module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Ordmap.Ordset | {
"line": 348,
"column": 64
} | {
"line": 348,
"column": 70
} | {
"line": 348,
"column": 70
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nl : Ordnode α\nx : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nhl : Valid' o₁ l ↑x\nhr : Valid' (↑x) r o₂\nH₁ : l.size = 0 → r.size ≤ 1\nH₂ : 1 ≤ l.size → 1 ≤ r.size → r.size ≤ delta * l.size\nH₃ : 2 * l.size ≤ 9 * r.size + 5 ∨ l.size ≤ 3\nr0 : r.size > 0\nl0 : l... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Invariants | {
"line": 703,
"column": 69
} | {
"line": 703,
"column": 75
} | {
"line": 703,
"column": 75
} | [
{
"pp": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : l.Balanced\nhr : r.Balanced\nsl : l.Sized\nsr : r.Sized\nl1 : 1 ≤ l.size\na✝ : 1 ≤ r.size\nl' : ℕ\ne : Raised l' l.size\nH : l' + r.size ≤ 1\n⊢ 0 < delta",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"Nat.instMulZero... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Ordmap.Invariants | {
"line": 703,
"column": 69
} | {
"line": 703,
"column": 75
} | {
"line": 703,
"column": 75
} | [
{
"pp": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : l.Balanced\nhr : r.Balanced\nsl : l.Sized\nsr : r.Sized\nl1 : 1 ≤ l.size\na✝ : 1 ≤ r.size\nl' : ℕ\ne : Raised l' l.size\nH : l' + r.size ≤ 1\n⊢ 0 < delta",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"Nat.instMulZero... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Invariants | {
"line": 703,
"column": 69
} | {
"line": 703,
"column": 75
} | {
"line": 703,
"column": 75
} | [
{
"pp": "α : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\nhl : l.Balanced\nhr : r.Balanced\nsl : l.Sized\nsr : r.Sized\nl1 : 1 ≤ l.size\na✝ : 1 ≤ r.size\nl' : ℕ\ne : Raised l' l.size\nH : l' + r.size ≤ 1\n⊢ 0 < delta",
"ppTerm": "?m.271",
"assigned": true,
"usedConstants": [
"Nat.instMulZero... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Ordset | {
"line": 402,
"column": 70
} | {
"line": 403,
"column": 65
} | {
"line": 405,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\nt : Ordnode α\nh : t.Valid\n⊢ t.eraseMax.Valid",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Ordnode.Valid.dual_iff",
"Eq.mpr",
"Ordnode.eraseMin",
"Ordnode",
"Ordnode.eraseMin.valid",
"congrArg",
"Ordno... | [] | by
rw [Valid.dual_iff, dual_eraseMax]; exact eraseMin.valid h.dual | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.QPF.Multivariate.Constructions.Fix | {
"line": 74,
"column": 33
} | {
"line": 74,
"column": 51
} | {
"line": 74,
"column": 52
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : F (α ::: β) → β\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\n⊢ g (abs ⟨a, splitFun f' (recF g ∘ f)⟩) = g (abs ((TypeVec.id ::: recF g) <$$> ⟨a, splitFun f' f⟩))",
"ppTerm": "?m.76",
... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : F (α ::: β) → β\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\n⊢ g (abs ⟨a, splitFun f' (recF g ∘ f)⟩) = g (abs ⟨a, (TypeVec.id ::: recF g) ⊚ splitFun f' f⟩)"
] | MvPFunctor.map_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 272,
"column": 40
} | {
"line": 272,
"column": 58
} | {
"line": 272,
"column": 59
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nr : Cofix F α → Cofix F α → Prop\nh : ∀ (x y : Cofix F α), r x y → LiftR (α.RelLast r) x.dest y.dest\nx y : Cofix F α\nrxy : r x y\na : (P F).A\nf₀ f₁ : (P F).B a ⟹ fun a ↦ (α ::: Cofix F α) a\ndxeq : x.dest = MvQPF.abs ⟨a, f₀⟩\nd... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nr : Cofix F α → Cofix F α → Prop\nh : ∀ (x y : Cofix F α), r x y → LiftR (α.RelLast r) x.dest y.dest\nx y : Cofix F α\nrxy : r x y\na : (P F).A\nf₀ f₁ : (P F).B a ⟹ fun a ↦ (α ::: Cofix F α) a\ndxeq : x.dest = MvQPF.abs ⟨a, f₀⟩\ndyeq : y.dest... | MvPFunctor.map_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Fix | {
"line": 208,
"column": 6
} | {
"line": 208,
"column": 24
} | {
"line": 208,
"column": 25
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : F (α ::: β) → β\nx : F (α ::: Fix F α)\nthis : recF g ∘ fixToW = rec g\na : (P F).A\nf : (P F).B a ⟹ α ::: Fix F α\nh : repr x = ⟨a, f⟩\n⊢ recF g ((P F).wMk' ((TypeVec.id ::: fixToW) <$$> ⟨a, f⟩)) = g ((TypeVec.id ... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng : F (α ::: β) → β\nx : F (α ::: Fix F α)\nthis : recF g ∘ fixToW = rec g\na : (P F).A\nf : (P F).B a ⟹ α ::: Fix F α\nh : repr x = ⟨a, f⟩\n⊢ recF g ((P F).wMk' ⟨a, (TypeVec.id ::: fixToW) ⊚ f⟩) = g ((TypeVec.id ::: rec g) <$$> x... | MvPFunctor.map_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Ordmap.Ordset | {
"line": 504,
"column": 55
} | {
"line": 504,
"column": 66
} | {
"line": 504,
"column": 66
} | [
{
"pp": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nf : α → α\nx : α\nhf : ∀ (y : α), x ≤ y ∧ y ≤ x → x ≤ f y ∧ f y ≤ x\nsz : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nh : Valid' o₁ (node sz l y r) o₂\nbl : nil.Bounded o₁ ↑x\nb... | [
"α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nf : α → α\nx : α\nhf : ∀ (y : α), x ≤ y ∧ y ≤ x → x ≤ f y ∧ f y ≤ x\nsz : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nh : Valid' o₁ (node sz l y r) o₂\nbl : nil.Bounded o₁ ↑x\nbr : nil.Boun... | h.2.size_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Ordmap.Ordset | {
"line": 511,
"column": 55
} | {
"line": 511,
"column": 66
} | {
"line": 511,
"column": 66
} | [
{
"pp": "α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nf : α → α\nx : α\nhf : ∀ (y : α), x ≤ y ∧ y ≤ x → x ≤ f y ∧ f y ≤ x\nsz : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nh : Valid' o₁ (node sz l y r) o₂\nbl : nil.Bounded o₁ ↑x\nb... | [
"α : Type u_1\ninst✝² : Preorder α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nf : α → α\nx : α\nhf : ∀ (y : α), x ≤ y ∧ y ≤ x → x ≤ f y ∧ f y ≤ x\nsz : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\no₁ : WithBot α\no₂ : WithTop α\nh : Valid' o₁ (node sz l y r) o₂\nbl : nil.Bounded o₁ ↑x\nbr : nil.Boun... | h.2.size_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Ordmap.Ordset | {
"line": 546,
"column": 4
} | {
"line": 546,
"column": 12
} | {
"line": 546,
"column": 12
} | [
{
"pp": "case nil.coe\nα : Type u_1\ninst✝¹ : Preorder α\nβ : Type u_2\ninst✝ : Preorder β\nf : α → β\nf_strict_mono : StrictMono f\na₂ : WithTop α\na✝ : α\nh : Valid' (↑a✝) nil a₂\n⊢ nil.Bounded (Option.map f ↑a✝) (Option.map f a₂)",
"ppTerm": "?nil.coe",
"assigned": true,
"usedConstants": [
... | [
"case nil.coe.top\nα : Type u_1\ninst✝¹ : Preorder α\nβ : Type u_2\ninst✝ : Preorder β\nf : α → β\nf_strict_mono : StrictMono f\na✝ : α\nh : Valid' (↑a✝) nil ⊤\n⊢ nil.Bounded (Option.map f ↑a✝) (Option.map f ⊤)",
"case nil.coe.coe\nα : Type u_1\ninst✝¹ : Preorder α\nβ : Type u_2\ninst✝ : Preorder β\nf : α → β\nf_... | cases a₂ | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Data.QPF.Multivariate.Constructions.Fix | {
"line": 237,
"column": 8
} | {
"line": 237,
"column": 28
} | {
"line": 237,
"column": 28
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng₁ g₂ : Fix F α → β\nh : ∀ (x : F (α ::: Fix F α)), (TypeVec.id ::: g₁) <$$> x = (TypeVec.id ::: g₂) <$$> x → g₁ (mk x) = g₂ (mk x)\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\nih : ∀ (i : (P ... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng₁ g₂ : Fix F α → β\nh : ∀ (x : F (α ::: Fix F α)), (TypeVec.id ::: g₁) <$$> x = (TypeVec.id ::: g₂) <$$> x → g₁ (mk x) = g₂ (mk x)\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\nih : ∀ (i : (P F).last.B a)... | ← Fix.ind_aux a f' f | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Fix | {
"line": 239,
"column": 30
} | {
"line": 239,
"column": 48
} | {
