module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.NumberTheory.ZetaValues | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 10
} | {
"line": 464,
"column": 0
} | [
{
"pp": "⊢ 4 ≠ 1",
"ppTerm": "?m.116",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"instDecidableEqNat",
"OfNat.ofNat",
"Decida... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ZetaValues | {
"line": 473,
"column": 75
} | {
"line": 473,
"column": 81
} | {
"line": 473,
"column": 82
} | [
{
"pp": "this : 1 / 4 = (algebraMap ℚ ℝ) (1 / 4)\n⊢ 2 * 1 + 1 = 3",
"ppTerm": "?m.185",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"id",
"instMulNat",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Nat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.ZetaValues | {
"line": 473,
"column": 75
} | {
"line": 473,
"column": 81
} | {
"line": 473,
"column": 82
} | [
{
"pp": "this : 1 / 4 = (algebraMap ℚ ℝ) (1 / 4)\n⊢ 2 * 1 + 1 = 3",
"ppTerm": "?m.185",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"id",
"instMulNat",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Nat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ZetaValues | {
"line": 473,
"column": 75
} | {
"line": 473,
"column": 81
} | {
"line": 473,
"column": 82
} | [
{
"pp": "this : 1 / 4 = (algebraMap ℚ ℝ) (1 / 4)\n⊢ 2 * 1 + 1 = 3",
"ppTerm": "?m.185",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"of_decide_eq_true",
"id",
"instMulNat",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Nat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LSeries.Injectivity | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 62
} | {
"line": 108,
"column": 2
} | [
{
"pp": "f : ℕ → ℂ\nn : ℕ\nh : ∀ m ≤ n, f m = 0\nha : abscissaOfAbsConv f < ⊤\ny : ℝ\nhay : abscissaOfAbsConv f < ↑y\nhyt : ↑y < ⊤\nF : ℝ → ℕ → ℂ := fun x ↦ {m | n + 1 < m}.indicator fun m ↦ f m / (↑m / (↑n + 1)) ^ ↑x\nhF₀ : ∀ (x : ℝ) {m : ℕ}, m ≤ n + 1 → F x m = 0\nhF : ∀ (x : ℝ) {m : ℕ}, m ≠ n + 1 → F x m = (... | [
"f : ℕ → ℂ\nn : ℕ\nh : ∀ m ≤ n, f m = 0\nha : abscissaOfAbsConv f < ⊤\ny : ℝ\nhay : abscissaOfAbsConv f < ↑y\nhyt : ↑y < ⊤\nF : ℝ → ℕ → ℂ := fun x ↦ {m | n + 1 < m}.indicator fun m ↦ f m / (↑m / (↑n + 1)) ^ ↑x\nhF₀ : ∀ (x : ℝ) {m : ℕ}, m ≤ n + 1 → F x m = 0\nhF : ∀ (x : ℝ) {m : ℕ}, m ≠ n + 1 → F x m = (↑n + 1) ^ ↑x... | rw [show (0 : ℂ) = tsum (fun _ : ℕ ↦ 0) from tsum_zero.symm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.LSeries.PrimesInAP | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 69
} | {
"line": 355,
"column": 2
} | [
{
"pp": "q : ℕ\na : ZMod q\ninst✝ : NeZero q\nha : IsUnit a\ns : ℂ\nhs : 1 < s.re\n⊢ LFunctionResidueClassAux a s = (fun s ↦ L (fun n ↦ ↑(residueClass a n)) s - (↑q.totient)⁻¹ / (s - 1)) s",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"DirichletCharacter.fintype",
"Eq.mpr",
... | [
"q : ℕ\na : ZMod q\ninst✝ : NeZero q\nha : IsUnit a\ns : ℂ\nhs : 1 < s.re\n⊢ (↑q.totient)⁻¹ *\n (-deriv (LFunctionTrivChar₁ q) s / LFunctionTrivChar₁ q s -\n ∑ χ ∈ {1}ᶜ, χ a⁻¹ * deriv (LFunction χ) s / LFunction χ s) =\n -(↑q.totient)⁻¹ * ∑ χ, χ a⁻¹ * (deriv (LFunction χ) s / LFunction χ s) - (↑q.tot... | simp only [LSeries_residueClass_eq ha hs, LFunctionResidueClassAux] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 37,
"column": 59
} | {
"line": 37,
"column": 65
} | {
"line": 37,
"column": 65
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ZMod p\nhap : a ≠ 0\nhe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x ≠ 0 ∧ x ≤ p / 2\nx✝ : ℕ\nhx : x✝ ∈ Ico 1 (p / 2).succ\n⊢ 1 < 2",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"B... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 37,
"column": 59
} | {
"line": 37,
"column": 65
} | {
"line": 37,
"column": 65
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ZMod p\nhap : a ≠ 0\nhe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x ≠ 0 ∧ x ≤ p / 2\nx✝ : ℕ\nhx : x✝ ∈ Ico 1 (p / 2).succ\n⊢ 1 < 2",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"B... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 37,
"column": 59
} | {
"line": 37,
"column": 65
} | {
"line": 37,
"column": 65
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ZMod p\nhap : a ≠ 0\nhe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x ≠ 0 ∧ x ≤ p / 2\nx✝ : ℕ\nhx : x✝ ∈ Ico 1 (p / 2).succ\n⊢ 1 < 2",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"B... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 40,
"column": 2
} | {
"line": 43,
"column": 100
} | {
"line": 44,
"column": 2
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ZMod p\nhap : a ≠ 0\nhe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x ≠ 0 ∧ x ≤ p / 2\nhep : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x < p\nhpe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → ¬p ∣ x\n⊢ Multiset.map (fun x ↦ (a * ↑x).valMinAbs.natAbs) (Ico 1 (p / 2).succ).val =\n Mult... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\na : ZMod p\nhap : a ≠ 0\nhe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x ≠ 0 ∧ x ≤ p / 2\nhep : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → x < p\nhpe : ∀ {x : ℕ}, x ∈ Ico 1 (p / 2).succ → ¬p ∣ x\nhmem : ∀ x ∈ Ico 1 (p / 2).succ, (a * ↑x).valMinAbs.natAbs ∈ Ico 1 (p / 2).succ\n⊢ Multiset.map (fu... | have hmem : ∀ (x : ℕ) (_ : x ∈ Ico 1 (p / 2).succ),
