module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.NumberTheory.LucasLehmer | {
"line": 406,
"column": 4
} | {
"line": 406,
"column": 44
} | [
{
"pp": "k : ℕ\ninst✝ : Fact (Nat.Prime (2 * k + 1))\nleg3 : legendreSym (2 * k + 1) 3 = -1\nq : ℕ := 2 * k + 1\n⊢ 3 ^ k = -1",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"Field.toDivisionRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 413,
"column": 36
} | {
"line": 415,
"column": 10
} | [
{
"pp": "q : ℕ\ninst✝ : Fact (Nat.Prime q)\nodd : Odd q\nleg3 : legendreSym q 3 = -1\n⊢ (1 + α) ^ (q + 1) = -2",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMu... | by
rw [pow_succ, one_add_α_pow_q odd leg3, mul_comm, ← _root_.sq_sub_sq, α_sq]
norm_num | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.LucasLehmer | {
"line": 497,
"column": 6
} | {
"line": 497,
"column": 19
} | [
{
"pp": "p' : ℕ\nh : sZMod (p' + 2) (p' + 2 - 2) = 0\n⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1",
"usedConstants": [
"Int.cast",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"HSub.hSub",
"Eq.mp",
"instSub... | sZMod_eq_s p' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 498,
"column": 44
} | {
"line": 498,
"column": 91
} | [
{
"pp": "p' : ℕ\nh : ↑(s (p' + 2 - 2)) = 0\n⊢ 2 ^ (p' + 2) - 1 ∣ s p'",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 527,
"column": 2
} | {
"line": 527,
"column": 13
} | [
{
"pp": "p' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\nk : ℤ\nw : ω ^ 2 ^ (p' + 1) = ↑k * 0 * ω ^ 2 ^ p' - 1\n⊢ ω ^ 2 ^ (p' + 1) = -1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 690,
"column": 2
} | {
"line": 690,
"column": 13
} | [
{
"pp": "p : ℕ\nhp : 1 < p\nh : sModNatTR (2 ^ p - 1) (p - 2) ≠ 0\n⊢ ¬↑(sModNatTR (2 ^ p - 1) (p - 2)) = 0",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
"Int",
"Nat.cast",
"Monoid.toPo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.MahlerMeasure | {
"line": 61,
"column": 6
} | {
"line": 61,
"column": 17
} | [
{
"pp": "case refine_1\nn : ℕ\nB₁ B₂ : Fin (n + 1) → ℝ\np : ↑(boxPoly n B₁ B₂)\nprop : ∀ (i : Fin (n + 1)), B₁ i ≤ ↑((↑p).coeff ↑i) ∧ ↑((↑p).coeff ↑i) ≤ B₂ i\n⊢ (toFn (n + 1)) ↑p ∈ ↑(Finset.Icc (fun x ↦ ⌈B₁ x⌉) fun x ↦ ⌊B₂ x⌋)",
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 29
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nH K : Subgroup G\nhHK : H ≤ K\n⊢ ∀ (s : Set ↥H),\n (∃ a,\n IsOpen[inst✝] a ∧\n Subtype.val ⁻¹' Subtype.val ⁻¹' a =\n ⇑{ toFun := fun g ↦ ⟨↑↑g, ⋯⟩, invFun := fun g ↦ ⟨⟨↑g, ⋯⟩, ⋯⟩, left_inv := ⋯, right_inv := ⋯,\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.MahlerMeasure | {
"line": 214,
"column": 2
} | {
"line": 214,
"column": 70
} | [
{
"pp": "p : ℤ[X]\nh : (map (castRingHom ℂ) p).mahlerMeasure = 1\nz : ℂ\nhz₀ : z ≠ 0\nhz : z ∈ p.aroots ℂ\n⊢ ∃ n, 0 < n ∧ IsPrimitiveRoot z n",
"usedConstants": [
"Polynomial.pow_eq_one_of_mahlerMeasure_eq_one"
]
}
] | obtain ⟨_, _, hz_pow⟩ := pow_eq_one_of_mahlerMeasure_eq_one h hz₀ hz | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 141,
"column": 4
} | {
"line": 143,
"column": 21
} | [
{
"pp": "case mp\nN : ℕ\nA : ↥(Gamma0 N)\nha : ↑(↑↑A 1 1) = 1\nadet : ↑(↑↑A 0 0) * ↑(↑↑A 1 1) - ↑(↑↑A 0 1) * ↑(↑↑A 1 0) = 1\n⊢ ↑(↑↑A 0 0) = 1 ∧ ↑(↑↑A 1 1) = 1 ∧ ↑(↑↑A 1 0) = 0",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Matrix.SpecialLinearGroup",
"ZMod.commRing",
"_private.Mat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.ArchimedeanDiscrete | {
"line": 72,
"column": 26
} | {
"line": 73,
"column": 90
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : CommGroup G\ninst✝⁴ : LinearOrder G\ninst✝³ : IsOrderedMonoid G\ninst✝² : TopologicalSpace G\ninst✝¹ : OrderTopology G\ninst✝ : MulArchimedean G\nH : Subgroup G\na✝ : Nontrivial G\nthis : Dense ↑H ∨ ∃ a, zpowers a = H\nhA : DiscreteTopology ↥H\nh : Dense ↑H\n⊢ H = ⊤",
"usedCo... | by
rw [← coe_eq_univ, ← (dense_iff_closure_eq.mp h), H.isClosed_of_discrete.closure_eq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 263,
"column": 6
} | {
"line": 263,
"column": 17
} | [
{
"pp": "g : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nA₁ : Matrix (Fin 2) (Fin 2) ℚ := ↑g\nA₂ : Matrix (Fin 2) (Fin 2) ℚ := ↑g⁻¹\nhA₁₂ : A₁ * A₂ = 1\na₁ : ℕ := A₁.den\na₂ : ℕ := A₂.den\nx✝ : SL(2, ℤ)\ny : Matrix (Fin 2) (Fin 2) ℤ\nhy : y.det = 1\nhy' : ↑((SpecialLinearGroup.map (Int.castRingHom (ZMod (a₁ * a₂ * M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 264,
"column": 4
} | {
"line": 264,
"column": 55
} | [
{