"line": 239,
"column": 49
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng₁ g₂ : Fix F α → β\nh : ∀ (x : F (α ::: Fix F α)), (TypeVec.id ::: g₁) <$$> x = (TypeVec.id ::: g₂) <$$> x → g₁ (mk x) = g₂ (mk x)\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\nih : ∀ (i : (P ... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Type u\ng₁ g₂ : Fix F α → β\nh : ∀ (x : F (α ::: Fix F α)), (TypeVec.id ::: g₁) <$$> x = (TypeVec.id ::: g₂) <$$> x → g₁ (mk x) = g₂ (mk x)\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\nih : ∀ (i : (P F).last.B a)... | MvPFunctor.map_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 42
} | {
"line": 338,
"column": 0
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nx y : Cofix F α\nh : x.dest = y.dest\n⊢ x = y",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"TypeVec.append1",
"MvQPF.Cofix.mk",
"MvQPF.Cofix.... | [] | rw [← Cofix.mk_dest x, h, Cofix.mk_dest] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 42
} | {
"line": 338,
"column": 0
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nx y : Cofix F α\nh : x.dest = y.dest\n⊢ x = y",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"TypeVec.append1",
"MvQPF.Cofix.mk",
"MvQPF.Cofix.... | [] | rw [← Cofix.mk_dest x, h, Cofix.mk_dest] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 42
} | {
"line": 338,
"column": 0
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nx y : Cofix F α\nh : x.dest = y.dest\n⊢ x = y",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"TypeVec.append1",
"MvQPF.Cofix.mk",
"MvQPF.Cofix.... | [] | rw [← Cofix.mk_dest x, h, Cofix.mk_dest] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Multivariate.Constructions.Fix | {
"line": 282,
"column": 8
} | {
"line": 282,
"column": 28
} | {
"line": 282,
"column": 28
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\np : Fix F α → Prop\nh : ∀ (x : F (α ::: Fix F α)), LiftP (α.PredLast p) x → p (mk x)\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\nih : ∀ (i : (P F).last.B a), p (Quot.mk (⇑(wSetoid α)) (f i))\n⊢ p ⟦(P F).... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\np : Fix F α → Prop\nh : ∀ (x : F (α ::: Fix F α)), LiftP (α.PredLast p) x → p (mk x)\na : (P F).A\nf' : (P F).drop.B a ⟹ α\nf : (P F).last.B a → (P F).W α\nih : ∀ (i : (P F).last.B a), p (Quot.mk (⇑(wSetoid α)) (f i))\n⊢ p (mk (abs ⟨a, (P F).... | ← Fix.ind_aux a f' f | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Fix | {
"line": 313,
"column": 4
} | {
"line": 313,
"column": 8
} | {
"line": 314,
"column": 4
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Fix F α → Type u\ng : (x : F (α ::: Sigma β)) → β (mk ((TypeVec.id ::: Sigma.fst) <$$> x))\nx : Fix F α\ny : Sigma β := rec (fun i ↦ ⟨mk ((TypeVec.id ::: Sigma.fst) <$$> i), g i⟩) x\n⊢ x = y.fst",
"ppTerm": "?m.52",
"a... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα : TypeVec.{u} n\nβ : Fix F α → Type u\ng : (x : F (α ::: Sigma β)) → β (mk ((TypeVec.id ::: Sigma.fst) <$$> x))\nx : Fix F α\ny : Sigma β := ⋯\n⊢ y.fst = x"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 486,
"column": 4
} | {
"line": 486,
"column": 8
} | {
"line": 487,
"column": 4
} | [
{
"pp": "F₂ : Type u → Type u\nq₂ : QPF F₂\nF₁ : Type u → Type u\nq₁ : QPF F₁\nα β : Type u\nf : α → β\nb : (P F₂).A\nh : (P F₂).B b → (P F₁).A\ng :\n { A := (a₂ : (P F₂).A) × ((P F₂).B a₂ → (P F₁).A), B := fun a₂a₁ ↦ (u : (P F₂).B a₂a₁.fst) × (P F₁).B (a₂a₁.snd u) }.B\n ⟨b, h⟩ →\n α\n⊢ abs\n ⟨({ ... | [
"F₂ : Type u → Type u\nq₂ : QPF F₂\nF₁ : Type u → Type u\nq₁ : QPF F₁\nα β : Type u\nf : α → β\nb : (P F₂).A\nh : (P F₂).B b → (P F₁).A\ng :\n { A := (a₂ : (P F₂).A) × ((P F₂).B a₂ → (P F₁).A), B := fun a₂a₁ ↦ (u : (P F₂).B a₂a₁.fst) × (P F₁).B (a₂a₁.snd u) }.B\n ⟨b, h⟩ →\n α\n⊢ f <$> abs ⟨b, fun x ↦ abs ⟨... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 488,
"column": 6
} | {
"line": 488,
"column": 10
} | {
"line": 489,
"column": 6
} | [
{
"pp": "F₂ : Type u → Type u\nq₂ : QPF F₂\nF₁ : Type u → Type u\nq₁ : QPF F₁\nα β : Type u\nf : α → β\nb : (P F₂).A\nh : (P F₂).B b → (P F₁).A\ng :\n { A := (a₂ : (P F₂).A) × ((P F₂).B a₂ → (P F₁).A), B := fun a₂a₁ ↦ (u : (P F₂).B a₂a₁.fst) × (P F₁).B (a₂a₁.snd u) }.B\n ⟨b, h⟩ →\n α\n⊢ f <$> abs ⟨b, f... | [
"F₂ : Type u → Type u\nq₂ : QPF F₂\nF₁ : Type u → Type u\nq₁ : QPF F₁\nα β : Type u\nf : α → β\nb : (P F₂).A\nh : (P F₂).B b → (P F₁).A\ng :\n { A := (a₂ : (P F₂).A) × ((P F₂).B a₂ → (P F₁).A), B := fun a₂a₁ ↦ (u : (P F₂).B a₂a₁.fst) × (P F₁).B (a₂a₁.snd u) }.B\n ⟨b, h⟩ →\n α\n⊢ ?a = f <$> abs ⟨b, fun x ↦ ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 624,
"column": 2
} | {
"line": 625,
"column": 59
} | {
"line": 626,
"column": 2
} | [
{
"pp": "case mp\nF : Type u → Type u\nq : QPF F\n⊢ SuppPreservation → IsUniform",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PFunctor.supp_eq",
"PFunctor.A",
"PFunctor.Obj",
"congrArg",
"Set.univ",
"PFunctor.B",
"id",
"QPF.... | [
"case mpr\nF : Type u → Type u\nq : QPF F\n⊢ IsUniform → SuppPreservation"
] | · intro h α a a' f f' h'
rw [← PFunctor.supp_eq, ← PFunctor.supp_eq, ← h, h', h] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Real.Sign | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 57
} | {
"line": 108,
"column": 2
} | [
{
"pp": "case inl\nr : ℝ\nhn : r < 0\n⊢ r⁻¹.sign = r.sign",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"IsOrdered... | [
"case inr.inl\n⊢ 0⁻¹.sign = sign 0",
"case inr.inr\nr : ℝ\nhp : 0 < r\n⊢ r⁻¹.sign = r.sign"
] | · rw [sign_of_neg hn, sign_of_neg (inv_lt_zero.mpr hn)] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Set.Enumerate | {
"line": 56,
"column": 8
} | {
"line": 58,
"column": 36
} | {
"line": 60,
"column": 0
} | [
{
"pp": "case some.succ\nα : Type u_1\nsel : Set α → Option α\ns : Set α\nn : ℕ\nh : enumerate sel s (n + 1) = none\nval✝ : α\nhs : sel s = some val✝\nm' : ℕ\nhm : n + 1 ≤ m' + 1\n⊢ enumerate sel s (m' + 1) = none",
"ppTerm": "?some.succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | simp only [enumerate, hs] at h ⊢
have hm : n ≤ m' := Nat.le_of_succ_le_succ hm
exact enumerate_eq_none h hm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Enumerate | {
"line": 56,
"column": 8
} | {
"line": 58,
"column": 36
} | {
"line": 60,
"column": 0
} | [
{
"pp": "case some.succ\nα : Type u_1\nsel : Set α → Option α\ns : Set α\nn : ℕ\nh : enumerate sel s (n + 1) = none\nval✝ : α\nhs : sel s = some val✝\nm' : ℕ\nhm : n + 1 ≤ m' + 1\n⊢ enumerate sel s (m' + 1) = none",
"ppTerm": "?some.succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | simp only [enumerate, hs] at h ⊢
have hm : n ≤ m' := Nat.le_of_succ_le_succ hm
exact enumerate_eq_none h hm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Seq.Parallel | {
"line": 81,
"column": 6
} | {
"line": 83,
"column": 20
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case cons.inl\nα : Type u\nlem1 :\n ∀ (l : List (Computation α)) (S : WSeq (Computation α)),\n (∃ a, parallel.aux2 l = Sum.inl a) → (corec parallel.aux1 (l, S)).Terminates\nc✝ : Computation α\nT : c✝.Terminates\na : α\nS : WSeq (Computation α)\nc : Computation α\nl : List (Computation α)\nIH : pure... | [] | rw [← e]
simp only [parallel.aux2, rmap, List.foldr_cons, destruct_pure]
split <;> simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Seq.Parallel | {
"line": 81,
"column": 6
} | {
"line": 83,
"column": 20
} | {
"line": 84,
"column": 4
} | [
{
"pp": "case cons.inl\nα : Type u\nlem1 :\n ∀ (l : List (Computation α)) (S : WSeq (Computation α)),\n (∃ a, parallel.aux2 l = Sum.inl a) → (corec parallel.aux1 (l, S)).Terminates\nc✝ : Computation α\nT : c✝.Terminates\na : α\nS : WSeq (Computation α)\nc : Computation α\nl : List (Computation α)\nIH : pure... | [] | rw [← e]
