module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 94,
"column": 4
} | {
"line": 95,
"column": 41
} | {
"line": 95,
"column": 42
} | [
{
"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",
"ppTerm": "?m.66",
"assigned": false,
"usedConstants": [],
"usedFVars":... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 56
} | {
"line": 108,
"column": 57
} | [
{
"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",
"ppTer... | [
"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⊢ γ ∈ Γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 59
} | {
"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",
"ppTer... | [] | simpa using hγ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 59
} | {
"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",
"ppTer... | [] | simpa using hγ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 108,
"column": 45
} | {
"line": 108,
"column": 59
} | {
"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",
"ppTer... | [] | simpa using hγ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 287,
"column": 4
} | {
"line": 287,
"column": 41
} | {
"line": 287,
"column": 42
} | [
{
"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",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"H... | [
"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 * j) = ⇑f ∣[k] g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Identities | {
"line": 45,
"column": 2
} | {
"line": 45,
"column": 51
} | {
"line": 45,
"column": 52
} | [
{
"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",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Real",
"Matrix.SpecialLine... | [
"N : ℕ\nk n : ℤ\nf : SlashInvariantForm (Subgroup.map (mapGL ℝ) Γ(N)) k\nz : ℍ\n⊢ f (↑N * ↑n +ᵥ z) = f z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 263,
"column": 6
} | {
"line": 263,
"column": 36
} | {
"line": 263,
"column": 37
} | [
{
"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",
... | [
"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.Identities | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 78
} | {
"line": 61,
"column": 4
} | [
{
"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",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Real",
"InvOneClass.toOne",
"Subg... | [
"case mpr.mul\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⊢ ∀ (x y : GL (Fin 2) ℝ),\n x ∈ Subgroup.closure s → y ∈ Subgroup.closure s → f ∣[k] x = f → f ∣[k] y = f → f ∣[k] (x * y) = f",
"case mpr.... | 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": 304,
"column": 38
} | {
"line": 304,
"column": 49
} | {
"line": 304,
"column": 50
} | [
{
"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",
"ppTerm": "?m.49",
"assigned": true,
"usedConst... | [
"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⊢ ↑(↑g 0 1) = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 38
} | {
"line": 311,
"column": 39
} | [
{
"pp": "⊢ (mapGL ℝ).range.strictPeriods = AddSubgroup.zmultiples 1",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"Subgroup.map",
"AddGroupWithOne.toAddGroup",
"congrArg",
"M... | [
"⊢ (map (mapGL ℝ) ⊤).strictPeriods = AddSubgroup.zmultiples 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 355,
"column": 2
} | {
"line": 355,
"column": 38
} | {
"line": 355,
"column": 39
} | [
{
"pp": "⊢ (mapGL ℝ).range.strictWidthInfty = 1",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"Subgroup.map",
"congrArg",
"Matrix",
"instDecidableEqFin",
"MonoidHom.ran... | [
"⊢ (map (mapGL ℝ) ⊤).strictWidthInfty = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 375,
"column": 4
} | {
"line": 375,
"column": 66
} | {
"line": 375,
"column": 67
} | [
{
"pp": "case inl\n𝒢 : Subgroup (GL (Fin 2) ℝ)\nh : upperRightHom 𝒢.widthInfty ∈ 𝒢\n⊢ 2 * 𝒢.widthInfty ∈ 𝒢.strictPeriods",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"Matrix",
"instDecid... | [
"case inl\n𝒢 : Subgroup (GL (Fin 2) ℝ)\nh : upperRightHom 𝒢.widthInfty ∈ 𝒢\n⊢ upperRightHom (2 * 𝒢.widthInfty) ∈ 𝒢"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 375,
"column": 4
} | {
"line": 375,
"column": 66
} | {
"line": 375,
"column": 67
} | [
{
"pp": "case inr\n𝒢 : Subgroup (GL (Fin 2) ℝ)\nh : -upperRightHom 𝒢.widthInfty ∈ 𝒢\n⊢ 2 * 𝒢.widthInfty ∈ 𝒢.strictPeriods",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"Matrix",
"instDeci... | [
"case inr\n𝒢 : Subgroup (GL (Fin 2) ℝ)\nh : -upperRightHom 𝒢.widthInfty ∈ 𝒢\n⊢ upperRightHom (2 * 𝒢.widthInfty) ∈ 𝒢"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 383,
"column": 6
} | {
"line": 383,
"column": 17
} | {
"line": 383,
"column": 18
} | [
{
"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... | [
"case mp.refine_1\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ninst✝¹ : DiscreteTopology ↥𝒢.strictPeriods\ninst✝ : 𝒢.HasDetPlusMinusOne\nh : 0 < 𝒢.strictWidthInfty\n⊢ ¬𝒢.strictWidthInfty = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 399,
"column": 11
} | {
"line": 399,
"column": 62
} | {
"line": 399,
"column": 63
} | [
{
"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",
"ppTerm": "?m.185",
"assigned": true,
"usedConstants": [
"Eq.mpr"... | [
"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 x ^ 2 ∈ 𝒢"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 403,
"column": 2
} | {
"line": 404,
"column": 9
} | {
"line": 404,
"column": 10
} | [
{
"pp": "𝒢 : Subgroup (GL (Fin 2) ℝ)\ninst✝ : 𝒢.IsArithmetic\n⊢ IsCusp ∞ 𝒢",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"OnePoint.infty",
"Matrix",
"Real.instRatCast",
"R... | [
"𝒢 : Subgroup (GL (Fin 2) ℝ)\ninst✝ : 𝒢.IsArithmetic\n⊢ ∃ y, OnePoint.map Rat.cast y = ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 463,
