module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Rat.Star | {
"line": 41,
"column": 2
} | {
"line": 41,
"column": 23
} | {
"line": 41,
"column": 24
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = ⊤",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ closure (range fun x ↦ x * x) = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Star | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 23
} | {
"line": 60,
"column": 24
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = nonneg ℚ",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ closure (range fun x ↦ x * x) = nonneg ℚ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Star | {
"line": 59,
"column": 92
} | {
"line": 60,
"column": 75
} | {
"line": 62,
"column": 0
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = nonneg ℚ",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"even_two",
"AddMonoid.toAddZeroClass",
"Rat",
"Rat.instAddLeftMono",... | [] | by
simpa only [sq] using addSubmonoid_closure_range_pow two_ne_zero even_two | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Set.Enumerate | {
"line": 68,
"column": 6
} | {
"line": 70,
"column": 17
} | {
"line": 72,
"column": 0
} | [
{
"pp": "case some\nα : Type u_1\nsel : Set α → Option α\nh_sel : ∀ (s : Set α) (a : α), sel s = some a → a ∈ s\ns : Set α\nn : ℕ\na a' : α\nh : sel s = some a'\n⊢ (do\n let a ← some a'\n enumerate sel (s \\ {a}) n) =\n some a →\n a ∈ s",
"ppTerm": "?some",
"assigned": true,
"u... | [] | exact fun h' : enumerate sel (s \ {a'}) n = some a ↦
have : a ∈ s \ {a'} := enumerate_mem h_sel h'
this.left | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Set.Finite.List | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 31
} | {
"line": 35,
"column": 32
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\nn : ℕ\n⊢ {l | l.length ≤ n}.Finite",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Finite α\nn : ℕ\n⊢ {l | l.length ≤ n}.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 246,
"column": 20
} | {
"line": 246,
"column": 31
} | {
"line": 246,
"column": 32
} | [
{
"pp": "case think\nα : Type u\nc : Computation (WSeq α)\nc1 c2 : Computation (Option (α × WSeq α))\nh : c1 = c2 ∨ ∃ c, c1 = (flatten c).destruct ∧ c2 = c.bind destruct\nc' : Computation (WSeq α)\n⊢ BisimO (fun c1 c2 ↦ c1 = c2 ∨ ∃ c, c1 = (flatten c).destruct ∧ c2 = c.bind destruct)\n (flatten c'.think).des... | [
"case think\nα : Type u\nc : Computation (WSeq α)\nc1 c2 : Computation (Option (α × WSeq α))\nh : c1 = c2 ∨ ∃ c, c1 = (flatten c).destruct ∧ c2 = c.bind destruct\nc' : Computation (WSeq α)\n⊢ (flatten c').destruct = c'.bind destruct ∨\n ∃ c, (flatten c').destruct = (flatten c).destruct ∧ c'.bind destruct = c.bin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 204,
"column": 48
} | {
"line": 204,
"column": 70
} | {
"line": 204,
"column": 71
} | [
{
"pp": "α : Type u\nβ : Type v\nR : α → β → Prop\ns✝ : WSeq α\nt✝ : WSeq β\nH : LiftRel R s✝ t✝\nn : ℕ\na✝ : Option (α × WSeq α)\nb✝ : Option (β × WSeq β)\no : LiftRelO R (LiftRel R) a✝ b✝\na : α\ns : WSeq α\nb : β\nt : WSeq β\nleft✝ : R a b\nh2 : LiftRel R s t\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) (... | [
"α : Type u\nβ : Type v\nR : α → β → Prop\ns✝ : WSeq α\nt✝ : WSeq β\nH : LiftRel R s✝ t✝\nn : ℕ\na✝ : Option (α × WSeq α)\nb✝ : Option (β × WSeq β)\no : LiftRelO R (LiftRel R) a✝ b✝\na : α\ns : WSeq α\nb : β\nt : WSeq β\nleft✝ : R a b\nh2 : LiftRel R s t\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) s.destruct t.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Setoid.Partition.Card | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 14
} | {
"line": 66,
"column": 2
} | [
{
"pp": "α : Type u_1\nP : Set (Set α)\nhP : IsPartition P\ns : Set α\nhs : s.Finite\nhst : ∀ (t : Set α), (s ∩ t).Finite\nhst' : ∀ (t : Set α), Nat.card ↑(s ∩ t) = ⋯.toFinset.card\nf : ↑(Function.support fun t ↦ (s ∩ ↑t).ncard) → ↑s := ⋯\nhf : ∀ (t : ↑(Function.support fun t ↦ (s ∩ ↑t).ncard)), ↑↑t ∈ P ∧ ↑(f t... | [
"α : Type u_1\nP : Set (Set α)\nhP : IsPartition P\ns : Set α\nhs : s.Finite\nhst : ∀ (t : Set α), (s ∩ t).Finite\nhst' : ∀ (t : Set α), Nat.card ↑(s ∩ t) = ⋯.toFinset.card\nf : ↑(Function.support fun t ↦ (s ∩ ↑t).ncard) → ↑s :=\n fun x ↦\n match x with\n | ⟨t, ht⟩ => ⟨Exists.choose ⋯, ⋯⟩\nhf : ∀ (t : ↑(Func... | intro t t' h | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Data.WSeq.Basic | {
"line": 462,
"column": 30
} | {
"line": 462,
"column": 41
} | {
"line": 462,
"column": 42
} | [
{
"pp": "α : Type u\na : α\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get 0\n⊢ a ∈ nil",
"ppTerm": "?m.61",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\na : α\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get 0\n⊢ a ∈ nil"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 462,
"column": 30
} | {
"line": 462,
"column": 41
} | {
"line": 462,
"column": 42
} | [
{
"pp": "α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get (n✝ + 1)\n⊢ a ∈ nil",
"ppTerm": "?m.85",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get (n✝ + 1)\n⊢ a ∈ nil"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 463,
"column": 80
} | {
"line": 463,
"column": 91
} | {
"line": 463,
"column": 92
} | [
{
"pp": "α : Type u\na x✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get 0\n⊢ a ∈ s✝",
"ppTerm": "?m.122",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\na x✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get 0\n⊢ a ∈ s✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 463,
"column": 80
} | {
"line": 463,
"column": 91
} | {
"line": 463,
"column": 92
} | [
{
"pp": "α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nx✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get (n✝ + 1)\n⊢ a ∈ s✝",
"ppTerm": "?m.140",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nx✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get (n✝ + 1)\n⊢ a ∈ s✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sigma.Interval | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 24
} | {
"line": 134,
"column": 0
} | [
{
"pp": "case inr\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Preorder (α i)\ninst✝ : (i : ι) → LocallyFiniteOrderTop (α i)\nx✝¹ x✝ : (i : ι) × α i\ni : ι\na : α i\nj : ι\nb : α j\nhij : i ≠ j\n⊢ (⟨j, b⟩ ∈\n match ⟨i, a⟩ with\n | ⟨i, a⟩ => Finset.map (Embedding.sigmaMk i) (Ioi a)) ↔\n ⟨i, a... | [] | · simp [hij, lt_def] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.String.Basic | {
"line": 62,
"column": 17