simp only [parallel.aux2, rmap, List.foldr_cons, destruct_pure]
split <;> simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.WSeq.Basic | {
"line": 280,
"column": 2
} | {
"line": 280,
"column": 6
} | {
"line": 281,
"column": 2
} | [
{
"pp": "α : Type u\ns : WSeq α\nn : ℕ\n⊢ s.tail.drop n = s.drop (1 + n)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Stream'.WSeq.drop",
"instOfNatNat",
"instHAdd",
"Stream'.WSeq.tail",
"HAdd.hAdd",
"Nat",
"Stream'.WSeq",
"instAddNat",
... | [
"α : Type u\ns : WSeq α\nn : ℕ\n⊢ s.drop (1 + n) = s.tail.drop n"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.Data.Seq.Parallel | {
"line": 117,
"column": 6
} | {
"line": 117,
"column": 63
} | {
"line": 117,
"column": 64
} | [
{
"pp": "case inr\nα : Type u\nlem1 :\n ∀ (l : List (Computation α)) (S : WSeq (Computation α)),\n (∃ a, parallel.aux2 l = Sum.inl a) → (corec parallel.aux1 (l, S)).Terminates\nc : Computation α\nT : c.Terminates\ns : Computation α\nIH : ∀ {l : List (Computation α)} {S : WSeq (Computation α)}, s ∈ l → (core... | [
"case inr.none\nα : Type u\nlem1 :\n ∀ (l : List (Computation α)) (S : WSeq (Computation α)),\n (∃ a, parallel.aux2 l = Sum.inl a) → (corec parallel.aux1 (l, S)).Terminates\nc : Computation α\nT : c.Terminates\ns : Computation α\nIH : ∀ {l : List (Computation α)} {S : WSeq (Computation α)}, s ∈ l → (corec paral... | rcases Seq.destruct S with (_ | ⟨_ | c, S'⟩) <;> apply IH | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.WSeq.Basic | {
"line": 409,
"column": 4
} | {
"line": 409,
"column": 12
} | {
"line": 410,
"column": 4
} | [
{
"pp": "case some\nα : Type u\nC : WSeq α → Prop\na : α\ns : WSeq α\nM : a ∈ s\nh1 : ∀ (b : α) (s' : WSeq α), a = b ∨ C s' → C (cons b s')\nh2 : ∀ (s : WSeq α), C s → C s.think\ns' : Seq (Option α)\nb : α\nh : some a = some b ∨ C s'\n⊢ C (Seq.cons (some b) s')",
"ppTerm": "?some",
"assigned": true,
... | [
"case some\nα : Type u\nC : WSeq α → Prop\na : α\ns : WSeq α\nM : a ∈ s\nh1 : ∀ (b : α) (s' : WSeq α), a = b ∨ C s' → C (cons b s')\nh2 : ∀ (s : WSeq α), C s → C s.think\ns' : Seq (Option α)\nb : α\nh : some a = some b ∨ C s'\n⊢ a = b ∨ C s'"
] | apply h1 | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.WSeq.Relation | {
"line": 263,
"column": 4
} | {
"line": 263,
"column": 21
} | {
"line": 264,
"column": 2
} | [
{
"pp": "case h1\nα : Type u\nc : Computation (WSeq α)\ns : WSeq α\nh : s ∈ c\n⊢ flatten (Computation.pure s) ~ʷ s",
"ppTerm": "?h1",
"assigned": true,
"usedConstants": [
"congrArg",
"Stream'.WSeq.flatten",
"_private.Mathlib.Data.WSeq.Relation.0.Stream'.WSeq.flatten_equiv._simp_1_1... | [] | simp [Equiv.refl] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.WSeq.Relation | {
"line": 263,
"column": 4
} | {
"line": 263,
"column": 21
} | {
"line": 264,
"column": 2
} | [
{
"pp": "case h1\nα : Type u\nc : Computation (WSeq α)\ns : WSeq α\nh : s ∈ c\n⊢ flatten (Computation.pure s) ~ʷ s",
"ppTerm": "?h1",
"assigned": true,
"usedConstants": [
"congrArg",
"Stream'.WSeq.flatten",
"_private.Mathlib.Data.WSeq.Relation.0.Stream'.WSeq.flatten_equiv._simp_1_1... | [] | simp [Equiv.refl] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.WSeq.Relation | {
"line": 263,
"column": 4
} | {
"line": 263,
"column": 21
} | {
"line": 264,
"column": 2
} | [
{
"pp": "case h1\nα : Type u\nc : Computation (WSeq α)\ns : WSeq α\nh : s ∈ c\n⊢ flatten (Computation.pure s) ~ʷ s",
"ppTerm": "?h1",
"assigned": true,
"usedConstants": [
"congrArg",
"Stream'.WSeq.flatten",
"_private.Mathlib.Data.WSeq.Relation.0.Stream'.WSeq.flatten_equiv._simp_1_1... | [] | simp [Equiv.refl] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Seq.Parallel | {
"line": 134,
"column": 4
} | {
"line": 140,
"column": 20
} | {
"line": 141,
"column": 4
} | [
{
"pp": "case inr.inl\nα : Type u\nS✝ : WSeq (Computation α)\nc✝ : Computation α\nh✝ : c✝ ∈ S✝\nT✝ : c✝.Terminates\nl : List (Computation α)\nS : Stream'.Seq (Option (Computation α))\nc : Computation α\nT : c.Terminates\na✝ : some (some c) = S.get? 0\nH : S.destruct = some (some c, S.tail)\na : α\nh : parallel.... | [
"case inr.inr\nα : Type u\nS✝ : WSeq (Computation α)\nc✝ : Computation α\nh✝ : c✝ ∈ S✝\nT✝ : c✝.Terminates\nl : List (Computation α)\nS : Stream'.Seq (Option (Computation α))\nc : Computation α\nT : c.Terminates\na : some (some c) = S.get? 0\nH : S.destruct = some (some c, S.tail)\nl' : List (Computation α)\nh : pa... | · have C : corec parallel.aux1 (l, S) = pure a := by
apply destruct_eq_pure
rw [corec_eq, parallel.aux1]
rw [h]
simp only [rmap]
rw [C]
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Seq.Parallel | {
"line": 152,
"column": 4
} | {
"line": 158,
"column": 20
} | {
"line": 159,
"column": 4
} | [
{
"pp": "case inr.inl\nα : Type u\nS✝ : WSeq (Computation α)\nc✝ : Computation α\nh✝ : c✝ ∈ S✝\nT✝ : c✝.Terminates\nn : ℕ\nIH :\n ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),\n c ∈ l ∨ some (some c) = S.get? n → c.Terminates → (corec parallel.aux1 (l, S)).Term... | [
"case inr.inr\nα : Type u\nS✝ : WSeq (Computation α)\nc✝ : Computation α\nh✝ : c✝ ∈ S✝\nT✝ : c✝.Terminates\nn : ℕ\nIH :\n ∀ (l : List (Computation α)) (S : Stream'.Seq (Option (Computation α))) (c : Computation α),\n c ∈ l ∨ some (some c) = S.get? n → c.Terminates → (corec parallel.aux1 (l, S)).Terminates\nl : ... | · have C : corec parallel.aux1 (l, S) = pure a := by
apply destruct_eq_pure
rw [corec_eq, parallel.aux1]
rw [h]
simp only [rmap]
rw [C]
infer_instance | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.WSeq.Basic | {
"line": 636,
"column": 4
} | {
"line": 636,
"column": 34
} | {
"line": 637,
"column": 4
} | [
{
"pp": "α : Type u\ns : Seq α\n⊢ (match\n match Option.map (fun a' ↦ (a', (some <$> s).tail)) (some <$> s.get? 0) with\n | none => Sum.inl none\n | some (none, s') => Sum.inr s'\n | some (some a, s') => Sum.inl (some (a, s')) with\n | Sum.inl a => Sum.inl a\n | Sum.inr b =>\n Sum... | [
"case none\nα : Type u\ns : Seq α\n⊢ (match\n match Option.map (fun a' ↦ (a', (some <$> s).tail)) (some <$> none) with\n | none => Sum.inl none\n | some (none, s') => Sum.inr s'\n | some (some a, s') => Sum.inl (some (a, s')) with\n | Sum.inl a => Sum.inl a\n | Sum.inr b =>\n Sum.inr\... | rcases Seq.get? s 0 with - | a | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Data.String.Basic | {
"line": 94,
"column": 16
} | {
"line": 94,
"column": 22
} | {
"line": 95,
"column": 2
} | [
{
"pp": "case nil.nil\n⊢ (if { s := ofList [], i := 0 }.hasNext = true then\n if { s := ofList [], i := 0 }.hasNext = true then\n if { s := ofList [], i := 0 }.curr = { s := ofList [], i := 0 }.curr then\n ltb { s := ofList [], i := 0 }.next { s := ofList [], i := 0 }.next\n ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.Sym.NatCard | {
"line": 34,
"column": 2
} | {
"line": 34,
"column": 28
} | {
"line": 35,
"column": 2
} | [
{
"pp": "α : Type u_1\nk : ℕ\n⊢ Nat.card (Sym α k) = (Nat.card α).multichoose k",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"Finite",
"finite_or_infinite",
"Nat.card",
"Or.casesOn",
"Nat",
"Sym",
"Eq.refl",
"Or.inl",
"Or",
"Inf... | [
"case inl\nα : Type u_1\nk : ℕ\nh✝ : Finite α\n⊢ Nat.card (Sym α k) = (Nat.card α).multichoose k",
"case inr\nα : Type u_1\nk : ℕ\nh✝ : Infinite α\n⊢ Nat.card (Sym α k) = (Nat.card α).multichoose k"
] | cases finite_or_infinite α | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Data.Sym.NatCard | {
"line": 64,
"column": 2
} | {
"line": 64,
"column": 28
} | {
"line": 65,
"column": 2
} | [
{
"pp": "α : Type u_1\n⊢ Nat.card { a // ¬a.IsDiag } = (Nat.card α).choose 2",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Nat.choose",
