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