprime (s i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 496,
"column": 2
} | {
"line": 496,
"column": 22
} | {
"line": 496,
"column": 23
} | [
{
"pp": "α : Type u_2\nf g : Perm α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : f.IsCycle\nhg : g.IsCycle\nh : f.support ⊆ g.support\nh' : ∀ x ∈ f.support, f x = g x\nthis : f.support = g.support\n⊢ ∀ x ∈ g.support, f x = g x",
"ppTerm": "?m.167",
"assigned": true,
"usedConstants": [
"Eq.... | [
"α : Type u_2\nf g : Perm α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : f.IsCycle\nhg : g.IsCycle\nh : f.support ⊆ g.support\nh' : ∀ x ∈ f.support, f x = g x\nthis : f.support = g.support\n⊢ ∀ (x : α), ¬f x = x → f x = g x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 528,
"column": 6
} | {
"line": 528,
"column": 17
} | {
"line": 528,
"column": 18
} | [
{
"pp": "case neg\nα : Type u_2\nf : Perm α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : f.IsCycle\nn : ℕ\nz : α\nhz : ¬f z = z\nk : ℕ\nhx : (f ^ k) z ∈ f.support\nH : (f ^ k) z ∉ (f ^ n).support\n⊢ (f ^ n) ((f ^ k) z) = (f ^ k) (1 z)",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [
"case neg\nα : Type u_2\nf : Perm α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhf : f.IsCycle\nn : ℕ\nz : α\nhz : ¬f z = z\nk : ℕ\nhx : (f ^ k) z ∈ f.support\nH : (f ^ k) z ∉ (f ^ n).support\n⊢ (f ^ n) ((f ^ k) z) = (f ^ k) z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 670,
"column": 69
} | {
"line": 671,
"column": 50
} | {
"line": 673,
"column": 0
} | [
{
"pp": "α : Type u_2\ns : Set α\n⊢ IsCycleOn 1 s ↔ s.Subsingleton",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"congrArg",
"Membership.mem",
"Equiv.Perm.sameCycle_one._simp_1",
"Equiv.Perm.SameCycle",
... | [] | by
simp [IsCycleOn, Set.bijOn_id, Set.Subsingleton] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 723,
"column": 16
} | {
"line": 723,
"column": 27
} | {
"line": 723,
"column": 28
} | [
{
"pp": "α : Type u_2\nf : Perm α\ns : Set α\nx : α\nhf : f.IsCycleOn s\nhx : f x ∈ s\n⊢ x ∈ s",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nf : Perm α\ns : Set α\nx : α\nhf : f.IsCycleOn s\nhx : f x ∈ s\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 857,
"column": 4
} | {
"line": 857,
"column": 15
} | {
"line": 857,
"column": 16
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns : Finset α\nx : α\nhx : x ∈ s.toList.formPerm.support\n⊢ x ∈ s",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\ns : Finset α\nx : α\nhx : x ∈ s.toList.formPerm.support\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 872,
"column": 6
} | {
"line": 872,
"column": 17
} | {
"line": 872,
"column": 18
} | [
{
"pp": "α : Type u_2\ns : Set α\nhs : s.Countable\nhs' : s.Finite\nx : α\nhx : x ∈ {x | hs'.toFinset.toList.formPerm x ≠ x}\n⊢ x ∈ s",
"ppTerm": "?m.39",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\ns : Set α\nhs : s.Countable\nhs' : s.Finite\nx : α\nhx : x ∈ {x | hs'.toFinset.toList.formPerm x ≠ x}\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 871,
"column": 4
} | {
"line": 872,
"column": 51
} | {
"line": 873,
"column": 4
} | [
{
"pp": "case inl\nα : Type u_2\ns : Set α\nhs : s.Countable\nhs' : s.Finite\n⊢ ∃ f, f.IsCycleOn s ∧ {x | f x ≠ x} ⊆ s",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Equiv.instEquivLike",
"Finset",
"setOf",
"Classical.propDecidable",
"Membership.mem",
"... | [
