module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 141,
"column": 47
} | {
"line": 141,
"column": 58
} | {
"line": 141,
"column": 59
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhodd : Odd (Nat.card V)\n⊢ Odd (Nat.card ↑(⊤.deleteVerts ∅).verts)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Subgraph",
"Set.univ",
"Odd",
"Set.Elem",
... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhodd : Odd (Nat.card V)\n⊢ Odd (Nat.card V)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 141,
"column": 2
} | {
"line": 141,
"column": 68
} | {
"line": 143,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhodd : Odd (Nat.card V)\n⊢ 0 < (⊤.deleteVerts ∅).coe.oddComponents.ncard",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instNontrivial",
"co... | [] | exact ((odd_ncard_oddComponents _).mpr <| by simpa using hodd).pos | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 172,
"column": 42
} | {
"line": 173,
"column": 9
} | {
"line": 173,
"column": 10
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfectMat... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfectMatching\nhM1xb... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Tiling.Tile | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 49
} | {
"line": 242,
"column": 50
} | [
{
"pp": "G : Type u_1\nX : Type u_2\nιₚ : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G X\nps : Protoset G X ιₚ\ng : G\npt : PlacedTile ps\na b : G\nr : a⁻¹ * b ∈ Subgroup.map (MulAction.stabilizer G ↑(↑ps pt.index)).subtype (↑ps pt.index).symmetries\n⊢ { index := pt.index, groupElts := ↑(g * a) }.groupElts ≍... | [
"G : Type u_1\nX : Type u_2\nιₚ : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G X\nps : Protoset G X ιₚ\ng : G\npt : PlacedTile ps\na b : G\nr : a⁻¹ * b ∈ Subgroup.map (MulAction.stabilizer G ↑(↑ps pt.index)).subtype (↑ps pt.index).symmetries\n⊢ ∃ (x : (a⁻¹ * b) • ↑(↑ps pt.index) = ↑(↑ps pt.index)), ⟨a⁻¹ * b, ⋯⟩ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Young.SemistandardTableau | {
"line": 71,
"column": 4
} | {
"line": 73,
"column": 9
} | {
"line": 75,
"column": 0
} | [
{
"pp": "μ : YoungDiagram\nT T' : SemistandardYoungTableau μ\nh : T.entry = T'.entry\n⊢ T = T'",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"YoungDiagram",
"SemistandardYoungTableau.mk",
"Membership.mem",
"Eq.rec",
"Prod.mk",
"instOfNatNat",
"LE... | [] | cases T
cases T'
congr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Young.SemistandardTableau | {
"line": 71,
"column": 4
} | {
"line": 73,
"column": 9
} | {
"line": 75,
"column": 0
} | [
{
"pp": "μ : YoungDiagram\nT T' : SemistandardYoungTableau μ\nh : T.entry = T'.entry\n⊢ T = T'",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"YoungDiagram",
"SemistandardYoungTableau.mk",
"Membership.mem",
"Eq.rec",
"Prod.mk",
"instOfNatNat",
"LE... | [] | cases T
cases T'
congr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.Young.YoungDiagram | {
"line": 450,
"column": 2
} | {
"line": 450,
"column": 54
} | {
"line": 450,
"column": 55
} | [
{
"pp": "μ : YoungDiagram\ni j : ℕ\n⊢ (∃ (_ : i < μ.colLen 0), j < μ.rowLen i) ↔ (i, j) ∈ μ",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self._simp_1_4",
"YoungDiagram",... | [
"μ : YoungDiagram\ni j : ℕ\n⊢ j < μ.rowLen i → 0 < μ.rowLen i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.Basic | {
"line": 366,
"column": 42
} | {
"line": 366,
"column": 66
} | {
"line": 366,
"column": 66
} | [
{
"pp": "⊢ Primrec₂ Nat.pair",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.Primrec",
"Denumerable.prod",
"Equiv.instEquivLike",
"congrArg",
"Primcodable.ofDenumerable",
"Nat.unpair",
"Option.some",
"Option.encodable",
... | [
"⊢ Nat.Primrec fun n ↦ n + 1"
] | simp [Primrec₂, Primrec] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 227,
"column": 4
} | {
"line": 227,
"column": 87
} | {
"line": 227,
"column": 87
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfectMat... | [
"case refine_1\nV : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfect... | refine ⟨x', hx', p'.takeUntil x' hx'p, hp'.1.isPath_takeUntil hx'p, ?_, fun h ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.Primrec.Basic | {
"line": 608,
"column": 2
} | {
"line": 608,
"column": 32
} | {
"line": 608,
"column": 33
} | [
{
"pp": "α : Type u_1\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable σ\nc : α → Prop\ninst✝ : DecidablePred c\nf g : α → σ\nhc : PrimrecPred c\nhf : Primrec f\nhg : Primrec g\n⊢ Primrec fun a ↦ if c a then f a else g a",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"us... | [
"α : Type u_1\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable σ\nc : α → Prop\ninst✝ : DecidablePred c\nf g : α → σ\nhc : PrimrecPred c\nhf : Primrec f\nhg : Primrec g\n⊢ Primrec fun a ↦ if c a then f a else g a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.Basic | {
"line": 665,
"column": 10
} | {
"line": 665,
"column": 21
} | {
"line": 665,
"column": 22
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\np : α → β → Prop\ninst✝ : DecidableRel p\nhp : PrimrecRel p\nf : α → β\nhf : Primrec f\n⊢ PrimrecPred fun a ↦ (fun b ↦ decide (p a b)) (f a) = true",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\np : α → β → Prop\ninst✝ : DecidableRel p\nhp : PrimrecRel p\nf : α → β\nhf : Primrec f\n⊢ PrimrecPred fun a ↦ p a (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.Basic | {
"line": 839,
"column": 20
} | {
"line": 839,
"column": 31
} | {
"line": 839,
"column": 32
} | [
{
"pp": "α : Type u_1\ninst✝ : Primcodable α\n⊢ PrimrecPred fun p ↦ (fun a ↦ decide (encode a = p.1)) p.2 = true",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Primcodable.ofDenumerable",
"id",
"Prod.fst",
"Primcodable.prod",
... | [
"α : Type u_1\ninst✝ : Primcodable α\n⊢ PrimrecPred fun p ↦ encode p.2 = p.1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 76,
"column": 10
} | {
"line": 76,
"column": 17
} | {
"line": 77,
"column": 10
} | [
{
"pp": "case inr.inl\np : ℕ →. Bool\nm : ℕ\nIH : (y : ℕ) → lbp p y m → (∀ n < y, false ∈ p n) → { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }\nal : ∀ n < m, false ∈ p n\nn : ℕ\nh₁ : true ∈ p n\nh₂ : ∀ k < n, (p k).Dom\nh₃ : m = n\n⊢ (p m).Dom",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": ... | [