} | {
"line": 62,
"column": 28
} | {
"line": 62,
"column": 29
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := ofList s₂.s.toList, i... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := s₂.s, i := s₂.i }.hasNext = true"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 62,
"column": 45
} | {
"line": 62,
"column": 56
} | {
"line": 62,
"column": 57
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := ofList s₁.s.toList, i... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := s₁.s, i := s₁.i }.hasNext = true"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 376,
"column": 8
} | {
"line": 376,
"column": 19
} | {
"line": 376,
"column": 20
} | [
{
"pp": "case some.some\nα : Type u\nβ : Type v\nR : α → β → Prop\ns1✝ s2 : WSeq α\nt1✝ t2 : WSeq β\nh1 : LiftRel R s1✝ t1✝\nh2 : LiftRel R s2 t2\ns✝ : WSeq α\nt✝ : WSeq β\nh✝¹ : (fun s t ↦ LiftRel R s t ∨ ∃ s1 t1, s = s1.append s2 ∧ t = t1.append t2 ∧ LiftRel R s1 t1) s✝ t✝\ns1 : WSeq α\nt1 : WSeq β\nh✝ : Lift... | [
"case some.some\nα : Type u\nβ : Type v\nR : α → β → Prop\ns1✝ s2 : WSeq α\nt1✝ t2 : WSeq β\nh1 : LiftRel R s1✝ t1✝\nh2 : LiftRel R s2 t2\ns✝ : WSeq α\nt✝ : WSeq β\nh✝¹ : (fun s t ↦ LiftRel R s t ∨ ∃ s1 t1, s = s1.append s2 ∧ t = t1.append t2 ∧ LiftRel R s1 t1) s✝ t✝\ns1 : WSeq α\nt1 : WSeq β\nh✝ : LiftRel R s1 t1\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 65,
"column": 6
} | {
"line": 65,
"column": 78
} | {
"line": 65,
"column": 79
} | [
{
"pp": "case case1.hc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := ofList... | [
"case case1.hc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ Pos.Raw.get s₁.s s₁.i = P... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 68,
"column": 17
} | {
"line": 68,
"column": 28
} | {
"line": 68,
"column": 29
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := ofList s₂.s.toList, i := s₂.i }.hasNext = true",
"ppTerm": "?m.131",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := s₂.s, i := s₂.i }.hasNext = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 68,
"column": 45
} | {
"line": 68,
"column": 56
} | {
"line": 68,
"column": 57
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := ofList s₁.s.toList, i := s₁.i }.hasNext = true",
"ppTerm": "?m.144",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := s₁.s, i := s₁.i }.hasNext = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 70,
"column": 6
} | {
"line": 70,
"column": 78
} | {
"line": 70,
"column": 79
} | [
{
"pp": "case case2.hnc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ ¬{ s := ofList (c :: s₁.s.toList), i := s₁.i + c }.curr = { s := ofList (c :: s₂.s.toList), i := s₂.i + c }.curr",
"ppTerm": "?case2.hnc",
"assigned": true,
"usedCons... | [
"case case2.hnc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ ¬Pos.Raw.get s₁.s s₁.i = Pos.Raw.get s₂.s s₂.i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 73,
"column": 17
} | {
"line": 73,
"column": 28
} | {
"line": 73,
"column": 29
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ { s := ofList s₂.s.toList, i := s₂.i }.hasNext = true",
"ppTerm": "?m.186",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
"String",
"... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ { s := s₂.s, i := s₂.i }.hasNext = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 73,
"column": 45
} | {
"line": 73,
"column": 56
} | {
"line": 73,
"column": 57
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ ¬{ s := ofList s₁.s.toList, i := s₁.i }.hasNext = true",
"ppTerm": "?m.199",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
"String",
... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ { s := s₁.s, i := s₁.i }.hasNext = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 75,
"column": 62
} | {
"line": 75,
"column": 73
} | {
"line": 75,
"column": 74
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : ¬s₂.hasNext = true\n⊢ ¬{ s := ofList s₂.s.toList, i := s₂.i }.hasNext = true",
"ppTerm": "?m.227",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
"String",
"String.Legacy.Iterator.... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : ¬s₂.hasNext = true\n⊢ { s := s₂.s, i := s₂.i }.hasNext = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 799,
"column": 20
} | {
"line": 799,
"column": 31
} | {
"line": 799,
"column": 32
} | [
{
"pp": "case bisim.nil.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct (nil.append (map f (cons s S).join))) (Seq.destruct (nil.append (map (map f) ... | [
"case bisim.nil.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ ∃ s_1 S_1,\n (map f s).append (map f S.join) = s_1.append (map f S_1.join) ∧\n (map f s).append (map (map f) S).join = s_1.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 800,
"column": 19
} | {
"line": 800,
"column": 30
} | {
"line": 800,
"column": 31
} | [
{
"pp": "case bisim.nil.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct (nil.append (map f S.think.join))) (Seq.destruct (nil.append (map (map f) S.think).join))",
"ppTerm":... | [
"case bisim.nil.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\n⊢ ∃ s S_1, map f S.join = s.append (map f S_1.join) ∧ (map (map f) S).join = s.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 801,
"column": 6
} | {
"line": 801,
"column": 17
} | {
"line": 801,
"column": 18
} | [
{
"pp": "case bisim.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\nx✝ : β\ns✝ : WSeq β\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct ((cons x✝ s✝).append (map f S.join))) (Seq.destruct ((cons x✝ s✝).append (map (map f) S).... | [
"case bisim.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\nx✝ : β\ns✝ : WSeq β\n⊢ ∃ s S_1,\n s✝.append (map f S.join) = s.append (map f S_1.join) ∧\n s✝.append (map (map f) S).join = s.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 802,
"column": 6
} | {
"line": 802,
"column": 17
} | {
"line": 802,
"column": 18
} | [
{
"pp": "case bisim.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\ns✝ : WSeq β\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct (s✝.think.append (map f S.join))) (Seq.destruct (s✝.think.append (map (map f) S).join))",
"p... | [
"case bisim.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\ns✝ : WSeq β\n⊢ ∃ s S_1,\n s✝.append (map f S.join) = s.append (map f S_1.join) ∧\n s✝.append (map (map f) S).join = s.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Sym2.Finsupp | {
"line": 33,
"column": 2
} | {
"line": 33,
"column": 13
} | {
"line": 33,
"column": 14
} | [
{