(a * x : ZMod p).valMinAbs.natAbs ∈ Ico 1 (p / 2).succ := by
intro x hx
simp [hap, CharP.cast_eq_zero_iff (ZMod p) p, hpe hx, one_le_iff_ne_zero, natAbs_valMinAbs_le _] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 53
} | {
"line": 209,
"column": 54
} | [
{
"pp": "a : ℤ\nb : ℕ\nh : a.gcd ↑b = 1\n⊢ J(a | b) ^ 2 = 1",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"jacobiSym.eq_one_or_neg_one",
"id",
"Int.instNegInt",
"instOfNatNat",
"Int",
"NPow.toPow",
"Or.casesOn",
... | [
"case inl\na : ℤ\nb : ℕ\nh : a.gcd ↑b = 1\nh₁ : J(a | b) = 1\n⊢ 1 ^ 2 = 1",
"case inr\na : ℤ\nb : ℕ\nh : a.gcd ↑b = 1\nh₁ : J(a | b) = -1\n⊢ (-1) ^ 2 = 1"
] | rcases eq_one_or_neg_one h with h₁ | h₁ <;> rw [h₁] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.NumberTheory.LSeries.SumCoeff | {
"line": 163,
"column": 60
} | {
"line": 163,
"column": 90
} | {
"line": 165,
"column": 0
} | [
{
"pp": "f : ℕ → ℝ\nr : ℝ\nhr : 0 ≤ r\ns : ℂ\nhs : r < s.re\nhO : (fun n ↦ ∑ k ∈ Icc 1 n, f k) =O[atTop] fun n ↦ ↑n ^ r\nhf : ∀ (n : ℕ), 0 ≤ f n\nx✝ : ℕ\n⊢ ∑ k ∈ Icc 1 x✝, f k = ∑ k ∈ Icc 1 x✝, ‖↑(f k)‖",
"ppTerm": "?m.103",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Real",
... | [] | by simp [abs_of_nonneg (hf _)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 90,
"column": 39
} | {
"line": 90,
"column": 45
} | {
"line": 90,
"column": 45
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\nhap : ↑a ≠ 0\n⊢ 1 < 2",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 90,
"column": 39
} | {
"line": 90,
"column": 45
} | {
"line": 90,
"column": 45
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\nhap : ↑a ≠ 0\n⊢ 1 < 2",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 90,
"column": 39
} | {
"line": 90,
"column": 45
} | {
"line": 90,
"column": 45
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\na : ℤ\nhap : ↑a ≠ 0\n⊢ 1 < 2",
"ppTerm": "?m.98",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 290,
"column": 75
} | {
"line": 290,
"column": 81
} | {
"line": 292,
"column": 0
} | [
{
"pp": "a : ℤ\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nh : J(a | p) = 1\n⊢ ¬1 = -1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Int.instNegInt",
"Int",
"Bool.true",
"instOf... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 336,
"column": 37
} | {
"line": 336,
"column": 43
} | {
"line": 336,
"column": 43
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha4 : 4 * a % 4 = 0\nthis : (↑2).gcd ↑b = 1\n⊢ 4 ≠ 0",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"inst... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 336,
"column": 37
} | {
"line": 336,
"column": 43
} | {
"line": 336,
"column": 43
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha4 : 4 * a % 4 = 0\nthis : (↑2).gcd ↑b = 1\n⊢ 4 ≠ 0",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"inst... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 336,
"column": 37
} | {
"line": 336,
"column": 43
} | {
"line": 336,
"column": 43
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha4 : 4 * a % 4 = 0\nthis : (↑2).gcd ↑b = 1\n⊢ 4 ≠ 0",
"ppTerm": "?m.70",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"inst... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 337,
"column": 8
} | {
"line": 337,
"column": 14
} | {
"line": 337,
"column": 15
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha4 : 4 * a % 4 = 0\nthis : (↑2).gcd ↑b = 1\n⊢ 4 = ↑2 ^ 2",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"NPow.toPow",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 337,
"column": 8
} | {
"line": 337,
"column": 14
} | {
"line": 337,
"column": 15
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha4 : 4 * a % 4 = 0\nthis : (↑2).gcd ↑b = 1\n⊢ 4 = ↑2 ^ 2",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"NPow.toPow",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 337,
"column": 8
} | {
"line": 337,
"column": 14
} | {
"line": 337,
"column": 15
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha4 : 4 * a % 4 = 0\nthis : (↑2).gcd ↑b = 1\n⊢ 4 = ↑2 ^ 2",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"NPow.toPow",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 342,
"column": 23
} | {
"line": 342,
"column": 29
} | {
"line": 342,
"column": 29
} | [
{
"pp": "b : ℕ\nhb : Odd b\n⊢ 4 % 4 = 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"instHMod",
"Int",
"Bool.true",
"HMod.hMod",
"instOfNat",
"Bool",
"Int.instMod",
"Eq.r... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 342,
"column": 23
} | {
"line": 342,
"column": 29
} | {
"line": 342,
"column": 29
} | [
{
"pp": "b : ℕ\nhb : Odd b\n⊢ 4 % 4 = 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"instHMod",
"Int",
"Bool.true",
"HMod.hMod",
"instOfNat",
"Bool",
"Int.instMod",
"Eq.r... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 342,
"column": 23
} | {
"line": 342,
"column": 29
} | {
"line": 342,
"column": 29
} | [
{
"pp": "b : ℕ\nhb : Odd b\n⊢ 4 % 4 = 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"instHMod",
"Int",
"Bool.true",
"HMod.hMod",
"instOfNat",
"Bool",
"Int.instMod",
"Eq.r... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 348,