"case inl\nα : Type u_2\ns : Set α\nhs : s.Countable\nhs' : s.Finite\n⊢ hs'.toFinset.toList.formPerm.IsCycleOn s"
] | refine ⟨hs'.toFinset.toList.formPerm, ?_, fun x hx => by
simpa using List.mem_of_formPerm_apply_ne hx⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.GroupTheory.Perm.Sign | {
"line": 532,
"column": 6
} | {
"line": 532,
"column": 80
} | {
"line": 532,
"column": 81
} | [
{
"pp": "α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\na : α\nσ : Perm β\nx✝¹ x✝ : α × β\na₁ : α\nb₁ : β\nhab₁ : (prodExtendRight a σ) (a₁, b₁) ≠ (a₁, b₁)\na₂ : α\nb₂ : β\nhab₂ : (prodExtendRight a σ) (a₂, b₂) ≠ (a₂, b₂)\nh : (a₁, b₁).2 = (a₂, b₂)... | [
"α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\na : α\nσ : Perm β\nx✝¹ x✝ : α × β\na₁ : α\nb₁ : β\nhab₁ : (prodExtendRight a σ) (a₁, b₁) ≠ (a₁, b₁)\na₂ : α\nb₂ : β\nhab₂ : (prodExtendRight a σ) (a₂, b₂) ≠ (a₂, b₂)\nh : (a₁, b₁).2 = (a₂, b₂).2\n⊢ b₁ = b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Basic | {
"line": 1050,
"column": 4
} | {
"line": 1050,
"column": 36
} | {
"line": 1050,
"column": 37
} | [
{
"pp": "case mp\nα : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng c : Perm α\ns : Finset α\nhg : ∀ (x : α), g x ∈ s ↔ x ∈ s\nhc : c.support ⊆ s\nn : ℤ\nh : c ^ n = ofSubtype (g.subtypePerm hg)\nx : α\nhx : x ∈ s\n⊢ ↑((c.subtypePerm ⋯ ^ n) ⟨x, hx⟩) = ↑((g.subtypePerm hg) ⟨x, hx⟩)",
"ppTerm": "?mp"... | [
"case mp\nα : Type u_2\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\ng c : Perm α\ns : Finset α\nhg : ∀ (x : α), g x ∈ s ↔ x ∈ s\nhc : c.support ⊆ s\nn : ℤ\nh : c ^ n = ofSubtype (g.subtypePerm hg)\nx : α\nhx : x ∈ s\n⊢ (ofSubtype (g.subtypePerm hg)) x = g x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Sign | {
"line": 536,
"column": 2
} | {
"line": 536,
"column": 52
} | {
"line": 537,
"column": 2
} | [
{
"pp": "α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nσ : α → Perm β\n⊢ sign (prodCongrRight σ) = ∏ k, sign (σ k)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Int.instCommMonoid",
"Equiv.prodCongrRight",
... | [
"α : Type u\ninst✝³ : DecidableEq α\nβ : Type v\ninst✝² : Fintype α\ninst✝¹ : DecidableEq β\ninst✝ : Fintype β\nσ : α → Perm β\nl : List α\nhl : l.Nodup\nmem_l : ∀ (x : α), x ∈ l\n⊢ sign (prodCongrRight σ) = ∏ k, sign (σ k)"
] | obtain ⟨l, hl, mem_l⟩ := Finite.exists_univ_list α | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 203,
"column": 6
} | {
"line": 203,
"column": 17
} | {
"line": 203,
"column": 18
} | [
{
"pp": "case pos\nα : Type u_2\nf : Perm α\nx : α\ninst✝² : DecidableRel f.SameCycle\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhx : ¬f x = x\nk : ℤ\n⊢ ¬(f ^ k) x ∉ f.support ↔ True",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.support",
"Equiv.i... | [
"case pos\nα : Type u_2\nf : Perm α\nx : α\ninst✝² : DecidableRel f.SameCycle\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhx : ¬f x = x\nk : ℤ\n⊢ ¬f x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 204,
"column": 6
} | {
"line": 204,
"column": 22
} | {
"line": 204,
"column": 23
} | [
{
"pp": "case neg\nα : Type u_2\nf : Perm α\nx y : α\ninst✝² : DecidableRel f.SameCycle\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhx : ¬f x = x\nhy : ¬f.SameCycle x y\n⊢ y ≠ y ↔ f.SameCycle x y ∧ x ∈ f.support",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.P... | [
"case neg\nα : Type u_2\nf : Perm α\nx y : α\ninst✝² : DecidableRel f.SameCycle\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nhx : ¬f x = x\nhy : ¬f.SameCycle x y\n⊢ ¬f.SameCycle x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Sign | {