"Finite",
"finite_or_infinite",
"Subtype",
"Nat.card",
"instOfNatNat",
"Or.casesOn",
"Nat",
"Eq.re... | [
"case inl\nα : Type u_1\nh✝ : Finite α\n⊢ Nat.card { a // ¬a.IsDiag } = (Nat.card α).choose 2",
"case inr\nα : Type u_1\nh✝ : Infinite α\n⊢ Nat.card { a // ¬a.IsDiag } = (Nat.card α).choose 2"
] | cases finite_or_infinite α | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Data.Sym.NatCard | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 28
} | {
"line": 79,
"column": 2
} | [
{
"pp": "α : Type u_1\n⊢ Nat.card (Sym2 α) = (Nat.card α + 1).choose 2",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Nat.choose",
"Finite",
"finite_or_infinite",
"Nat.card",
"instOfNatNat",
"Or.casesOn",
"instHAdd",
"HAdd.hAdd",
"Nat... | [
"case inl\nα : Type u_1\nh✝ : Finite α\n⊢ Nat.card (Sym2 α) = (Nat.card α + 1).choose 2",
"case inr\nα : Type u_1\nh✝ : Infinite α\n⊢ Nat.card (Sym2 α) = (Nat.card α + 1).choose 2"
] | cases finite_or_infinite α | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Data.Seq.Parallel | {
"line": 328,
"column": 2
} | {
"line": 330,
"column": 47
} | {
"line": 332,
"column": 0
} | [
{
"pp": "α : Type u\nS : WSeq (Computation α)\na : α\nH : ∀ s ∈ S, s ~> a\nc : Computation α\ncs : c ∈ S\nac : a ∈ c\n⊢ a ∈ parallel S",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Computation.terminates_parallel",
"Computation.parallel",
"Computation.parallel_promises... | [] | haveI := terminates_of_mem ac
haveI := terminates_parallel cs
exact mem_of_promises _ (parallel_promises H) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Seq.Parallel | {
"line": 328,
"column": 2
} | {
"line": 330,
"column": 47
} | {
"line": 332,
"column": 0
} | [
{
"pp": "α : Type u\nS : WSeq (Computation α)\na : α\nH : ∀ s ∈ S, s ~> a\nc : Computation α\ncs : c ∈ S\nac : a ∈ c\n⊢ a ∈ parallel S",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Computation.terminates_parallel",
"Computation.parallel",
"Computation.parallel_promises... | [] | haveI := terminates_of_mem ac
haveI := terminates_parallel cs
exact mem_of_promises _ (parallel_promises H) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Vector.Snoc | {
"line": 65,
"column": 4
} | {
"line": 65,
"column": 23
} | {
"line": 66,
"column": 4
} | [
{
"pp": "case succ\nα : Type u_1\nn✝ : ℕ\nval : α\nn : ℕ\nih : replicate (n + 1) val = (replicate n val).snoc val\n⊢ replicate (n + 1 + 1) val = (replicate (n + 1) val).snoc val",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.Vector.replicate_s... | [
"case succ\nα : Type u_1\nn✝ : ℕ\nval : α\nn : ℕ\nih : replicate (n + 1) val = (replicate n val).snoc val\n⊢ val ::ᵥ replicate (n + 1) val = (replicate (n + 1) val).snoc val"
] | rw [replicate_succ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Vector.Snoc | {
"line": 66,
"column": 17
} | {
"line": 66,
"column": 36
} | {
"line": 67,
"column": 4
} | [
{
"pp": "α : Type u_1\nn✝ : ℕ\nval : α\nn : ℕ\nih : replicate (n + 1) val = (replicate n val).snoc val\n| (replicate (n + 1) val).snoc val",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"List.Vector.replicate_succ",
"List.Vector",
"instOfNatNat",
... | [
"α : Type u_1\nn✝ : ℕ\nval : α\nn : ℕ\nih : replicate (n + 1) val = (replicate n val).snoc val\n| (val ::ᵥ replicate n val).snoc val"
] | rw [replicate_succ] | Lean.Parser.Tactic.Conv._aux_Init_Conv___macroRules_Lean_Parser_Tactic_Conv_convRw___1 | Lean.Parser.Tactic.Conv.convRw__ |
Mathlib.Data.UInt | {
"line": 158,
"column": 85
} | {
"line": 158,
"column": 91
} | {
"line": 158,
"column": 91
} | [
{
"pp": "n : UInt8\n⊢ 2 ^ 8 < 55296",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"instPowNat",
"of_decide_eq_true",
"id",
"instOfNatNat",
"instNatPowNat",
"Bool.true",
"HPow.hPow",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.Data.UInt | {
"line": 158,
"column": 85
} | {
"line": 158,
"column": 91
} | {
"line": 158,
"column": 91
} | [
{
"pp": "n : UInt8\n⊢ 2 ^ 8 < 55296",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"instPowNat",
"of_decide_eq_true",
"id",
"instOfNatNat",
"instNatPowNat",
"Bool.true",
"HPow.hPow",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.UInt | {
"line": 158,
"column": 85
} | {
"line": 158,
"column": 91
} | {
"line": 158,
"column": 91
} | [
{
"pp": "n : UInt8\n⊢ 2 ^ 8 < 55296",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"instPowNat",
"of_decide_eq_true",
"id",
"instOfNatNat",
"instNatPowNat",
"Bool.true",
"HPow.hPow",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Dynamics.Ergodic.Ergodic | {
"line": 190,
"column": 26
} | {
"line": 190,
"column": 53
} | {
"line": 190,
"column": 54
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ne : α ≃ᵐ α\nhe : Ergodic (⇑e) μ\ns : Set α\nhsm : MeasurableSet s\nhs : ⇑e.symm ⁻¹' s = s\n| ⇑e ⁻¹' ⇑e.symm ⁻¹' s",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"MeasurableEquiv.instEquivLike",
"congrArg",
"Mea... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\ne : α ≃ᵐ α\nhe : Ergodic (⇑e) μ\ns : Set α\nhsm : MeasurableSet s\nhs : ⇑e.symm ⁻¹' s = s\n| ⇑e ⁻¹' ⇑e '' s"
] | ← e.image_eq_preimage_symm, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.Dynamics.Circle.RotationNumber.TranslationNumber | {
"line": 454,
"column": 71
} | {
"line": 456,
"column": 32
} | {
"line": 457,
"column": 4
} | [
{
"pp": "f g₁ g₂ : CircleDeg1Lift\nh : Semiconj ⇑f ⇑g₁ ⇑g₂\n⊢ dist (g₁ 0) (f (g₁ 0) - f 0) + dist (f (g₁ 0) - f 0) (g₂ 0) =\n dist (f 0 + g₁ 0) (f (g₁ 0)) + dist (g₂ 0 + f 0) (g₂ (f 0))",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"Real",
"Real.lattice",
"Real.instZ... | [] | by
simp only [h.eq, Real.dist_eq, sub_sub, add_comm (f 0), sub_sub_eq_add_sub,
abs_sub_comm (g₂ (f 0))] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Dynamics.Ergodic.Action.OfMinimal | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 75
} | {
"line": 60,
"column": 2
} | [
{
"pp": "M : Type u_1\ninst✝⁹ : TopologicalSpace M\nX : Type u_2\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : R1Space X\ninst✝⁶ : MeasurableSpace X\ninst✝⁵ : BorelSpace X\ninst✝⁴ : SMul M X\ninst✝³ : ContinuousSMul M X\nμ : Measure X\ninst✝² : IsFiniteMeasure μ\ninst✝¹ : μ.InnerRegular\ninst✝ : ErgodicSMul M X μ\ns :... | [
"M : Type u_1\ninst✝⁹ : TopologicalSpace M\nX : Type u_2\ninst✝⁸ : TopologicalSpace X\ninst✝⁷ : R1Space X\ninst✝⁶ : MeasurableSpace X\ninst✝⁵ : BorelSpace X\ninst✝⁴ : SMul M X\ninst✝³ : ContinuousSMul M X\nμ : Measure X\ninst✝² : IsFiniteMeasure μ\ninst✝¹ : μ.InnerRegular\ninst✝ : ErgodicSMul M X μ\ns : Set X\nhsm ... | rwa [dense_iff_closure_eq, IsClosed.closure_eq, eq_univ_iff_forall] at hd | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Dynamics.Ergodic.Conservative | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 39
} | {
"line": 103,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : MeasurableSpace α\nf : α → α\ns : Set α\nμ : Measure α\nhf : Conservative f μ\nhsm : NullMeasurableSet s μ\nhs₀ : μ s ≠ 0\nt : Set α\nhsub : t ⊆ s\nhtm : MeasurableSet t\nhts : t =ᵐ[μ] s\nx : α\nhxt : x ∈ t\nm : ℕ\nhm₀ : m ≠ 0\nhmt : f^[m] x ∈ t\n⊢ ∃ x ∈ s, ∃ m, m ≠ 0 ∧ f^[m] x ∈ ... | [] | exact ⟨x, hsub hxt, m, hm₀, hsub hmt⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Group.AddCircle | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 78
} | {
"line": 81,
"column": 2
} | [
{
"pp": "case refine_3\nT : 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\n⊢ ∀ (g : ↥G), QuasiMeasurePreser... | [] | exact fun g => quasiMeasurePreserving_add_left (G := AddCircle T) volume g | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Group.AddCircle | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 78