"pp": "g : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nA₁ : Matrix (Fin 2) (Fin 2) ℚ := ↑g\nA₂ : Matrix (Fin 2) (Fin 2) ℚ := ↑g⁻¹\nhA₁₂ : A₁ * A₂ = 1\na₁ : ℕ := A₁.den\na₂ : ℕ := A₂.den\nx✝ : SL(2, ℤ)\ny : Matrix (Fin 2) (Fin 2) ℤ\nhy : y.det = 1\nhy' : y.map Int.cast = 1\n⊢ ∃ k, y = 1 + (a₁ * a₂ * M) • k",
"u... | use Matrix.of fun i j ↦ (y - 1) i j / (a₁ * a₂ * M) | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 48,
"column": 2
} | {
"line": 48,
"column": 69
} | [
{
"pp": "n : Type u_1\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq n\nR : Type u_2\ninst✝² : CommRing R\nΓ : Subgroup (GL n R)\ninst✝¹ : LinearOrder R\ninst✝ : IsOrderedRing R\nh : ∀ {g : GL n R}, g ∈ Γ → |↑(GeneralLinearGroup.det g)| = 1\n⊢ ∀ {g : GL n R}, g ∈ Γ → GeneralLinearGroup.det g = 1 ∨ GeneralLinearGroup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 271,
"column": 4
} | {
"line": 272,
"column": 25
} | [
{
"pp": "case h.a\ng : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nA₁ : Matrix (Fin 2) (Fin 2) ℚ := ↑g\nA₂ : Matrix (Fin 2) (Fin 2) ℚ := ↑g⁻¹\nhA₁₂ : A₁ * A₂ = 1\na₁ : ℕ := A₁.den\na₂ : ℕ := A₂.den\nx✝ : SL(2, ℤ)\ny : Matrix (Fin 2) (Fin 2) ℤ\nhy : y.det = 1\nhy' : (y - 1).map Int.cast = 0\ni j : Fin 2\n⊢ ↑a₁ * ↑a₂ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 96,
"column": 4
} | {
"line": 97,
"column": 59
} | [
{
"pp": "case mp\nΓ : Subgroup SL(2, ℤ)\nx✝ : (map (mapGL ℝ) Γ).IsArithmetic\nh : (map (mapGL ℝ) Γ).Commensurable (mapGL ℝ).range\n⊢ Γ.index ≠ 0",
"usedConstants": [
"Matrix.SpecialLinearGroup",
"instDecidableEqFin",
"Matrix.SpecialLinearGroup.instGroup",
"id",
"Ne",
"ins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 96,
"column": 4
} | {
"line": 97,
"column": 59
} | [
{
"pp": "case mpr\nΓ : Subgroup SL(2, ℤ)\nx✝ : Γ.FiniteIndex\nh : Γ.index ≠ 0\n⊢ (map (mapGL ℝ) Γ).Commensurable (mapGL ℝ).range",
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"False",
"Nat.instMulZeroClass",
"Real.partialOrder",
"Real",
"CommRing",
"Matrix... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 25
} | [
{
"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\n⊢ |↑(GeneralLinearGroup.det g ^ n)| = 1",
"usedConstants": [
... | obtain ⟨t, ht⟩ := hgn.1 | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 188,
"column": 38
} | {
"line": 188,
"column": 49
} | [
{
"pp": "n : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_2\ninst✝ : Ring R\n𝒢 : Subgroup (GL n R)\nhG : -1 ∈ 𝒢\ng : GL n R\nhg : g ∈ 𝒢.adjoinNegOne\nh : -g ∈ 𝒢\n⊢ g ∈ 𝒢",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 289,
"column": 30
} | {
"line": 290,
"column": 24
} | [
{
"pp": "g : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nA₁ : Matrix (Fin 2) (Fin 2) ℚ := ↑g\nA₂ : Matrix (Fin 2) (Fin 2) ℚ := ↑g⁻¹\nhA₁₂ : A₁ * A₂ = 1\na₁ : ℕ := A₁.den\na₂ : ℕ := A₂.den\nx✝ : SL(2, ℤ)\ny : Matrix (Fin 2) (Fin 2) ℤ\nhy : y.det = 1\nhy' : ⟨y, hy⟩ ∈ Γ(a₁ * a₂ * M)\nk : Matrix (Fin 2) (Fin 2) ℤ\nhk : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 233,
"column": 4
} | {
"line": 233,
"column": 44
} | [
{
"pp": "case inr\nn : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_3\ninst✝ : CommRing R\n𝒢 : Subgroup (GL n R)\nhn : Even (Fintype.card n)\nx✝ : 𝒢.HasDetOne\ng : GL n R\nhg : -g ∈ 𝒢\n⊢ GeneralLinearGroup.det g = 1",
"usedConstants": [
"Units.val",
"Eq.mpr",
"MulOne... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | {
"line": 136,
"column": 6
} | {
"line": 137,
"column": 13
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : DecidableEq K\ng : GL (Fin 2) K\nh : ![↑g 0 0, ↑g 1 0] = 0\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 60
} | [
{
"pp": "case right\ng : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nN : ℕ\nhN : N ≠ 0\nh : ∀ x ∈ Γ(N), g * (mapGL ℚ) x * g⁻¹ ∈ Subgroup.map (mapGL ℚ) Γ(M)\nx : SL(2, ℤ)\nhx : x ∈ Γ(N)\nz : SL(2, ℤ)\nhz : z ∈ ↑Γ(M)\nhz' : (mapGL ℚ) z = g * (mapGL ℚ) x * g⁻¹\n⊢ (mapGL ℝ) z = toConjAct ((GeneralLinearGroup.map (Rat.ca... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | {
"line": 205,
"column": 6
} | {
"line": 206,
"column": 13
} | [
{
"pp": "case neg\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : DecidableEq K\ng : GL (Fin 2) K\ninst✝ : NeZero 2\nhg : ↑g ∉ Set.range ⇑(Matrix.scalar (Fin 2))\nhdisc : (↑g 0 0 + ↑g 1 1) ^ 2 - 4 * (↑g 0 0 * ↑g 1 1 - ↑g 0 1 * ↑g 1 0) = 0\nc : K\nhc : ¬↑g 1 0 = 0\nthis : discrim (↑g 1 0) (↑g 1 1 - ↑g 0 0) (-↑g 0 1) =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 323,
"column": 4
} | {
"line": 323,
"column": 34
} | [
{