"pp": "case mk\nα : Type u_1\nM₀ : Type u_2\ninst✝ : CommMonoidWithZero M₀\nf : α →₀ M₀\np : Sym2 α\na b : α\nhp : ¬f a * f b = 0\n⊢ Quot.mk (Rel α) (a, b) ∈ f.support.sym2",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Sym2.Rel",
... | [
"case mk\nα : Type u_1\nM₀ : Type u_2\ninst✝ : CommMonoidWithZero M₀\nf : α →₀ M₀\np : Sym2 α\na b : α\nhp : ¬f a * f b = 0\n⊢ ¬f a = 0 ∧ ¬f b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 440,
"column": 8
} | {
"line": 440,
"column": 19
} | {
"line": 440,
"column": 20
} | [
{
"pp": "α : Type u\nβ : Type v\nR : α → β → Prop\nS✝ : WSeq (WSeq α)\nT✝ : WSeq (WSeq β)\nh✝ : LiftRel (LiftRel R) S✝ T✝\ns1 : WSeq α\ns2 : WSeq β\nx✝ :\n (fun s1 s2 ↦ ∃ s t S T, s1 = s.append S.join ∧ s2 = t.append T.join ∧ LiftRel R s t ∧ LiftRel (LiftRel R) S T) s1 s2\ns✝ : WSeq α\nt✝ : WSeq β\nS : WSeq (W... | [
"α : Type u\nβ : Type v\nR : α → β → Prop\nS✝ : WSeq (WSeq α)\nT✝ : WSeq (WSeq β)\nh✝ : LiftRel (LiftRel R) S✝ T✝\ns1 : WSeq α\ns2 : WSeq β\nx✝ :\n (fun s1 s2 ↦ ∃ s t S T, s1 = s.append S.join ∧ s2 = t.append T.join ∧ LiftRel R s t ∧ LiftRel (LiftRel R) S T) s1 s2\ns✝ : WSeq α\nt✝ : WSeq β\nS : WSeq (WSeq α)\nT : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 468,
"column": 56
} | {
"line": 468,
"column": 73
} | {
"line": 468,
"column": 74
} | [
{
"pp": "α : Type u\ns : WSeq α\n⊢ (ret s).join ~ʷ s",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Stream'.WSeq.join",
"congrArg",
"Stream'.WSeq.cons",
"Stream'.WSeq.ofList_cons",
"id",
"Stream'.WSeq.join_cons",
"Stream'.WSeq.thin... | [
"α : Type u\ns : WSeq α\n⊢ s.think ~ʷ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 515,
"column": 18
} | {
"line": 515,
"column": 29
} | {
"line": 515,
"column": 30
} | [
{
"pp": "case nil.cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nT : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ LiftRelAux (LiftRelO Eq fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join... | [
"case nil.cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nT : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ ∃ s_1 S_1 T_1,\n (s.append (S.append T).join).destruct = (s_1.append (S_1.append T_1).join).destruct ∧\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 517,
"column": 16
} | {
"line": 517,
"column": 27
} | {
"line": 517,
"column": 28
} | [
{
"pp": "case cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\na : α\ns : WSeq α\n⊢ LiftRelAux (LiftRelO Eq fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join... | [
"case cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\na : α\ns : WSeq α\n⊢ ∃ s_1 S_1 T_1,\n s.append (S.append T).join = s_1.append (S_1.append T_1).join ∧\n s.append (S.join.append T.join) = s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 518,
"column": 15
} | {
"line": 518,
"column": 26
} | {
"line": 518,
"column": 27
} | [
{
"pp": "case think\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\ns : WSeq α\n⊢ LiftRelAux (LiftRelO Eq fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join))\n ... | [
"case think\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\ns : WSeq α\n⊢ ∃ s_1 S_1 T_1,\n (s.append (S.append T).join).destruct = (s_1.append (S_1.append T_1).join).destruct ∧\n (s.append (S.join.a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Parallel | {
"line": 277,
"column": 39
} | {
"line": 277,
"column": 50
} | {
"line": 277,
"column": 51
} | [
{
"pp": "case inr.nil\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (L... | [
"case inr.nil\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (List.map (map... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Parallel | {
"line": 277,
"column": 39
} | {
"line": 277,
"column": 50
} | {
"line": 277,
"column": 51
} | [
{
"pp": "case inr.cons\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (... | [
"case inr.cons\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (List.map (ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Parallel | {
"line": 277,
"column": 39
} | {
"line": 277,
"column": 50
} | {
"line": 277,
"column": 51
} | [
{
"pp": "case inr.think\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap ... | [
"case inr.think\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (List.map (m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 561,
"column": 22
} | {
"line": 561,
"column": 33
} | {
"line": 561,
"column": 34
} | [
{
"pp": "case nil.cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ LiftRelAux\n (LiftRelO... | [
"case nil.cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ ∃ s_1 S_1 SS_1,\n (s.append (S.app... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 563,
"column": 20
} | {
"line": 563,
"column": 31
} | {
"line": 563,
"column": 32
} | [
{
"pp": "case cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\na : α\ns : WSeq α\n⊢ LiftRelAux\n (LiftR... | [
"case cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\na : α\ns : WSeq α\n⊢ ∃ s_1 S_1 SS_1,\n s.append (S.a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 564,
"column": 19
} | {
"line": 564,
"column": 30
} | {
"line": 564,
"column": 31
} | [
{
"pp": "case think\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\n⊢ LiftRelAux\n (LiftRelO Eq... | [
"case think\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\n⊢ ∃ s_1 S_1 SS_1,\n (s.append (S.append... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.Mem | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 71
} | {
"line": 71,
"column": 72
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nb : β\nv : Vector α 0\nf : α → β\n⊢ ¬b ∈ (map f v).toList",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.Vector.map",
"List.Vector.eq_nil",
"List.Vector",
"Membership.mem",
"id",
... | [
"α : Type u_1\nβ : Type u_2\nb : β\nv : Vector α 0\nf : α → β\n⊢ ¬b ∈ []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sum.Interval | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 28
} | {
"line": 190,
"column": 2
} | [
{
"pp": "case refine_4.inl.inr\nα₁ : Type u_1\nα₂ : Type u_2\nβ₁ : Type u_3\nβ₂ : Type u_4\nγ₁ : Type u_5\nγ₂ : Type u_6\nf₁ : α₁ → β₁ → Finset γ₁\nf₂ : α₂ → β₂ → Finset γ₂\ng₁ : α₁ → β₂ → Finset γ₁\ng₂ : α₁ → β₂ → Finset γ₂\nval✝¹ : α₁\nval✝ : β₂\nh :\n (∀ (a₁ : α₁) (b₁ : β₁), inl val✝¹ = inl a₁ → inr val✝ = ... | [
"case refine_4.inr.inl\nα₁ : Type u_1\nα₂ : Type u_2\nβ₁ : Type u_3\nβ₂ : Type u_4\nγ₁ : Type u_5\nγ₂ : Type u_6\nf₁ : α₁ → β₁ → Finset γ₁\nf₂ : α₂ → β₂ → Finset γ₂\ng₁ : α₁ → β₂ → Finset γ₁\ng₂ : α₁ → β₂ → Finset γ₂\nval✝¹ : α₂\nval✝ : β₁\nh :\n (∀ (a₁ : α₁) (b₁ : β₁), inr val✝¹ = inl a₁ → inl val✝ = inl b₁ → f₁ ... | · simp [h.2.1 _ _ rfl rfl] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Vector.MapLemmas | {