"case inr.inl\np : ℕ →. Bool\nm : ℕ\nIH : (y : ℕ) → lbp p y m → (∀ n < y, false ∈ p n) → { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }\nal : ∀ n < m, false ∈ p n\nn : ℕ\nh₁ : true ∈ p n\nh₂ : ∀ k < n, (p k).Dom\nh₃ : m = n\n⊢ (p n).Dom"
] | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Computability.Partrec | {
"line": 147,
"column": 23
} | {
"line": 147,
"column": 34
} | {
"line": 147,
"column": 35
} | [
{
"pp": "α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\n⊢ true ∈ (fun n ↦ ↑(Option.some (f n).isSome)) (Nat.find h')",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Part.some",
... | [
"α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\n⊢ (f (Nat.find h')).isSome = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 15
} | {
"line": 150,
"column": 16
} | [
{
"pp": "α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\nfd : (rfind fun n ↦ ↑(Option.some (f n).isSome)).Dom\nthis : true ∈ ↑(Option.some (f ((rfind fun n ↦ ↑(Option.some (f n).isSome)).get fd)).isSome)\n⊢ ((fun b ↦ (fun n ↦ ↑(f n)) ((rfin... | [
"α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\nfd : (rfind fun n ↦ ↑(Option.some (f n).isSome)).Dom\nthis : true ∈ ↑(Option.some (f ((rfind fun n ↦ ↑(Option.some (f n).isSome)).get fd)).isSome)\n⊢ (f ((rfind fun n ↦ Part.some (f n).isSome).ge... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 341,
"column": 39
} | {
"line": 341,
"column": 50
} | {
"line": 341,
"column": 51
} | [
{
"pp": "β : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝¹ : DecidableE... | [
"β : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝¹ : DecidableEq β\nmapGrap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 32
} | {
"line": 413,
"column": 33
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α →. β\ng : α → β → σ\nhf : Partrec f\nhg : Computable₂ g\n⊢ Partrec fun a ↦ Part.map (g a) (f a)",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α →. β\ng : α → β → σ\nhf : Partrec f\nhg : Computable₂ g\n⊢ Partrec fun a ↦ Part.map (g a) (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 346,
"column": 41
} | {
"line": 346,
"column": 52
} | {
"line": 346,
"column": 53
} | [
{
"pp": "β : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝ : DecidableEq... | [
"β : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝ : DecidableEq β\nmapGraph... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 348,
"column": 10
} | {
"line": 348,
"column": 46
} | {
"line": 348,
"column": 47
} | [
{
"pp": "case cons\nβ : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝ : ... | [
"case cons\nβ : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝ : DecidableEq ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 354,
"column": 22
} | {
"line": 354,
"column": 41
} | {
"line": 354,
"column": 42
} | [
{
"pp": "case zero\nβ : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝ : ... | [
"case zero\nβ : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\nthis✝ : DecidableEq ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 532,
"column": 27
} | {
"line": 532,
"column": 49
} | {
"line": 532,
"column": 50
} | [
{
"pp": "α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\nh : Nat.Partrec fun n ↦ (↑(decode₂ α n)).bind fun a ↦ Part.map encode (f a)\n⊢ Partrec fun a ↦ Part.map encode (f a)",
"ppTerm": "?m.94",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\nh : Nat.Partrec fun n ↦ (↑(decode₂ α n)).bind fun a ↦ Part.map encode (f a)\n⊢ Partrec fun a ↦ Part.map encode (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 539,
"column": 28
} | {
"line": 539,
"column": 39
} | {
"line": 539,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝ : Primcodable α\nn : ℕ\n⊢ Primrec fun a ↦ (a.1 ::ᵥ a.2).toList",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.Vector",
"id",
"Primcodable.vector",
"List.Vector.toList_cons",
"Prod.fst",
... | [
"α : Type u_1\ninst✝ : Primcodable α\nn : ℕ\n⊢ Primrec fun a ↦ a.1 :: a.2.toList"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 559,
"column": 4
} | {
"line": 559,
"column": 15
} | {
"line": 559,
"column": 16
} | [
{
"pp": "α : Type u_1\nσ : Type u_3\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nn : ℕ\nf : Fin (n + 1) → α → σ\nhf : ∀ (i : Fin (n + 1)), Primrec (f i)\n⊢ Primrec fun a ↦ List.ofFn fun i ↦ f i a",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1"... | [
"α : Type u_1\nσ : Type u_3\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nn : ℕ\nf : Fin (n + 1) → α → σ\nhf : ∀ (i : Fin (n + 1)), Primrec (f i)\n⊢ Primrec fun a ↦ f 0 a :: List.ofFn fun i ↦ f i.succ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 664,
"column": 2
} | {
"line": 664,
"column": 13
} | {
"line": 664,
"column": 14
} | [
{
"pp": "f : ℕ → ℕ → ℕ\nhf : Primrec' fun v ↦ f v.head v.tail.head\nn : ℕ\ng h : List.Vector ℕ n → ℕ\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ f (g v) (h v)",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℕ → ℕ → ℕ\nhf : Primrec' fun v ↦ f v.head v.tail.head\nn : ℕ\ng h : List.Vector ℕ n → ℕ\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ f (g v) (h v)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 668,
"column": 2
} | {
"line": 668,
"column": 13
} | {
"line": 668,
"column": 14
} | [
{
"pp": "n : ℕ\nf g : List.Vector ℕ n → ℕ\nh : List.Vector ℕ (n + 2) → ℕ\nhf : Primrec' f\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ Nat.rec (g v) (fun y IH ↦ h (y ::ᵥ IH ::ᵥ v)) (f v)",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"n : ℕ\nf g : List.Vector ℕ n → ℕ\nh : List.Vector ℕ (n + 2) → ℕ\nhf : Primrec' f\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ Nat.rec (g v) (fun y IH ↦ h (y ::ᵥ IH ::ᵥ v)) (f v)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 681,
"column": 2
} | {
"line": 681,
"column": 13
} | {
"line": 681,
"column": 14
} | [
{
"pp": "this : Primrec' fun v ↦ (fun a b ↦ b - a) v.head v.tail.head\n⊢ Primrec' fun v ↦ v.head - v.tail.head",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"this : Primrec' fun v ↦ (fun a b ↦ b - a) v.head v.tail.head\n⊢ Primrec' fun v ↦ v.head - v.tail.head"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 760,
"column": 8
} | {
"line": 760,
"column": 23
} | {
"line": 760,
"column": 24
} | [
{