"column": 37
} | {
"line": 348,
"column": 43
} | {
"line": 348,
"column": 43
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha2 : 2 * a % 2 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"instOfNat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 348,
"column": 37
} | {
"line": 348,
"column": 43
} | {
"line": 348,
"column": 43
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha2 : 2 * a % 2 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"instOfNat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 348,
"column": 37
} | {
"line": 348,
"column": 43
} | {
"line": 348,
"column": 43
} | [
{
"pp": "b : ℕ\nhb2 : b % 2 = 1\na : ℤ\nha2 : 2 * a % 2 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Int.instDecidableEq",
"id",
"Ne",
"Int",
"Bool.true",
"instOfNat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 186,
"column": 47
} | {
"line": 186,
"column": 53
} | {
"line": 186,
"column": 53
} | [
{
"pp": "p q : ℕ\nhp : Fact (Nat.Prime p)\nhq0 : ↑q ≠ 0\nhswap :\n #({x ∈ Ico 1 (q / 2).succ ×ˢ Ico 1 (p / 2).succ | x.2 * q ≤ x.1 * p}) =\n #({x ∈ Ico 1 (p / 2).succ ×ˢ Ico 1 (q / 2).succ | x.1 * q ≤ x.2 * p})\nx : ℕ × ℕ\nhx : x ∈ Ico 1 (p / 2).succ ×ˢ Ico 1 (q / 2).succ\nhpq : x.2 * p ≤ x.1 * q\nhqp : x.1... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 186,
"column": 47
} | {
"line": 186,
"column": 53
} | {
"line": 186,
"column": 53
} | [
{
"pp": "p q : ℕ\nhp : Fact (Nat.Prime p)\nhq0 : ↑q ≠ 0\nhswap :\n #({x ∈ Ico 1 (q / 2).succ ×ˢ Ico 1 (p / 2).succ | x.2 * q ≤ x.1 * p}) =\n #({x ∈ Ico 1 (p / 2).succ ×ˢ Ico 1 (q / 2).succ | x.1 * q ≤ x.2 * p})\nx : ℕ × ℕ\nhx : x ∈ Ico 1 (p / 2).succ ×ˢ Ico 1 (q / 2).succ\nhpq : x.2 * p ≤ x.1 * q\nhqp : x.1... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas | {
"line": 186,
"column": 47
} | {
"line": 186,
"column": 53
} | {
"line": 186,
"column": 53
} | [
{
"pp": "p q : ℕ\nhp : Fact (Nat.Prime p)\nhq0 : ↑q ≠ 0\nhswap :\n #({x ∈ Ico 1 (q / 2).succ ×ˢ Ico 1 (p / 2).succ | x.2 * q ≤ x.1 * p}) =\n #({x ∈ Ico 1 (p / 2).succ ×ˢ Ico 1 (q / 2).succ | x.1 * q ≤ x.2 * p})\nx : ℕ × ℕ\nhx : x ∈ Ico 1 (p / 2).succ ×ˢ Ico 1 (q / 2).succ\nhpq : x.2 * p ≤ x.1 * q\nhqp : x.1... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 411,
"column": 66
} | {
"line": 411,
"column": 70
} | {
"line": 411,
"column": 70
} | [
{
"pp": "case e'_2.e'_6\na✝ b : ℕ\nha : Odd a✝\nhb : Odd b\na : ℕ\n⊢ 1 = J(↑1 | a)",
"ppTerm": "?e'_2.e'_6",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Nat.instMulOneClass",
"Int",
"Nat.cast",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemir... | [
"case e'_2.e'_6\na✝ b : ℕ\nha : Odd a✝\nhb : Odd b\na : ℕ\n⊢ J(↑1 | a) = 1"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 411,
"column": 66
} | {
"line": 411,
"column": 70
} | {
"line": 411,
"column": 70
} | [
{
"pp": "case e'_2.e'_6\na✝ b : ℕ\nha : Odd a✝\nhb : Odd b\na : ℕ\n⊢ 1 = J(↑1 | a)",
"ppTerm": "?e'_2.e'_6",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Nat.instMulOneClass",
"Int",
"Nat.cast",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemir... | [
"case e'_2.e'_6\na✝ b : ℕ\nha : Odd a✝\nhb : Odd b\na : ℕ\n⊢ J(↑1 | a) = 1"
] | symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 411,
"column": 66
} | {
"line": 411,
"column": 70
} | {
"line": 411,
"column": 70
} | [
{
"pp": "case e'_2.e'_6\na✝ b : ℕ\nha : Odd a✝\nhb : Odd b\na : ℕ\n⊢ 1 = J(↑1 | a)",
"ppTerm": "?e'_2.e'_6",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Nat.instMulOneClass",
"Int",
"Nat.cast",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemir... | [
"case e'_2.e'_6\na✝ b : ℕ\nha : Odd a✝\nhb : Odd b\na : ℕ\n⊢ J(↑1 | a) = 1"
] | symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 462,
"column": 66
} | {
"line": 462,
"column": 72
} | {
"line": 462,
"column": 72
} | [
{
"pp": "a b : ℕ\nhb : Odd b\nha₀ : a ≠ 0\n⊢ Even 4",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instAddNat",
"Eq.refl... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 462,
"column": 66
} | {
"line": 462,
"column": 72
} | {
"line": 462,
"column": 72
} | [
{
"pp": "a b : ℕ\nhb : Odd b\nha₀ : a ≠ 0\n⊢ Even 4",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instAddNat",
"Eq.refl... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 462,
"column": 66
} | {
"line": 462,
"column": 72
} | {
"line": 462,
"column": 72
} | [
{
"pp": "a b : ℕ\nhb : Odd b\nha₀ : a ≠ 0\n⊢ Even 4",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instAddNat",
"Eq.refl... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 478,
"column": 29
} | {
"line": 478,
"column": 41
} | {
"line": 478,
"column": 41
} | [
{
"pp": "case h\na b : ℕ\nhb : Odd b\nha₀ : a ≠ 0\nhb' : Odd (b % (4 * a))\na' : ℕ\nha₁' : ¬2 ∣ a'\nha₁ : Odd a'\ne : ℕ\nha₂ : a = 2 ^ (e + 1) * a'\n⊢ 4 * (2 ^ (e + 1) * a') = 8 * (2 ^ e * a')",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"HMul.hMul... | [
"case h\na b : ℕ\nhb : Odd b\nha₀ : a ≠ 0\nhb' : Odd (b % (4 * a))\na' : ℕ\nha₁' : ¬2 ∣ a'\nha₁ : Odd a'\ne : ℕ\nha₂ : a = 2 ^ (e + 1) * a'\n⊢ 4 * (2 ^ e * 2 * a') = 8 * (2 ^ e * a')"
] | Nat.pow_succ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 484,
"column": 75
} | {