} | {
"line": 81,
"column": 2
} | [
{
"pp": "case refine_3\nT : 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\n⊢ ∀ (g : ↥G), QuasiMeasurePreser... | [] | exact fun g => quasiMeasurePreserving_add_left (G := AddCircle T) volume g | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Group.AddCircle | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 78
} | {
"line": 81,
"column": 2
} | [
{
"pp": "case refine_3\nT : 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\n⊢ ∀ (g : ↥G), QuasiMeasurePreser... | [] | exact fun g => quasiMeasurePreserving_add_left (G := AddCircle T) volume g | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 168,
"column": 40
} | {
"line": 171,
"column": 10
} | {
"line": 173,
"column": 0
} | [
{
"pp": "A : Type u_1\nG : Type u_2\ninst✝¹ : Monoid G\ninst✝ : TopologicalSpace A\ng : G\n⊢ Continuous[Pi.topologicalSpace, Pi.topologicalSpace] (mulShift g)",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Continuous",
"HMul.hMul",
"Pi.topologicalSpace",
"Monoid.to... | [] | by
-- coordinate projections are continuous; composition preserves continuity
unfold mulShift
fun_prop | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Dynamics.SymbolicDynamics.Basic | {
"line": 544,
"column": 2
} | {
"line": 544,
"column": 83
} | {
"line": 546,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝⁴ : TopologicalSpace A\ninst✝³ : Inhabited A\nG : Type u_2\ninst✝² : Monoid G\ninst✝¹ : IsLeftCancelMul G\ninst✝ : DiscreteTopology A\nF : Set (Pattern A G)\nh_eq : {x | ∀ p ∈ F, ∀ (v : G), ¬p.mulOccursInAt x v} = ⋂ p ∈ F, ⋂ v, {x | ¬p.mulOccursInAt x v}\np : Pattern A G\nhp : p ∈ F\... | [] | simpa [this, isClosed_compl_iff] using isOpen_mulOccursInAt (A := A) (G := G) p v | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | {
"line": 330,
"column": 41
} | {
"line": 331,
"column": 71
} | {
"line": 333,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝ : μ.HaveLebesgueDecomposition ν\nhμν : μ ≪ ν\ns : Set α\nhs : MeasurableSet s\n⊢ ∫⁻ (x : α) in s, μ.rnDeriv ν x ∂ν = μ s",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure.withDen... | [] | by
rw [← withDensity_apply _ hs, Measure.withDensity_rnDeriv_eq _ _ hμν] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Dynamics.TopologicalEntropy.Semiconj | {
"line": 71,
"column": 7
} | {
"line": 71,
"column": 34
} | {
"line": 71,
"column": 34
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ns F : Set X\nV : SetRel Y Y\nS : X → X\nT : Y → Y\nφ : X → Y\nn : ℕ\nh : Semiconj φ S T\nh' : IsDynCoverOf S F (map φ φ ⁻¹' V) n s\nx : X\nhx : x ∈ F\ny : X\nhy : y ∈ s\nhxy : (x, y) ∈ dynEntourage S (map φ φ ⁻¹' V) n\n⊢ (x, y) ∈ map φ φ ⁻¹' dynEntourage T V n",
"ppTerm"... | [
"X : Type u_1\nY : Type u_2\ns F : Set X\nV : SetRel Y Y\nS : X → X\nT : Y → Y\nφ : X → Y\nn : ℕ\nh : Semiconj φ S T\nh' : IsDynCoverOf S F (map φ φ ⁻¹' V) n s\nx : X\nhx : x ∈ F\ny : X\nhy : y ∈ s\nhxy : (x, y) ∈ dynEntourage S (map φ φ ⁻¹' V) n\n⊢ (x, y) ∈ dynEntourage S (map φ φ ⁻¹' V) n"
] | h.preimage_dynEntourage V n | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Dynamics.TopologicalEntropy.Subset | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 71
} | {
"line": 118,
"column": 0
} | [
{
"pp": "case inr\nX : Type u_1\nT : X → X\nV : SetRel X X\ninst✝ : UniformSpace X\nh : Continuous T\nF : Set X\nU : SetRel X X\nV_uni : V ∈ 𝓤 X\nn : ℕ\nh' : coverMincard T F U n < ⊤\ns : Finset X\ns_cover : IsDynCoverOf T F U n ↑s\ns_coverMincard : ↑s.card = coverMincard T F U n\n⊢ coverMincard T (closure F) ... | [] | exact s_coverMincard ▸ (s_cover.closure h V_uni).coverMincard_le_card | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Dynamics.TopologicalEntropy.Semiconj | {
"line": 213,
"column": 6
} | {
"line": 213,
"column": 42
} | {
"line": 213,
"column": 42
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : UniformSpace X\ninst✝ : UniformSpace Y\nS : X → X\nT : Y → Y\nφ : X → Y\nh : Semiconj φ S T\nF G : Set X\nh' : UniformContinuousOn φ G\nhF : F ⊆ G\nhG : MapsTo S G G\n⊢ coverEntropy T (φ '' F) ≤ coverEntropy S F",
"ppTerm": "?m.19",
"assigned": true,
"us... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : UniformSpace X\ninst✝ : UniformSpace Y\nS : X → X\nT : Y → Y\nφ : X → Y\nh : Semiconj φ S T\nF G : Set X\nh' : UniformContinuousOn φ G\nhF : F ⊆ G\nhG : MapsTo S G G\n⊢ coverEntropy T (φ '' F) ≤ coverEntropy (MapsTo.restrict S G G hG) (val ⁻¹' F)"
] | ← coverEntropy_restrict_subset hF hG | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.AbelRuffini | {
"line": 56,
"column": 33
} | {
"line": 56,
"column": 51
} | {
"line": 56,
"column": 51
} | [
{
"pp": "case h₂\nF : Type u_1\ninst✝ : Field F\ns : Multiset F[X]\nhs : ∀ p ∈ s, IsSolvable p.Gal\np : F[X]\nt : Multiset F[X]\nhps : p ∈ s\na✝ : t ⊆ s\nht : IsSolvable t.prod.Gal\n⊢ IsSolvable (p ::ₘ t).prod.Gal",
"ppTerm": "?h₂",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"IsSolva... | [
"case h₂\nF : Type u_1\ninst✝ : Field F\ns : Multiset F[X]\nhs : ∀ p ∈ s, IsSolvable p.Gal\np : F[X]\nt : Multiset F[X]\nhps : p ∈ s\na✝ : t ⊆ s\nht : IsSolvable t.prod.Gal\n⊢ IsSolvable (p * t.prod).Gal"
] | Multiset.prod_cons | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym | {
"line": 529,
"column": 4
} | {
"line": 529,
"column": 8
} | {
"line": 530,
"column": 4
} | [
{
"pp": "case refine_1\nα : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nf : α → β\nhf : MeasurableEmbedding f\nμ ν : Measure α\ninst✝¹ : SigmaFinite μ\ninst✝ : SigmaFinite ν\nthis✝¹ : SigmaFinite (map f ν)\nthis✝ : SigmaFinite (map f (μ.singularPart ν))\nthis : SigmaFinite (map f (ν.w... | [
"case refine_1\nα : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nmβ : MeasurableSpace β\nf : α → β\nhf : MeasurableEmbedding f\nμ ν : Measure α\ninst✝¹ : SigmaFinite μ\ninst✝ : SigmaFinite ν\nthis✝¹ : SigmaFinite (map f ν)\nthis✝ : SigmaFinite (map f (μ.singularPart ν))\nthis : SigmaFinite (map f (ν.withDensity (... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.ModelTheory.LanguageMap | {
"line": 364,
"column": 2
} | {
"line": 364,
"column": 34
} | {
"line": 365,
"column": 2
} | [
{
"pp": "M : Type w\nα : Type u'\nβ : Type v'\nf : α → β\nfα : α → M\nfβ : β → M\nh : fβ ∘ f = fα\n⊢ (LHom.constantsOnMap f).IsExpansionOn M",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"FirstOrder.Language.constantsOn.structure"
],
"usedFVars": [
"M",
"α",
... | [
"M : Type w\nα : Type u'\nβ : Type v'\nf : α → β\nfα : α → M\nfβ : β → M\nh : fβ ∘ f = fα\nthis : (constantsOn α).Structure M := constantsOn.structure fα\n⊢ (LHom.constantsOnMap f).IsExpansionOn M"
] | letI := constantsOn.structure fα | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLetI___1 | Lean.Parser.Tactic.tacticLetI__ |
Mathlib.ModelTheory.Basic | {
"line": 690,
"column": 66
} | {
"line": 691,
"column": 59
} | {
"line": 693,
"column": 0
} | [
{
"pp": "L : Language\nM : Type w\nN : Type w'\ninst✝¹ : L.Structure M\ninst✝ : L.Structure N\nf : M ≃[L] N\n⊢ f.symm.toEmbedding.comp f.toEmbedding = Embedding.refl L M",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FirstOrder.Language.Equiv.comp_toEmbedding",
... | [] | by
rw [← comp_toEmbedding, symm_comp_self, refl_toEmbedding] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.ModelTheory.Algebra.Ring.Basic | {
"line": 134,
"column": 30
} | {
"line": 134,
"column": 36
} | {
"line": 134,
"column": 36
} | [
{
"pp": "α : Type u_1\n⊢ (↑[Sum.inl ⟨2, add⟩, Sum.inl ⟨2, mul⟩, Sum.inl ⟨1, neg⟩, Sum.inl ⟨0, zero⟩, Sum.inl ⟨0, one⟩]).Nodup",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"FirstOrder.Language.ring",
"of_decide_eq_true",
"Multiset.Nodup",