"pp": "g : GL (Fin 2) ℚ\nt : ConjAct (GL (Fin 2) ℝ) := (toConjAct ((GeneralLinearGroup.map (Rat.castHom ℝ)) g))⁻¹\nN : ℕ\nhN : N ≠ 0\nhN' : toConjAct ((GeneralLinearGroup.map (Rat.castHom ℝ)) g) • Subgroup.map (mapGL ℝ) Γ(N) ≤ (mapGL ℝ).range\nthis : Γ(N) ≤ comap (mapGL ℝ) (t • (mapGL ℝ).range ⊓ (mapGL ℝ).ran... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 325,
"column": 2
} | {
"line": 325,
"column": 51
} | [
{
"pp": "case index_ne_zero\ng : GL (Fin 2) ℚ\nt : ConjAct (GL (Fin 2) ℝ) := (toConjAct ((GeneralLinearGroup.map (Rat.castHom ℝ)) g))⁻¹\nN : ℕ\nhN : N ≠ 0\nhN' : toConjAct ((GeneralLinearGroup.map (Rat.castHom ℝ)) g) • Subgroup.map (mapGL ℝ) Γ(N) ≤ (mapGL ℝ).range\nk : SL(2, ℤ)\nhk : k ∈ Γ(N)\n⊢ k ∈ comap (mapG... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | {
"line": 234,
"column": 8
} | {
"line": 235,
"column": 15
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : DecidableEq K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\ng : GL (Fin 2) K\nhg : g.IsElliptic\nc : K\nh : g • ↑c = ↑c\n⊢ ↑g 1 0 * (c * c) + (↑g 1 1 + -↑g 0 0) * c + -↑g 0 1 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashActions | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 39
} | [
{
"pp": "β : Type u_1\nG : Type u_2\nα : Type u_3\ninst✝² : Group G\ninst✝¹ : AddGroup α\ninst✝ : SlashAction β G α\nk : β\ng : G\na : α\nh : (a ∣[k] g) ∣[k] g⁻¹ = 0 ∣[k] g⁻¹\n⊢ a = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashActions | {
"line": 185,
"column": 2
} | {
"line": 185,
"column": 13
} | [
{
"pp": "A : SL(2, ℤ)\n⊢ 1 ∣[0] Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) A) = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashActions | {
"line": 258,
"column": 2
} | {
"line": 258,
"column": 36
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : Nonempty ι\nk : ℤ\ng : GL (Fin 2) ℝ\nf : ι → ℍ → ℂ\nthis : 0 < Fintype.card ι\n⊢ (∏ i, f i) ∣[k * ↑(Fintype.card ι)] g = |↑(Matrix.GeneralLinearGroup.det g)| ^ (Fintype.card ι - 1) • ∏ i, f i ∣[k] g",
"usedConstants": [
"Units.val",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 94,
"column": 4
} | {
"line": 95,
"column": 41
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝² : FunLike F ℍ ℂ\nk : ℤ\ninst✝¹ : Γ.HasDetOne\ninst✝ : SlashInvariantFormClass F Γ k\nf : F\nγ : GL (Fin 2) ℝ\nhγ : γ ∈ Γ\nz : ℍ\n⊢ f (γ • z) = f z * denom γ ↑z ^ k",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 56
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\nΓ : Subgroup SL(2, ℤ)\ninst✝ : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ) k\nf : F\nγ : SL(2, ℤ)\nhγ : γ ∈ Γ\nz : ℍ\n⊢ (Matrix.SpecialLinearGroup.mapGL ℝ) γ ∈ Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 59
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\nΓ : Subgroup SL(2, ℤ)\ninst✝ : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ) k\nf : F\nγ : SL(2, ℤ)\nhγ : γ ∈ Γ\nz : ℍ\n⊢ (Matrix.SpecialLinearGroup.mapGL ℝ) γ ∈ Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ",
"usedC... | simpa using hγ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 59
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\nΓ : Subgroup SL(2, ℤ)\ninst✝ : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ) k\nf : F\nγ : SL(2, ℤ)\nhγ : γ ∈ Γ\nz : ℍ\n⊢ (Matrix.SpecialLinearGroup.mapGL ℝ) γ ∈ Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ",
"usedC... | simpa using hγ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 59
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\nΓ : Subgroup SL(2, ℤ)\ninst✝ : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ) k\nf : F\nγ : SL(2, ℤ)\nhγ : γ ∈ Γ\nz : ℍ\n⊢ (Matrix.SpecialLinearGroup.mapGL ℝ) γ ∈ Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ",
"usedC... | simpa using hγ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 41
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\ninst✝¹ : FunLike F ℍ ℂ\ninst✝ : SlashInvariantFormClass F Γ k\nf : F\ng j : GL (Fin 2) ℝ\nhj : g * j * g⁻¹ ∈ Γ\n⊢ (⇑f ∣[k] g) ∣[k] j = ⇑f ∣[k] g",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"outParam",
"Monoid.to... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 32,
"column": 2
} | {
"line": 33,
"column": 9
} | [
{
"pp": "g : GL (Fin 2) ℝ\nf : ℍ → ℂ\nk : ℤ\nhg : ↑g 1 0 = 0\nhf : Tendsto (fun x ↦ ‖f x‖) atImInfty (nhds 0)\n⊢ Tendsto (fun x ↦ ‖(f ∣[k] g) x‖) atImInfty (nhds 0)",
"usedConstants": [
"UpperHalfPlane.glAction",
"Norm.norm",
"Units.val",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 68,
"column": 16
} | {
"line": 68,
"column": 27
} | [
{