"column": 26
} | {
"line": 463,
"column": 37
} | {
"line": 463,
"column": 38
} | [
{
"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)",
"ppTerm": "?m.89",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 68,
"column": 41
} | {
"line": 68,
"column": 52
} | {
"line": 68,
"column": 53
} | [
{
"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))",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"Left.neg_pos_iff._simp_1",
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"Mon... | [
"f : ℍ → ℂ\nhf : MDiff f\nk : ℤ\ng : GL (Fin 2) ℝ\nhg : (↑g).det < 0\n⊢ (↑g).det < 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 201,
"column": 27
} | {
"line": 201,
"column": 38
} | {
"line": 201,
"column": 39
} | [
{
"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",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
... | [
"Γ : Subgroup (GL (Fin 2) ℝ)\nk : ℤ\nf g : ModularForm Γ k\nc✝ : OnePoint ℝ\nhc : IsCusp c✝ Γ\n⊢ c✝.IsBoundedAt (⇑f + ⇑g) k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 213,
"column": 34
} | {
"line": 213,
"column": 45
} | {
"line": 213,
"column": 46
} | [
{
"pp": "Γ : 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⊢ IsBoundedAtImInfty (toFun 0 ∣[k] g)",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
"SlashInvariantForm.instIsZeroApplyUpperHa... | [
"Γ : 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⊢ IsBoundedAtImInfty 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 239,
"column": 25
} | {
"line": 239,
"column": 36
} | {
"line": 239,
"column": 37
} | [
{
"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",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"instHSMul",
"instSMulOfMul",
"Complex.instMul",
"... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 244,
"column": 16
} | {
"line": 244,
"column": 27
} | {
"line": 244,
"column": 28
} | [
{
"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)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
"ModularForm",
... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 246,
"column": 6
} | {
"line": 248,
"column": 13
} | {
"line": 248,
"column": 14
} | [
{
"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)",
"ppT... | [
"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⊢ ((σ g) (c • 1) • ⇑f ∣[k] g) =O[atImInfty] 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 28
} | {
"line": 82,
"column": 29
} | [
{
"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",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Function.Periodic.qParam",
"UpperHalfPlane.coe",
"UpperHalfPlane.cuspFunction",
"id",
"Compl... | [
"h : ℝ\nf : ℍ → ℂ\nτ : ℍ\nhh : h ≠ 0\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\n⊢ Periodic.cuspFunction h (f ∘ ↑ofComplex) (𝕢 h ↑τ) = f τ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 266,
"column": 16
} | {
"line": 266,
"column": 27
} | {
"line": 266,
"column": 28
} | [
{
"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)",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
"ModularForm"... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 106,
"column": 8
} | {
"line": 106,
"column": 34
} | {
"line": 106,
"column": 35
} | [
{
"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",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",... | [
"h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\n⊢ {x | ‖x‖ < 1} ∈ 𝓝 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 15
} | {
"line": 114,
"column": 16
} | [
{
"pp": "h : 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",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Function.Periodic.qParam",
"UpperHalfPlane.coe",
... | [
"h : 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 (𝕢 h ↑τ) = f τ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 20
} | {
"line": 115,
"column": 21
} | [
{
"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))",
"ppTerm": "?m.49",
"assigned": false,
"usedConstants": [],
"usedFVars": ... | [
"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))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 386,
"column": 29
} | {
"line": 386,
"column": 40
} | {
"line": 386,
"column": 41
} | [
{
"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",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"SlashInvariantForm... | [
"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 (⇑f + ⇑g) k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 413,
"column": 25
} | {
"line": 413,
"column": 36
} | {
"line": 413,
"column": 37
} | [
{
"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",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"instHSMul",
"instSMulOfMul",
"Complex.ins... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 417,
"column": 16
} | {
"line": 417,
"column": 27
} | {
"line": 417,
"column": 28
} | [
{
"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)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
"Eq.m... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 439,
"column": 16
} | {
"line": 439,
"column": 27
} | {
"line": 439,
"column": 28
} | [
{
"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)",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"SlashInvariantForm",
"E... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 130,
"column": 32
} | {
"line": 130,
"column": 43
} | {
"line": 130,
"column": 44
} | [
{
"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",
"ppTerm": "?m.181",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
... | [
"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.im ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 609,