"line": 484,
"column": 81
} | {
"line": 484,
"column": 81
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : Odd b\nha : a = -↑a.natAbs\n⊢ Even 4",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instAddNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 484,
"column": 75
} | {
"line": 484,
"column": 81
} | {
"line": 484,
"column": 81
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : Odd b\nha : a = -↑a.natAbs\n⊢ Even 4",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instAddNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 484,
"column": 75
} | {
"line": 484,
"column": 81
} | {
"line": 484,
"column": 81
} | [
{
"pp": "a : ℤ\nb : ℕ\nhb : Odd b\nha : a = -↑a.natAbs\n⊢ Even 4",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidablePredEven",
"Bool.true",
"Nat",
"Even",
"Bool",
"instAddNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 511,
"column": 72
} | {
"line": 511,
"column": 78
} | {
"line": 511,
"column": 78
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : a % 4 = 0\n⊢ 0 < 4",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNa... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 511,
"column": 72
} | {
"line": 511,
"column": 78
} | {
"line": 511,
"column": 78
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : a % 4 = 0\n⊢ 0 < 4",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNa... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 511,
"column": 72
} | {
"line": 511,
"column": 78
} | {
"line": 511,
"column": 78
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : a % 4 = 0\n⊢ 0 < 4",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNa... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 514,
"column": 72
} | {
"line": 514,
"column": 78
} | {
"line": 514,
"column": 78
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 0 < 2",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 514,
"column": 72
} | {
"line": 514,
"column": 78
} | {
"line": 514,
"column": 78
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 0 < 2",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 514,
"column": 72
} | {
"line": 514,
"column": 78
} | {
"line": 514,
"column": 78
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 0 < 2",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 523,
"column": 32
} | {
"line": 523,
"column": 38
} | {
"line": 523,
"column": 38
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : a % 4 = 0\n⊢ 1 < 4",
"ppTerm": "?m.168",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 523,
"column": 32
} | {
"line": 523,
"column": 38
} | {
"line": 523,
"column": 38
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : a % 4 = 0\n⊢ 1 < 4",
"ppTerm": "?m.168",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 523,
"column": 32
} | {
"line": 523,
"column": 38
} | {
"line": 523,
"column": 38
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : a % 4 = 0\n⊢ 1 < 4",
"ppTerm": "?m.168",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 524,
"column": 32
} | {
"line": 524,
"column": 38
} | {
"line": 524,
"column": 38
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 1 < 2",
"ppTerm": "?m.170",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.ref... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 524,
"column": 32
} | {
"line": 524,
"column": 38
} | {
"line": 524,
"column": 38
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 1 < 2",
"ppTerm": "?m.170",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.ref... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 524,
"column": 32
} | {
"line": 524,
"column": 38
} | {
"line": 524,
"column": 38
} | [
{
"pp": "a b : ℕ\nflip : Bool\nha0 : a > 0\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 1 < 2",
"ppTerm": "?m.170",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.ref... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 533,
"column": 42
} | {
"line": 533,
"column": 48
} | {
"line": 533,
"column": 48
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : a % 4 = 0\n⊢ 1 < 4",
"ppTerm": "?m.61",
"assigned": ... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 533,
"column": 42
} | {
"line": 533,
"column": 48
} | {
"line": 533,
"column": 48
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : a % 4 = 0\n⊢ 1 < 4",
"ppTerm": "?m.61",
"assigned": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 533,
"column": 42
} | {
"line": 533,
"column": 48
} | {
"line": 533,
"column": 48
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : a % 4 = 0\n⊢ 1 < 4",
"ppTerm": "?m.61",
"assigned": ... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 536,
"column": 42
} | {
"line": 536,
"column": 48
} | {
"line": 536,
"column": 48
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 1 < 2",
"ppTerm": "?m.91"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 536,
"column": 42
} | {
"line": 536,
"column": 48
} | {
"line": 536,
"column": 48
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 1 < 2",
"ppTerm": "?m.91"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 536,
"column": 42
} | {
"line": 536,
"column": 48
} | {
"line": 536,
"column": 48
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : ¬a % 4 = 0\nha2 : a % 2 = 0\n⊢ 1 < 2",