"pp": "case refine_2.inl.refine_1\nα : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂✝ : b ∈ f.fix a₂\nIH :\n ... | [
"case refine_2.inl.refine_1\nα : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂✝ : b ∈ f.fix a₂\nIH :\n ∀ (a'' : α),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 754,
"column": 4
} | {
"line": 754,
"column": 15
} | {
"line": 755,
"column": 6
} | [
{
"pp": "case prec\nn : ℕ\nf✝¹ : List.Vector ℕ n → ℕ\nf f✝ g✝ : ℕ → ℕ\na✝¹ : Nat.Primrec f✝\na✝ : Nat.Primrec g✝\nhf : Primrec' fun v ↦ f✝ v.head\nhg : Primrec' fun v ↦ g✝ v.head\n⊢ Primrec' fun v ↦ unpaired (fun z n ↦ Nat.rec (f✝ z) (fun y IH ↦ g✝ (pair z (pair y IH))) n) v.head",
"ppTerm": "?prec",
"a... | [
"case prec\nn : ℕ\nf✝¹ : List.Vector ℕ n → ℕ\nf f✝ g✝ : ℕ → ℕ\na✝¹ : Nat.Primrec f✝\na✝ : Nat.Primrec g✝\nhf : Primrec' fun v ↦ f✝ v.head\nhg : Primrec' fun v ↦ g✝ v.head\n⊢ Primrec' fun v ↦ Nat.rec (f✝ (unpair v.head).1) (fun y IH ↦ g✝ (pair (unpair v.head).1 (pair y IH))) (unpair v.head).2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 774,
"column": 15
} | {
"line": 774,
"column": 26
} | {
"line": 774,
"column": 27
} | [
{
"pp": "m n : ℕ\nf : List.Vector ℕ m → List.Vector ℕ n\nh : Vec f\n⊢ Primrec f",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : List.Vector ℕ m → List.Vector ℕ n\nh : Vec f\n⊢ Primrec f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 762,
"column": 33
} | {
"line": 762,
"column": 48
} | {
"line": 762,
"column": 49
} | [
{
"pp": "α : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂ : b ∈ f.fix a₂\nIH :\n ∀ (a'' : α),\n Sum.inr a''... | [
"α : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂ : b ∈ f.fix a₂\nIH :\n ∀ (a'' : α),\n Sum.inr a'' ∈ f a₂ →\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 125,
"column": 23
} | {
"line": 125,
"column": 34
} | {
"line": 125,
"column": 35
} | [
{
"pp": "n₁ n₂ : ℕ\nh : n₁ < n₂\n⊢ ack 0 n₁ < ack 0 n₂",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Eq.mpr",
"ack",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeft... | [
"n₁ n₂ : ℕ\nh : n₁ < n₂\n⊢ n₁ < n₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 157,
"column": 19
} | {
"line": 157,
"column": 30
} | {
"line": 157,
"column": 31
} | [
{
"pp": "m : ℕ\n⊢ m + 1 + 0 < ack (m + 1) 0",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"AddMonoid.toAddZeroClass",
"ack_succ_zero",
"Nat.instAddMonoid",
"id",
"instOfNatNat",
"instHAdd",
"HAdd.hAd... | [
"m : ℕ\n⊢ m + 1 < ack m 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 179,
"column": 32
} | {
"line": 179,
"column": 43
} | {
"line": 179,
"column": 44
} | [
{
"pp": "m : ℕ\n_h : 0 < m + 1\n⊢ ack 0 0 < ack (m + 1) 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"AddMonoid.toAddZeroClass",
"ack_succ_zero",
"Nat.instAddMonoid",
"id",
"instOfNatNat",
"zero_add",
... | [
"m : ℕ\n_h : 0 < m + 1\n⊢ 1 < ack m 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 187,
"column": 4
} | {
"line": 187,
"column": 15
} | {
"line": 187,
"column": 16
} | [
{
"pp": "m₁ m₂ : ℕ\nh : m₁ + 1 < m₂ + 1\n⊢ ack (m₁ + 1) 0 < ack (m₂ + 1) 0",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"ack_succ_zero",
"id",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"congr"... | [
"m₁ m₂ : ℕ\nh : m₁ + 1 < m₂ + 1\n⊢ ack m₁ 1 < ack m₂ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 236,
"column": 15
} | {
"line": 236,
"column": 26
} | {
"line": 236,
"column": 27
} | [
{
"pp": "n : ℕ\n⊢ (ack 0 n + 1) ^ 2 ≤ ack (0 + 3) n",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"Nat.instAddMonoid",
"ack_three",
"id",
"i... | [
"n : ℕ\n⊢ (n + 1 + 1) ^ 2 ≤ 2 ^ (n + 3) - 3"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 780,
"column": 29
} | {
"line": 780,
"column": 44
} | {
"line": 780,
"column": 45
} | [
{
"pp": "α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ ⊕ α\nhf : Partrec f\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nhF : Partrec₂ F\np : α → ℕ → Part Bool := fun a n ↦ Part.ma... | [
"α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ ⊕ α\nhf : Partrec f\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nhF : Partrec₂ F\np : α → ℕ → Part Bool := fun a n ↦ Part.map (fun s ↦ S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 312,
"column": 8
} | {
"line": 313,
"column": 26
} | {
"line": 314,
"column": 8
} | [
{
"pp": "case inl\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : ?m.338 < m\n⊢ ack (b + 4) (max m (pair n (rec (f m) (fun y IH ↦ g... | [
"case inr\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : m ≤ pair n (rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n)\n⊢ ack (b + 4) (... | · rw [max_eq_left h₁.le]
gcongr <;> omega | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.Ackermann | {
"line": 319,
"column": 10
} | {
"line": 322,
"column": 57
} | {
"line": 323,
"column": 8
} | [
{
"pp": "case inr.inl\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : m ≤ pair n (rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n)\... | [] | rw [max_eq_left h₂.le, add_assoc]
exact
ack_le_ack (Nat.add_le_add (le_max_right a b) <| by simp)
((le_succ n).trans <| self_le_add_left _ _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.Ackermann | {
"line": 319,
"column": 10
} | {
"line": 322,
"column": 57
} | {
"line": 323,
"column": 8
} | [
{
"pp": "case inr.inl\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : m ≤ pair n (rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n)\... | [] | rw [max_eq_left h₂.le, add_assoc]
exact
ack_le_ack (Nat.add_le_add (le_max_right a b) <| by simp)
((le_succ n).trans <| self_le_add_left _ _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 289,
"column": 10
} | {
"line": 289,
"column": 39
} | {
"line": 289,
"column": 40
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\nh' : ∀ (K : Gmax.deleteUniver... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\nh' : ∀ (K : Gmax.deleteUniversalVerts.coe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 113,
"column": 19
} | {
"line": 113,
"column": 77
} | {
"line": 114,
"column": 6
} | [
{