"column": 4
} | {
"line": 609,
"column": 63
} | {
"line": 610,
"column": 4
} | [
{
"pp": "case succ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝ : Γ.HasDetPlusMinusOne\nk : ℤ\nf : ModularForm Γ k\nn : ℕ\nih : ⟨n • k, GradedMonoid.GMonoid.gnpow n f⟩ = ⟨↑n * k, f.pow n⟩\n⊢ ⟨(n + 1) • k, GradedMonoid.GMonoid.gnpow (n + 1) f⟩ = ⟨↑(n + 1) * k, f.pow (n + 1)⟩",
"ppTerm": "?succ",
"assigned": true,... | [
"case succ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝ : Γ.HasDetPlusMinusOne\nk : ℤ\nf : ModularForm Γ k\nn : ℕ\nih : ⟨n • k, GradedMonoid.GMonoid.gnpow n f⟩ = ⟨↑n * k, f.pow n⟩\n⊢ ⟨n • ⟨k, f⟩.fst, GradedMonoid.GMonoid.gnpow n ⟨k, f⟩.snd⟩ * ⟨k, f⟩ = ⟨↑(n + 1) * k, f.pow (n + 1)⟩"
] | refine (GradedMonoid.GMonoid.gnpow_succ' n ⟨k, f⟩).trans ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 611,
"column": 4
} | {
"line": 612,
"column": 35
} | {
"line": 614,
"column": 0
} | [
{
"pp": "case succ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝ : Γ.HasDetPlusMinusOne\nk : ℤ\nf : ModularForm Γ k\nn : ℕ\nih : ⟨n • k, GradedMonoid.GMonoid.gnpow n f⟩ = ⟨↑n * k, f.pow n⟩\n⊢ ⟨↑n * k, f.pow n⟩ * ⟨k, f⟩ = ⟨↑(n + 1) * k, f.pow (n + 1)⟩",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
... | [] | exact gradedMonoid_eq_of_cast (show ((n : ℤ) * k + k = (n + 1) * k) by ring)
(ModularForm.ext fun _ ↦ rfl) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 186,
"column": 10
} | {
"line": 186,
"column": 21
} | {
"line": 186,
"column": 22
} | [
{
"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.56 ∈ ball 0 1",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"N... | [
"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.56‖ < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 194,
"column": 2
} | {
"line": 194,
"column": 46
} | {
"line": 195,
"column": 4
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nτ : ℍ\nthis : ‖𝕢 h ↑τ‖ < 1\n⊢ HasSum (fun m ↦ (PowerSeries.coeff m) (qExpansion h f) • 𝕢 h ↑τ ^ m) (f τ)",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Norm... | [
"h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nτ : ℍ\nthis : ‖𝕢 h ↑τ‖ < 1\n⊢ HasSum (fun m ↦ (PowerSeries.coeff m) (qExpansion h f) * 𝕢 h ↑τ ^ m) (f τ)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 665,
"column": 4
} | {
"line": 665,
"column": 30
} | {
"line": 665,
"column": 31
} | [
{
"pp": "k : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nf : F\ninst✝ : ModularFormClass F Γ k\ng : GL (Fin 2) ℝ\nc : OnePoint ℝ\nhc : IsCusp c (toConjAct g⁻¹ • Γ)\nγ : GL (Fin 2) ℝ\nhγ : γ • ∞ = c\n⊢ IsCusp ((g * γ) • ∞) Γ",
"ppTerm": "?m.80",
"assigned": true,
"usedConsta... | [
"k : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nf : F\ninst✝ : ModularFormClass F Γ k\ng : GL (Fin 2) ℝ\nc : OnePoint ℝ\nhc : IsCusp c (toConjAct g⁻¹ • Γ)\nγ : GL (Fin 2) ℝ\nhγ : γ • ∞ = c\n⊢ IsCusp (g • c) Γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 228,
"column": 8
} | {
"line": 228,
"column": 19
} | {
"line": 228,
"column": 20
} | [
{
"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",
"ppTerm": "?m.97",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Rea... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 683,
"column": 4
} | {
"line": 683,
"column": 30
} | {
"line": 683,
"column": 31
} | [
{
"pp": "k : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nf : F\ninst✝ : CuspFormClass F Γ k\ng : GL (Fin 2) ℝ\nc : OnePoint ℝ\nhc : IsCusp c (toConjAct g⁻¹ • Γ)\nγ : GL (Fin 2) ℝ\nhγ : γ • ∞ = c\n⊢ IsCusp ((g * γ) • ∞) Γ",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants... | [
"k : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nf : F\ninst✝ : CuspFormClass F Γ k\ng : GL (Fin 2) ℝ\nc : OnePoint ℝ\nhc : IsCusp c (toConjAct g⁻¹ • Γ)\nγ : GL (Fin 2) ℝ\nhγ : γ • ∞ = c\n⊢ IsCusp (g • c) Γ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Basic | {
"line": 699,
"column": 6
} | {
"line": 700,
"column": 9
} | {
"line": 700,
"column": 10
} | [
{
"pp": "k : ?m.1\nF : Sort ?u.11\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝¹ : FunLike F ℍ ℂ\nf : F\ninst✝ : Γ.IsArithmetic\n⊢ IsCusp ∞ Γ",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"OnePoint.inft... | [
"k : ?m.1\nF : Sort ?u.11\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝¹ : FunLike F ℍ ℂ\nf : F\ninst✝ : Γ.IsArithmetic\n⊢ ∃ y, OnePoint.map Rat.cast y = ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 239,
"column": 65
} | {
"line": 239,
"column": 76
} | {
"line": 239,
"column": 77
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\np : Fin 2 → ℤ\nhp : IsCoprime (p 0) (p 1)\nhg : ↑g 1 = p\nnonZ1 : ↑(p 0) ^ 2 + ↑(p 1) ^ 2 ≠ 0\nh : Int.cast ∘ p = 0\ni : Fin 2\n⊢ p i = 0 i",
"ppTerm": "?m.193",
"assigned": true,
"usedConstants": [
"CommSemiring.toSemiring",
"id",
"Pi.instZero",
... | [
"g : SL(2, ℤ)\nz : ℍ\np : Fin 2 → ℤ\nhp : IsCoprime (p 0) (p 1)\nhg : ↑g 1 = p\nnonZ1 : ↑(p 0) ^ 2 + ↑(p 1) ^ 2 ≠ 0\nh : Int.cast ∘ p = 0\ni : Fin 2\n⊢ p i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 240,
"column": 45
} | {
"line": 240,
"column": 56
} | {
"line": 240,
"column": 57
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\np : Fin 2 → ℤ\nhp : IsCoprime (p 0) (p 1)\nhg : ↑g 1 = p\nnonZ1 : ↑(p 0) ^ 2 + ↑(p 1) ^ 2 ≠ 0\nthis : Int.cast ∘ p ≠ 0\n⊢ ↑(p 0) * ↑z + ↑(p 1) ≠ 0",
"ppTerm": "?m.224",
"assigned": true,
"usedConstants": [
"Int.cast",
"HMul.hMul",
"UpperHalfPlane.coe",... | [
"g : SL(2, ℤ)\nz : ℍ\np : Fin 2 → ℤ\nhp : IsCoprime (p 0) (p 1)\nhg : ↑g 1 = p\nnonZ1 : ↑(p 0) ^ 2 + ↑(p 1) ^ 2 ≠ 0\nthis : Int.cast ∘ p ≠ 0\n⊢ ¬↑(p 0) * ↑z + ↑(p 1) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 250,