"line": 622,
"column": 85
} | {
"line": 624,
"column": 68
} | {
"line": 626,
"column": 0
} | [
{
"pp": "α : Type u\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\n⊢ (ofSign 1).disjUnion (ofSign (-1)) ⋯ = univ",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCom... | [] | by
ext σ
simp_rw [mem_disjUnion, mem_ofSign, Int.units_eq_one_or, mem_univ] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 262,
"column": 35
} | {
"line": 262,
"column": 46
} | {
"line": 262,
"column": 47
} | [
{
"pp": "α : Type u_2\nf : Perm α\nx : α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nh : f x ≠ x\n⊢ 2 ≤ #(f.cycleOf x).support",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_2\nf : Perm α\nx : α\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nh : f x ≠ x\n⊢ 2 ≤ #(f.cycleOf x).support"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.GCD | {
"line": 215,
"column": 50
} | {
"line": 215,
"column": 61
} | {
"line": 215,
"column": 62
} | [
{
"pp": "n : ℤ\nd : ℕ\nhi : Invertible ↑d\nh : n.natAbs.gcd d = 1\n⊢ d ≠ 0",
"ppTerm": "?m.124",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
],
"usedFVars": [
"d"
],
"usedGoals": [
{
"new": tr... | [
"n : ℤ\nd : ℕ\nhi : Invertible ↑d\nh : n.natAbs.gcd d = 1\n⊢ ¬d = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.GCD | {
"line": 224,
"column": 50
} | {
"line": 224,
"column": 61
} | {
"line": 224,
"column": 62
} | [
{
"pp": "n : ℤ\nd : ℕ\nhi : Invertible ↑d\nh : n.natAbs.gcd d = 1\n⊢ d ≠ 0",
"ppTerm": "?m.124",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
],
"usedFVars": [
"d"
],
"usedGoals": [
{
"new": tr... | [
"n : ℤ\nd : ℕ\nhi : Invertible ↑d\nh : n.natAbs.gcd d = 1\n⊢ ¬d = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Option | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | {
"line": 54,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\nσ : Perm (Option α)\nx : Option α\nthis : Option.map (⇑(removeNone σ)) x = (swap none (σ none)) (σ x)\n⊢ (removeNone σ).optionCongr x = (swap none (σ none) * σ) x",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.inst... | [
"α : Type u_1\ninst✝ : DecidableEq α\nσ : Perm (Option α)\nx : Option α\nthis : Option.map (⇑(removeNone σ)) x = (swap none (σ none)) (σ x)\n⊢ Option.map (⇑(removeNone σ)) x = (swap none (σ none)) (σ x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.NoncommPiCoprod | {
"line": 310,
"column": 2
} | {
"line": 310,
"column": 13
} | {
"line": 311,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\nι : Type u_2\nH : ι → Subgroup G\nhcomm : Pairwise fun i j ↦ ∀ (x y : G), x ∈ H i → y ∈ H j → Commute x y\ninst✝¹ : Finite ι\ninst✝ : (i : ι) → Fintype ↥(H i)\nhcoprime : Pairwise fun i j ↦ (Fintype.card ↥(H i)).Coprime (Fintype.card ↥(H j))\n⊢ iSupIndep H",
"ppTerm"... | [
"G : Type u_1\ninst✝² : Group G\nι : Type u_2\nH : ι → Subgroup G\nhcomm : Pairwise fun i j ↦ ∀ (x y : G), x ∈ H i → y ∈ H j → Commute x y\ninst✝¹ : Finite ι\ninst✝ : (i : ι) → Fintype ↥(H i)\nhcoprime : Pairwise fun i j ↦ (Fintype.card ↥(H i)).Coprime (Fintype.card ↥(H j))\n⊢ iSupIndep H"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.NoncommPiCoprod | {
"line": 341,
"column": 4
} | {
"line": 341,
"column": 15
} | {
"line": 341,
"column": 16
} | [
{