"line": 64,
"column": 67
} | {
"line": 64,
"column": 78
} | {
"line": 64,
"column": 79
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ : Type u_5\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\ns : σ\ns₁ : σ₁\ns₂ : σ₂\nxs : Vector α n\nf₁✝ : β → σ₁ → σ₁ × γ\nf₂✝ : α → σ₂ → σ₂ × β\np : β → Prop\nf₁ : (b : β) → p b → γ\nf₂ : α → β\nH : ∀ (x : β), x ∈ (map f₂ xs).toList → p x\... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ : Type u_5\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\ns : σ\ns₁ : σ₁\ns₂ : σ₂\nxs : Vector α n\nf₁✝ : β → σ₁ → σ₁ × γ\nf₂✝ : α → σ₂ → σ₂ × β\np : β → Prop\nf₁ : (b : β) → p b → γ\nf₂ : α → β\nH : ∀ (x : β), x ∈ (map f₂ xs).toList → p x\n⊢ ∀ (x : α)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 55
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f xs = (mapAccumr (fun x x_1 ↦ ((), f x)) xs ()).2",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unit.unit",
"List.Vector.mapAccumr",
"List.Vector.mapAccumr_snoc",
"congrArg",
"Li... | [] | induction xs using Vector.revInductionOn <;> simp_all | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 55
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f xs = (mapAccumr (fun x x_1 ↦ ((), f x)) xs ()).2",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unit.unit",
"List.Vector.mapAccumr",
"List.Vector.mapAccumr_snoc",
"congrArg",
"Li... | [] | induction xs using Vector.revInductionOn <;> simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 55
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f xs = (mapAccumr (fun x x_1 ↦ ((), f x)) xs ()).2",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unit.unit",
"List.Vector.mapAccumr",
"List.Vector.mapAccumr_snoc",
"congrArg",
"Li... | [] | induction xs using Vector.revInductionOn <;> simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Vector.MapLemmas | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 26
} | {
"line": 253,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (s : σ), s ∈ S → (f a s).1 ∈ S\nout : ∀ (a : α) (s s' : σ), s ∈ S → s' ∈ S → (f a s).2 = (f a s').2\n⊢ ∃ R, R s₀ () ∧ ∀ {s : σ} {q : Unit} (a : α), R s q → R (f a s).... | [
"case right\nα : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (s : σ), s ∈ S → (f a s).1 ∈ S\nout : ∀ (a : α) (s s' : σ), s ∈ S → s' ∈ S → (f a s).2 = (f a s').2\n⊢ ∀ {s : σ} {q : Unit} (a : α), s ∈ S → (f a s).1 ∈ S ∧ (f a s).2... | use fun s _ => s ∈ S, h₀ | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Data.Vector.MapLemmas | {
"line": 270,
"column": 2
} | {
"line": 270,
"column": 26
} | {
"line": 271,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × γ\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (b : β) (s : σ), s ∈ S → (f a b s).1 ∈ S\nout : ∀ (a : α) (b : β) (s s' : σ), s ∈ S → s' ∈ S → (f a b s).2 = (f a b s').2\n⊢ ∃ R,\n... | [
"case right\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × γ\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (b : β) (s : σ), s ∈ S → (f a b s).1 ∈ S\nout : ∀ (a : α) (b : β) (s s' : σ), s ∈ S → s' ∈ S → (f a b s).2 = (f a b s').2\n⊢ ∀ {s :... | use fun s _ => s ∈ S, h₀ | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Data.Vector3 | {
"line": 190,
"column": 2
} | {
"line": 190,
"column": 18
} | {
"line": 190,
"column": 19
} | [
{
"pp": "case refine_2\nα : Type u_1\nm n : ℕ\na : α\nt✝ : Vector3 α m\nv : Vector3 α n\ni : Fin2 (n + 1)\ne : n + 1 + m = n + m + 1\nk : ℕ\nb : α\nt : Vector3 α k\nIH : ∀ (x : n + 1 + k = n + k + 1), insert a (t +-+ v) (Eq.recOn x (i.add k)) = Eq.recOn x (t +-+ insert a v i)\nx✝ : n + 1 + (k + 1) = n + (k + 1)... | [
"case refine_2\nα : Type u_1\nm n : ℕ\na : α\nt✝ : Vector3 α m\nv : Vector3 α n\ni : Fin2 (n + 1)\ne : n + 1 + m = n + m + 1\nk : ℕ\nb : α\nt : Vector3 α k\nIH : ∀ (x : n + 1 + k = n + k + 1), insert a (t +-+ v) (Eq.recOn x (i.add k)) = Eq.recOn x (t +-+ insert a v i)\nx✝ : n + 1 + (k + 1) = n + (k + 1) + 1\ne' : n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector3 | {
"line": 254,
"column": 6
} | {
"line": 254,
"column": 17
} | {
"line": 254,
"column": 18
} | [
{
"pp": "case refine_2.refine_1\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\n⊢ p a",
"ppTerm": "?refine_2.refine_1",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"case refine_2.refine_1\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\n⊢ p a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector3 | {
"line": 255,
"column": 6
} | {
"line": 255,
"column": 17
} | {
"line": 255,
"column": 18
} | [
{
"pp": "case refine_2.refine_2\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\ni : Fin2 n\n⊢ p (v i)",
"ppTerm": "?refine_2.refine_2",
"assigned": false,
"usedConstants": ... | [
"case refine_2.refine_2\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\ni : Fin2 n\n⊢ p (v i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Defs | {
"line": 243,
"column": 16
} | {
"line": 243,
"column": 27
} | {
"line": 243,
"column": 28
} | [
{
"pp": "case cons\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\na : α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.i... | [
"case cons\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\na : α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.inr (n, s')\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Defs | {
"line": 244,
"column": 15
} | {
"line": 244,
"column": 26
} | {
"line": 244,
"column": 27
} | [
{
"pp": "case think\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.inr (n,... | [
"case think\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.inr (n, s')\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SemiconjSup | {
"line": 68,
"column": 14
} | {
"line": 68,
"column": 43
} | {
"line": 68,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → α\nh : IsOrderRightAdjoint f g\ne : β ≃o γ\ny : γ\n⊢ IsLUB {x | (⇑e ∘ f) x ≤ y} ((g ∘ ⇑e.symm) y)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"setOf... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → α\nh : IsOrderRightAdjoint f g\ne : β ≃o γ\ny : γ\n⊢ IsLUB {x | e (f x) ≤ y} (g (e.symm y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SemiconjSup | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 24
} | {
"line": 102,
"column": 25
} | [
{