"column": 6
} | {
"line": 250,
"column": 77
} | {
"line": 251,
"column": 8
} | [
{
"pp": "case r_le.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)\nr : NNReal\nhr : ↑r < 1\nhr' : ↑r ≠ 0\nthis : FiniteDimensional ℝ ℂ := ⋯\n⊢ Summable fun n ↦ ‖FormalMultilinearSeries.ofScalars ℂ c n‖ * ↑r ^ n",
"ppTerm": "?r_le.inr",
"assigned": ... | [
"case r_le.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)\nr : NNReal\nhr : ↑r < 1\nhr' : ↑r ≠ 0\nthis : FiniteDimensional ℝ ℂ := Module.Basis.finiteDimensional_of_finite basisOneI\n⊢ Summable fun n ↦ ↑r ^ n * ‖c n‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 251,
"column": 68
} | {
"line": 251,
"column": 79
} | {
"line": 251,
"column": 80
} | [
{
"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",
"ppTerm": "?m.152",
"assigned": true,
"usedConstants": ... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 89,
"column": 2
} | {
"line": 90,
"column": 9
} | {
"line": 90,
"column": 10
} | [
{
"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) =... | [
"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) = petersson k... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 55,
"column": 4
} | {
"line": 57,
"column": 11
} | {
"line": 57,
"column": 12
} | [
{
"pp": "E : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nD : ℝ\nhD : D > 0\ny : ℝ\nhy : ∀ (b : ℝ), y ≤ b → ∀ (a : ℍ), a.im = b → ‖f a‖ ≤ D * a.im ^ t\nhfm : Continuou... | [
"E : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nD : ℝ\nhD : D > 0\ny : ℝ\nhy : ∀ (b : ℝ), y ≤ b → ∀ (a : ℍ), a.im = b → ‖f a‖ ≤ D * a.im ^ t\nhfm : ContinuousOn (fun τ ↦... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 257,
"column": 6
} | {
"line": 257,
"column": 43
} | {
"line": 257,
"column": 44
} | [
{
"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 + 0))",
"ppTerm": "?hasSum.inl",
"assigned": true,
"... | [
"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 ↦ if n = 0 then c 0 else 0) (c 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 258,
"column": 6
} | {
"line": 259,
"column": 13
} | {
"line": 259,
"column": 14
} | [
{
"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) (0 + y))",
"ppTerm": "?hasSum.inr",
"as... | [
"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 ↦ c n * y ^ n) (cuspFunction h f y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Petersson | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 13
} | {
"line": 115,
"column": 14
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 274,
"column": 4
} | {
"line": 274,
"column": 48
} | {
"line": 275,
"column": 6
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nc : ℕ → ℂ\nhh : 0 < h\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nhfeq : f = fun τ ↦ update (cuspFunction h f) 0 (c 0) (𝕢 h ↑τ)\n⊢ Tendsto (fun τ ↦ update (cuspFunction h f) 0 (c 0) (𝕢 h ↑τ)) atImInfty (𝓝 (c 0))",
"ppTerm": "?m.81",
"assigned": false,
"us... | [
"h : ℝ\nf : ℍ → ℂ\nc : ℕ → ℂ\nhh : 0 < h\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nhfeq : f = fun τ ↦ update (cuspFunction h f) 0 (c 0) (𝕢 h ↑τ)\n⊢ Tendsto (fun τ ↦ update (cuspFunction h f) 0 (c 0) (𝕢 h ↑τ)) atImInfty (𝓝 (c 0))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 40,
"column": 4
} | {
"line": 41,
"column": 11
} | {
"line": 41,
"column": 12
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : SlashInvariantFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nτ : ℍ\nγ : SL(2, ℤ)\nhγ : 1 / 2 ≤ (γ • τ).im\nhdenom : ‖denom (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ≤ 1\n... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : SlashInvariantFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nτ : ℍ\nγ : SL(2, ℤ)\nhγ : 1 / 2 ≤ (γ • τ).im\nhdenom : ‖denom (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ≤ 1\nthis : Slash... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 53,
"column": 4
} | {
"line": 53,
"column": 46
} | {
"line": 53,
"column": 47
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : SlashInvariantFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nf : F\nc : ℂ\nhf : ⇑f = Function.const ℍ c\nthis✝ : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ(1)) k\nhI : c = ↑UpperHalfPlane.I ^ k * c\nh2I2 :... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : SlashInvariantFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nf : F\nc : ℂ\nhf : ⇑f = Function.const ℍ c\nthis✝ : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ(1)) k\nhI : c = ↑UpperHalfPlane.I ^ k * c\nh2I2 : c = ↑(⟨2, ⋯... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 294,
"column": 4
} | {
"line": 294,
"column": 29
} | {
"line": 294,
"column": 30
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nH1 : HasFPowerSeriesOnBall (update (cuspFunction h f) 0 (c 0)) (FormalMultilinearSeries.ofScalars ℂ c) 0 1\nL1 : ContinuousAt (update (cuspFunction h f) 0 (... | [
"h : ℝ\nf : ℍ → ℂ\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nH1 : HasFPowerSeriesOnBall (update (cuspFunction h f) 0 (c 0)) (FormalMultilinearSeries.ofScalars ℂ c) 0 1\nL1 : ContinuousAt (update (cuspFunction h f) 0 (c 0)) 0\nL2 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | {
"line": 54,
"column": 14
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : SlashInvariantFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nf : F\nc : ℂ\nhf : ⇑f = Function.const ℍ c\nthis : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ(1)) k\nhI : c = ↑UpperHalfPlane.I ^ k * c\nh2I2 : ... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : SlashInvariantFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nf : F\nc : ℂ\nhf : ⇑f = Function.const ℍ c\nthis : SlashInvariantFormClass F (Subgroup.map (Matrix.SpecialLinearGroup.mapGL ℝ) Γ(1)) k\nhI : c = ↑UpperHalfPlane.I ^ k * c\nh2I2 : c = ↑(⟨2, ⋯⟩... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 81,