"pp": "case hind\nG : Type u_1\ninst✝¹ : Group G\nι : Type u_2\nH : ι → Subgroup G\ninst✝ : Fintype ι\nhcomm : Pairwise fun i j ↦ ∀ (x y : G), x ∈ H i → y ∈ H j → Commute x y\nhind : iSupIndep H\n⊢ iSupIndep fun i ↦ (H i).subtype.range",
"ppTerm": "?hind",
"assigned": true,
"usedConstants": [
... | [
"case hind\nG : Type u_1\ninst✝¹ : Group G\nι : Type u_2\nH : ι → Subgroup G\ninst✝ : Fintype ι\nhcomm : Pairwise fun i j ↦ ∀ (x y : G), x ∈ H i → y ∈ H j → Commute x y\nhind : iSupIndep H\n⊢ iSupIndep fun i ↦ H i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 13
} | {
"line": 149,
"column": 14
} | [
{
"pp": "case h\nn : ℕ\ni j : Fin n\nh : i < j\n⊢ j ∉ Set.range ⇑(castLEEmb ⋯)",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Fin.cycleRange._proof_2",
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"congrArg",
"Fin.castLE",
"PartialOrder.toPreorder",
... | [
"case h\nn : ℕ\ni j : Fin n\nh : i < j\n⊢ i < j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 163,
"column": 6
} | {
"line": 163,
"column": 64
} | {
"line": 163,
"column": 65
} | [
{
"pp": "n : ℕ\ni j : Fin n\ninst✝ : NeZero n\nh : i ≤ j\niin : i ∈ Set.range ⇑(castLEEmb ⋯)\nthis : (castLEEmb ⋯).toEquivRange (i.castLT ⋯) = ⟨i, iin⟩\nch : i = j\n⊢ (castLEEmb ⋯).toEquivRange.symm ⟨i, iin⟩ = last ↑j",
"ppTerm": "?m.119",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"n : ℕ\ni j : Fin n\ninst✝ : NeZero n\nh : i ≤ j\niin : i ∈ Set.range ⇑(castLEEmb ⋯)\nthis : (castLEEmb ⋯).toEquivRange (i.castLT ⋯) = ⟨i, iin⟩\nch : i = j\n⊢ i.castLT ⋯ = last ↑j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 36
} | {
"line": 175,
"column": 2
} | [
{
"pp": "case zero\ni j : Fin 0\nh : i ≤ j\n⊢ ↑(j.cycleRange i) = if i = j then 0 else ↑i + 1",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"le_rfl",
"Equiv.instEquivLike",
"instDecidableEqFin",
"Fin.pos",
"Preorder.toLE",
"instOfNatNat",
"LE.le"... | [] | exact absurd le_rfl j.pos.not_ge | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.GroupTheory.Perm.Fin | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 36
} | {
"line": 175,
"column": 2
} | [
{
"pp": "case zero\ni j : Fin 0\nh : i ≤ j\n⊢ ↑(j.cycleRange i) = if i = j then 0 else ↑i + 1",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"le_rfl",
"Equiv.instEquivLike",
"instDecidableEqFin",
"Fin.pos",
"Preorder.toLE",
"instOfNatNat",
"LE.le"... | [] | exact absurd le_rfl j.pos.not_ge | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Fin | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 36
} | {
"line": 175,
"column": 2
} | [
{
"pp": "case zero\ni j : Fin 0\nh : i ≤ j\n⊢ ↑(j.cycleRange i) = if i = j then 0 else ↑i + 1",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"le_rfl",
"Equiv.instEquivLike",
"instDecidableEqFin",
"Fin.pos",
"Preorder.toLE",
"instOfNatNat",
"LE.le"... | [] | exact absurd le_rfl j.pos.not_ge | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Fin | {
"line": 238,
"column": 6
} | {
"line": 238,
"column": 24
} | {
"line": 238,
"column": 25
} | [
{
"pp": "case succ.inl.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhlt : j < i\nthis : (j + 1).castSucc = j.succ\n⊢ ↑(j + 1).castSucc < ↑i.succ",
"ppTerm": "?succ.inl.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Preorder.toLT",
"Nat.instOne",
"Fin.succ"... | [
"case succ.inl.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhlt : j < i\nthis : (j + 1).castSucc = j.succ\n⊢ j < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 240,
"column": 4
} | {