"ppTerm": "?m.91"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 543,
"column": 57
} | {
"line": 543,
"column": 63
} | {
"line": 543,
"column": 63
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : ¬a % 4 = 0\nha2 : ¬a % 2 = 0\nha1 : ¬a = 1\nhba : b % a = 0\... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 543,
"column": 57
} | {
"line": 543,
"column": 63
} | {
"line": 543,
"column": 63
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : ¬a % 4 = 0\nha2 : ¬a % 2 = 0\nha1 : ¬a = 1\nhba : b % a = 0\... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 543,
"column": 57
} | {
"line": 543,
"column": 63
} | {
"line": 543,
"column": 63
} | [
{
"pp": "a : ℕ\nIH :\n ∀ m < a,\n ∀ {b : ℕ} {flip : Bool} {ha0 : m > 0},\n b % 2 = 1 → b > 1 → fastJacobiSymAux m b flip ha0 = if flip = true then -J(↑m | b) else J(↑m | b)\nb : ℕ\nflip : Bool\nha0 : a > 0\nhb2 : b % 2 = 1\nhb1 : b > 1\nha4 : ¬a % 4 = 0\nha2 : ¬a % 2 = 0\nha1 : ¬a = 1\nhba : b % a = 0\... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 583,
"column": 25
} | {
"line": 583,
"column": 31
} | {
"line": 583,
"column": 31
} | [
{
"pp": "a : ℤ\nha2 : ¬a % 2 = 0\nb : ℕ\nIH : ∀ m < 2 * b, J(a | m) = fastJacobiSym a m\nhb0 : ¬2 * b = 0\nhb2 : 2 * b % 2 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 583,
"column": 25
} | {
"line": 583,
"column": 31
} | {
"line": 583,
"column": 31
} | [
{
"pp": "a : ℤ\nha2 : ¬a % 2 = 0\nb : ℕ\nIH : ∀ m < 2 * b, J(a | m) = fastJacobiSym a m\nhb0 : ¬2 * b = 0\nhb2 : 2 * b % 2 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 583,
"column": 25
} | {
"line": 583,
"column": 31
} | {
"line": 583,
"column": 31
} | [
{
"pp": "a : ℤ\nha2 : ¬a % 2 = 0\nb : ℕ\nIH : ∀ m < 2 * b, J(a | m) = fastJacobiSym a m\nhb0 : ¬2 * b = 0\nhb2 : 2 * b % 2 = 0\n⊢ 2 ≠ 0",
"ppTerm": "?m.162",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 584,
"column": 32
} | {
"line": 584,
"column": 38
} | {
"line": 584,
"column": 38
} | [
{
"pp": "a : ℤ\nha2 : ¬a % 2 = 0\nb : ℕ\nIH : ∀ m < 2 * b, J(a | m) = fastJacobiSym a m\nhb0 : ¬2 * b = 0\nhb2 : 2 * b % 2 = 0\n⊢ 0 < 2",
"ppTerm": "?m.171",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 584,
"column": 32
} | {
"line": 584,
"column": 38
} | {
"line": 584,
"column": 38
} | [
{
"pp": "a : ℤ\nha2 : ¬a % 2 = 0\nb : ℕ\nIH : ∀ m < 2 * b, J(a | m) = fastJacobiSym a m\nhb0 : ¬2 * b = 0\nhb2 : 2 * b % 2 = 0\n⊢ 0 < 2",
"ppTerm": "?m.171",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 584,
"column": 32
} | {
"line": 584,
"column": 38
} | {
"line": 584,
"column": 38
} | [
{
"pp": "a : ℤ\nha2 : ¬a % 2 = 0\nb : ℕ\nIH : ∀ m < 2 * b, J(a | m) = fastJacobiSym a m\nhb0 : ¬2 * b = 0\nhb2 : 2 * b % 2 = 0\n⊢ 0 < 2",
"ppTerm": "?m.171",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | {
"line": 587,
"column": 2
} | {
"line": 587,
"column": 89
} | {
"line": 588,
"column": 2
} | [
{
"pp": "case pos\na : ℤ\nb : ℕ\nIH : ∀ m < b, J(a | m) = fastJacobiSym a m\nhb0 : ¬b = 0\nhb2 : ¬b % 2 = 0\nhb1 : ¬b = 1\nhab : a % ↑b = 0\n⊢ J(a | b) = 0",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"jacobiSym.mod_left",
"id",
"instH... | [
"case neg\na : ℤ\nb : ℕ\nIH : ∀ m < b, J(a | m) = fastJacobiSym a m\nhb0 : ¬b = 0\nhb2 : ¬b % 2 = 0\nhb1 : ¬b = 1\nhab : ¬a % ↑b = 0\n⊢ J(a | b) = fastJacobiSymAux (a % ↑b).natAbs b false ⋯"
] | · rw [mod_left, hab, zero_left (lt_of_le_of_ne (Nat.pos_of_ne_zero hb0) (Ne.symm hb1))] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.LucasLehmer | {
"line": 489,
"column": 4
} | {
"line": 489,
"column": 25
} | {
"line": 490,
"column": 2
} | [
{
"pp": "case refine_1\np' : ℕ\n⊢ 1 < p' + 2",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Nat.le_add_left",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Nat.succ"
],
"usedFVars": [
"p'"
],
"usedGoals": []
}
] | [] | exact le_add_left _ _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.LucasLehmer | {
"line": 489,
"column": 4
} | {
"line": 489,
"column": 25
} | {
"line": 490,
"column": 2
} | [
{
"pp": "case refine_1\np' : ℕ\n⊢ 1 < p' + 2",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Nat.le_add_left",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Nat.succ"
],
"usedFVars": [
"p'"
],
"usedGoals": []
}
] | [] | exact le_add_left _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LucasLehmer | {
"line": 489,
"column": 4
} | {
"line": 489,
"column": 25
} | {
"line": 490,
"column": 2
} | [
{
"pp": "case refine_1\np' : ℕ\n⊢ 1 < p' + 2",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Nat.le_add_left",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Nat.succ"
],
"usedFVars": [
"p'"
],
"usedGoals": []
}
] | [] | exact le_add_left _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LucasLehmer | {
"line": 510,
"column": 52
} | {
"line": 510,
"column": 58
} | {
"line": 510,
"column": 58
} | [
{
"pp": "p' : ℕ\nk : ℤ\nt : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)\nh : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1\n⊢ 0 < 2",
"ppTerm": "?m.423",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.LucasLehmer | {
"line": 510,
"column": 52
} | {
"line": 510,
"column": 58
} | {
"line": 510,
"column": 58
} | [
{