"column": 6
} | {
"line": 81,
"column": 16
} | {
"line": 81,
"column": 16
} | [
{
"pp": "E : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nhf_inv : ∀ (g : SL(2, ℤ)) (τ : ℍ), f (g • τ) = f τ\nF : ℝ\nτ : ℍ\ng : SL(2, ℤ)\nhF𝒟 : ‖f (g • τ)... | [
"E : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nhf_inv : ∀ (g : SL(2, ℤ)) (τ : ℍ), f (g • τ) = f τ\nF : ℝ\nτ : ℍ\ng : SL(2, ℤ)\nhF𝒟 : ‖f τ‖ ≤ F * (g • τ).im... | hf_inv g τ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 82,
"column": 20
} | {
"line": 82,
"column": 48
} | {
"line": 82,
"column": 49
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nhq : 0 ∈ Metric.ball 0 1\n⊢ ‖0‖ ≤ rexp (-π)",
"ppTerm": "?m.133",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm"... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nhq : 0 ∈ Metric.ball 0 1\n⊢ 0 ≤ rexp (-π)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 86,
"column": 11
} | {
"line": 87,
"column": 64
} | {
"line": 87,
"column": 65
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nq : ℂ\nhq : q ∈ Metric.ball 0 1\nhq' : q ≠ 0\nξ : ℍ\nhξ : 1 / 2 ≤ ξ.im\nhξ₂ : ‖f { coe := invQParam 1 q, coe_im_pos := ⋯ }‖ ≤ ‖f ξ‖\n⊢ ‖UpperHalfPlane.cuspFunction 1 (... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nq : ℂ\nhq : q ∈ Metric.ball 0 1\nhq' : q ≠ 0\nξ : ℍ\nhξ : 1 / 2 ≤ ξ.im\nhξ₂ : ‖f { coe := invQParam 1 q, coe_im_pos := ⋯ }‖ ≤ ‖f ξ‖\n⊢ ‖UpperHalfPlane.cuspFunction 1 (⇑f) q‖ ≤ ‖Up... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 318,
"column": 48
} | {
"line": 318,
"column": 59
} | {
"line": 318,
"column": 60
} | [
{
"pp": "z : ℍ\n⊢ (T • z).re = z.re + 1",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Real",
"instHSMul",
"Matrix.SpecialLinearGroup",
"UpperHalfPlane.SLAction",
"instDecidableEqFin",
"ModularGroup.T",
"id",
"Real.instRing",
"instOfN... | [
"z : ℍ\n⊢ (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) T) • z).re = z.re + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 320,
"column": 44
} | {
"line": 320,
"column": 55
} | {
"line": 320,
"column": 56
} | [
{
"pp": "z : ℍ\n⊢ (T • z).im = z.im",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Real",
"instHSMul",
"Matrix.SpecialLinearGroup",
"UpperHalfPlane.SLAction",
"instDecidableEqFin",
"ModularGroup.T",
"id",
"Real.instRing",
"instOfNatNa... | [
"z : ℍ\n⊢ (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) T) • z).im = z.im"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 93,
"column": 4
} | {
"line": 93,
"column": 15
} | {
"line": 93,
"column": 16
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nz : ℍ\n⊢ 𝕢 1 ↑z ∈ Metric.ball 0 1",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"E... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nz : ℍ\n⊢ ‖𝕢 1 ↑z‖ < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 324,
"column": 50
} | {
"line": 324,
"column": 61
} | {
"line": 324,
"column": 62
} | [
{
"pp": "z : ℍ\n⊢ (T⁻¹ • z).im = z.im",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"UpperHalfPlane.glAction",
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"Real",
"DivInvMonoid.toInv",
"instHSMul",
"Matrix.SpecialLinearGroup",
"MonoidHom.inst... | [
"z : ℍ\n⊢ ((toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) T))⁻¹ • z).im = z.im"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 94,
"column": 2
} | {
"line": 95,
"column": 9
} | {
"line": 95,
"column": 10
} | [
{
"pp": "F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nz : ℍ\nhQ : 𝕢 1 ↑z ∈ Metric.ball 0 1\n⊢ f z = Function.const ℍ (UpperHalfPlane.cuspFunction 1 (⇑f) 0) z",
"ppTerm": "?m.57",
"assigned": true,
"usedConsta... | [
"F : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nk : ℤ\ninst✝ : ModularFormClass F (Matrix.SpecialLinearGroup.mapGL ℝ).range k\nhk : k ≤ 0\nf : F\nz : ℍ\nhQ : 𝕢 1 ↑z ∈ Metric.ball 0 1\n⊢ UpperHalfPlane.cuspFunction 1 (⇑f) (𝕢 1 ↑z) = UpperHalfPlane.cuspFunction 1 (⇑f) 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 317,
"column": 70
} | {
"line": 317,
"column": 81
} | {
"line": 317,
"column": 82
} | [
{
"pp": "k : ℤ\nF : Type u_1\ninst✝ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\nf✝ : F\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nn : ℕ\nt : ℝ\nht : 0 < t\nu : ℝ\n⊢ 0 < (↑u + ↑t * ↑I).im",
"ppTerm": "?m.83",
"assigned": true,
... | [
"k : ℤ\nF : Type u_1\ninst✝ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\nf✝ : F\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nn : ℕ\nt : ℝ\nht : 0 < t\nu : ℝ\n⊢ 0 < t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 321,
"column": 50
} | {
"line": 321,
"column": 71
} | {
"line": 321,
"column": 72
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nn : ℕ\nt : ℝ\nht : 0 < t\nR : ℝ := rexp (-2 * π * t / h)\nhR0 : 0 < R\n⊢ -2 * π * t / h < 0",
"ppTerm": "?m.125",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtrac... | [
"h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nn : ℕ\nt : ℝ\nht : 0 < t\nR : ℝ := rexp (-2 * π * t / h)\nhR0 : 0 < R\n⊢ 0 < 2 * π * t / h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.Basic | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 38
} | {
"line": 117,
"column": 39
} | [
{
"pp": "k : ℤ\nhk : k < 0\nf : ModularForm (Matrix.SpecialLinearGroup.mapGL ℝ).range k\n⊢ 1 • f = 0",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"ModularForm",
"Eq.mpr",