"pp": "f : ℝ → ℝ\nhf✝ : GrowsPolynomially f\nhf' : ∀ (a : ℝ), ∃ b, a ≤ b ∧ f b = 0\nc₁ : ℝ\nhc₁_mem : c₁ > 0\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhf : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nx : ℝ\nhx : ∀ (y : ℝ), x ≤ y → ∀ u ∈ Set.Icc (1 / 2 * y) y, f u ∈ Set.Icc (c₁ * f ... | [] | by simp only [neg_add, ← sub_eq_add_neg] at hz; exact hz.2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 302,
"column": 6
} | {
"line": 302,
"column": 47
} | {
"line": 302,
"column": 48
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\nhc : ¬Fintype.card ↑Gmax.univ... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\nhc : ¬Fintype.card ↑Gmax.universalVerts <... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 13
} | {
"line": 130,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\n⊢ ∀ᶠ (x : ℕ) in atTop, ‖↑(r i x) - b i * ↑x‖ ≤ ↑x / log ↑x ^ 2",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"Norm.norm",
... | [
"α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\n⊢ ∃ a, ∀ (b_1 : ℕ), a ≤ b_1 → |↑(r i b_1) - b i * ↑b_1| ≤ ↑b_1 / log ↑b_1 ^ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 15
} | {
"line": 94,
"column": 16
} | [
{
"pp": "p x : ℝ\nhx : 1 < x\nhderiv : deriv (fun x ↦ 1 - ε x) x = x⁻¹ / log x ^ 2\n⊢ deriv (fun x ↦ x ^ p) x * (1 - ε x) + x ^ p * deriv (fun x ↦ 1 - ε x) x =\n p * x ^ (p - 1) * (1 - ε x) + x ^ p * (x⁻¹ / log x ^ 2)",
"ppTerm": "?m.399",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"p x : ℝ\nhx : 1 < x\nhderiv : deriv (fun x ↦ 1 - ε x) x = x⁻¹ / log x ^ 2\n⊢ deriv (fun x ↦ x ^ p) x * (1 - ε x) + x ^ p * (x⁻¹ / log x ^ 2) =\n p * x ^ (p - 1) * (1 - ε x) + x ^ p * (x⁻¹ / log x ^ 2)"
] | hderiv, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 51
} | {
"line": 226,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nq : ℝ → ℝ\nhq_diff : DifferentiableOn ℝ q (Set.Ioi 1)\nhq_poly : GrowsPolynomially fun x ↦ ‖deriv q x‖\ni : α\nb' : ℝ := b (min_bi b) / 2\nhb_pos : 0 < b'\nhb_lt_on... | [
"α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nq : ℝ → ℝ\nhq_diff : DifferentiableOn ℝ q (Set.Ioi 1)\nhq_poly : GrowsPolynomially fun x ↦ ‖deriv q x‖\ni : α\nb' : ℝ := b (min_bi b) / 2\nhb_pos : 0 < b'\nhb_lt_one : b' < 1\n... | have hb : b' ∈ Set.Ioo 0 1 := ⟨hb_pos, hb_lt_one⟩ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 219,
"column": 93
} | {
"line": 248,
"column": 33
} | {
"line": 250,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nq : ℝ → ℝ\nhq_diff : DifferentiableOn ℝ q (Set.Ioi 1)\nhq_poly : GrowsPolynomially fun x ↦ ‖deriv q x‖\ni : α\n⊢ (fun n ↦ q ↑(r i n) - q (b i * ↑n)) =O[atTop] fun n... | [] | by
let b' := b (min_bi b) / 2
have hb_pos : 0 < b' := by have := R.b_pos (min_bi b); positivity
have hb_lt_one : b' < 1 := calc b (min_bi b) / 2
_ < b (min_bi b) := div_two_lt_of_pos (R.b_pos (min_bi b))
_ < 1 := R.b_lt_one (min_bi b)
have hb : b' ∈ Set.Ioo 0 1 := ⟨hb_pos, hb_lt_one⟩
have hb' (i) : b'... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 169,
"column": 4
} | {
"line": 169,
"column": 49
} | {
"line": 170,
"column": 4
} | [
{
"pp": "f : ℝ → ℝ\nhf : GrowsPolynomially f\nc₁ : ℝ\nleft✝¹ : c₁ > 0\nc₂ : ℝ\nleft✝ : c₂ > 0\nh : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhlt : c₁ < c₂\nx : ℝ\nhx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhx_nonneg : 0 ≤ x\nh' : 3 / 4 * x... | [
"f : ℝ → ℝ\nhf : GrowsPolynomially f\nc₁ : ℝ\nleft✝¹ : c₁ > 0\nc₂ : ℝ\nleft✝ : c₂ > 0\nh : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhlt : c₁ < c₂\nx : ℝ\nhx : ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nhx_nonneg : 0 ≤ x\nh' : 3 / 4 * x ∈ Set.Icc (... | have hu' : 0 ≤ (c₂ - c₁) * f x := by linarith | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 467,
"column": 56
} | {
"line": 467,
"column": 84
} | {
"line": 469,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\n⊢ (fun n ↦ -log (b i) / (log ↑n * log ↑n)) = fun n ↦ -log (b i) / log ↑n ^ 2",
"ppTerm": "?m.187",
"assigned": true,
"usedConstants": [
"Eq... | [] | ext; congr 1; rw [← pow_two] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 467,
"column": 56
} | {
"line": 467,
"column": 84
} | {
"line": 469,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\n⊢ (fun n ↦ -log (b i) / (log ↑n * log ↑n)) = fun n ↦ -log (b i) / log ↑n ^ 2",
"ppTerm": "?m.187",
"assigned": true,
"usedConstants": [
"Eq... | [] | ext; congr 1; rw [← pow_two] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.PartrecCode | {
"line": 421,
"column": 2
} | {
"line": 428,
"column": 52
} | {
"line": 429,
"column": 2
} | [
{
"pp": "α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nc : α → Code\nhc : Computable c\nz : α → σ\nhz : Computable z\ns : α → σ\nhs : Computable s\nl : α → σ\nhl : Computable l\nr : α → σ\nhr : Computable r\npr : α → Code × Code × σ × σ → σ\nhpr : Computable₂ pr\nco : α → Code × Cod... | [
"α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nc : α → Code\nhc : Computable c\nz : α → σ\nhz : Computable z\ns : α → σ\nhs : Computable s\nl : α → σ\nhl : Computable l\nr : α → σ\nhr : Computable r\npr : α → Code × Code × σ × σ → σ\nhpr : Computable₂ pr\nco : α → Code × Code × σ × σ → ... | have : Computable₂ G := .mk <|
nat_casesOn (list_length.comp snd) (option_some_iff.2 (hz.comp fst)) <| .mk <|
nat_casesOn snd (option_some_iff.2 (hs.comp (fst.comp fst))) <| .mk <|
nat_casesOn snd (option_some_iff.2 (hl.comp (fst.comp <| fst.comp fst))) <| .mk <|
nat_casesOn snd (option_some_iff.2 (hr.c... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 581,
"column": 8
} | {
"line": 584,
"column": 82
} | {
"line": 586,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nn : ℕ\nhn : 0 < n\n⊢ ↑n ^ p a b * (1 + 0) ≤ asympBound g a b n",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"AkraBazziRecurrence.asym... | [] | simp only [asympBound_def']
gcongr n ^ p a b * (1 + ?_)
have := R.g_nonneg
aesop (add safe Real.rpow_nonneg, safe div_nonneg, safe Finset.sum_nonneg) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 581,
"column": 8
} | {
"line": 584,
"column": 82
} | {
"line": 586,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nn : ℕ\nhn : 0 < n\n⊢ ↑n ^ p a b * (1 + 0) ≤ asympBound g a b n",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"AkraBazziRecurrence.asym... | [] | simp only [asympBound_def']
gcongr n ^ p a b * (1 + ?_)
have := R.g_nonneg
aesop (add safe Real.rpow_nonneg, safe div_nonneg, safe Finset.sum_nonneg) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 631,