"line": 241,
"column": 24
} | {
"line": 242,
"column": 2
} | [
{
"pp": "case succ.inr.inl.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nheq : j = i\n⊢ castSucc 0 < i.succ",
"ppTerm": "?succ.inr.inl.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Fin.succ",
"congrArg",
"id",
"Fin.instOfNat",
"instOfNatNat",
... | [] | · rw [Fin.castSucc_zero]
apply Fin.succ_pos | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.GroupTheory.Perm.Fin | {
"line": 245,
"column": 6
} | {
"line": 245,
"column": 41
} | {
"line": 245,
"column": 42
} | [
{
"pp": "case succ.inr.inr.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhgt : i < j\n⊢ i.succ ≤ j.castSucc",
"ppTerm": "?succ.inr.inr.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"Fin.succ",
"_private.Mathlib.GroupTheory.Perm.Fin.0.Fin.succAbove_... | [
"case succ.inr.inr.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhgt : i < j\n⊢ i < j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 245,
"column": 6
} | {
"line": 245,
"column": 45
} | {
"line": 247,
"column": 0
} | [
{
"pp": "case succ.inr.inr.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhgt : i < j\n⊢ i.succ ≤ j.castSucc",
"ppTerm": "?succ.inr.inr.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"Fin.succ",
"_private.Mathlib.GroupTheory.Perm.Fin.0.Fin.succAbove_... | [] | simpa [Fin.le_iff_val_le_val] using hgt | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.GroupTheory.Perm.Fin | {
"line": 245,
"column": 6
} | {
"line": 245,
"column": 45
} | {
"line": 247,
"column": 0
} | [
{
"pp": "case succ.inr.inr.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhgt : i < j\n⊢ i.succ ≤ j.castSucc",
"ppTerm": "?succ.inr.inr.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"Fin.succ",
"_private.Mathlib.GroupTheory.Perm.Fin.0.Fin.succAbove_... | [] | simpa [Fin.le_iff_val_le_val] using hgt | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Fin | {
"line": 245,
"column": 6
} | {
"line": 245,
"column": 45
} | {
"line": 247,
"column": 0
} | [
{
"pp": "case succ.inr.inr.h\nn✝ : ℕ\ni j : Fin (n✝ + 1)\nhgt : i < j\n⊢ i.succ ≤ j.castSucc",
"ppTerm": "?succ.inr.inr.h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Nat.instOne",
"Fin.succ",
"_private.Mathlib.GroupTheory.Perm.Fin.0.Fin.succAbove_... | [] | simpa [Fin.le_iff_val_le_val] using hgt | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Fin | {
"line": 352,
"column": 4
} | {
"line": 352,
"column": 21
} | {
"line": 352,
"column": 22
} | [
{
"pp": "case pos\nn : ℕ\ni j k : Fin n\nh : k < i\nhij : i ≤ j\n⊢ (i.cycleIcc j) k = k",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.instSub",
"Equiv.instEquivLike",
"Equiv.Perm.extendDomain",
"congrArg",
"instDecidableEqFin",
"HS... | [
"case pos\nn : ℕ\ni j k : Fin n\nh : k < i\nhij : i ≤ j\n⊢ (((j - i).castLT ⋯).cycleRange.extendDomain (natAdd_castLEEmb ⋯).toEquivRange) k = k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 370,
"column": 6
} | {
"line": 370,
"column": 33
} | {
"line": 370,
"column": 34
} | [
{
"pp": "n : ℕ\ni j k : Fin n\nh : j < k\nhij : i ≤ j\nkin : k ∈ Set.range ⇑(natAdd_castLEEmb ⋯)\n⊢ ((addNatEmb (n - (n - ↑i))).trans (finCongr ⋯).toEmbedding).toEquivRange.symm ⟨k, kin⟩ = subNat (↑i) (Fin.cast ⋯ k) ⋯",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Set.mem_range_sel... | [
"n : ℕ\ni j k : Fin n\nh : j < k\nhij : i ≤ j\nkin : k ∈ Set.range ⇑(natAdd_castLEEmb ⋯)\n⊢ k = Fin.cast ⋯ ((subNat (↑i) (Fin.cast ⋯ k) ⋯).addNat (n - (n - ↑i)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 387,