"pp": "c : OnePoint ℝ\nf : ℍ → ℂ\nk : ℤ\nf' : ℍ → ℂ\nhf : c.IsBoundedAt f k\nhf' : c.IsBoundedAt f' k\ng : GL (Fin 2) ℝ\nhg : g • ∞ = c\n⊢ IsBoundedAtImInfty ((f + f') ∣[k] g)",
"usedConstants": [
"Eq.mpr",
"UpperHalfPlane.IsBoundedAtImInfty",
"Real",
"AddMonoid.toAddSemigroup",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 72,
"column": 16
} | {
"line": 72,
"column": 27
} | [
{
"pp": "c : OnePoint ℝ\nf : ℍ → ℂ\nk : ℤ\nf' : ℍ → ℂ\nhf : c.IsZeroAt f k\nhf' : c.IsZeroAt f' k\ng : GL (Fin 2) ℝ\nhg : g • ∞ = c\n⊢ IsZeroAtImInfty ((f + f') ∣[k] g)",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"AddMonoid.toAddSemigroup",
"co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 75,
"column": 14
} | {
"line": 75,
"column": 25
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nh : ∞.IsBoundedAt f k\n⊢ IsBoundedAtImInfty f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 78,
"column": 14
} | {
"line": 78,
"column": 25
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nh : ∞.IsZeroAt f k\n⊢ IsZeroAtImInfty f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 98,
"column": 4
} | {
"line": 98,
"column": 61
} | [
{
"pp": "case mp\nf : ℍ → ℂ\nk : ℤ\nγ : SL(2, ℤ)\nhc : IsCusp ((mapGL ℝ) γ • ∞) (mapGL ℝ).range\n⊢ ((mapGL ℝ) γ • ∞).IsBoundedAt f k → ∃ γ_1, (mapGL ℝ) γ_1 • ∞ = (mapGL ℝ) γ • ∞ ∧ IsBoundedAtImInfty (f ∣[k] γ_1)",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"OnePoint.IsBoundedAt"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 61
} | [
{
"pp": "case mpr\nf : ℍ → ℂ\nk : ℤ\nγ : SL(2, ℤ)\nb : IsBoundedAtImInfty (f ∣[k] γ)\nhc : IsCusp ((mapGL ℝ) γ • ∞) (mapGL ℝ).range\n⊢ ((mapGL ℝ) γ • ∞).IsBoundedAt f k",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"OnePoint.IsBoundedAt",
"UpperHalfPlane.IsBoundedAtImInfty"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 106,
"column": 4
} | {
"line": 106,
"column": 55
} | [
{
"pp": "case mp\nf : ℍ → ℂ\nk : ℤ\nγ : SL(2, ℤ)\nhc : IsCusp ((mapGL ℝ) γ • ∞) (mapGL ℝ).range\n⊢ ((mapGL ℝ) γ • ∞).IsZeroAt f k → ∃ γ_1, (mapGL ℝ) γ_1 • ∞ = (mapGL ℝ) γ • ∞ ∧ IsZeroAtImInfty (f ∣[k] γ_1)",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"NormedCommRing.toSeminormed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 55
} | [
{
"pp": "case mpr\nf : ℍ → ℂ\nk : ℤ\nγ : SL(2, ℤ)\nb : IsZeroAtImInfty (f ∣[k] γ)\nhc : IsCusp ((mapGL ℝ) γ • ∞) (mapGL ℝ).range\n⊢ ((mapGL ℝ) γ • ∞).IsZeroAt f k",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 112,
"column": 27
} | {
"line": 112,
"column": 38
} | [
{
"pp": "c : OnePoint ℝ\nf : ℍ → ℂ\nk : ℤ\nhc✝ : IsCusp c (mapGL ℝ).range\nhc : c.IsBoundedAt f k\nx✝ : SL(2, ℤ)\nhγ : (mapGL ℝ) x✝ • ∞ = c\n⊢ IsBoundedAtImInfty (f ∣[k] x✝)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 66,
"column": 4
} | {
"line": 66,
"column": 40
} | [
{
"pp": "case refine_1\nc : OnePoint ℝ\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ng p : GL (Fin 2) ℝ\nhp𝒢 : p ∈ 𝒢\nhpp : p.IsParabolic\nhpc : p • c = c\n⊢ (ConjAct.toConjAct g • p).IsParabolic",
"usedConstants": [
"Matrix.GeneralLinearGroup.isParabolic_conj_iff._simp_1",
"Eq.mpr",
"Real",
"ins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 59
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nγ : SL(2, ℤ)\nhc : IsCusp ((mapGL ℝ) γ • ∞) (mapGL ℝ).range\nh : ∀ (γ_1 : SL(2, ℤ)), (mapGL ℝ) γ_1 • ∞ = (mapGL ℝ) γ • ∞ → IsBoundedAtImInfty (f ∣[k] γ_1)\n⊢ ((mapGL ℝ) γ • ∞).IsBoundedAt f k",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"OnePoint.IsBou... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 118,
"column": 27
} | {
"line": 118,
"column": 38
} | [
{
"pp": "c : OnePoint ℝ\nf : ℍ → ℂ\nk : ℤ\nhc✝ : IsCusp c (mapGL ℝ).range\nhc : c.IsZeroAt f k\nx✝ : SL(2, ℤ)\nhγ : (mapGL ℝ) x✝ • ∞ = c\n⊢ IsZeroAtImInfty (f ∣[k] x✝)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 53
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nγ : SL(2, ℤ)\nhc : IsCusp ((mapGL ℝ) γ • ∞) (mapGL ℝ).range\nh : ∀ (γ_1 : SL(2, ℤ)), (mapGL ℝ) γ_1 • ∞ = (mapGL ℝ) γ • ∞ → IsZeroAtImInfty (f ∣[k] γ_1)\n⊢ ((mapGL ℝ) γ • ∞).IsZeroAt f k",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"NormedCommRing.toSem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 48
} | [
{
"pp": "case refine_2\nc : OnePoint ℝ\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ng p : GL (Fin 2) ℝ\nhp𝒢 : p ∈ 𝒢\nhpp : p.IsParabolic\nhpc : p • c = c\n⊢ (ConjAct.toConjAct g • p) • g • c = g • c",
"usedConstants": [
"OnePoint.instGLAction",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