"column": 14
} | {
"line": 631,
"column": 26
} | {
"line": 631,
"column": 27
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nc₁ : ℝ\nhc₁_mem : c₁ ∈ Set.Ioo 0 1\nhc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁... | [
"α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nc₁ : ℝ\nhc₁_mem : c₁ ∈ Set.Ioo 0 1\nhc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, g... | mul_comm c₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 355,
"column": 14
} | {
"line": 355,
"column": 37
} | {
"line": 356,
"column": 14
} | [
{
"pp": "case hbc\nf g : ℝ → ℝ\nhf✝¹ : GrowsPolynomially f\nhg✝¹ : GrowsPolynomially g\nhf'✝ : 0 ≤ᶠ[atTop] f\nhg'✝ : 0 ≤ᶠ[atTop] g\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nc₁ : ℝ\nhc₁_mem : c₁ > 0\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhf✝ : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nc₃ : ℝ\nhc... | [
"case hbc\nf g : ℝ → ℝ\nhf✝¹ : GrowsPolynomially f\nhg✝¹ : GrowsPolynomially g\nhf'✝ : 0 ≤ᶠ[atTop] f\nhg'✝ : 0 ≤ᶠ[atTop] g\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nc₁ : ℝ\nhc₁_mem : c₁ > 0\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhf✝ : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (b * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nc₃ : ℝ\nhc₃_mem : c₃ >... | · exact min_le_left _ _ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.PartrecCode | {
"line": 547,
"column": 6
} | {
"line": 548,
"column": 29
} | {
"line": 549,
"column": 4
} | [
{
"pp": "case refine_1.comp\nf f✝ g✝ : ℕ →. ℕ\npf : Nat.Partrec f✝\npg : Nat.Partrec g✝\nhf : ∃ c, c.eval = f✝\nhg : ∃ c, c.eval = g✝\n⊢ ∃ c, c.eval = fun n ↦ g✝ n >>= f✝",
"ppTerm": "?refine_1.comp",
"assigned": true,
"usedConstants": [
"Part",
"Nat.Partrec",
"PFun",
"Exists... | [] | rcases hf with ⟨cf, rfl⟩; rcases hg with ⟨cg, rfl⟩
exact ⟨comp cf cg, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.PartrecCode | {
"line": 547,
"column": 6
} | {
"line": 548,
"column": 29
} | {
"line": 549,
"column": 4
} | [
{
"pp": "case refine_1.comp\nf f✝ g✝ : ℕ →. ℕ\npf : Nat.Partrec f✝\npg : Nat.Partrec g✝\nhf : ∃ c, c.eval = f✝\nhg : ∃ c, c.eval = g✝\n⊢ ∃ c, c.eval = fun n ↦ g✝ n >>= f✝",
"ppTerm": "?refine_1.comp",
"assigned": true,
"usedConstants": [
"Part",
"Nat.Partrec",
"PFun",
"Exists... | [] | rcases hf with ⟨cf, rfl⟩; rcases hg with ⟨cg, rfl⟩
exact ⟨comp cf cg, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.PartrecCode | {
"line": 612,
"column": 4
} | {
"line": 612,
"column": 41
} | {
"line": 612,
"column": 42
} | [
{
"pp": "k : ℕ\nc : Code\nn x : ℕ\nh : x ∈ evaln (k + 1) c n\n⊢ ∀ {o : Option ℕ},\n (x ∈ do\n guard (n ≤ k)\n o) →\n n < k + 1",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"guard",
"Eq.mpr",
"instAlternativeOption",
"congrArg",
"Option... | [
"k : ℕ\nc : Code\nn x : ℕ\nh : x ∈ evaln (k + 1) c n\n⊢ n ≤ k → n < k + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 675,
"column": 33
} | {
"line": 675,
"column": 50
} | {
"line": 675,
"column": 50
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nc₁ : ℝ\nhc₁_mem : c₁ ∈ Set.Ioo 0 1\nhc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁... | [
"α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nc₁ : ℝ\nhc₁_mem : c₁ ∈ Set.Ioo 0 1\nhc₁ : ∀ᶠ (n : ℕ) in atTop, ∀ (i : α), c₁ * ↑n ≤ ↑(r i n)\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhc₂ : ∀ᶠ (n : ℕ) in atTop, ∀ u ∈ Set.Icc (c₁ * ↑n) ↑n, c... | have := hc₃_mem.2 | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.PartrecCode | {
"line": 660,
"column": 14
} | {
"line": 660,
"column": 52
} | {
"line": 660,
"column": 53
} | [
{
"pp": "case zero\nk n x : ℕ\nleft✝ : n ≤ k\nh : 0 = x\n⊢ x ∈ pure 0 n",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Part",
"Eq.mpr",
"PFun",
"Monad.toApplicative",
"Membership.mem",
"PFun.monad",
"id",
"Part.instMember... | [
"case zero\nk n x : ℕ\nleft✝ : n ≤ k\nh : 0 = x\n⊢ x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 660,
"column": 14
} | {
"line": 660,
"column": 52
} | {
"line": 660,
"column": 53
} | [
{
"pp": "case succ\nk n x : ℕ\nleft✝ : n ≤ k\nh : n + 1 = x\n⊢ x = n + 1",
"ppTerm": "?succ",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case succ\nk n x : ℕ\nleft✝ : n ≤ k\nh : n + 1 = x\n⊢ x = n + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 660,
"column": 14
} | {
"line": 660,
"column": 52
} | {
"line": 660,
"column": 53
} | [
{
"pp": "case left\nk n x : ℕ\nleft✝ : n ≤ k\nh : (unpair n).1 = x\n⊢ x = (unpair n).1",
"ppTerm": "?left",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case left\nk n x : ℕ\nleft✝ : n ≤ k\nh : (unpair n).1 = x\n⊢ x = (unpair n).1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 660,
"column": 14
} | {
"line": 660,
"column": 52
} | {
"line": 660,
"column": 53
} | [
{
"pp": "case right\nk n x : ℕ\nleft✝ : n ≤ k\nh : (unpair n).2 = x\n⊢ x = (unpair n).2",
"ppTerm": "?right",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case right\nk n x : ℕ\nleft✝ : n ≤ k\nh : (unpair n).2 = x\n⊢ x = (unpair n).2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 681,
"column": 18
} | {
"line": 681,
"column": 34
} | {
"line": 681,
"column": 35
} | [
{
"pp": "k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn x : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : m = 0\nh₂ : (unpair n).2 = x\n⊢ 0 ∈ cf.eval (Nat.pair (unpair n).1 (0 + (unpair n).2))",
"ppTerm": "?m.420",
"assigned": true,
"usedConstants": [... | [
"k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn x : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : m = 0\nh₂ : (unpair n).2 = x\n⊢ 0 ∈ cf.eval n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 686,
"column": 22
} | {
"line": 686,
"column": 59
} | {
"line": 686,
"column": 60
} | [
{
"pp": "k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : ¬m = 0\ny : ℕ\nhy₁ : 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + ((unpair n).2 + 1)))\nhy₂ : ∀ {m : ℕ}, m < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m + ((unpair ... | [
"k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : ¬m = 0\ny : ℕ\nhy₁ : 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + ((unpair n).2 + 1)))\nhy₂ : ∀ {m : ℕ}, m < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m + ((unpair n).2 + 1))),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 689,