"FirstOrder.ringFunc.mul"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.ModelTheory.Algebra.Ring.Basic | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 24
} | {
"line": 139,
"column": 4
} | [
{
"pp": "case inl.add\nα : Type u_1\n⊢ Sum.inl ⟨2, add⟩ ∈\n { val := ↑[Sum.inl ⟨2, add⟩, Sum.inl ⟨2, mul⟩, Sum.inl ⟨1, neg⟩, Sum.inl ⟨0, zero⟩, Sum.inl ⟨0, one⟩],\n nodup := instFintypeSymbolsRing._proof_1 }",
"ppTerm": "?inl.add",
"assigned": true,
"usedConstants": [
"FirstOrder.Langu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.ModelTheory.Algebra.Ring.Basic | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 24
} | {
"line": 139,
"column": 4
} | [
{
"pp": "case inl.mul\nα : Type u_1\n⊢ Sum.inl ⟨2, mul⟩ ∈\n { val := ↑[Sum.inl ⟨2, add⟩, Sum.inl ⟨2, mul⟩, Sum.inl ⟨1, neg⟩, Sum.inl ⟨0, zero⟩, Sum.inl ⟨0, one⟩],\n nodup := instFintypeSymbolsRing._proof_1 }",
"ppTerm": "?inl.mul",
"assigned": true,
"usedConstants": [
"FirstOrder.Langu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.ModelTheory.Algebra.Ring.Basic | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 24
} | {
"line": 139,
"column": 4
} | [
{
"pp": "case inl.neg\nα : Type u_1\n⊢ Sum.inl ⟨1, neg⟩ ∈\n { val := ↑[Sum.inl ⟨2, add⟩, Sum.inl ⟨2, mul⟩, Sum.inl ⟨1, neg⟩, Sum.inl ⟨0, zero⟩, Sum.inl ⟨0, one⟩],\n nodup := instFintypeSymbolsRing._proof_1 }",
"ppTerm": "?inl.neg",
"assigned": true,
"usedConstants": [
"FirstOrder.Langu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.ModelTheory.Algebra.Ring.Basic | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 24
} | {
"line": 139,
"column": 4
} | [
{
"pp": "case inl.zero\nα : Type u_1\n⊢ Sum.inl ⟨0, zero⟩ ∈\n { val := ↑[Sum.inl ⟨2, add⟩, Sum.inl ⟨2, mul⟩, Sum.inl ⟨1, neg⟩, Sum.inl ⟨0, zero⟩, Sum.inl ⟨0, one⟩],\n nodup := instFintypeSymbolsRing._proof_1 }",
"ppTerm": "?inl.zero",
"assigned": true,
"usedConstants": [
"FirstOrder.La... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.ModelTheory.Algebra.Ring.Basic | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 24
} | {
"line": 139,
"column": 4
} | [
{
"pp": "case inl.one\nα : Type u_1\n⊢ Sum.inl ⟨0, one⟩ ∈\n { val := ↑[Sum.inl ⟨2, add⟩, Sum.inl ⟨2, mul⟩, Sum.inl ⟨1, neg⟩, Sum.inl ⟨0, zero⟩, Sum.inl ⟨0, one⟩],\n nodup := instFintypeSymbolsRing._proof_1 }",
"ppTerm": "?inl.one",
"assigned": true,
"usedConstants": [
"FirstOrder.Langu... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.ModelTheory.Semantics | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 37
} | {
"line": 112,
"column": 0
} | [
{
"pp": "L : Language\nM : Type w\ninst✝ : L.Structure M\nα : Type u'\nf : L.Functions 1\nt : L.Term α\nv : α → M\ni : Fin 1\n⊢ realize v (![t] i) = ![realize v t] i",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"congrArg",
"FirstOrder.Language.Term",
"Matrix.cons_val_f... | [] | simp only [Matrix.cons_val_fin_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.FieldTheory.AbelRuffini | {
"line": 224,
"column": 52
} | {
"line": 224,
"column": 71
} | {
"line": 224,
"column": 72
} | [
{
"pp": "case refine_1\nF : Type u_1\nE : Type u_2\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nx : E\nn : ℕ\nhn : n ≠ 0\np : F[X]\nh1 : p ≠ 0\nh2 : (aeval (x ^ n)) p = 0\nh : p.leadingCoeff * (X ^ n).leadingCoeff ^ p.natDegree = 0\n⊢ p.leadingCoeff = 0",
"ppTerm": "?refine_1",
"assigned": ... | [
"case refine_1\nF : Type u_1\nE : Type u_2\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nx : E\nn : ℕ\nhn : n ≠ 0\np : F[X]\nh1 : p ≠ 0\nh2 : (aeval (x ^ n)) p = 0\nh : p.leadingCoeff * 1 ^ p.natDegree = 0\n⊢ p.leadingCoeff = 0",
"case refine_1\nF : Type u_1\nE : Type u_2\ninst✝² : Field F\ninst✝¹ : F... | leadingCoeff_X_pow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.ModelTheory.Semantics | {
"line": 309,
"column": 2
} | {
"line": 309,
"column": 37
} | {
"line": 311,
"column": 0
} | [
{
"pp": "L : Language\nM : Type w\ninst✝ : L.Structure M\nα : Type u'\nl : ℕ\nv : α → M\nxs : Fin l → M\nR : L.Relations 1\nt : L.Term (α ⊕ Fin l)\nx✝ : Fin 1\n⊢ realize (Sum.elim v xs) (![t] x✝) = ![realize (Sum.elim v xs) t] x✝",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"congr... | [] | simp only [Matrix.cons_val_fin_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.FieldTheory.AbelRuffini | {
"line": 285,
"column": 6
} | {
"line": 285,
"column": 30
} | {
"line": 286,
"column": 6
} | [
{
"pp": "case hq.refine_2\nF : Type u_1\nE : Type u_2\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nx : E\nhx : x ∈ solvableByRad F E\nn : ℕ\nhn : n ≠ 0\nhα : IsSolvable (minpoly F (x ^ n)).Gal\np : F[X] := minpoly F (x ^ n)\nhp : p.comp (X ^ n) ≠ 0\ns : Multiset p.SplittingField\nhs :\n map (algeb... | [
"case hq.refine_2\nF : Type u_1\nE : Type u_2\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nx : E\nhx : x ∈ solvableByRad F E\nn : ℕ\nhn : n ≠ 0\nhα : IsSolvable (minpoly F (x ^ n)).Gal\np : F[X] := minpoly F (x ^ n)\nhp : p.comp (X ^ n) ≠ 0\ns : Multiset p.SplittingField\nhs :\n map (algebraMap F p.Sp... | obtain ⟨q, _, rfl⟩ := hq | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.ModelTheory.Semantics | {
"line": 349,
"column": 2
} | {
"line": 350,
"column": 53
} | {
"line": 352,
"column": 0
} | [
{
"pp": "L : Language\nM : Type w\ninst✝ : L.Structure M\nα : Type u'\nm n : ℕ\nh : m = n\nh' : m ≤ n\nφ : L.BoundedFormula α m\nv : α → M\nxs : Fin n → M\n⊢ (castLE h' φ).Realize v xs ↔ φ.Realize v (xs ∘ Fin.cast h)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"congrArg",
"... | [] | subst h
simp only [castLE_rfl, cast_refl, Function.comp_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.ModelTheory.Semantics | {
"line": 349,
"column": 2
} | {
"line": 350,
"column": 53
} | {
"line": 352,
"column": 0
} | [
{
"pp": "L : Language\nM : Type w\ninst✝ : L.Structure M\nα : Type u'\nm n : ℕ\nh : m = n\nh' : m ≤ n\nφ : L.BoundedFormula α m\nv : α → M\nxs : Fin n → M\n⊢ (castLE h' φ).Realize v xs ↔ φ.Realize v (xs ∘ Fin.cast h)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"congrArg",
"... | [] | subst h
simp only [castLE_rfl, cast_refl, Function.comp_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.ModelTheory.Semantics | {
"line": 560,
"column": 2
} | {
"line": 560,
"column": 37
} | {
"line": 562,
"column": 0
} | [
{
"pp": "L : Language\nM : Type w\ninst✝ : L.Structure M\nα : Type u'\nv : α → M\nR : L.Relations 1\nt : L.Term α\nx✝ : Fin 1\n⊢ Term.realize v (![t] x✝) = ![Term.realize v t] x✝",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"congrArg",
"FirstOrder.Language.Term",
"Matr... | [] | simp only [Matrix.cons_val_fin_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.ModelTheory.Definability | {
"line": 151,
"column": 66
} | {
"line": 154,
"column": 6
} | {
"line": 156,
"column": 0
} | [
{
"pp": "M : Type w\nA : Set M\nL : Language\ninst✝¹ : L.Structure M\nα : Type u₁\nι : Type u_2\ninst✝ : Finite ι\nf : ι → Set (α → M)\nhf : ∀ (i : ι), A.Definable L (f i)\n⊢ A.Definable L (⋂ i, f i)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fintype.ofFinite",
... | [] | by
haveI := Fintype.ofFinite ι
convert! definable_finset_inf hf Finset.univ using 1
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.ModelTheory.Definability | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 24
} | {
"line": 209,
"column": 4
} | [
{
"pp": "case mpr\nM : Type w\nA : Set M\nL : Language\ninst✝ : L.Structure M\nα : Type u₁\ns : Set (α → M)\n⊢ (∃ A0, ↑A0 ⊆ A ∧ (↑A0).Definable L s) → A.Definable L s",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Set.Definable",
"Finset",
"Exists",
"LE.le",
... | [