... | · simp [ConjAct.toConjAct_smul, mul_smul, hpc] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.ModularForms.Identities | {
"line": 45,
"column": 2
} | {
"line": 45,
"column": 51
} | [
{
"pp": "N : ℕ\nk n : ℤ\nf : SlashInvariantForm (Subgroup.map (mapGL ℝ) Γ(N)) k\nz : ℍ\n⊢ f (↑(↑N * n) +ᵥ z) = f z",
"usedConstants": [
"SlashInvariantForm",
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Real",
"Matrix.SpecialLinearGroup",
"HMul.hMul",
"AddMonoid... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Identities | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 78
} | [
{
"pp": "case mpr\nf : ℍ → ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\ns : Set (GL (Fin 2) ℝ)\nhΓ : Γ = Subgroup.closure s\nk : ℤ\nh : ∀ γ ∈ s, f ∣[k] γ = f\nγ : GL (Fin 2) ℝ\nhγ : γ ∈ Γ\n⊢ f ∣[k] γ = f",
"usedConstants": [
"Real",
"InvOneClass.toOne",
"Subgroup.closure",
"DivInvOneMonoid.toInvO... | apply Subgroup.closure_induction (p := fun γ _ ↦ f ∣[k] γ = f) h (by simp) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 90,
"column": 4
} | {
"line": 90,
"column": 45
} | [
{
"pp": "case h𝒢'\n𝒢 𝒢' : Subgroup (GL (Fin 2) ℝ)\nh𝒢 : 𝒢.Commensurable 𝒢'\nc : OnePoint ℝ\n⊢ (𝒢 ⊓ 𝒢').relIndex 𝒢' ≠ 0",
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"Matrix",
"instDecidableEqFin",
"CompleteLattice.toConditionallyCompleteLattice",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 91,
"column": 4
} | {
"line": 91,
"column": 44
} | [
{
"pp": "case h𝒢'\n𝒢 𝒢' : Subgroup (GL (Fin 2) ℝ)\nh𝒢 : 𝒢.Commensurable 𝒢'\nc : OnePoint ℝ\n⊢ (𝒢 ⊓ 𝒢').relIndex 𝒢 ≠ 0",
"usedConstants": [
"Eq.mpr",
"Subgroup.inf_relIndex_left",
"Real",
"congrArg",
"Matrix",
"instDecidableEqFin",
"CompleteLattice.toConditi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 50
} | [
{
"pp": "case mp\nc : OnePoint ℝ\ng : SL(2, ℤ)\nhgp : ((mapGL ℝ) g).IsParabolic\nhgc : (mapGL ℝ) g • c = c\n⊢ c ∈ Set.range (OnePoint.map Rat.cast)",
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"Real.partialOrder",
"Real",
"instHSMul",
"Matrix.SpecialLinearGroup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 125,
"column": 47
} | {
"line": 125,
"column": 75
} | [
{
"pp": "a✝ : SL(2, ℤ)\nx✝ : ↑((mapGL ℝ) ModularGroup.T) ∈ Set.range ⇑(Matrix.scalar (Fin 2))\na : ℝ\nha : (Matrix.scalar (Fin 2)) a = ↑((mapGL ℝ) ModularGroup.T)\n⊢ 0 = 1",
"usedConstants": [
"Eq.mpr",
"False",
"Real",
"Real.instZero",
"id",
"Real.instFloorRing",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 263,
"column": 6
} | {
"line": 263,
"column": 36
} | [
{
"pp": "case neg.inr\nR : Type u_1\ninst✝ : Ring R\n𝒢 : Subgroup (GL (Fin 2) R)\nh✝ : 𝒢.strictPeriods < 𝒢.periods\nu b : R\nhu_mem : upperRightHom u ∈ 𝒢 ∨ -upperRightHom u ∈ 𝒢\nhu_notMem : upperRightHom u ∉ 𝒢\nh : -upperRightHom b ∈ 𝒢\n⊢ upperRightHom b * upperRightHom u ∈ 𝒢 ∨ upperRightHom b ∈ 𝒢",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 304,
"column": 38
} | {
"line": 304,
"column": 49
} | [
{
"pp": "Γ : Subgroup SL(2, ℤ)\nhΓ : ModularGroup.T ∈ Γ\nx : ℝ\nx✝ : ∃ x_1 ∈ Γ, (algebraMap ℤ ℝ).mapMatrix ↑x_1 = ↑(upperRightHom x)\ng : SL(2, ℤ)\nleft✝ : g ∈ Γ\nhg : (algebraMap ℤ ℝ).mapMatrix ↑g = ↑(upperRightHom x)\n⊢ (fun x ↦ x • 1) (↑g 0 1) = x",
"usedConstants": [
"Int.cast",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 38
} | [
{
"pp": "⊢ (mapGL ℝ).range.strictPeriods = AddSubgroup.zmultiples 1",
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"Subgroup.map",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Matrix",
"instDecidableEqFin",
"Mo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 355,
"column": 2
} | {
"line": 355,
"column": 38
} | [
{
"pp": "⊢ (mapGL ℝ).range.strictWidthInfty = 1",
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"Subgroup.map",
"congrArg",
"Matrix",
"instDecidableEqFin",
"MonoidHom.range_eq_map",
"Real.semiring",
"Mat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 375,
"column": 4
} | {
"line": 375,
"column": 66
} | [
{
"pp": "case inl\n𝒢 : Subgroup (GL (Fin 2) ℝ)\nh : upperRightHom 𝒢.widthInfty ∈ 𝒢\n⊢ 2 * 𝒢.widthInfty ∈ 𝒢.strictPeriods",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"Matrix",
"instDecidableEqFin",
"Nat.instAtLeastTwoHAddOfN... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 375,
"column": 4
} | {
"line": 375,
"column": 66
} | [
{
"pp": "case inr\n𝒢 : Subgroup (GL (Fin 2) ℝ)\nh : -upperRightHom 𝒢.widthInfty ∈ 𝒢\n⊢ 2 * 𝒢.widthInfty ∈ 𝒢.strictPeriods",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"Matrix",
"instDecidableEqFin",