"pp": "α : Type u_1\nG : Type u_4\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' ↦ (f₁ g')⁻¹ ((f₂ g') x)) (h x)\ng : G\ny : α\nthis : IsLUB (range ((⇑(f₁ g) ∘ fun g' ↦ (f₁ g')⁻¹ ((f₂ g') y)) ∘ ⇑(Equiv.mulRight g))) ((f₁ g) (h y))\n⊢ IsLUB (range f... | [
"α : Type u_1\nG : Type u_4\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' ↦ (f₁ g')⁻¹ ((f₂ g') x)) (h x)\ng : G\ny : α\nthis : IsLUB (range ((⇑(f₁ g) ∘ fun g' ↦ (f₁ g')⁻¹ ((f₂ g') y)) ∘ ⇑(Equiv.mulRight g))) ((f₁ g) (h y))\n⊢ IsLUB (range fun g' ↦ (f₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Ergodic | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 41
} | {
"line": 63,
"column": 42
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhfs : f ⁻¹' s = s\n⊢ s =ᵐ[μ] ∅ ∨ s =ᵐ[μ] univ",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhfs : f ⁻¹' s = s\n⊢ s =ᵐ[μ] ∅ ∨ s =ᵐ[μ] univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Ergodic | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 13
} | {
"line": 67,
"column": 14
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ μ s = 0 ∨ μ sᶜ = 0",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ μ s = 0 ∨ μ sᶜ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Ergodic | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 18
} | {
"line": 76,
"column": 19
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\ninst✝ : IsProbabilityMeasure μ\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ μ s = 0 ∨ μ s = 1",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\ninst✝ : IsProbabilityMeasure μ\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ μ s = 0 ∨ μ s = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Action.Basic | {
"line": 72,
"column": 4
} | {
"line": 72,
"column": 36
} | {
"line": 72,
"column": 37
} | [
{
"pp": "G : Type u_1\nα : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : Group G\ninst✝¹ : MulAction G α\ninst✝ : ErgodicSMul G α μ\ns : Set α\nhm : NullMeasurableSet s μ\nh : ∀ (g : G), g • s =ᵐ[μ] s\ng : G\n⊢ (fun x ↦ g • x) ⁻¹' s =ᵐ[μ] s",
"ppTerm": "?m.30",
"assigned": true,
"usedCons... | [
"G : Type u_1\nα : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : Group G\ninst✝¹ : MulAction G α\ninst✝ : ErgodicSMul G α μ\ns : Set α\nhm : NullMeasurableSet s μ\nh : ∀ (g : G), g • s =ᵐ[μ] s\ng : G\n⊢ g⁻¹ • s =ᵐ[μ] s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Action.Regular | {
"line": 38,
"column": 2
} | {
"line": 38,
"column": 19
} | {
"line": 38,
"column": 20
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableMul₂ G\ninst✝² : MeasurableInv G\nμ : Measure G\ninst✝¹ : SFinite μ\ninst✝ : μ.IsMulLeftInvariant\ns : Set G\nhsm : MeasurableSet s\nhs : ∀ (g : G), (fun x ↦ g • x) ⁻¹' s =ᵐ[μ] s\nhμs : ∃ᵐ (x : G) ∂μ, x ∈ s\na : G\nhas : a ∈... | [
"G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableMul₂ G\ninst✝² : MeasurableInv G\nμ : Measure G\ninst✝¹ : SFinite μ\ninst✝ : μ.IsMulLeftInvariant\ns : Set G\nhsm : MeasurableSet s\nhs : ∀ (g : G), (fun x ↦ g • x) ⁻¹' s =ᵐ[μ] s\nhμs : ∃ᵐ (x : G) ∂μ, x ∈ s\na : G\nhas : a ∈ s\nha : ∀ᵐ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Action.Regular | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 19
} | {
"line": 53,
"column": 20
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableMul₂ G\ninst✝² : MeasurableInv G\nμ : Measure G\ninst✝¹ : SFinite μ\ninst✝ : μ.IsMulRightInvariant\ns : Set G\nhsm : MeasurableSet s\nhs : ∀ (g : Gᵐᵒᵖ), (fun x ↦ g • x) ⁻¹' s =ᵐ[μ] s\nhμs : ∃ᵐ (x : G) ∂μ, x ∈ s\na : G\nhas :... | [
"G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : MeasurableMul₂ G\ninst✝² : MeasurableInv G\nμ : Measure G\ninst✝¹ : SFinite μ\ninst✝ : μ.IsMulRightInvariant\ns : Set G\nhsm : MeasurableSet s\nhs : ∀ (g : Gᵐᵒᵖ), (fun x ↦ g • x) ⁻¹' s =ᵐ[μ] s\nhμs : ∃ᵐ (x : G) ∂μ, x ∈ s\na : G\nhas : a ∈ s\nha :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 203,
"column": 35
} | {
"line": 203,
"column": 46
} | {
"line": 203,
"column": 47
} | [
{
"pp": "f✝ g : CircleDeg1Lift\nf : CircleDeg1Liftˣ\na✝ b✝ : ℝ\nh :\n { toFun := ⇑↑f, invFun := ⇑↑f⁻¹, left_inv := ⋯, right_inv := ⋯ } a✝ ≤\n { toFun := ⇑↑f, invFun := ⇑↑f⁻¹, left_inv := ⋯, right_inv := ⋯ } b✝\n⊢ a✝ ≤ b✝",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"f✝ g : CircleDeg1Lift\nf : CircleDeg1Liftˣ\na✝ b✝ : ℝ\nh :\n { toFun := ⇑↑f, invFun := ⇑↑f⁻¹, left_inv := ⋯, right_inv := ⋯ } a✝ ≤\n { toFun := ⇑↑f, invFun := ⇑↑f⁻¹, left_inv := ⋯, right_inv := ⋯ } b✝\n⊢ a✝ ≤ b✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 48
} | {
"line": 292,
"column": 49
} | [
{
"pp": "f : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ⇑f fun x ↦ ↑n + x",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ⇑f fun x ↦ ↑n + x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 303,
"column": 17
} | {
"line": 303,
"column": 45
} | {
"line": 303,
"column": 46
} | [
{
"pp": "f : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ⇑f fun x ↦ x + ↑-[n+1]",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real",
"AddMonoid.toAddSemigro... | [
"f : CircleDeg1Lift\nn : ℕ\n⊢ Function.Commute ⇑f fun x ↦ x + (-1 + -↑n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 306,
"column": 2
} | {
"line": 306,
"column": 39
} | {
"line": 306,
"column": 40
} | [
{
"pp": "f : CircleDeg1Lift\nn : ℤ\n⊢ Function.Commute ⇑f fun x ↦ ↑n + x",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nn : ℤ\n⊢ Function.Commute ⇑f fun x ↦ ↑n + x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 476,
"column": 6
} | {
"line": 476,
"column": 34
} | {
"line": 476,
"column": 35
} | [
{
"pp": "f : CircleDeg1Lift\n⊢ Tendsto (fun x ↦ x - 1) atTop atTop",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddGroupWithOne.t... | [
"f : CircleDeg1Lift\n⊢ Tendsto (fun x ↦ x + -1) atTop atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 494,
"column": 2
} | {
"line": 494,
"column": 52
} | {
"line": 495,
"column": 4
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : f x ≤ x + ↑m\nn : ℕ\n⊢ (⇑f)^[n] x ≤ x + ↑n * ↑m",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : f x ≤ x + ↑m\nn : ℕ\n⊢ (⇑f)^[n] x ≤ x + ↑n * ↑m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 499,
"column": 2
} | {
"line": 499,
"column": 52
} | {
"line": 500,
"column": 4
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : x + ↑m ≤ f x\nn : ℕ\n⊢ x + ↑n * ↑m ≤ (⇑f)^[n] x",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : x + ↑m ≤ f x\nn : ℕ\n⊢ x + ↑n * ↑m ≤ (⇑f)^[n] x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 504,
"column": 2
} | {
"line": 504,
"column": 52
} | {
"line": 504,
"column": 53