"case mpr\nM : Type w\nA : Set M\nL : Language\ninst✝ : L.Structure M\nα : Type u₁\ns : Set (α → M)\nA0 : Finset M\nhA0 : ↑A0 ⊆ A\nhd : (↑A0).Definable L s\n⊢ A.Definable L s"
] | rintro ⟨A0, hA0, hd⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.RingTheory.Nullstellensatz | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 63
} | {
"line": 180,
"column": 2
} | [
{
"pp": "k : Type u_1\nK : Type u_2\ninst✝⁴ : Field k\ninst✝³ : Field K\ninst✝² : Algebra k K\nσ : Type u_3\ninst✝¹ : IsAlgClosed K\ninst✝ : Finite σ\nI J : Ideal (MvPolynomial σ k)\nhJI : I ≤ J\nhJ : J.IsMaximal\nx : σ → K\nhx : J = vanishingIdeal k {x}\n⊢ vanishingIdeal k (zeroLocus K I) ≤ J",
"ppTerm": "... | [
"k : Type u_1\nK : Type u_2\ninst✝⁴ : Field k\ninst✝³ : Field K\ninst✝² : Algebra k K\nσ : Type u_3\ninst✝¹ : IsAlgClosed K\ninst✝ : Finite σ\nI J : Ideal (MvPolynomial σ k)\nhJI : I ≤ J\nhJ : J.IsMaximal\nx : σ → K\nhx : J = vanishingIdeal k {x}\ny : σ → K\nhy : y ∈ {x}\np : MvPolynomial σ k\nhp : p ∈ I\n⊢ (aeval ... | refine hx.symm ▸ vanishingIdeal_anti_mono fun y hy p hp => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.ModelTheory.Satisfiability | {
"line": 336,
"column": 4
} | {
"line": 338,
"column": 70
} | {
"line": 340,
"column": 0
} | [
{
"pp": "case refine_2\nL : Language\nT : L.Theory\nα : Type w\nφ : L.Formula α\nh : (L.lhomWithConstants α).onTheory T ⊨ᵇ Formula.equivSentence φ\nM : T.ModelType\nv : α → ↑M\n⊢ φ.Realize v",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"FirstOrder.Language.Sen... | [] | letI : (constantsOn α).Structure M := constantsOn.structure v
have : M ⊨ (L.lhomWithConstants α).onTheory T := (LHom.onTheory_model _ _).2 inferInstance
exact (Formula.realize_equivSentence _ _).1 (h.realize_sentence M) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.ModelTheory.Satisfiability | {
"line": 336,
"column": 4
} | {
"line": 338,
"column": 70
} | {
"line": 340,
"column": 0
} | [
{
"pp": "case refine_2\nL : Language\nT : L.Theory\nα : Type w\nφ : L.Formula α\nh : (L.lhomWithConstants α).onTheory T ⊨ᵇ Formula.equivSentence φ\nM : T.ModelType\nv : α → ↑M\n⊢ φ.Realize v",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"FirstOrder.Language.Sen... | [] | letI : (constantsOn α).Structure M := constantsOn.structure v
have : M ⊨ (L.lhomWithConstants α).onTheory T := (LHom.onTheory_model _ _).2 inferInstance
exact (Formula.realize_equivSentence _ _).1 (h.realize_sentence M) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.ModelTheory.Satisfiability | {
"line": 435,
"column": 4
} | {
"line": 435,
"column": 20
} | {
"line": 436,
"column": 4
} | [
{
"pp": "case mpr\nL : Language\nT : L.Theory\n⊢ (T.IsSatisfiable ∧ ∀ (M N : T.ModelType), ↑M ≅[L] ↑N) → T.IsComplete",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"FirstOrder.Language.Theory.ModelType",
"FirstOrder.Language.Theory.IsSatisfiable",
"FirstOrder.Language.Th... | [
"case mpr\nL : Language\nT : L.Theory\nhsat : T.IsSatisfiable\nh : ∀ (M N : T.ModelType), ↑M ≅[L] ↑N\n⊢ T.IsComplete"
] | rintro ⟨hsat, h⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.ModelTheory.Satisfiability | {
"line": 486,
"column": 27
} | {
"line": 486,
"column": 44
} | {
"line": 486,
"column": 45
} | [
{
"pp": "L : Language\nM : Type w\ninst✝ : L.Structure M\nφ : L.Sentence\n⊢ φ ∈ {φ | M ⊨ φ} ∨ Formula.not φ ∈ {φ | M ⊨ φ}",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"FirstOrder.Language.Sentence.Realize",
"setOf",
"Membership.mem",
"FirstOrder.Language.Theory",... | [
"L : Language\nM : Type w\ninst✝ : L.Structure M\nφ : L.Sentence\n⊢ M ⊨ φ ∨ M ⊨ Formula.not φ"
] | Set.mem_setOf_eq, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.ModelTheory.Satisfiability | {
"line": 536,
"column": 6
} | {
"line": 536,
"column": 94
} | {
"line": 536,
"column": 94
} | [
{
"pp": "this : Language.empty.Structure ℕ\n⊢ Language.empty.infiniteTheory.ModelType",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"FirstOrder.Language.empty",
"FirstOrder.Language.infiniteTheory",
"FirstOrder.Language.model_infiniteTheory_iff",
... | [] | exact ((model_infiniteTheory_iff Language.empty).2 (inferInstance : Infinite ℕ)).bundled | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.GroupTheory.OreLocalization.Cardinality | {
"line": 105,
"column": 27
} | {
"line": 105,
"column": 36
} | {
"line": 105,
"column": 37
} | [
{
"pp": "R : Type u\ninst✝² : Monoid R\nS : Submonoid R\ninst✝¹ : OreSet S\nX : Type v\ninst✝ : MulAction R X\nhc : ∀ (s s' : ↥S), Commute s s'\nh✝ : Infinite X\nkey : ∀ (x : X) (s s' : ↥S), s • x = s' • x → Commute s s' → x /ₒ s = x /ₒ s'\ni : X × ↥S → OreLocalization S X := fun x ↦ x.1 /ₒ x.2\nhsurj : Surject... | [
"R : Type u\ninst✝² : Monoid R\nS : Submonoid R\ninst✝¹ : OreSet S\nX : Type v\ninst✝ : MulAction R X\nhc : ∀ (s s' : ↥S), Commute s s'\nh✝ : Infinite X\nkey : ∀ (x : X) (s s' : ↥S), s • x = s' • x → Commute s s' → x /ₒ s = x /ₒ s'\ni : X × ↥S → OreLocalization S X := fun x ↦ x.1 /ₒ x.2\nhsurj : Surjective i\nhi : ... | lift_id', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.SetTheory.Cardinal.Divisibility | {
"line": 52,
"column": 2
} | {
"line": 52,
"column": 46
} | {
"line": 53,
"column": 2
} | [
{
"pp": "case inr\na : Cardinal.{u}\nh : ∀ (y : Cardinal.{u}), a ∣ y\nha : a ≠ 0\nt : Cardinal.{u}\nht : 1 = a * t\n⊢ a = 1",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"mul_eq_one_iff_of_one_le",
"MulOne.toOne",
"Semigroup.toMul",
"HMul.hMul",
"Cardinal.ins... | [
"case inr\na : Cardinal.{u}\nh : ∀ (y : Cardinal.{u}), a ∣ y\nha : a ≠ 0\nt : Cardinal.{u}\nht : a = 1 ∧ t = 1\n⊢ a = 1",
"case inr.ha\na : Cardinal.{u}\nh : ∀ (y : Cardinal.{u}), a ∣ y\nha : a ≠ 0\nt : Cardinal.{u}\nht : a * t = 1\n⊢ 1 ≤ a",
"case inr.hb\na : Cardinal.{u}\nh : ∀ (y : Cardinal.{u}), a ∣ y\nha :... | rw [eq_comm, mul_eq_one_iff_of_one_le] at ht | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.Cardinal.Divisibility | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 39
} | {
"line": 112,
"column": 2
} | [
{
"pp": "case refine_2\nn : ℕ\nh : ∀ (a b : Cardinal.{u_1}), ↑n ∣ a * b → ↑n ∣ a ∨ ↑n ∣ b\nb c : ℕ\nhbc : n ∣ b * c\n⊢ n ∣ b ∨ n ∣ c",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Nat.cast_mul._simp_1",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Dvd.dvd",
"HM... | [
"case refine_3\nn : ℕ\nh : ∀ (a b : ℕ), n ∣ a * b → n ∣ a ∨ n ∣ b\nb c : Cardinal.{u_1}\nhbc : ↑n ∣ b * c\n⊢ ↑n ∣ b ∨ ↑n ∣ c"
] | · exact mod_cast h b c (mod_cast hbc) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.SetTheory.Cardinal.Divisibility | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 47
} | {
"line": 139,
"column": 2
} | [
{
"pp": "case pos\na : Cardinal.{u_1}\nh : ℵ₀ ≤ a\n⊢ IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n, a = ↑n ∧ IsPrimePow n",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Cardinal",
"congrArg",
"true_or",
"IsPrimePow",
"Exists",
"Cardinal.aleph0",
"LE.le",
"Na... | [
"case neg\na : Cardinal.{u_1}\nh : ¬ℵ₀ ≤ a\n⊢ IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n, a = ↑n ∧ IsPrimePow n"
] | · simp [h, (prime_of_aleph0_le h).isPrimePow] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Separation.Connected | {
"line": 25,
"column": 2
} | {
"line": 28,
"column": 35
} | {
"line": 30,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nh : TotallyDisconnectedSpace X\n⊢ T1Space X",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Filter.instMembership",
"Eq.mpr",
"Continuous",
"totallyDisconnectedSpace_iff_connectedComponent_singlet... | [] | rw [((t1Space_TFAE X).out 0 1 :)]
intro x
rw [← totallyDisconnectedSpace_iff_connectedComponent_singleton.mp h x]
exact isClosed_connectedComponent | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Separation.Connected | {