"Subgroup.instHasDetOneRangeSpecialLinearGroupGeneralLinearGroupMapGL",
"MonoidHom.range",
... | [
"k : ℤ\nhk : k < 0\nf : ModularForm (Matrix.SpecialLinearGroup.mapGL ℝ).range k\n⊢ ⇑f = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 82
} | {
"line": 93,
"column": 83
} | [
{
"pp": "E : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nhf_inv : ∀ (g : SL(2, ℤ)) (τ : ℍ), f (g • τ) = f τ\nF : ℝ\nτ : ℍ\ng : SL(2, ℤ)\nhF𝒟 : ‖f τ‖ ≤ F ... | [
"E : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nhf_inv : ∀ (g : SL(2, ℤ)) (τ : ℍ), f (g • τ) = f τ\nF : ℝ\nτ : ℍ\ng : SL(2, ℤ)\nhF𝒟 : ‖f τ‖ ≤ F * (g • τ).im... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 23
} | {
"line": 97,
"column": 24
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nhf_inv : ∀ (g : SL(2, ℤ)) (τ : ℍ), f (g • τ) = f τ\nF : ℝ\nτ : ℍ\ng : SL(2, ℤ)\nhF𝒟 : ... | [
"case pos\nE : Type u_1\ninst✝ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : f =O[atImInfty] fun z ↦ z.im ^ t\nhf_inv : ∀ (g : SL(2, ℤ)) (τ : ℍ), f (g • τ) = f τ\nF : ℝ\nτ : ℍ\ng : SL(2, ℤ)\nhF𝒟 : ‖f τ‖ ≤ F * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 339,
"column": 45
} | {
"line": 339,
"column": 79
} | {
"line": 340,
"column": 4
} | [
{
"pp": "g : SL(2, ℤ)\nhc : ↑g 1 0 = 0\nhad : ↑g 0 0 * ↑g 1 1 = 1\nha : ↑g 0 0 = -1\nhd : ↑g 1 1 = -1\nthis : g = -T ^ (-↑g 0 1)\nz : ℍ\n⊢ g • z = T ^ (-↑g 0 1) • z",
"ppTerm": "?m.915",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Fintype.card_fin_two",
"instHSMul... | [] | conv_lhs => rw [this, SL_neg_smul] | Mathlib.Tactic.Conv._aux_Mathlib_Tactic_Conv___macroRules_Mathlib_Tactic_Conv_convLHS_1 | Mathlib.Tactic.Conv.convLHS |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 13
} | {
"line": 156,
"column": 14
} | [
{
"pp": "r : ℕ\ninst✝ : NeZero r\nv : Fin 2 → ℤ\nhab : finGcdMap v = r\nA : SL(2, ℤ)\nhvr : v = r • (v / ↑r)\n⊢ finGcdMap (r • (v / ↑r) ᵥ* ↑A) = r",
"ppTerm": "?m.307",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"NonAssocSemiring.toAddCommMonoidWithOne"... | [
"r : ℕ\ninst✝ : NeZero r\nv : Fin 2 → ℤ\nhab : finGcdMap v = r\nA : SL(2, ℤ)\nhvr : v = r • (v / ↑r)\n⊢ finGcdMap (↑r * (v / ↑r) ᵥ* ↑A) = r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 330,
"column": 30
} | {
"line": 330,
"column": 41
} | {
"line": 330,
"column": 42
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nn : ℕ\nt : ℝ\nht : 0 < t\nR : ℝ := rexp (-2 * π * t / h)\nhR0 : 0 < R\nhR1 : R < 1\nu : ℝ\n⊢ 0 < (↑u + ↑t * ↑I).im",
"ppTerm": "?m.248",
"assigned": true,
"usedConstants": [
... | [
"h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nn : ℕ\nt : ℝ\nht : 0 < t\nR : ℝ := rexp (-2 * π * t / h)\nhR0 : 0 < R\nhR1 : R < 1\nu : ℝ\n⊢ 0 < t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 355,
"column": 2
} | {
"line": 355,
"column": 33
} | {
"line": 355,
"column": 34
} | [
{
"pp": "z : ℍ\nh : 1 < normSq ↑z\n⊢ normSq\n ((↑((algebraMap ℤ ℝ) (↑S 0 0)) * ↑z + ↑((algebraMap ℤ ℝ) (↑S 0 1))) /\n (↑((algebraMap ℤ ℝ) (↑S 1 0)) * ↑z + ↑((algebraMap ℤ ℝ) (↑S 1 1)))) <\n 1",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid... | [
"z : ℍ\nh : 1 < normSq ↑z\n⊢ (normSq ↑z)⁻¹ < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 395,
"column": 45
} | {
"line": 395,
"column": 79
} | {
"line": 395,
"column": 80
} | [
{
"pp": "z : ℍ\nh : z ∈ 𝒟ᵒ\n⊢ 1 < z.re * z.re + z.im * z.im",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"z : ℍ\nh : z ∈ 𝒟ᵒ\n⊢ 1 < z.re * z.re + z.im * z.im"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 401,
"column": 45
} | {
"line": 401,
"column": 79
} | {
"line": 401,
"column": 80
} | [
{
"pp": "τ : ℍ\nh : τ ∈ 𝒟\n⊢ 1 ≤ τ.re * τ.re + τ.im * τ.im",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"τ : ℍ\nh : τ ∈ 𝒟\n⊢ 1 ≤ τ.re * τ.re + τ.im * τ.im"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 437,
"column": 4
} | {
"line": 437,
"column": 27
} | {
"line": 437,
"column": 28
} | [
{
"pp": "z : ℍ\ng₀ : SL(2, ℤ)\nhg₀ : ∀ (g' : SL(2, ℤ)), (g' • z).im ≤ (g₀ • z).im\ng : SL(2, ℤ)\nhg : ↑g 1 = ↑g₀ 1\nhg' : ∀ (g' : SL(2, ℤ)), ↑g 1 = ↑g' 1 → |(g • z).re| ≤ |(g' • z).re|\nhg'' : (g • z).im = (g₀ • z).im\n⊢ ∀ (g' : SL(2, ℤ)), (g' • z).im ≤ (g • z).im",
"ppTerm": "?m.81",
"assigned": true,
... | [
"z : ℍ\ng₀ : SL(2, ℤ)\nhg₀ : ∀ (g' : SL(2, ℤ)), (g' • z).im ≤ (g₀ • z).im\ng : SL(2, ℤ)\nhg : ↑g 1 = ↑g₀ 1\nhg' : ∀ (g' : SL(2, ℤ)), ↑g 1 = ↑g' 1 → |(g • z).re| ≤ |(g' • z).re|\nhg'' : (g • z).im = (g₀ • z).im\n⊢ ∀ (g' : SL(2, ℤ)), (g' • z).im ≤ (g₀ • z).im"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 89
} | {
"line": 137,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : ∀ (g : SL(2, ℤ)), (fun τ ↦ f (g • τ)) =O[atImInfty] fun z ↦ z.im ^ t\nΓ : Subgroup SL(2, ℤ)\ninst✝ : Γ.FiniteIndex\nhf_inv : ∀ g ∈... | [
"E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\nf : ℍ → E\nhf_cont : Continuous[_, PseudoMetricSpace.toUniformSpace.toTopologicalSpace] f\nt : ℝ\nht : 0 ≤ t\nhf_infinity : ∀ (g : SL(2, ℤ)), (fun τ ↦ f (g • τ)) =O[atImInfty] fun z ↦ z.im ^ t\nΓ : Subgroup SL(2, ℤ)\ninst✝ : Γ.FiniteIndex\nhf_inv : ∀ g ∈ Γ, ∀ (τ : ℍ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.Defs | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 13
} | {
"line": 198,
"column": 14
} | [
{
"pp": "k : ℤ\ni : Fin 2 → ℤ\nA : SL(2, ℤ)\nz : ℍ\nh :\n ∀ (a b c d u v : ℂ),\n c * ↑z + d ≠ 0 →\n (u * ((a * ↑z + b) / (c * ↑z + d)) + v) ^ (-k) =\n (c * ↑z + d) ^ k * ((u * a + v * c) * ↑z + (u * b + v * d)) ^ (-k)\n⊢ (↑(i 0) *\n ((↑((algebraMap ℤ ℝ) (↑A 0 0)) * ↑z + ↑((algebraMap ℤ ... | [