"column": 23
} | {
"line": 689,
"column": 34
} | {
"line": 689,
"column": 35
} | [
{
"pp": "k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : ¬m = 0\ny : ℕ\nhy₁ : 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + ((unpair n).2 + 1)))\nhy₂ : ∀ {m : ℕ}, m < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m + ((unpair ... | [
"k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : ¬m = 0\ny : ℕ\nhy₁ : 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + ((unpair n).2 + 1)))\nhy₂ : ∀ {m : ℕ}, m < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m + ((unpair n).2 + 1))),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 691,
"column": 23
} | {
"line": 691,
"column": 60
} | {
"line": 691,
"column": 61
} | [
{
"pp": "k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : ¬m = 0\ny : ℕ\nhy₁ : 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + ((unpair n).2 + 1)))\nhy₂ : ∀ {m : ℕ}, m < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m + ((unpair ... | [
"k : ℕ\ncf : Code\nhf : ∀ (n x : ℕ), x ∈ evaln (k + 1) cf n → x ∈ cf.eval n\nn : ℕ\nleft✝ : n ≤ k\nm : ℕ\nh₁ : evaln (k + 1) cf n = some m\nm0 : ¬m = 0\ny : ℕ\nhy₁ : 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + ((unpair n).2 + 1)))\nhy₂ : ∀ {m : ℕ}, m < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m + ((unpair n).2 + 1))),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 720,
"column": 4
} | {
"line": 720,
"column": 38
} | {
"line": 720,
"column": 39
} | [
{
"pp": "case prec\ncf cg : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nhg : ∀ {n x : ℕ}, x ∈ cg.eval n → ∃ k, x ∈ evaln (k + 1) cg n\nn x n₁ n₂ : ℕ\n⊢ x ∈ Nat.rec (cf.eval n₁) (fun y IH ↦ IH.bind fun i ↦ cg.eval (Nat.pair n₁ (Nat.pair y i))) n₂ →\n ∃ k,\n n ≤ k ∧\n Nat.r... | [] | induction n₂ generalizing x n with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Computability.PartrecCode | {
"line": 753,
"column": 27
} | {
"line": 753,
"column": 85
} | {
"line": 753,
"column": 86
} | [
{
"pp": "cf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (Nat.pair (unp... | [
"cf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (Nat.pair (unpair n).1 m)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 755,
"column": 10
} | {
"line": 755,
"column": 68
} | {
"line": 756,
"column": 12
} | [
{
"pp": "cf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (Nat.pair (unp... | [
"cf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (Nat.pair (unpair n).1 m)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 763,
"column": 6
} | {
"line": 763,
"column": 47
} | {
"line": 764,
"column": 8
} | [
{
"pp": "case right\ncf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (N... | [
"case right\ncf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (Nat.pair (unp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Language | {
"line": 260,
"column": 10
} | {
"line": 260,
"column": 25
} | {
"line": 260,
"column": 25
} | [
{
"pp": "case succ.mpr.cons.refl\nα : Type u_1\nl : Language α\na : List α\nS : List (List α)\nhS : ∀ y ∈ a :: S, y ∈ l\nihn : ∀ {x : List α}, x ∈ l ^ S.length ↔ ∃ S_1, x = S_1.flatten ∧ S_1.length = S.length ∧ ∀ y ∈ S_1, y ∈ l\n⊢ ∃ a_1 ∈ l, ∃ b, (∃ S_1, b = S_1.flatten ∧ S_1.length = S.length ∧ ∀ y ∈ S_1, y ∈ ... | [
"case succ.mpr.cons.refl\nα : Type u_1\nl : Language α\na : List α\nS : List (List α)\nhS : a ∈ l ∧ ∀ x ∈ S, x ∈ l\nihn : ∀ {x : List α}, x ∈ l ^ S.length ↔ ∃ S_1, x = S_1.flatten ∧ S_1.length = S.length ∧ ∀ y ∈ S_1, y ∈ l\n⊢ ∃ a_1 ∈ l, ∃ b, (∃ S_1, b = S_1.flatten ∧ S_1.length = S.length ∧ ∀ y ∈ S_1, y ∈ l) ∧ a_1 ... | forall_mem_cons | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Computability.Language | {
"line": 308,
"column": 4
} | {
"line": 320,
"column": 58
} | {
"line": 321,
"column": 4
} | [
{
"pp": "case a\nα : Type u_1\nl m n : Language α\nhm : [] ∉ m\nh : l = m * l + n\n⊢ l ≤ m∗ * n",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"MulOne.toOne",
"Semigroup.toMul",
"Language.instOne",
"HMul.hMul",
"Language.instAdd... | [
"case a\nα : Type u_1\nl m n : Language α\nhm : [] ∉ m\nh : l = m * l + n\n⊢ m∗ * n ≤ l"
] | · intro x hx
induction hlen : x.length using Nat.strong_induction_on generalizing x with | _ _ ih
subst hlen
rw [h] at hx
obtain hx | hx := hx
· obtain ⟨a, ha, b, hb, rfl⟩ := mem_mul.mp hx
rw [length_append] at ih
have hal : 0 < a.length := length_pos_iff.mpr <| ne_of_mem_o... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.ContextFreeGrammar | {
"line": 71,
"column": 2
} | {
"line": 78,
"column": 8
} | {
"line": 80,
"column": 0
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nu v : List (Symbol T N)\nhr : r.Rewrites u v\n⊢ ∃ p q, u = p ++ [Symbol.nonterminal r.input] ++ q ∧ v = p ++ r.output ++ q",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"ContextFreeRule.Rewrites",
"Symbol",
"... | [] | induction hr with
| head s =>
use [], s
simp
| cons x _ ih =>
rcases ih with ⟨p', q', rfl, rfl⟩
use x :: p', q'
simp | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Computability.ContextFreeGrammar | {
"line": 71,
"column": 2
} | {
"line": 78,
"column": 8
} | {
"line": 80,
"column": 0
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nu v : List (Symbol T N)\nhr : r.Rewrites u v\n⊢ ∃ p q, u = p ++ [Symbol.nonterminal r.input] ++ q ∧ v = p ++ r.output ++ q",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"ContextFreeRule.Rewrites",
"Symbol",
"... | [] | induction hr with
| head s =>
use [], s
simp
| cons x _ ih =>
rcases ih with ⟨p', q', rfl, rfl⟩
use x :: p', q'
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.ContextFreeGrammar | {
"line": 71,
"column": 2
} | {
"line": 78,
"column": 8
} | {
"line": 80,
"column": 0
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nu v : List (Symbol T N)\nhr : r.Rewrites u v\n⊢ ∃ p q, u = p ++ [Symbol.nonterminal r.input] ++ q ∧ v = p ++ r.output ++ q",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"ContextFreeRule.Rewrites",
"Symbol",
"... | [] | induction hr with
| head s =>
use [], s
simp
| cons x _ ih =>
rcases ih with ⟨p', q', rfl, rfl⟩
use x :: p', q'
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.ContextFreeGrammar | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 13