"line": 25,
"column": 2
} | {
"line": 28,
"column": 35
} | {
"line": 30,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nh : TotallyDisconnectedSpace X\n⊢ T1Space X",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Filter.instMembership",
"Eq.mpr",
"Continuous",
"totallyDisconnectedSpace_iff_connectedComponent_singlet... | [] | rw [((t1Space_TFAE X).out 0 1 :)]
intro x
rw [← totallyDisconnectedSpace_iff_connectedComponent_singleton.mp h x]
exact isClosed_connectedComponent | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.CardinalEmb | {
"line": 167,
"column": 34
} | {
"line": 167,
"column": 45
} | {
"line": 167,
"column": 46
} | [
{
"pp": "F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nrank_inf : Fact (ℵ₀ ≤ Module.rank F E)\ninst✝ : Algebra.IsAlgebraic F E\n⊢ ⨆ i, adjoin F (⇑b '' Iio (φ i)) = ⊤",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"IntermediateField... | [
"F : Type u\nE : Type v\ninst✝³ : Field F\ninst✝² : Field E\ninst✝¹ : Algebra F E\nrank_inf : Fact (ℵ₀ ≤ Module.rank F E)\ninst✝ : Algebra.IsAlgebraic F E\n⊢ ⊤ ≤ ⨆ i, adjoin F (⇑b '' Iio (φ i))"
] | eq_top_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.FieldTheory.Isaacs | {
"line": 83,
"column": 69
} | {
"line": 83,
"column": 91
} | {
"line": 83,
"column": 91
} | [
{
"pp": "F : Type u_1\nE : Type u_2\nK : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Field K\ninst✝¹ : Algebra F E\ninst✝ : Algebra F K\nalg : Algebra.IsAlgebraic F E\nh : ∀ (x : E), ∃ y, minpoly F x = minpoly F y\nx : E\ny : K\nhy : minpoly F x = minpoly F y\n⊢ (aeval y) (minpoly F x) = 0",
"ppT... | [] | rw [hy, minpoly.aeval] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.FieldTheory.Isaacs | {
"line": 83,
"column": 69
} | {
"line": 83,
"column": 91
} | {
"line": 83,
"column": 91
} | [
{
"pp": "F : Type u_1\nE : Type u_2\nK : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Field K\ninst✝¹ : Algebra F E\ninst✝ : Algebra F K\nalg : Algebra.IsAlgebraic F E\nh : ∀ (x : E), ∃ y, minpoly F x = minpoly F y\nx : E\ny : K\nhy : minpoly F x = minpoly F y\n⊢ (aeval y) (minpoly F x) = 0",
"ppT... | [] | rw [hy, minpoly.aeval] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.FieldTheory.Isaacs | {
"line": 83,
"column": 69
} | {
"line": 83,
"column": 91
} | {
"line": 83,
"column": 91
} | [
{
"pp": "F : Type u_1\nE : Type u_2\nK : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field E\ninst✝² : Field K\ninst✝¹ : Algebra F E\ninst✝ : Algebra F K\nalg : Algebra.IsAlgebraic F E\nh : ∀ (x : E), ∃ y, minpoly F x = minpoly F y\nx : E\ny : K\nhy : minpoly F x = minpoly F y\n⊢ (aeval y) (minpoly F x) = 0",
"ppT... | [] | rw [hy, minpoly.aeval] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.FieldTheory.IsPerfectClosure | {
"line": 465,
"column": 18
} | {
"line": 465,
"column": 43
} | {
"line": 465,
"column": 43
} | [
{
"pp": "K : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝⁹ : CommRing K\ninst✝⁸ : CommRing L\ninst✝⁷ : CommRing M\ni : K →+* L\nj : K →+* M\np : ℕ\ninst✝⁶ : ExpChar M p\ninst✝⁵ : ExpChar K p\ninst✝⁴ : ExpChar L p\ninst✝³ : PerfectRing L p\ninst✝² : IsPerfectClosure i p\ninst✝¹ : PerfectRing M p\ninst✝ : IsPerfec... | [
"K : Type u_1\nL : Type u_2\nM : Type u_3\ninst✝⁹ : CommRing K\ninst✝⁸ : CommRing L\ninst✝⁷ : CommRing M\ni : K →+* L\nj : K →+* M\np : ℕ\ninst✝⁶ : ExpChar M p\ninst✝⁵ : ExpChar K p\ninst✝⁴ : ExpChar L p\ninst✝³ : PerfectRing L p\ninst✝² : IsPerfectClosure i p\ninst✝¹ : PerfectRing M p\ninst✝ : IsPerfectClosure j p... | equiv_apply j i p _ _ _ h | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.AlgebraicIndependent.RankAndCardinality | {
"line": 84,
"column": 30
} | {
"line": 84,
"column": 52
} | {
"line": 84,
"column": 52
} | [
{
"pp": "case neg\nF : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B : IntermediateField F E\nhA : Algebra.Transcendental F ↥A\nhB : Algebra.Transcendental F ↥B\nthis✝¹ : Algebra.Transcendental F ↥(A ⊔ B)\nthis✝ : Infinite ↥A\nthis : Infinite ↥B\n⊢ #↥(adjoin F (↑A ∪ ↑B)) ≤ max... | [
"case neg\nF : Type u\nE : Type v\ninst✝² : Field F\ninst✝¹ : Field E\ninst✝ : Algebra F E\nA B : IntermediateField F E\nhA : Algebra.Transcendental F ↥A\nhB : Algebra.Transcendental F ↥B\nthis✝¹ : Algebra.Transcendental F ↥(A ⊔ B)\nthis✝ : Infinite ↥A\nthis : Infinite ↥B\n⊢ Cardinal.lift.{u, v} #↥(adjoin F (↑A ∪ ↑... | ← Cardinal.lift_le.{u} | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 322,
"column": 8
} | {
"line": 322,
"column": 19
} | {
"line": 322,
"column": 20
} | [
{
"pp": "case adjoin_rootSet'\nK : Type u\ninst✝ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na : K\nH : Irreducible (X ^ n - C a)\nthis✝ : Fact (Irreducible (X ^ n - C a))\nthis : Algebra K K[n√a] := ⋯\n⊢ Algebra.adjoin K ((X ^ n - C a).rootSet K[n√a]) = ⊤",
"ppTerm": "?adjoin_rootSet'",
"assi... | [
"case adjoin_rootSet'\nK : Type u\ninst✝ : Field K\nn : ℕ\nhζ : (primitiveRoots n K).Nonempty\na : K\nH : Irreducible (X ^ n - C a)\nthis✝ : Fact (Irreducible (X ^ n - C a))\nthis : Algebra K K[n√a] := inferInstance\n⊢ ⊤ ≤ Algebra.adjoin K ((X ^ n - C a).rootSet K[n√a])"
] | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 522,
"column": 10
} | {
"line": 522,
"column": 41
} | {
"line": 523,
"column": 8
} | [
{
"pp": "case refine_2\nK : Type u\ninst✝³ : Field K\nL : Type u_1\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : FiniteDimensional K L\na : K\nα : L\nha : α ^ finrank K L = (algebraMap K L) a\nhα : K⟮α⟯ = ⊤\nq : K [X]\nhq : q.Monic\nhq' : (aeval α) q = 0\n⊢ (X ^ finrank K L - C a).degree ≤ (minpoly K α).degr... | [
"case refine_2\nK : Type u\ninst✝³ : Field K\nL : Type u_1\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : FiniteDimensional K L\na : K\nα : L\nha : α ^ finrank K L = (algebraMap K L) a\nhα : K⟮α⟯ = ⊤\nq : K [X]\nhq : q.Monic\nhq' : (aeval α) q = 0\n⊢ ↑(finrank K L) ≤ (minpoly K α).degree"
] | degree_X_pow_sub_C finrank_pos, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.KummerExtension | {
"line": 538,
"column": 8
} | {
"line": 538,
"column": 19
} | {
"line": 538,
"column": 20
} | [
{
"pp": "case adjoin_rootSet'\nK : Type u\ninst✝³ : Field K\nL : Type u_1\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : FiniteDimensional K L\nhK : (primitiveRoots (finrank K L) K).Nonempty\na : K\nα : L\nha : α ^ finrank K L = (algebraMap K L) a\nhα : K⟮α⟯ = ⊤\n⊢ Algebra.adjoin K ((X ^ finrank K L - C a).ro... | [
"case adjoin_rootSet'\nK : Type u\ninst✝³ : Field K\nL : Type u_1\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : FiniteDimensional K L\nhK : (primitiveRoots (finrank K L) K).Nonempty\na : K\nα : L\nha : α ^ finrank K L = (algebraMap K L) a\nhα : K⟮α⟯ = ⊤\n⊢ ⊤ ≤ Algebra.adjoin K ((X ^ finrank K L - C a).rootSet L)... | eq_top_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Minpoly.ConjRootClass | {
"line": 192,
"column": 76
} | {
"line": 199,
"column": 24
} | {
"line": 201,
"column": 0
} | [
{
"pp": "K : Type u_1\nL : Type u_2\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : Algebra.IsSeparable K L\ninst✝¹ : Normal K L\nc : ConjRootClass K L\ninst✝ : Fintype ↑c.carrier\n⊢ map (algebraMap K L) c.minpoly = ∏ x ∈ c.carrier.toFinset, (X - C x)",
"ppTerm": "?m.65",
"assigned":... | [] | by
classical
simp_rw [← rootSet_minpoly_eq_carrier, Finset.prod_eq_multiset_prod, rootSet_def,
Finset.toFinset_coe, Multiset.toFinset_val]
rw [Multiset.dedup_eq_self.mpr (nodup_roots c.separable_minpoly.map),
prod_multiset_X_sub_C_of_monic_of_roots_card_eq (c.monic_minpoly.map _)]
rw [← splits_iff_card_... | [anonymous] | Lean.Parser.Term.byTactic |
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