"Nat.instAtLeastTwoHAddOf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 383,
"column": 6
} | {
"line": 383,
"column": 17
} | [
{
"pp": "case mp.refine_1\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ninst✝¹ : DiscreteTopology ↥𝒢.strictPeriods\ninst✝ : 𝒢.HasDetPlusMinusOne\nh : 0 < 𝒢.strictWidthInfty\n⊢ ↑(Additive.toMul (upperRightHom.toAddMonoidHom 𝒢.strictWidthInfty)) 0 0 =\n ↑(Additive.toMul (upperRightHom.toAddMonoidHom 𝒢.strictWidthInfty... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 399,
"column": 11
} | {
"line": 399,
"column": 62
} | [
{
"pp": "𝒢 : Subgroup (GL (Fin 2) ℝ)\ninst✝¹ : DiscreteTopology ↥𝒢.strictPeriods\ninst✝ : 𝒢.HasDetPlusMinusOne\nx : ℝ\nhx : x ≠ 0\nhgg : -upperRightHom x ∈ 𝒢\nhgi : ↑(-upperRightHom x) 1 0 = 0\n⊢ upperRightHom (2 • x) ∈ 𝒢",
"usedConstants": [
"Eq.mpr",
"AddChar.map_nsmul_eq_pow",
"Rea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 403,
"column": 2
} | {
"line": 404,
"column": 9
} | [
{
"pp": "𝒢 : Subgroup (GL (Fin 2) ℝ)\ninst✝ : 𝒢.IsArithmetic\n⊢ IsCusp ∞ 𝒢",
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"OnePoint.infty",
"Matrix",
"Real.instRatCast",
"Rat",
"instDecidableEqFin",
"Membe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 459,
"column": 26
} | {
"line": 459,
"column": 37
} | [
{
"pp": "N : ℕ\nx : ℝ\nthis : AddSubgroup.zmultiples ↑N = AddSubgroup.map (Int.castAddHom ℝ) (AddSubgroup.zmultiples ↑N)\ng : SL(2, ℤ)\nhx : (mapGL ℝ) g = upperRightHom x\nhg : ↑(↑g 0 1) = 0\n⊢ x = ↑(↑g 0 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 89,
"column": 2
} | {
"line": 90,
"column": 9
} | [
{
"pp": "F : Type u_1\nF' : Type u_2\ninst✝⁴ : FunLike F ℍ ℂ\ninst✝³ : FunLike F' ℍ ℂ\nk : ℤ\ng : GL (Fin 2) ℝ\nτ : ℍ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝² : Γ.HasDetOne\ninst✝¹ : SlashInvariantFormClass F Γ k\nf : F\ninst✝ : SlashInvariantFormClass F' Γ k\nf' : F'\nhg : g ∈ Γ\n⊢ petersson k (⇑f) (⇑f') (g • τ) =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | [
{
"pp": "case right.a\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\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 45,
"column": 2
} | {
"line": 45,
"column": 38
} | [
{
"pp": "f : ℍ → ℂ\nhf : MDiff f\nk : ℤ\ng : GL (Fin 2) ℝ\nhg : 0 < ↑(Matrix.GeneralLinearGroup.det g)\n⊢ MDiff fun x ↦ (σ g) (f (g • x))",
"usedConstants": [
"UpperHalfPlane.glAction",
"NormedCommRing.toNormedRing",
"Units.val",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 28
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nτ : ℍ\nhh : h ≠ 0\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\n⊢ cuspFunction h f (𝕢 h ↑τ) = f τ",
"usedConstants": [
"Function.Periodic.qParam",
"UpperHalfPlane.coe",
"UpperHalfPlane.cuspFunction",
"id",
"Complex",
"Eq"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 105,
"column": 8
} | {
"line": 105,
"column": 34
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\n⊢ ball 0 1 ∈ 𝓝 0",
"usedConstants": [
"Filter.instMembership",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 15
} | [
{
"pp": "case h\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h f) 0\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nτ : ℍ\n⊢ (cuspFunction h f ∘ fun τ ↦ 𝕢 h ↑τ) τ = f τ",
"usedConstants": [
"Function.Periodic.qParam",
"UpperHalfPlane.coe",
"Function.comp",
"UpperHal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 20
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h f) 0\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nthis : (cuspFunction h f ∘ fun τ ↦ 𝕢 h ↑τ) = f\n⊢ Tendsto f atImInfty (𝓝 (cuspFunction h f 0))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 59,
"column": 32
} | {
"line": 59,
"column": 43
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nhf : DifferentiableOn ℂ (fun x ↦ f (↑ofComplex x)) {z | 0 < z.im}\nthis :\n Set.EqOn (fun x ↦ (starRingEnd ℂ) (f (↑ofComplex (-(starRingEnd ℂ) ↑(↑ofComplex x)))))\n (fun x ↦ (starRingEnd ℂ) (f (↑ofComplex (-(starRingEnd ℂ) x)))) {z | 0 < z.im}\nz : ℂ\nhz : z ∈ {z | 0 < z.im}\n⊢ 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 129,
"column": 32
} | {
"line": 129,
"column": 43
} | [
{
"pp": "k : ℤ\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\nf : F\ninst✝ : SlashInvariantFormClass F Γ k\nhΓ : h ∈ Γ.strictPeriods\nw : ℂ\nhw : w.im ≤ 0\n⊢ (w + ↑h).im ≤ 0",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 13