} | {
"line": 81,
"column": 14
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\n⊢ r.Rewrites [Symbol.nonterminal r.input] r.output",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\n⊢ r.Rewrites [Symbol.nonterminal r.input] r.output"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.ContextFreeGrammar | {
"line": 268,
"column": 23
} | {
"line": 268,
"column": 34
} | {
"line": 268,
"column": 35
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\ns : List (Symbol T N)\n⊢ r.reverse.Rewrites (Symbol.nonterminal r.input :: s).reverse (r.output ++ s).reverse",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"ContextFreeRule.Rewrites",
"Eq.mpr",
"Symbol",
... | [
"T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\ns : List (Symbol T N)\n⊢ r.reverse.Rewrites (s.reverse ++ [Symbol.nonterminal r.input]) (s.reverse ++ r.output.reverse)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.ContextFreeGrammar | {
"line": 269,
"column": 36
} | {
"line": 269,
"column": 47
} | {
"line": 269,
"column": 48
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nx : Symbol T N\nu v : List (Symbol T N)\nh : r.Rewrites u v\n⊢ r.reverse.Rewrites (x :: u).reverse (x :: v).reverse",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"ContextFreeRule.Rewrites",
"Eq.mpr",
"Symbol"... | [
"T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nx : Symbol T N\nu v : List (Symbol T N)\nh : r.Rewrites u v\n⊢ r.reverse.Rewrites (u.reverse ++ [x]) (v.reverse ++ [x])"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.ContextFreeGrammar | {
"line": 272,
"column": 14
} | {
"line": 272,
"column": 25
} | {
"line": 272,
"column": 26
} | [
{
"pp": "T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nu v : List (Symbol T N)\nh : r.reverse.Rewrites u.reverse v.reverse\n⊢ r.Rewrites u v",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"T : Type u_1\nN : Type u_2\nr : ContextFreeRule T N\nu v : List (Symbol T N)\nh : r.reverse.Rewrites u.reverse v.reverse\n⊢ r.Rewrites u v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.ContextFreeGrammar | {
"line": 350,
"column": 2
} | {
"line": 350,
"column": 13
} | {
"line": 350,
"column": 14
} | [
{
"pp": "T : Type u_1\nL : Language T\nh : L.reverse.IsContextFree\n⊢ L.IsContextFree",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"T : Type u_1\nL : Language T\nh : L.reverse.IsContextFree\n⊢ L.IsContextFree"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecCode | {
"line": 921,
"column": 4
} | {
"line": 921,
"column": 15
} | {
"line": 921,
"column": 16
} | [
{
"pp": "case neg\nk : ℕ\nc : Code\nn : ℕ\nkn : ¬n < k\n⊢ (List.range k).length ≤ n",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.length_range",
"id",
"List.range",
"LE.le",
"instLENat",
"Nat",
"congrFun'",... | [
"case neg\nk : ℕ\nc : Code\nn : ℕ\nkn : ¬n < k\n⊢ k ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Size | {
"line": 80,
"column": 94
} | {
"line": 88,
"column": 72
} | {
"line": 88,
"column": 72
} | [
{
"pp": "m n : ℕ\nh : m < 2 ^ n\n⊢ m.size ≤ n",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Nat.bit",
"instPowNat",
"Eq.mpr",
"congrArg",
"False.elim",
"Eq.mp",
"id",
"Nat.binaryRec'",
"Ne",
"instOfNatNat",
"LE.le",
... | [] | by
induction m using binaryRec' generalizing n with
| zero => simp
| bit b m e IH =>
rw [← Nat.bit_ne_zero_iff] at e
rw [size_bit e]
cases n with
| zero => exact (e (Nat.lt_one_iff.mp h)).elim
| succ n => exact succ_le_succ (IH (bit_lt_two_pow_succ_iff.mp h)) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Size | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 58
} | {
"line": 96,
"column": 59
} | [
{
"pp": "n : ℕ\n⊢ n.size = 0 ↔ n = 0",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\n⊢ n.size = 0 ↔ n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Size | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 42
} | {
"line": 99,
"column": 43
} | [
{
"pp": "n : ℕ\n⊢ (2 ^ n).size = n + 1",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\n⊢ (2 ^ n).size = n + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Bitwise | {
"line": 158,
"column": 25
} | {
"line": 158,
"column": 36
} | {
"line": 158,
"column": 37
} | [
{
"pp": "b : Bool\nn : ℕ\nhn : (∀ (i : ℕ), n.testBit i = false) → n = 0\nh : ∀ (i : ℕ), (bit b n).testBit i = false\n⊢ b = false",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"b : Bool\nn : ℕ\nhn : (∀ (i : ℕ), n.testBit i = false) → n = 0\nh : ∀ (i : ℕ), (bit b n).testBit i = false\n⊢ b = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Bitwise | {
"line": 312,
"column": 2
} | {
"line": 312,
"column": 38
} | {
"line": 313,
"column": 2
} | [
{
"pp": "m n : ℕ\n⊢ Even (m ^^^ n) ↔ (Even m ↔ Even n)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instXorOp",
"congrArg",
"_private.Mathlib.Data.Nat.Bitwise.0.Nat.even_xor._simp_1_1",
"id",
"Nat.instMod",
"instHMod",
"inst... | [
"m n : ℕ\n⊢ (m + n) % 2 = 0 ↔ (m % 2 = 0 ↔ n % 2 = 0)"
] | simp only [even_iff, xor_mod_two_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.PartrecCode | {
"line": 1042,
"column": 61
} | {
"line": 1042,
"column": 72
} | {
"line": 1042,
"column": 73
} | [
{
"pp": "x✝¹ x✝ : { f // Computable f }\nh : (fun f ↦ ⟨↑↑f, ⋯⟩) x✝¹ = (fun f ↦ ⟨↑↑f, ⋯⟩) x✝\n⊢ ↑↑x✝¹ = ↑↑x✝",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x✝¹ x✝ : { f // Computable f }\nh : (fun f ↦ ⟨↑↑f, ⋯⟩) x✝¹ = (fun f ↦ ⟨↑↑f, ⋯⟩) x✝\n⊢ ↑↑x✝¹ = ↑↑x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Encoding | {
"line": 125,
"column": 6
} | {
"line": 125,
"column": 24
} | {
"line": 125,
"column": 24
} | [
{
"pp": "case pos\nn : PosNum\n⊢ (if\n (match Num.pos n with\n | Num.zero => []\n | Num.pos n => encodePosNum n) =\n [] then\n Num.zero\n else ↑n) =\n Num.pos n",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"castPosNum",
... | [
"case pos\nn : PosNum\n⊢ (if\n (match Num.pos n with\n | Num.zero => []\n | Num.pos n => encodePosNum n) =\n [] then\n Num.zero\n else Num.pos n) =\n Num.pos n"
] | PosNum.cast_to_num | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.Lemmas | {
"line": 88,
"column": 12
} | {
"line": 88,
"column": 29
} | {
"line": 89,
"column": 2
} | [
{
"pp": "b : PosNum\n⊢ 1 + b.succ = (1 + b).succ",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"congrArg",