"k : ℤ\ni : Fin 2 → ℤ\nA : SL(2, ℤ)\nz : ℍ\nh :\n ∀ (a b c d u v : ℂ),\n c * ↑z + d ≠ 0 →\n (u * ((a * ↑z + b) / (c * ↑z + d)) + v) ^ (-k) =\n (c * ↑z + d) ^ k * ((u * a + v * c) * ↑z + (u * b + v * d)) ^ (-k)\n⊢ ((↑(i 0) * ((↑(↑A 0 0) * ↑z + ↑(↑A 0 1)) / (↑(↑A 1 0) * ↑z + ↑(↑A 1 1))) + ↑(i 1)) ^ k)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 181,
"column": 2
} | {
"line": 182,
"column": 9
} | {
"line": 182,
"column": 10
} | [
{
"pp": "k : ℤ\nhk : 0 ≤ k\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝⁴ : Γ.IsArithmetic\nF : Type u_2\nF' : Type u_3\nf : F\nf' : F'\ninst✝³ : FunLike F ℍ ℂ\ninst✝² : FunLike F' ℍ ℂ\ninst✝¹ : ModularFormClass F Γ k\ninst✝ : ModularFormClass F' Γ k\ng : SL(2, ℤ)\n⊢ (fun τ ↦ ‖petersson k (⇑f ∣[k] g) (⇑f' ∣[k] g) τ‖) =O[... | [
"k : ℤ\nhk : 0 ≤ k\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝⁴ : Γ.IsArithmetic\nF : Type u_2\nF' : Type u_3\nf : F\nf' : F'\ninst✝³ : FunLike F ℍ ℂ\ninst✝² : FunLike F' ℍ ℂ\ninst✝¹ : ModularFormClass F Γ k\ninst✝ : ModularFormClass F' Γ k\ng : SL(2, ℤ)\n⊢ (fun τ ↦ ‖(⇑f ∣[k] g) τ‖ * ‖(⇑f' ∣[k] g) τ‖ * τ.im ^ k) =O[atImInf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 351,
"column": 12
} | {
"line": 351,
"column": 23
} | {
"line": 351,
"column": 24
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nthis : (f ∘ ↑ofComplex) =O[I∞] (1 ∘ ↑ofComplex)\nz : ℂ\nhz : z ∈ Complex.im ⁻¹' Ioi 0\n⊢ DifferentiableAt ℂ (f ∘ ↑ofComplex) z",
"ppTerm": "?m.86",
"assigned": false,
"usedCons... | [
"h : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nthis : (f ∘ ↑ofComplex) =O[I∞] (1 ∘ ↑ofComplex)\nz : ℂ\nhz : z ∈ Complex.im ⁻¹' Ioi 0\n⊢ DifferentiableAt ℂ (f ∘ ↑ofComplex) z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 28
} | {
"line": 355,
"column": 4
} | [
{
"pp": "case e'_7\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nthis : (f ∘ ↑ofComplex) =O[I∞] (1 ∘ ↑ofComplex)\nx✝ : ℍ\n⊢ f x✝ - valueAtInfty f =\n ((fun z ↦ (f ∘ ↑ofComplex) z - Periodic.cuspFunction h (f ∘ ↑ofComplex) 0) ∘ UpperHalfPla... | [
"case e'_7\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nthis : (f ∘ ↑ofComplex) =O[I∞] (1 ∘ ↑ofComplex)\nx✝ : ℍ\n⊢ valueAtInfty f = Periodic.cuspFunction h (f ∘ ↑ofComplex) 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 372,
"column": 2
} | {
"line": 372,
"column": 39
} | {
"line": 372,
"column": 40
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhf : IsZeroAtImInfty f\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\n⊢ f =O[atImInfty] fun τ ↦ rexp (-2 * π * τ.im / h)",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"instHD... | [
"h : ℝ\nf : ℍ → ℂ\nhf : IsZeroAtImInfty f\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\n⊢ f =O[atImInfty] fun τ ↦ rexp (-(2 * π * τ.im) / h)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 381,
"column": 70
} | {
"line": 381,
"column": 81
} | {
"line": 381,
"column": 82
} | [
{
"pp": "k : ℤ\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\nf : F\ninst✝ : ModularFormClass F Γ k\nhh : 0 < h\nhΓ : h ∈ Γ.strictPeriods\nn : ℕ\nt : ℝ\nht : 0 < t\nu : ℝ\n⊢ 0 < (↑u + ↑t * I).im",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"Complex.mul_... | [
"k : ℤ\nF : Type u_1\ninst✝¹ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\nf : F\ninst✝ : ModularFormClass F Γ k\nhh : 0 < h\nhΓ : h ∈ Γ.strictPeriods\nn : ℕ\nt : ℝ\nht : 0 < t\nu : ℝ\n⊢ 0 < t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 39
} | {
"line": 407,
"column": 40
} | [
{
"pp": "k : ℤ\nF : Type u_1\ninst✝⁴ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nf : F\ninst✝³ : ModularFormClass F Γ k\ninst✝² : Γ.HasDetPlusMinusOne\ninst✝¹ : DiscreteTopology ↥Γ\ninst✝ : Fact (IsCusp OnePoint.infty Γ)\nhf : IsZeroAtImInfty ⇑f\n⊢ ∃ c > 0, ⇑f =O[atImInfty] fun τ ↦ rexp (-c * τ.im)",
"ppT... | [
"k : ℤ\nF : Type u_1\ninst✝⁴ : FunLike F ℍ ℂ\nΓ : Subgroup (GL (Fin 2) ℝ)\nf : F\ninst✝³ : ModularFormClass F Γ k\ninst✝² : Γ.HasDetPlusMinusOne\ninst✝¹ : DiscreteTopology ↥Γ\ninst✝ : Fact (IsCusp OnePoint.infty Γ)\nhf : IsZeroAtImInfty ⇑f\n⊢ ∃ c, 0 < c ∧ ⇑f =O[atImInfty] fun τ ↦ rexp (-(c * τ.im))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Bounds | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 35
} | {
"line": 208,
"column": 36
} | [
{
"pp": "k : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝⁴ : Γ.IsArithmetic\nF : Type u_2\nF' : Type u_3\nf : F\nf' : F'\ninst✝³ : FunLike F ℍ ℂ\ninst✝² : FunLike F' ℍ ℂ\ninst✝¹ : ModularFormClass F Γ k\ninst✝ : CuspFormClass F' Γ k\n⊢ ∃ C, ∀ (τ : ℍ), ‖petersson k (⇑f) (⇑f') τ‖ ≤ C",
"ppTerm": "?m.18",
"assign... | [
"k : ℤ\nΓ : Subgroup (GL (Fin 2) ℝ)\ninst✝⁴ : Γ.IsArithmetic\nF : Type u_2\nF' : Type u_3\nf : F\nf' : F'\ninst✝³ : FunLike F ℍ ℂ\ninst✝² : FunLike F' ℍ ℂ\ninst✝¹ : ModularFormClass F Γ k\ninst✝ : CuspFormClass F' Γ k\n⊢ ∃ C, ∀ (τ : ℍ), ‖petersson k (⇑f) (⇑f') τ‖ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 451,
"column": 65
} | {
"line": 453,
"column": 96
} | {
"line": 455,
"column": 0
} | [
{
"pp": "h : ℝ\nf g : ℂ → ℂ\nhfcts : ContinuousAt (Periodic.cuspFunction h f) 0\nhgcts : ContinuousAt (Periodic.cuspFunction h g) 0\n⊢ Periodic.cuspFunction h (f * g) 0 = Periodic.cuspFunction h f 0 * Periodic.cuspFunction h g 0",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [] | by
rw [Periodic.cuspFunction, update_self]
exact (Periodic.tendsto_nhds_zero hfcts).mul (Periodic.tendsto_nhds_zero hgcts) |>.limUnder_eq | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence | {
"line": 54,
"column": 2
} | {
"line": 55,
"column": 23
} | {
"line": 55,
"column": 24
} | [
{