"pp": "p' : ℕ\nk : ℤ\nt : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)\nh : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1\n⊢ 0 < 2",
"ppTerm": "?m.423",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LucasLehmer | {
"line": 510,
"column": 52
} | {
"line": 510,
"column": 58
} | {
"line": 510,
"column": 58
} | [
{
"pp": "p' : ℕ\nk : ℤ\nt : 2 ^ p' + 2 ^ p' = 2 ^ (p' + 1)\nh : ω ^ 2 ^ (p' + 1) = ↑k * ↑(2 ^ (p' + 2) - 1) * ω ^ 2 ^ p' - 1\n⊢ 0 < 2",
"ppTerm": "?m.423",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LucasLehmer | {
"line": 604,
"column": 37
} | {
"line": 604,
"column": 51
} | {
"line": 604,
"column": 51
} | [
{
"pp": "p' : ℕ\nw : 3 ≤ p' + 2\nhp : Nat.Prime (mersenne (p' + 2))\nthis : Fact (Nat.Prime (mersenne (p' + 2)))\nhp' : p' = p' + 2 - 2\n⊢ 4 ∣ mersenne (p' + 2) + 1",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"dvd_mul_left._simp_1",
"Dvd.dvd",
"HMul.hMul",
"Mono... | [] | simp [pow_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.LucasLehmer | {
"line": 604,
"column": 37
} | {
"line": 604,
"column": 51
} | {
"line": 604,
"column": 51
} | [
{
"pp": "p' : ℕ\nw : 3 ≤ p' + 2\nhp : Nat.Prime (mersenne (p' + 2))\nthis : Fact (Nat.Prime (mersenne (p' + 2)))\nhp' : p' = p' + 2 - 2\n⊢ 4 ∣ mersenne (p' + 2) + 1",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"dvd_mul_left._simp_1",
"Dvd.dvd",
"HMul.hMul",
"Mono... | [] | simp [pow_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LucasLehmer | {
"line": 604,
"column": 37
} | {
"line": 604,
"column": 51
} | {
"line": 604,
"column": 51
} | [
{
"pp": "p' : ℕ\nw : 3 ≤ p' + 2\nhp : Nat.Prime (mersenne (p' + 2))\nthis : Fact (Nat.Prime (mersenne (p' + 2)))\nhp' : p' = p' + 2 - 2\n⊢ 4 ∣ mersenne (p' + 2) + 1",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"dvd_mul_left._simp_1",
"Dvd.dvd",
"HMul.hMul",
"Mono... | [] | simp [pow_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LucasLehmer | {
"line": 605,
"column": 30
} | {
"line": 605,
"column": 57
} | {
"line": 605,
"column": 58
} | [
{
"pp": "p' : ℕ\nw : 3 ≤ p' + 2\nhp : Nat.Prime (mersenne (p' + 2))\nthis✝ : Fact (Nat.Prime (mersenne (p' + 2)))\nhp' : p' = p' + 2 - 2\nthis : X.ω ^ (2 ^ p' * 2 ^ 2 / 4) + X.ωb ^ (2 ^ p' * 2 ^ 2 / 4) = 0\n⊢ (X.ω ^ 2 ^ p' + X.ωb ^ 2 ^ p').1 = 0",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants... | [
"p' : ℕ\nw : 3 ≤ p' + 2\nhp : Nat.Prime (mersenne (p' + 2))\nthis✝ : Fact (Nat.Prime (mersenne (p' + 2)))\nhp' : p' = p' + 2 - 2\nthis : X.ω ^ (2 ^ p' * 4 / 4) + X.ωb ^ (2 ^ p' * 4 / 4) = 0\n⊢ (X.ω ^ 2 ^ p' + X.ωb ^ 2 ^ p').1 = 0"
] | show 2 ^ 2 = 4 by norm_num, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.MahlerMeasure | {
"line": 171,
"column": 60
} | {
"line": 177,
"column": 57
} | {
"line": 179,
"column": 0
} | [
{
"pp": "p : ℤ[X]\nh : (map (castRingHom ℂ) p).mahlerMeasure = 1\nz : ℂ\nhz : z ∈ p.aroots ℂ\n⊢ ‖z‖ ≤ 1",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"le_max_right",
"Real.instIsOrderedRing",
"Norm.norm",
"MulOne.toOne",
"Real.partialOrder",
"Real.inst... | [] | by
calc
‖z‖ ≤ max 1 ‖z‖ := le_max_right 1 ‖z‖
_ ≤ ((p.map (castRingHom ℂ)).roots.map (fun a ↦ max 1 ‖a‖)).prod :=
mem_le_prod_of_one_le (fun a ↦ le_max_left 1 ‖a‖) hz
_ ≤ 1 := by grind [prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff,
norm_leadingCoeff_eq_one_of_mahlerMeasure... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.LSeries.SumCoeff | {
"line": 355,
"column": 4
} | {
"line": 359,
"column": 82
} | {
"line": 360,
"column": 2
} | [
{
"pp": "case refine_2\nf : ℕ → ℂ\nl : ℂ\nhlim : Tendsto (fun n ↦ (∑ k ∈ Icc 1 n, f k) / ↑n) atTop (𝓝 l)\nhfS : ∀ (s : ℝ), 1 < s → LSeriesSummable f ↑s\nh₁ : ∀ {C ε : ℝ}, Tendsto (fun s ↦ (s - 1) * s * C + s * ε) (𝓝[>] 1) (𝓝 ε)\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) (𝓝[>] 1) fun s ↦ ‖(↑s - 1) * LSeries ... | [] | refine le_of_forall_pos_le_add fun ε hε ↦ ?_
rw [zero_add]
obtain ⟨C, hC₁, hC₂⟩ := LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_aux₃ hlim hfS hε
refine le_of_le_of_eq (limsup_le_limsup hC₂ ?_ h₁.isBoundedUnder_le) h₁.limsup_eq
exact isCoboundedUnder_le_of_eventually_le _ (univ_mem' fun _ ↦ norm_n... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LSeries.SumCoeff | {
"line": 355,
"column": 4
} | {
"line": 359,
"column": 82
} | {
"line": 360,
"column": 2
} | [
{
"pp": "case refine_2\nf : ℕ → ℂ\nl : ℂ\nhlim : Tendsto (fun n ↦ (∑ k ∈ Icc 1 n, f k) / ↑n) atTop (𝓝 l)\nhfS : ∀ (s : ℝ), 1 < s → LSeriesSummable f ↑s\nh₁ : ∀ {C ε : ℝ}, Tendsto (fun s ↦ (s - 1) * s * C + s * ε) (𝓝[>] 1) (𝓝 ε)\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) (𝓝[>] 1) fun s ↦ ‖(↑s - 1) * LSeries ... | [] | refine le_of_forall_pos_le_add fun ε hε ↦ ?_
rw [zero_add]
obtain ⟨C, hC₁, hC₂⟩ := LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div_aux₃ hlim hfS hε
refine le_of_le_of_eq (limsup_le_limsup hC₂ ?_ h₁.isBoundedUnder_le) h₁.limsup_eq
exact isCoboundedUnder_le_of_eventually_le _ (univ_mem' fun _ ↦ norm_n... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 113,
"column": 36
} | {
"line": 113,
"column": 94
} | {
"line": 114,
"column": 2
} | [
{