"PosNum.instAdd",
"instOnePosNum",
"PosNum.succ",
"instHAdd",
"HAdd.hAdd",
"congr",
"True",
"eq_self",
"of_eq_true",
... | [] | by simp [one_add] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.ReduceOption | {
"line": 41,
"column": 17
} | {
"line": 41,
"column": 96
} | {
"line": 41,
"column": 97
} | [
{
"pp": "case cons.none\nα : Type u_1\nβ : Type u_2\nf : α → β\ntl : List (Option α)\nhl : (map (Option.map f) tl).reduceOption = map f tl.reduceOption\n⊢ (map (Option.map f) (none :: tl)).reduceOption = map f (none :: tl).reduceOption",
"ppTerm": "?cons.none",
"assigned": true,
"usedConstants": [
... | [
"case cons.none\nα : Type u_1\nβ : Type u_2\nf : α → β\ntl : List (Option α)\nhl : (map (Option.map f) tl).reduceOption = map f tl.reduceOption\n⊢ (map (Option.map f) tl).reduceOption = map f tl.reduceOption"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.ReduceOption | {
"line": 41,
"column": 17
} | {
"line": 41,
"column": 96
} | {
"line": 41,
"column": 97
} | [
{
"pp": "case cons.some\nα : Type u_1\nβ : Type u_2\nf : α → β\ntl : List (Option α)\nhl : (map (Option.map f) tl).reduceOption = map f tl.reduceOption\nval✝ : α\n⊢ (map (Option.map f) (some val✝ :: tl)).reduceOption = map f (some val✝ :: tl).reduceOption",
"ppTerm": "?cons.some",
"assigned": true,
... | [
"case cons.some\nα : Type u_1\nβ : Type u_2\nf : α → β\ntl : List (Option α)\nhl : (map (Option.map f) tl).reduceOption = map f tl.reduceOption\nval✝ : α\n⊢ (map (Option.map f) tl).reduceOption = map f tl.reduceOption"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.ReduceOption | {
"line": 54,
"column": 2
} | {
"line": 59,
"column": 9
} | {
"line": 61,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List (Option α)\n⊢ l.reduceOption = [] ↔ ∃ n, l = replicate n none",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"List.filterMap_eq_nil_iff",
"congrArg",
"List.eq_replicate_of_mem",
"Membership.mem"... | [] | dsimp [reduceOption]
rw [filterMap_eq_nil_iff]
constructor
· intro h
exact ⟨l.length, eq_replicate_of_mem h⟩
· grind | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.ReduceOption | {
"line": 54,
"column": 2
} | {
"line": 59,
"column": 9
} | {
"line": 61,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : List (Option α)\n⊢ l.reduceOption = [] ↔ ∃ n, l = replicate n none",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.replicate",
"List.filterMap_eq_nil_iff",
"congrArg",
"List.eq_replicate_of_mem",
"Membership.mem"... | [] | dsimp [reduceOption]
rw [filterMap_eq_nil_iff]
constructor
· intro h
exact ⟨l.length, eq_replicate_of_mem h⟩
· grind | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.NFA | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 18
} | {
"line": 201,
"column": 2
} | [
{
"pp": "case mp.inr\nα : Type u\nσ : Type v\nM : NFA α σ\nS T : Set σ\nx : List α\ns : σ\nhs : s ∈ M.accept\nh : s ∈ M.evalFrom T x\n⊢ x ∈ M.acceptsFrom S ∪ M.acceptsFrom T",
"ppTerm": "?mp.inr",
"assigned": true,
"usedConstants": [
"NFA.evalFrom",
"Membership.mem",
"NFA.accept",
... | [] | · right; tauto | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Num.Lemmas | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 56
} | {
"line": 148,
"column": 4
} | [
{
"pp": "case lt\na b : PosNum\nthis : ↑a < ↑b\n⊢ ↑a + ↑a < ↑b + ↑b + 1",
"ppTerm": "?lt",
"assigned": true,
"usedConstants": [
"castPosNum",
"Nat.instOne",
"Nat.add_lt_add",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.le_succ_of_le",
"Nat... | [] | exact Nat.le_succ_of_le (Nat.add_lt_add this this) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Num.Lemmas | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 56
} | {
"line": 148,
"column": 4
} | [
{
"pp": "case lt\na b : PosNum\nthis : ↑a < ↑b\n⊢ ↑a + ↑a < ↑b + ↑b + 1",
"ppTerm": "?lt",
"assigned": true,
"usedConstants": [
"castPosNum",
"Nat.instOne",
"Nat.add_lt_add",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.le_succ_of_le",
"Nat... | [] | exact Nat.le_succ_of_le (Nat.add_lt_add this this) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.Lemmas | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 56
} | {
"line": 148,
"column": 4
} | [
{
"pp": "case lt\na b : PosNum\nthis : ↑a < ↑b\n⊢ ↑a + ↑a < ↑b + ↑b + 1",
"ppTerm": "?lt",
"assigned": true,
"usedConstants": [
"castPosNum",
"Nat.instOne",
"Nat.add_lt_add",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.le_succ_of_le",
"Nat... | [] | exact Nat.le_succ_of_le (Nat.add_lt_add this this) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.NFA | {
"line": 295,
"column": 25
} | {
"line": 295,
"column": 43
} | {
"line": 295,
"column": 44
} | [
{
"pp": "α : Type u\nσ : Type v\nM : NFA α σ\ns✝ t✝ : σ\nx✝ : List α\np : Nonempty (M.Path s✝ t✝ x✝)\nt s s' : σ\na : α\nx : List α\nh₁ : s' ∈ M.step s a\nh₂ : M.Path s' t x\n⊢ t ∈ M.evalFrom (M.stepSet {s} a) x",
"ppTerm": "?m.307",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NFA.st... | [
"α : Type u\nσ : Type v\nM : NFA α σ\ns✝ t✝ : σ\nx✝ : List α\np : Nonempty (M.Path s✝ t✝ x✝)\nt s s' : σ\na : α\nx : List α\nh₁ : s' ∈ M.step s a\nh₂ : M.Path s' t x\n⊢ t ∈ M.evalFrom (M.step s a) x"
] | stepSet_singleton, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.Lemmas | {
"line": 157,
"column": 6
} | {
"line": 157,
"column": 56
} | {
"line": 158,
"column": 2
} | [
{
"pp": "case gt\na b : PosNum\nthis : ↑b < ↑a\n⊢ ↑b + ↑b < ↑a + ↑a + 1",
"ppTerm": "?gt",
"assigned": true,
"usedConstants": [
"castPosNum",
"Nat.instOne",
"Nat.add_lt_add",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.le_succ_of_le",
"Nat... | [] | exact Nat.le_succ_of_le (Nat.add_lt_add this this) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Num.Lemmas | {
"line": 157,
"column": 6
} | {
"line": 157,
"column": 56
} | {
"line": 158,
"column": 2
} | [
{
"pp": "case gt\na b : PosNum\nthis : ↑b < ↑a\n⊢ ↑b + ↑b < ↑a + ↑a + 1",
"ppTerm": "?gt",
"assigned": true,
"usedConstants": [
"castPosNum",
"Nat.instOne",
"Nat.add_lt_add",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.le_succ_of_le",
"Nat... | [] | exact Nat.le_succ_of_le (Nat.add_lt_add this this) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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