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : f x = x + ↑m\nn : ℕ\n⊢ (⇑f)^[n] x = x + ↑n * ↑m",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nh : f x = x + ↑m\nn : ℕ\n⊢ (⇑f)^[n] x = x + ↑n * ↑m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 508,
"column": 2
} | {
"line": 508,
"column": 52
} | {
"line": 509,
"column": 4
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (⇑f)^[n] x ≤ x + ↑n * ↑m ↔ f x ≤ x + ↑m",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (⇑f)^[n] x ≤ x + ↑n * ↑m ↔ f x ≤ x + ↑m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 513,
"column": 2
} | {
"line": 513,
"column": 52
} | {
"line": 514,
"column": 4
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (⇑f)^[n] x < x + ↑n * ↑m ↔ f x < x + ↑m",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (⇑f)^[n] x < x + ↑n * ↑m ↔ f x < x + ↑m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 518,
"column": 2
} | {
"line": 518,
"column": 52
} | {
"line": 519,
"column": 4
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (⇑f)^[n] x = x + ↑n * ↑m ↔ f x = x + ↑m",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ (⇑f)^[n] x = x + ↑n * ↑m ↔ f x = x + ↑m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 523,
"column": 2
} | {
"line": 523,
"column": 27
} | {
"line": 523,
"column": 28
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ x + ↑n * ↑m ≤ (⇑f)^[n] x ↔ x + ↑m ≤ f x",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ x + ↑n * ↑m ≤ (⇑f)^[n] x ↔ x + ↑m ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 527,
"column": 2
} | {
"line": 527,
"column": 27
} | {
"line": 527,
"column": 28
} | [
{
"pp": "f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ x + ↑n * ↑m < (⇑f)^[n] x ↔ x + ↑m < f x",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : CircleDeg1Lift\nx : ℝ\nm : ℤ\nn : ℕ\nhn : 0 < n\n⊢ x + ↑n * ↑m < (⇑f)^[n] x ↔ x + ↑m < f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 566,
"column": 4
} | {
"line": 566,
"column": 64
} | {
"line": 567,
"column": 6
} | [
{
"pp": "f : CircleDeg1Lift\nτ' : ℝ\nh : Tendsto (fun n ↦ (⇑f)^[n] 0 / ↑n) atTop (𝓝 τ')\n⊢ Tendsto f.transnumAuxSeq atTop (𝓝 τ')",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"instHDiv",
"Real.instZero",
"congrArg",
"Nat.instMonoid"... | [
"f : CircleDeg1Lift\nτ' : ℝ\nh : Tendsto (fun n ↦ (⇑f)^[n] 0 / ↑n) atTop (𝓝 τ')\n⊢ Tendsto (fun n ↦ (⇑f)^[2 ^ n] 0 / 2 ^ n) atTop (𝓝 τ')"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 36
} | {
"line": 105,
"column": 37
} | [
{
"pp": "M : Type u_1\nX : Type u_2\ninst✝¹⁵ : Monoid M\ninst✝¹⁴ : SMul M X\ninst✝¹³ : TopologicalSpace X\ninst✝¹² : R1Space X\ninst✝¹¹ : MeasurableSpace X\ninst✝¹⁰ : BorelSpace X\nμ : Measure X\ninst✝⁹ : IsFiniteMeasure μ\ninst✝⁸ : μ.InnerRegular\nN : Type u_3\ninst✝⁷ : MulAction M N\ninst✝⁶ : Monoid N\ninst✝⁵... | [
"M : Type u_1\nX : Type u_2\ninst✝¹⁵ : Monoid M\ninst✝¹⁴ : SMul M X\ninst✝¹³ : TopologicalSpace X\ninst✝¹² : R1Space X\ninst✝¹¹ : MeasurableSpace X\ninst✝¹⁰ : BorelSpace X\nμ : Measure X\ninst✝⁹ : IsFiniteMeasure μ\ninst✝⁸ : μ.InnerRegular\nN : Type u_3\ninst✝⁷ : MulAction M N\ninst✝⁶ : Monoid N\ninst✝⁵ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 871,
"column": 4
} | {
"line": 871,
"column": 15
} | {
"line": 871,
"column": 16
} | [
{
"pp": "f₁ f₂ : CircleDeg1Liftˣ\nh : τ ↑f₁ = τ ↑f₂\nthis :\n ∀ (n : Multiplicative ℤ),\n τ (((Units.coeHom CircleDeg1Lift).comp ((zpowersHom CircleDeg1Liftˣ) f₁)) n) =\n τ (((Units.coeHom CircleDeg1Lift).comp ((zpowersHom CircleDeg1Liftˣ) f₂)) n)\nF : CircleDeg1Lift\nhF :\n ∀ (g : Multiplicative ℤ),\... | [
"f₁ f₂ : CircleDeg1Liftˣ\nh : τ ↑f₁ = τ ↑f₂\nthis :\n ∀ (n : Multiplicative ℤ),\n τ (((Units.coeHom CircleDeg1Lift).comp ((zpowersHom CircleDeg1Liftˣ) f₁)) n) =\n τ (((Units.coeHom CircleDeg1Lift).comp ((zpowersHom CircleDeg1Liftˣ) f₂)) n)\nF : CircleDeg1Lift\nhF :\n ∀ (g : Multiplicative ℤ),\n Semicon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 15
} | {
"line": 110,
"column": 16
} | [
{
"pp": "M : Type u_1\nX : Type u_2\ninst✝¹⁵ : Monoid M\ninst✝¹⁴ : SMul M X\ninst✝¹³ : TopologicalSpace X\ninst✝¹² : R1Space X\ninst✝¹¹ : MeasurableSpace X\ninst✝¹⁰ : BorelSpace X\nμ : Measure X\ninst✝⁹ : IsFiniteMeasure μ\ninst✝⁸ : μ.InnerRegular\nN : Type u_3\ninst✝⁷ : MulAction M N\ninst✝⁶ : Monoid N\ninst✝⁵... | [
"M : Type u_1\nX : Type u_2\ninst✝¹⁵ : Monoid M\ninst✝¹⁴ : SMul M X\ninst✝¹³ : TopologicalSpace X\ninst✝¹² : R1Space X\ninst✝¹¹ : MeasurableSpace X\ninst✝¹⁰ : BorelSpace X\nμ : Measure X\ninst✝⁹ : IsFiniteMeasure μ\ninst✝⁸ : μ.InnerRegular\nN : Type u_3\ninst✝⁷ : MulAction M N\ninst✝⁶ : Monoid N\ninst✝⁵ : Topologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Group.AddCircle | {
"line": 66,
"column": 30
} | {
"line": 66,
"column": 75
} | {
"line": 66,
"column": 76
} | [
{
"pp": "T : ℝ\nhT : Fact (0 < T)\nI : Set (AddCircle T)\nu x : AddCircle T\nhu : IsOfFinAddOrder u\nG : AddSubgroup (AddCircle T) := AddSubgroup.zmultiples u\nn : ℕ := addOrderOf u\nB : Set (AddCircle T) := ball x (T / (2 * ↑n))\nhI : I =ᵐ[volume] B\nhn : 1 ≤ ↑n\ng : AddCircle T\nhg : g ∈ G\nhg' : ⟨g, hg⟩ ≠ 0\... | [
"T : ℝ\nhT : Fact (0 < T)\nI : Set (AddCircle T)\nu x : AddCircle T\nhu : IsOfFinAddOrder u\nG : AddSubgroup (AddCircle T) := AddSubgroup.zmultiples u\nn : ℕ := addOrderOf u\nB : Set (AddCircle T) := ball x (T / (2 * ↑n))\nhI : I =ᵐ[volume] B\nhn : 1 ≤ ↑n\ng : AddCircle T\nhg : g ∈ G\nhg' : ⟨g, hg⟩ ≠ 0\n⊢ ¬g = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 138,
"column": 2
} | {
"line": 142,
"column": 52
} | {
"line": 144,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝¹¹ : Group G\ninst✝¹⁰ : TopologicalSpace G\ninst✝⁹ : ContinuousInv G\nX : Type u_2\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : R1Space X\ninst✝⁶ : MeasurableSpace X\ninst✝⁵ : BorelSpace X\ninst✝⁴ : MulAction G X\ninst✝³ : ContinuousSMul G X\ng : G\nhg : DenseRange fun x ↦ g ^ x\nμ : Measu... | [] | borelize G
refine ⟨measurePreserving_smul _ _, ⟨fun s hsm hs ↦ ?_⟩⟩
refine aeconst_of_dense_aestabilizer_smul hsm.nullMeasurableSet (hg.mono ?_)
rw [← Subgroup.coe_zpowers, SetLike.coe_subset_coe, ← Subgroup.zpowers_inv, Subgroup.zpowers_le,
MulAction.mem_aestabilizer, ← preimage_smul, hs] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 138,
"column": 2
} | {
"line": 142,
"column": 52
} | {