"column": 4
} | {
"line": 387,
"column": 31
} | {
"line": 387,
"column": 32
} | [
{
"pp": "n : ℕ\ni j k : Fin n\nhik : i ≤ k\nhkj : k ≤ j\ninst✝ : NeZero n\nhij : i ≤ j\nkin : k ∈ Set.range ⇑(natAdd_castLEEmb ⋯)\n⊢ ((addNatEmb (n - (n - ↑i))).trans (finCongr ⋯).toEmbedding).toEquivRange.symm ⟨k, kin⟩ = subNat (↑i) (Fin.cast ⋯ k) ⋯",
"ppTerm": "?m.80",
"assigned": true,
"usedConst... | [
"n : ℕ\ni j k : Fin n\nhik : i ≤ k\nhkj : k ≤ j\ninst✝ : NeZero n\nhij : i ≤ j\nkin : k ∈ Set.range ⇑(natAdd_castLEEmb ⋯)\n⊢ k = Fin.cast ⋯ ((subNat (↑i) (Fin.cast ⋯ k) ⋯).addNat (n - (n - ↑i)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 416,
"column": 8
} | {
"line": 416,
"column": 81
} | {
"line": 416,
"column": 82
} | [
{
"pp": "case refine_3\nι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nl✝¹ : List α\nf : Perm α\nh : ∀ {x : α}, f x ≠ x → x ∈ l✝¹\nl✝ : List α\ng : Perm α\nhfg : ∀ {x : α}, g x ≠ x → f.cycleOf x = g.cycleOf x\nx : α\nl : List α\nhg : ∀ {x_1 : α}, g x_1 ≠ x_1 → x_1 ∈ x :: l\... | [
"case refine_3\nι : Type u_1\nα : Type u_2\nβ : Type u_3\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nl✝¹ : List α\nf : Perm α\nh : ∀ {x : α}, f x ≠ x → x ∈ l✝¹\nl✝ : List α\ng : Perm α\nhfg : ∀ {x : α}, g x ≠ x → f.cycleOf x = g.cycleOf x\nx : α\nl : List α\nhg : ∀ {x_1 : α}, g x_1 ≠ x_1 → x_1 ∈ x :: l\nhx : ¬g x =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 430,
"column": 4
} | {
"line": 430,
"column": 29
} | {
"line": 431,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni j : Fin n\nhij✝ : i ≤ j\nhij : i < j\n⊢ Perm.sign (j.cycleIcc i) = 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"False",
"MonoidHom.instFunLike",
"Fin.not_le",
"Equiv.Perm.instOne",
"eq_false",
"MonoidHom"... | [] | simp [Fin.not_le.mpr hij] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.GroupTheory.Perm.Fin | {
"line": 430,
"column": 4
} | {
"line": 430,
"column": 29
} | {
"line": 431,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni j : Fin n\nhij✝ : i ≤ j\nhij : i < j\n⊢ Perm.sign (j.cycleIcc i) = 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"False",
"MonoidHom.instFunLike",
"Fin.not_le",
"Equiv.Perm.instOne",
"eq_false",
"MonoidHom"... | [] | simp [Fin.not_le.mpr hij] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.Perm.Fin | {
"line": 430,
"column": 4
} | {
"line": 430,
"column": 29
} | {
"line": 431,
"column": 2
} | [
{
"pp": "case inl\nn : ℕ\ni j : Fin n\nhij✝ : i ≤ j\nhij : i < j\n⊢ Perm.sign (j.cycleIcc i) = 1",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"False",
"MonoidHom.instFunLike",
"Fin.not_le",
"Equiv.Perm.instOne",
"eq_false",
"MonoidHom"... | [] | simp [Fin.not_le.mpr hij] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.GroupTheory.Perm.Fin | {
"line": 434,
"column": 2
} | {
"line": 434,
"column": 28
} | {
"line": 434,
"column": 29
} | [
{
"pp": "n : ℕ\ni j : Fin n\nhij : i < j\n⊢ (i.cycleIcc j).IsCycle",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fin.instSub",
"Equiv.Perm.extendDomain",
"congrArg",
"PartialOrder.toPreorder",
"instDecidableEqFin",
"HSub.hSub",
"l... | [
"n : ℕ\ni j : Fin n\nhij : i < j\n⊢ (((j - i).castLT ⋯).cycleRange.extendDomain (natAdd_castLEEmb ⋯).toEquivRange).IsCycle"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 439,
"column": 2
} | {
"line": 439,
"column": 74