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nhf : DifferentiableOn ℂ (fun x ↦ f (↑ofComplex x)) {z | 0 < z.im}\nthis✝¹ :\n Set.EqOn (fun x ↦ (starRingEnd ℂ) (f (↑ofComplex (-(starRingEnd ℂ) ↑(↑ofComplex x)))))\n (fun x ↦ (starRingEnd ℂ) (f (↑ofComplex (-(starRingEnd ℂ) x)))) {z | 0 < z.im}\nz : ℂ\nhz : z ∈ {z | 0 < z.im}\nth... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 68,
"column": 41
} | {
"line": 68,
"column": 52
} | [
{
"pp": "f : ℍ → ℂ\nhf : MDiff f\nk : ℤ\ng : GL (Fin 2) ℝ\nhg : (↑g).det < 0\n⊢ 0 < ↑(Matrix.GeneralLinearGroup.det (J * g))",
"usedConstants": [
"Left.neg_pos_iff._simp_1",
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"Real.parti... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 185,
"column": 10
} | {
"line": 185,
"column": 21
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nq : ℂ\nhq : ‖q‖ < 1\n⊢ ?m.60 ∈ ball 0 1",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 194,
"column": 2
} | {
"line": 194,
"column": 46
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nτ : ℍ\nthis✝ : 0 < 2 * π * τ.im / h\nthis : ‖𝕢 h ↑τ‖ < 1\n⊢ HasSum (fun m ↦ (PowerSeries.coeff m) (qExpansion h f) • 𝕢 h ↑τ ^ m) (f τ)",
"usedConstants": [
"NormedCommRing.toSe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 201,
"column": 27
} | {
"line": 201,
"column": 38
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nf g : ModularForm Γ k\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\n⊢ c✝.IsBoundedAt ({ toFun := ⇑f, slash_action_eq' := ⋯ } + { toFun := ⇑g, slash_action_eq' := ⋯ }).toFun k",
"usedConstants": [
"SlashInvariantForm",
"ModularForm",
"OnePoint.IsBoundedAt"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 245,
"column": 25
} | {
"line": 245,
"column": 36
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_1\ninst✝² : SMul α ℝ\ninst✝¹ : SMul α ℂ\ninst✝ : IsScalarTower α ℝ ℂ\na : α\ny z : ℂ\n⊢ (a • y) • z = a • y • z",
"usedConstants": [
"instHSMul",
"instSMulOfMul",
"Complex.instMul",
"id",
"HSMul.hSMul",
"Complex",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 228,
"column": 8
} | {
"line": 228,
"column": 19
} | [
{
"pp": "F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nhh : 0 < h\nhfper : Periodic (⇑f ∘ ↑ofComplex) ↑h\nhfhol : MDiff ⇑f\nhfbdd : IsBoundedAtImInfty ⇑f\nr : NNReal\nhr : ↑r < 1\n⊢ ‖↑↑r‖ < 1",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real",
"Preorder.toLT",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 250,
"column": 16
} | {
"line": 250,
"column": 27
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_1\ninst✝² : SMul α ℝ\ninst✝¹ : SMul α ℂ\ninst✝ : IsScalarTower α ℝ ℂ\nc : α\nf : ModularForm Γ k\n⊢ MDiff ⇑(c • f.toSlashInvariantForm)",
"usedConstants": [
"SlashInvariantForm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 13
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_1\ninst✝² : SMul α ℝ\ninst✝¹ : SMul α ℂ\ninst✝ : IsScalarTower α ℝ ℂ\nc : α\nf : ModularForm Γ k\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\ng : GL (Fin 2) ℝ\nhg : g • OnePoint.infty = c✝\n⊢ IsBoundedAtImInfty ((c • f.toSlashInvariantForm).toFun ∣[k] g)",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 236,
"column": 40
} | {
"line": 236,
"column": 97
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nc : ℕ → ℂ\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nq : ℂ\nhq : ‖q‖ < 1\nhq1 : q ≠ 0\nh1 : 0 < (Periodic.invQParam h q).im\nτ : ℍ := { coe := Periodic.invQParam h q, coe_im_pos := h1 }\nh2 : Periodic.cuspFunction h (f ∘ ↑ofComplex) q = (f ∘ ↑ofComplex) (Pe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 273,
"column": 16
} | {
"line": 273,
"column": 27
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_1\ninst✝² : SMul α ℂ\ninst✝¹ : IsScalarTower α ℂ ℂ\ninst✝ : Γ.HasDetOne\nc : α\nf : ModularForm Γ k\n⊢ MDiff ⇑(c • f.toSlashInvariantForm)",
"usedConstants": [
"SlashInvariantForm",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 293,
"column": 41
} | {
"line": 293,
"column": 52
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nf : ModularForm Γ k\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\ng : GL (Fin 2) ℝ\nhg : g • OnePoint.infty = c✝\n⊢ IsBoundedAtImInfty ((-f.toSlashInvariantForm).toFun ∣[k] g)",
"usedConstants": [
"SlashInvariantForm",
"AddGroup.toSubtractionMonoid",
"Mod... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 249,
"column": 6
} | {
"line": 249,
"column": 77
} | [
{
"pp": "case r_le.inr.h\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nc : ℕ → ℂ\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nr : NNReal\nhr : ↑r < 1\nhr' : ↑r ≠ 0\nthis : FiniteDimensional ℝ ℂ := ⋯\n⊢ Summable fun n ↦ ‖FormalMultilinearSeries.ofScalars ℂ c n‖ * ↑r ^ n",