"pp": "n✝ : Type u_1\ninst✝¹ : Fintype n✝\ninst✝ : DecidableEq n✝\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : Γ.IsArithmetic\ng : GL (Fin 2) ℝ\nhg : g ∈ Γ\nn : ℕ\nhn : 0 < n\nleft✝ : n ≤ (mapGL ℝ).range.relIndex Γ\nhgn : g ^ n ∈ (mapGL ℝ).range ⊓ Γ\nthis : |↑(GeneralLinearGroup.det g ^ n)| = 1\n⊢ |↑(GeneralLinearGroup.... | [] | simpa [← abs_pow, abs_pow_eq_one _ (Nat.ne_zero_of_lt hn)] | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 113,
"column": 36
} | {
"line": 113,
"column": 94
} | {
"line": 114,
"column": 2
} | [
{
"pp": "n✝ : Type u_1\ninst✝¹ : Fintype n✝\ninst✝ : DecidableEq n✝\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : Γ.IsArithmetic\ng : GL (Fin 2) ℝ\nhg : g ∈ Γ\nn : ℕ\nhn : 0 < n\nleft✝ : n ≤ (mapGL ℝ).range.relIndex Γ\nhgn : g ^ n ∈ (mapGL ℝ).range ⊓ Γ\nthis : |↑(GeneralLinearGroup.det g ^ n)| = 1\n⊢ |↑(GeneralLinearGroup.... | [] | simpa [← abs_pow, abs_pow_eq_one _ (Nat.ne_zero_of_lt hn)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 113,
"column": 36
} | {
"line": 113,
"column": 94
} | {
"line": 114,
"column": 2
} | [
{
"pp": "n✝ : Type u_1\ninst✝¹ : Fintype n✝\ninst✝ : DecidableEq n✝\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : Γ.IsArithmetic\ng : GL (Fin 2) ℝ\nhg : g ∈ Γ\nn : ℕ\nhn : 0 < n\nleft✝ : n ≤ (mapGL ℝ).range.relIndex Γ\nhgn : g ^ n ∈ (mapGL ℝ).range ⊓ Γ\nthis : |↑(GeneralLinearGroup.det g ^ n)| = 1\n⊢ |↑(GeneralLinearGroup.... | [] | simpa [← abs_pow, abs_pow_eq_one _ (Nat.ne_zero_of_lt hn)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 257,
"column": 8
} | {
"line": 257,
"column": 57
} | {
"line": 257,
"column": 57
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝ : Ring R\n𝒢 : Subgroup (GL (Fin 2) R)\nh : 𝒢.strictPeriods < 𝒢.periods\nu : R\nhu_mem : u ∈ 𝒢.periods\nhu_notMem : u ∉ 𝒢.strictPeriods\n⊢ 𝒢.strictPeriods.relIndex 𝒢.periods = 1 ∨ 𝒢.strictPeriods.relIndex 𝒢.periods = 2",
"ppTerm": "?neg✝",
"assigned": true,... | [
"case neg\nR : Type u_1\ninst✝ : Ring R\n𝒢 : Subgroup (GL (Fin 2) R)\nh : 𝒢.strictPeriods < 𝒢.periods\nu : R\nhu_mem : u ∈ 𝒢.periods\nhu_notMem : u ∉ 𝒢.strictPeriods\n⊢ 𝒢.strictPeriods.relIndex 𝒢.periods = 1 ∨\n ∃ a ∈ 𝒢.periods, a ∉ 𝒢.strictPeriods ∧ ∀ b ∈ 𝒢.periods, b + a ∈ 𝒢.strictPeriods ∨ b ∈ 𝒢.s... | AddSubgroup.relIndex_eq_two_iff_exists_notMem_and | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 38,
"column": 21
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 40
} | [
{
"pp": "case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℂ), a ≠ 0 ∨ 0 ≤ k",
"ppTerm": "?funProp.discharger",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"DivisionSemiring.toGroupWithZero",
"id",
"Ne",
... | [
"case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℂ), ¬a = 0 ∨ 0 ≤ k"
] | simp [im_ne_zero _] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 38,
"column": 21
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 40
} | [
{
"pp": "case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℂ), a ≠ 0 ∨ 0 ≤ k",
"ppTerm": "?funProp.discharger",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"DivisionSemiring.toGroupWithZero",
"id",
"Ne",
... | [
"case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℂ), ¬a = 0 ∨ 0 ≤ k"
] | simp [im_ne_zero _] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 38,
"column": 21
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 40
} | [
{
"pp": "case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℂ), a ≠ 0 ∨ 0 ≤ k",
"ppTerm": "?funProp.discharger",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"DivisionSemiring.toGroupWithZero",
"id",
"Ne",
... | [
"case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℂ), ¬a = 0 ∨ 0 ≤ k"
] | simp [im_ne_zero _] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 38,
"column": 21
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 40
} | [
{
"pp": "case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℍ), ↑a.im ≠ 0 ∨ 0 ≤ k",
"ppTerm": "?funProp.discharger",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Real",
"UpperHalfPlane.im_ne_zero"... | [] | simp [im_ne_zero _] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 38,
"column": 21
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 40
} | [
{
"pp": "case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℍ), ↑a.im ≠ 0 ∨ 0 ≤ k",
"ppTerm": "?funProp.discharger",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Real",
"UpperHalfPlane.im_ne_zero"... | [] | simp [im_ne_zero _] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 38,
"column": 21
} | {
"line": 38,
"column": 40
} | {
"line": 38,
"column": 40
} | [
{
"pp": "case funProp.discharger\nk : ℤ\nf f' : ℍ → ℂ\nhf : Continuous f\nhf' : Continuous f'\n⊢ ∀ (a : ℍ), ↑a.im ≠ 0 ∨ 0 ≤ k",
"ppTerm": "?funProp.discharger",
"assigned": true,
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"False",
"Real",
"UpperHalfPlane.im_ne_zero"... | [] | simp [im_ne_zero _] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Modular | {
"line": 180,
"column": 6
} | {
"line": 185,
"column": 33
} | {
"line": 185,
"column": 33
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\ncd : Fin 2 → ℤ\nhcd : IsCoprime (cd 0) (cd 1)\n⊢ (Fin 2 → ℝ) ≃ₗ[ℝ] Fin 2 → ℝ",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"Pi.Function.module",