} | {
"line": 439,
"column": 75
} | [
{
"pp": "n : ℕ\ni j : Fin n\nhij : i < j\n⊢ (i.cycleIcc j).cycleType = {↑j - ↑i + 1}",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Equiv.Perm.cycleType",
"Fin.instSub",
"Equiv.Perm.cycleType.congr_simp",
"Equiv.Perm.extendDomain",... | [
"n : ℕ\ni j : Fin n\nhij : i < j\n⊢ ↑(j - i) = ↑j - ↑i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Fin | {
"line": 443,
"column": 2
} | {
"line": 443,
"column": 13
} | {
"line": 443,
"column": 14
} | [
{
"pp": "n : ℕ\ni j : Fin n\nhij : i ≤ j\ninst✝ : NeZero n\n⊢ (j.cycleIcc i).cycleType = ∅",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.Perm.cycleType",
"Equiv.Perm.instOne",
"Equiv.Perm.cycleType_eq_zero._simp_1",
"instDecidableEqFin",
... | [
"n : ℕ\ni j : Fin n\nhij : i ≤ j\ninst✝ : NeZero n\n⊢ j.cycleIcc i = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 75,
"column": 4
} | {
"line": 75,
"column": 15
} | {
"line": 75,
"column": 16
} | [
{
"pp": "case h1\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nl : List (Perm α)\nh0 : l.prod = σ\nh1 : ∀ σ ∈ l, σ.IsCycle\nh2 : List.Pairwise Disjoint l\nhl : l.Nodup\n⊢ ∀ f ∈ l.toFinset, f.IsCycle",
"ppTerm": "?h1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case h1\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nl : List (Perm α)\nh0 : l.prod = σ\nh1 : ∀ σ ∈ l, σ.IsCycle\nh2 : List.Pairwise Disjoint l\nhl : l.Nodup\n⊢ ∀ f ∈ l, f.IsCycle"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 76,
"column": 4
} | {
"line": 76,
"column": 20
} | {
"line": 76,
"column": 21
} | [
{
"pp": "case h2\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nl : List (Perm α)\nh0 : l.prod = σ\nh1 : ∀ σ ∈ l, σ.IsCycle\nh2 : List.Pairwise Disjoint l\nhl : l.Nodup\n⊢ (↑l.toFinset).Pairwise Disjoint",
"ppTerm": "?h2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case h2\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nσ : Perm α\nl : List (Perm α)\nh0 : l.prod = σ\nh1 : ∀ σ ∈ l, σ.IsCycle\nh2 : List.Pairwise Disjoint l\nhl : l.Nodup\n⊢ List.Pairwise Disjoint l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Factors | {
"line": 545,
"column": 2
} | {
"line": 545,
"column": 56
} | {
"line": 546,
"column": 4
} | [
{
"pp": "α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf p : Perm α\nl : List (Perm α)\nhl : l.Nodup\nhl' : (∀ f ∈ l, f.IsCycle) ∧ List.Pairwise Disjoint l ∧ l.prod = f\n⊢ p ∈ l.toFinset ↔ p.IsCycle ∧ ∀ a ∈ p.support, p a = f a",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_2\ninst✝¹ : DecidableEq α\ninst✝ : Fintype α\nf p : Perm α\nl : List (Perm α)\nhl : l.Nodup\nhl' : (∀ f ∈ l, f.IsCycle) ∧ List.Pairwise Disjoint l ∧ l.prod = f\n⊢ p ∈ l ↔ p.IsCycle ∧ ∀ (a : α), ¬p a = a → p a = l.prod a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Perm.Cycle.Type | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 71
} | {
"line": 240,
"column": 72
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf g : Perm α\nhf : f ∈ g.cycleFactorsFinset\nhf' : f.IsCycle ∧ ∀ a ∈ f.support, f a = g a\n⊢ {f}.val ≤ g.cycleFactorsFinset.val",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset",
"PartialOr... | [
"α : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf g : Perm α\nhf : f ∈ g.cycleFactorsFinset\nhf' : f.IsCycle ∧ ∀ a ∈ f.support, f a = g a\n⊢ f ∈ g.cycleFactorsFinset"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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