"usedConstants": [
"NonUnitalNo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 341,
"column": 4
} | {
"line": 341,
"column": 27
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk k_1 k_2 : ℤ\ninst✝ : Γ.HasDetPlusMinusOne\nf : ModularForm Γ k_1\ng : ModularForm Γ k_2\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\nγ : GL (Fin 2) ℝ\nhγ : γ • OnePoint.infty = c✝\n⊢ IsBoundedAtImInfty ((f.mul g.toSlashInvariantForm).toFun ∣[k_1 + k_2] γ)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 250,
"column": 68
} | {
"line": 250,
"column": 79
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nc : ℕ → ℂ\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nr : NNReal\nhr : ↑r < 1\nhr' : ↑r ≠ 0\nthis : FiniteDimensional ℝ ℂ := Module.Basis.finiteDimensional_of_finite basisOneI\n⊢ ‖↑↑r‖ < 1",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 349,
"column": 30
} | {
"line": 350,
"column": 54
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nx : ℂ\ninst✝ : Γ.HasDetOne\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\ng : GL (Fin 2) ℝ\nhg : g • OnePoint.infty = c✝\n⊢ IsBoundedAtImInfty ((SlashInvariantForm.const x).toFun ∣[0] g)",
"usedConstants": [
"Int.instAddCommGroup",
"Units.val",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 361,
"column": 30
} | {
"line": 362,
"column": 54
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nx : ℝ\ninst✝ : Γ.HasDetPlusMinusOne\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\ng : GL (Fin 2) ℝ\nhg : g • OnePoint.infty = c✝\n⊢ IsBoundedAtImInfty ((SlashInvariantForm.constℝ x).toFun ∣[0] g)",
"usedConstants": [
"Int.instAddCommGroup",
"Units.val",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 410,
"column": 36
} | {
"line": 410,
"column": 47
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nf g : CuspForm Γ k\nc✝ : OnePoint ℝ\nA : IsCusp c✝ Γ\n⊢ c✝.IsZeroAt ({ toFun := ⇑f, slash_action_eq' := ⋯ } + { toFun := ⇑g, slash_action_eq' := ⋯ }).toFun k",
"usedConstants": [
"SlashInvariantForm",
"CuspFormClass.toSlashInvariantFormC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 423,
"column": 35
} | {
"line": 423,
"column": 46
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\ng : GL (Fin 2) ℝ\nhg : g • OnePoint.infty = c✝\n⊢ IsZeroAtImInfty (SlashInvariantForm.toFun 0 ∣[k] g)",
"usedConstants": [
"SlashInvariantForm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 439,
"column": 25
} | {
"line": 439,
"column": 36
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_2\ninst✝² : SMul α ℝ\ninst✝¹ : SMul α ℂ\ninst✝ : IsScalarTower α ℝ ℂ\na : α\ny z : ℂ\n⊢ (a • y) • z = a • y • z",
"usedConstants": [
"instHSMul",
"instSMulOfMul",
"Complex.instMul",
"id",
"HSMul.hSMul",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 443,
"column": 16
} | {
"line": 443,
"column": 27
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_2\ninst✝² : SMul α ℝ\ninst✝¹ : SMul α ℂ\ninst✝ : IsScalarTower α ℝ ℂ\nc : α\nf : CuspForm Γ k\n⊢ MDiff ⇑(c • f.toSlashInvariantForm)",
"usedConstants": [
"SlashInvariantForm",
"InnerProductSpace.toNormedSpace",
"NormedCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 466,
"column": 16
} | {
"line": 466,
"column": 27
} | [
{
"pp": "F : Type u_1\nΓ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nα : Type u_2\ninst✝² : SMul α ℂ\ninst✝¹ : IsScalarTower α ℂ ℂ\ninst✝ : Γ.HasDetOne\nc : α\nf : CuspForm Γ k\n⊢ MDiff ⇑(c • f.toSlashInvariantForm)",
"usedConstants": [
"SlashInvariantForm",
"InnerProductSpace.toNormedSpace",
"Norme... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 260,
"column": 6
} | {
"line": 260,
"column": 43
} | [
{
"pp": "case hasSum.inl\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nc : ℕ → ℂ\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nhy : ‖0‖ < 1\n⊢ HasSum (fun n ↦ (FormalMultilinearSeries.ofScalars ℂ c n) fun x ↦ 0) (update (cuspFunction h f) 0 (c 0) 0)",
"usedConstants": [
"Eq.mpr",
"InnerProductSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 261,
"column": 6
} | {
"line": 262,
"column": 13
} | [
{
"pp": "case hasSum.inr\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nc : ℕ → ℂ\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\ny : ℂ\nhy : ‖y‖ < 1\nhy' : y ≠ 0\n⊢ HasSum (fun n ↦ (FormalMultilinearSeries.ofScalars ℂ c n) fun x ↦ y) (update (cuspFunction h f) 0 (c 0) y)",
"usedConstants": [
"NonUnitalNon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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