"line": 144,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝¹¹ : Group G\ninst✝¹⁰ : TopologicalSpace G\ninst✝⁹ : ContinuousInv G\nX : Type u_2\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : R1Space X\ninst✝⁶ : MeasurableSpace X\ninst✝⁵ : BorelSpace X\ninst✝⁴ : MulAction G X\ninst✝³ : ContinuousSMul G X\ng : G\nhg : DenseRange fun x ↦ g ^ x\nμ : Measu... | [] | borelize G
refine ⟨measurePreserving_smul _ _, ⟨fun s hsm hs ↦ ?_⟩⟩
refine aeconst_of_dense_aestabilizer_smul hsm.nullMeasurableSet (hg.mono ?_)
rw [← Subgroup.coe_zpowers, SetLike.coe_subset_coe, ← Subgroup.zpowers_inv, Subgroup.zpowers_le,
MulAction.mem_aestabilizer, ← preimage_smul, hs] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 167,
"column": 4
} | {
"line": 167,
"column": 90
} | {
"line": 167,
"column": 91
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : MeasurableSpace G\ninst✝¹ : OpensMeasurableSpace G\nμ : Measure G\ninst✝ : μ.IsOpenPosMeasure\ng : G\nhg : Ergodic (fun x ↦ g * x) μ\na : G\nh : (range fun x ↦ g ^ x)ᶜ ∈ 𝓝 a\nthis :\n Tendsto\n (fu... | [
"G : Type u_1\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : MeasurableSpace G\ninst✝¹ : OpensMeasurableSpace G\nμ : Measure G\ninst✝ : μ.IsOpenPosMeasure\ng : G\nhg : Ergodic (fun x ↦ g * x) μ\na : G\nh : (range fun x ↦ g ^ x)ᶜ ∈ 𝓝 a\nthis :\n Tendsto\n (fun x ↦\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.CountableSeparating | {
"line": 42,
"column": 6
} | {
"line": 42,
"column": 33
} | {
"line": 42,
"column": 34
} | [
{
"pp": "case refine_3.inr\nX : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns✝ s : Set X\nhsc : s.Countable\nhsd : Dense s\nt : Set X := s ∪ {x | ∃ y, y ⋖ x}\nx y : X\nh : ∀ s ∈ Iio '' t, x ∈ s ↔ y ∈ s\nhne : x ≠ y\nthis : ∀ (x y : ... | [
"case refine_3.inr\nX : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns✝ s : Set X\nhsc : s.Countable\nhsd : Dense s\nt : Set X := s ∪ {x | ∃ y, y ⋖ x}\nx y : X\nh : ∀ s ∈ Iio '' t, x ∈ s ↔ y ∈ s\nhne : x ≠ y\nthis : ∀ (x y : X), (∀ s ∈ I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.CountableSeparating | {
"line": 45,
"column": 65
} | {
"line": 45,
"column": 76
} | {
"line": 45,
"column": 77
} | [
{
"pp": "X : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns✝ s : Set X\nhsc : s.Countable\nhsd : Dense s\nt : Set X := s ∪ {x | ∃ y, y ⋖ x}\nx y : X\nh : ∀ s ∈ Iio '' t, x ∈ s ↔ y ∈ s\nhne : x ≠ y\nhlt : x < y\nhe : Ioo x y = ∅\n⊢ ∀ ... | [
"X : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns✝ s : Set X\nhsc : s.Countable\nhsd : Dense s\nt : Set X := s ∪ {x | ∃ y, y ⋖ x}\nx y : X\nh : ∀ s ∈ Iio '' t, x ∈ s ↔ y ∈ s\nhne : x ≠ y\nhlt : x < y\nhe : Ioo x y = ∅\n⊢ ∀ ⦃c : X⦄, x <... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.CountableSeparating | {
"line": 49,
"column": 6
} | {
"line": 49,
"column": 35
} | {
"line": 49,
"column": 36
} | [
{
"pp": "case inr\nX : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns✝ s : Set X\nhsc : s.Countable\nhsd : Dense s\nt : Set X := s ∪ {x | ∃ y, y ⋖ x}\nx y : X\nh : ∀ s ∈ Iio '' t, x ∈ s ↔ y ∈ s\nhne✝ : x ≠ y\nhlt : x < y\nhne : (Ioo ... | [
"case inr\nX : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns✝ s : Set X\nhsc : s.Countable\nhsd : Dense s\nt : Set X := s ∪ {x | ∃ y, y ⋖ x}\nx y : X\nh : ∀ s ∈ Iio '' t, x ∈ s ↔ y ∈ s\nhne✝ : x ≠ y\nhlt : x < y\nhne : (Ioo x y).Nonempt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.CountableSeparating | {
"line": 56,
"column": 31
} | {
"line": 56,
"column": 73
} | {
"line": 56,
"column": 74
} | [
{
"pp": "X : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns : Set X\nt : Set (Set X)\nhtc : t.Countable\nht_sub : ∀ s ∈ t, s ∈ range Ioi\nht : ∀ x ∈ s, ∀ y ∈ s, (∀ s ∈ t, x ∈ s ↔ y ∈ s) → x = y\n⊢ ∀ s ∈ compl '' t, s ∈ range Iic",
... | [
"X : Type u_1\ninst✝³ : TopologicalSpace X\ninst✝² : LinearOrder X\ninst✝¹ : OrderTopology X\ninst✝ : SecondCountableTopology X\ns : Set X\nt : Set (Set X)\nhtc : t.Countable\nht_sub : ∀ s ∈ t, s ∈ range Ioi\nht : ∀ x ∈ s, ∀ y ∈ s, (∀ s ∈ t, x ∈ s ↔ y ∈ s) → x = y\n⊢ ∀ a ∈ t, ∃ y, Iic y = aᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.FixedPoints.Support | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 50
} | {
"line": 41,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nf : X → X\n⊢ HasCompactFixedSupport f ↔ ∃ K, IsClosed K ∧ IsCompact K ∧ (fixedPoints f)ᶜ ⊆ K",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Compl.compl",
"Function.fixedPoints",
"Exists",
"Function.HasCompactFixed... | [
"case refine_1\nX : Type u_1\ninst✝ : TopologicalSpace X\nf : X → X\nhf : HasCompactFixedSupport f\n⊢ ∃ K, IsClosed K ∧ IsCompact K ∧ (fixedPoints f)ᶜ ⊆ K",
"case refine_2\nX : Type u_1\ninst✝ : TopologicalSpace X\nf : X → X\nx✝ : ∃ K, IsClosed K ∧ IsCompact K ∧ (fixedPoints f)ᶜ ⊆ K\nK : Set X\nhK₁ : IsClosed K\n... | refine ⟨fun hf ↦ ?_, fun ⟨K, hK₁, hK₂, hf⟩ ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | {
"line": 166,
"column": 6
} | {
"line": 166,
"column": 23
} | {
"line": 168,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nν : Measure α\ninst✝¹ : μ.HaveLebesgueDecomposition ν\ninst✝ : SigmaFinite ν\nhμν : μ ≪ ν\nhf : AEMeasurable f ν\nhf_ne_zero : ∀ᵐ (x : α) ∂ν, f x ≠ 0\nhf_ne_top : ∀ᵐ (x : α) ∂ν, f x ≠ ∞\nthis : SigmaFinite (ν.withDensity f)\ns : Set α\nh... | [] | exact hf.restrict | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | {
"line": 166,
"column": 6
} | {
"line": 166,
"column": 23
} | {
"line": 168,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nν : Measure α\ninst✝¹ : μ.HaveLebesgueDecomposition ν\ninst✝ : SigmaFinite ν\nhμν : μ ≪ ν\nhf : AEMeasurable f ν\nhf_ne_zero : ∀ᵐ (x : α) ∂ν, f x ≠ 0\nhf_ne_top : ∀ᵐ (x : α) ∂ν, f x ≠ ∞\nthis : SigmaFinite (ν.withDensity f)\ns : Set α\nh... | [] | exact hf.restrict | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | {
"line": 166,
"column": 6
} | {
"line": 166,
"column": 23
} | {
"line": 168,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0∞\nν : Measure α\ninst✝¹ : μ.HaveLebesgueDecomposition ν\ninst✝ : SigmaFinite ν\nhμν : μ ≪ ν\nhf : AEMeasurable f ν\nhf_ne_zero : ∀ᵐ (x : α) ∂ν, f x ≠ 0\nhf_ne_top : ∀ᵐ (x : α) ∂ν, f x ≠ ∞\nthis : SigmaFinite (ν.withDensity f)\ns : Set α\nh... | [] | exact hf.restrict | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Dynamics.Ergodic.Extreme | {
"line": 51,
"column": 4
} | {
"line": 52,
"column": 60
} | {
"line": 53,
"column": 4
} | [
{
"pp": "case inr\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\nc : ℝ≥0∞\nhc : c ≠ ∞\nhf : MeasurePreserving f μ μ\nhc₀ : c ≠ 0\nthis✝ : IsFiniteMeasure μ\nS : Set (Measure X) := {ν | MeasurePreserving f ν ν ∧ ν univ = c}\nh : μ ∈ extremePoints ℝ≥0∞ S\nthis : ∀ {s : Set X}, MeasurableSet s → f... | [