"Matrix.GeneralLinearGroup.to... | [] | refine
LinearMap.GeneralLinearGroup.generalLinearEquiv ℝ (Fin 2 → ℝ)
(GeneralLinearGroup.toLin (planeConformalMatrix (cd 0 : ℝ) (-(cd 1 : ℝ)) ?_))
norm_cast
rw [neg_sq]
exact hcd.sq_add_sq_ne_zero | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Modular | {
"line": 180,
"column": 6
} | {
"line": 185,
"column": 33
} | {
"line": 185,
"column": 33
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\ncd : Fin 2 → ℤ\nhcd : IsCoprime (cd 0) (cd 1)\n⊢ (Fin 2 → ℝ) ≃ₗ[ℝ] Fin 2 → ℝ",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"Pi.Function.module",
"Matrix.GeneralLinearGroup.to... | [] | refine
LinearMap.GeneralLinearGroup.generalLinearEquiv ℝ (Fin 2 → ℝ)
(GeneralLinearGroup.toLin (planeConformalMatrix (cd 0 : ℝ) (-(cd 1 : ℝ)) ?_))
norm_cast
rw [neg_sq]
exact hcd.sq_add_sq_ne_zero | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 52
} | {
"line": 111,
"column": 2
} | [
{
"pp": "case right\nF : Type u_1\nF' : Type u_2\ninst✝⁶ : FunLike F ℍ ℂ\ninst✝⁵ : FunLike F' ℍ ℂ\nk : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝⁴ : Fact (IsCusp OnePoint.infty Γ)\ninst✝³ : Γ.HasDetPlusMinusOne\ninst✝² : DiscreteTopology ↥Γ\ninst✝¹ : ModularFormClass F Γ k\ninst✝ : ModularFormClass F' Γ k\nf : F\nh_... | [
"case right\nF : Type u_1\nF' : Type u_2\ninst✝⁶ : FunLike F ℍ ℂ\ninst✝⁵ : FunLike F' ℍ ℂ\nk : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝⁴ : Fact (IsCusp OnePoint.infty Γ)\ninst✝³ : Γ.HasDetPlusMinusOne\ninst✝² : DiscreteTopology ↥Γ\ninst✝¹ : ModularFormClass F Γ k\ninst✝ : ModularFormClass F' Γ k\nf : F\nh_bd : IsZeroA... | conv_rhs => enter [τ]; rw [← one_mul (Real.exp _)] | Mathlib.Tactic.Conv._aux_Mathlib_Tactic_Conv___macroRules_Mathlib_Tactic_Conv_convRHS_1 | Mathlib.Tactic.Conv.convRHS |
Mathlib.NumberTheory.Modular | {
"line": 331,
"column": 2
} | {
"line": 341,
"column": 82
} | {
"line": 344,
"column": 0
} | [
{
"pp": "g : SL(2, ℤ)\nhc : ↑g 1 0 = 0\n⊢ ∃ n, ∀ (z : ℍ), g • z = T ^ n • z",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"Real",
"Fintype.card_fin_two",
"instHSMul",
... | [] | have had := g.det_coe
replace had : g 0 0 * g 1 1 = 1 := by rw [det_fin_two, hc] at had; lia
rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
· use g 0 1
suffices g = T ^ g 0 1 by intro z; conv_lhs => rw [this]
ext i j; fin_cases i <;> fin_cases j <;>
simp [ha, hc, hd, coe_... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Modular | {
"line": 331,
"column": 2
} | {
"line": 341,
"column": 82
} | {
"line": 344,
"column": 0
} | [
{
"pp": "g : SL(2, ℤ)\nhc : ↑g 1 0 = 0\n⊢ ∃ n, ∀ (z : ℍ), g • z = T ^ n • z",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"Real",
"Fintype.card_fin_two",
"instHSMul",
... | [] | have had := g.det_coe
replace had : g 0 0 * g 1 1 = 1 := by rw [det_fin_two, hc] at had; lia
rcases Int.eq_one_or_neg_one_of_mul_eq_one' had with (⟨ha, hd⟩ | ⟨ha, hd⟩)
· use g 0 1
suffices g = T ^ g 0 1 by intro z; conv_lhs => rw [this]
ext i j; fin_cases i <;> fin_cases j <;>
simp [ha, hc, hd, coe_... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs | {
"line": 190,
"column": 74
} | {
"line": 198,
"column": 44
} | {
"line": 200,
"column": 0
} | [
{
"pp": "k : ℤ\ni : Fin 2 → ℤ\nA : SL(2, ℤ)\nz : ℍ\n⊢ eisSummand k i (A • z) =\n denom (SpecialLinearGroup.toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) A)) ↑z ^ k * eisSummand k (i ᵥ* ↑A) z",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_le... | [] | by
simp only [eisSummand, vecMul, vec2_dotProduct, denom, UpperHalfPlane.specialLinearGroup_apply]
have h (a b c d u v : ℂ) (hc : c * z + d ≠ 0) : (u * ((a * z + b) / (c * z + d)) + v) ^ (-k) =
(c * z + d) ^ k * ((u * a + v * c) * z + (u * b + v * d)) ^ (-k) := by
replace hc : z * c + d ≠ 0 := by convert!... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty | {
"line": 40,
"column": 59
} | {
"line": 46,
"column": 67
} | {
"line": 48,
"column": 0
} | [
{
"pp": "k : ℤ\nhk : 3 ≤ k\nz : ℍ\n⊢ Summable fun x ↦ ‖eisSummand k x z‖",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"Real.instIsOrderedRing",
"Norm.norm",
"Int.cast",
"SeminormedAddGroup.toNorm",
"Eq.m... | [] | by
have hk' : (2 : ℝ) < k := by norm_cast
apply ((summable_one_div_norm_rpow hk').mul_left <| r z ^ (-k : ℝ)).of_nonneg_of_le
(fun _ ↦ norm_nonneg _)
intro b
simp only [eisSummand, norm_zpow]
exact_mod_cast summand_bound z (show 0 ≤ (k : ℝ) by positivity) b | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Modular | {
"line": 498,
"column": 8
} | {
"line": 498,
"column": 18
} | {
"line": 498,
"column": 18
} | [
{
"pp": "g✝ : SL(2, ℤ)\nz✝ : ℍ\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhc : ↑g 1 0 = 0\nhd' : ↑g 1 1 = 1 ∨ ↑g 1 1 = -1\nhd : ↑g 1 1 = 1\nha : ↑g 0 0 = 1\nb : ℤ := ↑g 0 1\ni j : Fin 2\n⊢ ↑g i j = ↑(T ^ b) i j",
"ppTerm": "?m.457",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"g✝ : SL(2, ℤ)\nz✝ : ℍ\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhc : ↑g 1 0 = 0\nhd' : ↑g 1 1 = 1 ∨ ↑g 1 1 = -1\nhd : ↑g 1 1 = 1\nha : ↑g 0 0 = 1\nb : ℤ := ↑g 0 1\ni j : Fin 2\n⊢ ↑g i j = !![1, b; 0, 1] i j"
] | coe_T_zpow | Lean.Elab.Tactic.evalRewriteSeq | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.