"case inr\nX : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\nc : ℝ≥0∞\nhc : c ≠ ∞\nhf : MeasurePreserving f μ μ\nhc₀ : c ≠ 0\nthis✝ : IsFiniteMeasure μ\nS : Set (Measure X) := {ν | MeasurePreserving f ν ν ∧ ν univ = c}\nh : μ ∈ extremePoints ℝ≥0∞ S\nthis : ∀ {s : Set X}, MeasurableSet s → f ⁻¹' s = s →... | obtain ⟨hs, hs'⟩ : μ s ≠ 0 ∧ μ sᶜ ≠ 0 := by
simpa [eventuallyConst_set, ae_iff, and_comm] using! H | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 212,
"column": 2
} | {
"line": 212,
"column": 38
} | {
"line": 212,
"column": 39
} | [
{
"pp": "A : Type u_1\nG : Type u_2\ninst✝¹ : TopologicalSpace A\ninst✝ : DiscreteTopology A\nU : Finset G\nx : G → A\n⊢ IsOpen[Pi.topologicalSpace] (cylinder U x)",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.topologicalSpace",
"congrArg",
"Finset",
... | [
"A : Type u_1\nG : Type u_2\ninst✝¹ : TopologicalSpace A\ninst✝ : DiscreteTopology A\nU : Finset G\nx : G → A\n⊢ IsOpen[Pi.topologicalSpace] ((↑U).pi fun i ↦ {x i})"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 38
} | {
"line": 217,
"column": 39
} | [
{
"pp": "A : Type u_1\nG : Type u_2\ninst✝¹ : TopologicalSpace A\ninst✝ : T1Space A\nU : Finset G\nx : G → A\n⊢ IsClosed[Pi.topologicalSpace] (cylinder U x)",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.topologicalSpace",
"congrArg",
"Finset",
"... | [
"A : Type u_1\nG : Type u_2\ninst✝¹ : TopologicalSpace A\ninst✝ : T1Space A\nU : Finset G\nx : G → A\n⊢ IsClosed[Pi.topologicalSpace] ((↑U).pi fun i ↦ {x i})"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 378,
"column": 6
} | {
"line": 378,
"column": 36
} | {
"line": 378,
"column": 37
} | [
{
"pp": "A : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\nv h : G\nhmem : h ∈ Finset.image (fun x ↦ v * x) p.support\n⊢ ∃ w ∈ p.support, v * w = h",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"us... | [
"A : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\nv h : G\nhmem : h ∈ Finset.image (fun x ↦ v * x) p.support\n⊢ ∃ w ∈ p.support, v * w = h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 374,
"column": 2
} | {
"line": 381,
"column": 17
} | {
"line": 383,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\nv : G\n⊢ G → A",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"HMul.hMul",
"Monoid.toMulOneClass",
"Finset",
"Classic... | [] | intro h
if hmem : h ∈ p.support.image (v * ·) then
-- package existence of a preimage under (v * ·)
let ex : ∃ w, w ∈ p.support ∧ v * w = h := by
simpa [Finset.mem_image] using hmem
exact p.config (Classical.choose ex)
else
exact default | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 374,
"column": 2
} | {
"line": 381,
"column": 17
} | {
"line": 383,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\nv : G\n⊢ G → A",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"HMul.hMul",
"Monoid.toMulOneClass",
"Finset",
"Classic... | [] | intro h
if hmem : h ∈ p.support.image (v * ·) then
-- package existence of a preimage under (v * ·)
let ex : ∃ w, w ∈ p.support ∧ v * w = h := by
simpa [Finset.mem_image] using hmem
exact p.config (Classical.choose ex)
else
exact default | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 420,
"column": 4
} | {
"line": 420,
"column": 34
} | {
"line": 420,
"column": 35
} | [
{
"pp": "A : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\nv w : G\nhw : w ∈ p.support\nhmem : v * w ∈ Finset.image (fun x ↦ v * x) p.support\n⊢ ∃ w' ∈ p.support, v * w' = v * w",
"ppTerm": "?m.74",
"assigned": true,
"usedConstants": [
... | [
"A : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\nv w : G\nhw : w ∈ p.support\nhmem : v * w ∈ Finset.image (fun x ↦ v * x) p.support\n⊢ w ∈ p.support"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 461,
"column": 2
} | {
"line": 461,
"column": 38
} | {
"line": 461,
"column": 39
} | [
{
"pp": "A : Type u_3\nG : Type u_4\ninst✝¹ : Inhabited A\ninst✝ : Monoid G\nF : Set (Pattern A G)\nh : G\nx : G → A\np : Pattern A G\nhp : p ∈ F\ng : G\nhx : p.mulOccursInAt (mulShift h x) g\n⊢ p.mulOccursInAt x (h * g)",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [... | [
"A : Type u_3\nG : Type u_4\ninst✝¹ : Inhabited A\ninst✝ : Monoid G\nF : Set (Pattern A G)\nh : G\nx : G → A\np : Pattern A G\nhp : p ∈ F\ng : G\nhx : p.mulOccursInAt (mulShift h x) g\n⊢ p.mulOccursInAt x (h * g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 497,
"column": 4
} | {
"line": 497,
"column": 86
} | {
"line": 497,
"column": 87
} | [
{
"pp": "case mp\nA : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\ng : G\nx : G → A\nH : x ∈ {x | p.mulOccursInAt x g}\nw : G\nhw : w ∈ p.support\nhu : g * w ∈ Finset.image (fun x ↦ g * x) p.support\nhx : x (g * w) = p.config w\n⊢ x (g * w) = p.mul... | [
"case mp\nA : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\ng : G\nx : G → A\nH : x ∈ {x | p.mulOccursInAt x g}\nw : G\nhw : w ∈ p.support\nhu : g * w ∈ Finset.image (fun x ↦ g * x) p.support\nhx : x (g * w) = p.config w\n⊢ x (g * w) = p.config w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Extreme | {
"line": 67,
"column": 4
} | {
"line": 67,
"column": 47
} | {
"line": 67,
"column": 48
} | [
{
"pp": "X : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\nh : μ ∈ extremePoints ℝ≥0∞ {ν | MeasurePreserving f ν ν ∧ IsProbabilityMeasure ν}\n⊢ μ ∈ extremePoints ℝ≥0∞ {ν | MeasurePreserving f ν ν ∧ ν univ = 1}",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"X : Type u_1\nm : MeasurableSpace X\nμ : Measure X\nf : X → X\nh : μ ∈ extremePoints ℝ≥0∞ {ν | MeasurePreserving f ν ν ∧ IsProbabilityMeasure ν}\n⊢ μ ∈ extremePoints ℝ≥0∞ {ν | MeasurePreserving f ν ν ∧ ν univ = 1}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 504,
"column": 4
} | {
"line": 504,
"column": 86
} | {
"line": 504,
"column": 87
} | [
{
"pp": "case mpr\nA : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\ng : G\nx : G → A\nH : x ∈ cylinder (Finset.image (fun x ↦ g * x) p.support) (p.mulShift g)\nu : G\nhu : u ∈ p.support\nhx : x (g * u) = p.mulShift g (g * u)\n⊢ x (g * u) = p.config... | [
"case mpr\nA : Type u_1\ninst✝² : Inhabited A\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : IsLeftCancelMul G\np : Pattern A G\ng : G\nx : G → A\nH : x ∈ cylinder (Finset.image (fun x ↦ g * x) p.support) (p.mulShift g)\nu : G\nhu : u ∈ p.support\nhx : x (g * u) = p.mulShift g (g * u)\n⊢ x (g * u) = p.config u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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