"pp": "k : ℤ\nhk : 3 ≤ k\nN : ℕ\na : Fin 2 → ZMod N\nhk' : 2 < ↑k\np_sum : Summable fun x ↦ ‖↑x‖ ^ (-k)\nK : Set ℍ\nhK : IsCompact K\nA B : ℝ\nhB : 0 < B\nHABK : K ⊆ verticalStrip A B\np : ↑(gammaSet N 1 a)\nz : ℍ\nhz : z ∈ verticalStrip A B\n⊢ ‖eisSummand k (↑p) z‖ ≤ r { coe := { re := A, im := B }, coe_im_p... | [
"k : ℤ\nhk : 3 ≤ k\nN : ℕ\na : Fin 2 → ZMod N\nhk' : 2 < ↑k\np_sum : Summable fun x ↦ ‖↑x‖ ^ (-k)\nK : Set ℍ\nhK : IsCompact K\nA B : ℝ\nhB : 0 < B\nHABK : K ⊆ verticalStrip A B\np : ↑(gammaSet N 1 a)\nz : ℍ\nhz : z ∈ verticalStrip A B\n⊢ ‖↑(↑p 0) * ↑z + ↑(↑p 1)‖ ^ (-↑k) ≤ r { coe := { re := A, im := B }, coe_im_po... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 505,
"column": 2
} | {
"line": 505,
"column": 13
} | {
"line": 505,
"column": 14
} | [
{
"pp": "h : ℝ\nf : ℍ → ℂ\nhf : AnalyticAt ℂ (cuspFunction h f) 0\n⊢ qExpansion h (-f) = -qExpansion h f",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"h : ℝ\nf : ℍ → ℂ\nhf : AnalyticAt ℂ (cuspFunction h f) 0\n⊢ qExpansion h (-f) = -qExpansion h f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 517,
"column": 4
} | {
"line": 517,
"column": 50
} | {
"line": 517,
"column": 51
} | [
{
"pp": "h : ℝ\nf g : ℍ → ℂ\nhf : AnalyticAt ℂ (cuspFunction h f) 0\nhg : AnalyticAt ℂ (cuspFunction h g) 0\n⊢ AnalyticAt ℂ (cuspFunction h (-g)) 0",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Pi.instNeg",
"Complex.in... | [
"h : ℝ\nf g : ℍ → ℂ\nhf : AnalyticAt ℂ (cuspFunction h f) 0\nhg : AnalyticAt ℂ (cuspFunction h g) 0\n⊢ AnalyticAt ℂ (cuspFunction h g) 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 518,
"column": 2
} | {
"line": 518,
"column": 49
} | {
"line": 518,
"column": 50
} | [
{
"pp": "h : ℝ\nf g : ℍ → ℂ\nhf : AnalyticAt ℂ (cuspFunction h f) 0\nhg : AnalyticAt ℂ (cuspFunction h g) 0\nhg' : AnalyticAt ℂ (cuspFunction h (-g)) 0\n⊢ qExpansion h (f - g) = qExpansion h f - qExpansion h g",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"UpperHalf... | [
"h : ℝ\nf g : ℍ → ℂ\nhf : AnalyticAt ℂ (cuspFunction h f) 0\nhg : AnalyticAt ℂ (cuspFunction h g) 0\nhg' : AnalyticAt ℂ (cuspFunction h (-g)) 0\n⊢ qExpansion h (f + -g) = qExpansion h f + -qExpansion h g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 533,
"column": 4
} | {
"line": 533,
"column": 19
} | {
"line": 533,
"column": 20
} | [
{
"pp": "case mpr\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nH : f = 0\n⊢ qExpansion h f = 0",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MvPowerSeries.instZero",
"UpperHalfPlane.qExpans... | [
"case mpr\nh : ℝ\nf : ℍ → ℂ\nhh : 0 < h\nhfper : Periodic (f ∘ ↑ofComplex) ↑h\nhfhol : MDiff f\nhfbdd : IsBoundedAtImInfty f\nH : f = 0\n⊢ qExpansion h 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 616,
"column": 2
} | {
"line": 616,
"column": 23
} | {
"line": 618,
"column": 0
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\ninst✝ : Γ.HasDetPlusMinusOne\n⊢ qExpansion h ⇑1 = 1",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"ModularForm",
"UpperHalfPlane.qExpansion_one",
"UpperHalfPlane.qExpansion",
"congrArg",
"Int",
"Unit",
... | [] | simp [qExpansion_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 616,
"column": 2
} | {
"line": 616,
"column": 23
} | {
"line": 618,
"column": 0
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\ninst✝ : Γ.HasDetPlusMinusOne\n⊢ qExpansion h ⇑1 = 1",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"ModularForm",
"UpperHalfPlane.qExpansion_one",
"UpperHalfPlane.qExpansion",
"congrArg",
"Int",
"Unit",
... | [] | simp [qExpansion_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 616,
"column": 2
} | {
"line": 616,
"column": 23
} | {
"line": 618,
"column": 0
} | [
{
"pp": "Γ : Subgroup (GL (Fin 2) ℝ)\nh : ℝ\ninst✝ : Γ.HasDetPlusMinusOne\n⊢ qExpansion h ⇑1 = 1",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"ModularForm",
"UpperHalfPlane.qExpansion_one",
"UpperHalfPlane.qExpansion",
"congrArg",
"Int",
"Unit",
... | [] | simp [qExpansion_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Modular | {
"line": 488,
"column": 60
} | {
"line": 488,
"column": 71
} | {
"line": 488,
"column": 72
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhc : ↑g 1 0 = 0\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n ↑g 1 0 = 0 →\n 0 ≤ ↑g 1 1 → (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨ (g = T⁻¹ ∨ g = -T⁻¹) ∧ z.re = 1 / 2 ∨ g = 1 ∨ g = -1\nhd : ¬0 ≤ ↑g 1 1\n⊢ ↑(-g) 1 0 ... | [
"g : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhc : ↑g 1 0 = 0\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n ↑g 1 0 = 0 →\n 0 ≤ ↑g 1 1 → (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨ (g = T⁻¹ ∨ g = -T⁻¹) ∧ z.re = 1 / 2 ∨ g = 1 ∨ g = -1\nhd : ¬0 ≤ ↑g 1 1\n⊢ ↑g 1 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 489,
"column": 6
} | {
"line": 489,
"column": 17
} | {
"line": 489,
"column": 18
} | [
{
"pp": "case inr\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhc : ↑g 1 0 = 0\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n ↑g 1 0 = 0 →\n 0 ≤ ↑g 1 1 → (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨ (g = T⁻¹ ∨ g = -T⁻¹) ∧ z.re = 1 / 2 ∨ g = 1 ∨ g = -1\nhd : ¬0 ≤ ↑g 1 1\n⊢ ... | [
"case inr\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhc : ↑g 1 0 = 0\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n ↑g 1 0 = 0 →\n 0 ≤ ↑g 1 1 → (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨ (g = T⁻¹ ∨ g = -T⁻¹) ∧ z.re = 1 / 2 ∨ g = 1 ∨ g = -1\nhd : ¬0 ≤ ↑g 1 1\n⊢ ↑g 1 1 ≤ 0"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 723,
"column": 4
} | {
"line": 724,
"column": 11
} | {
"line": 724,
"column": 12
} | [
{
"pp": "F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h ⇑f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nh1 : HasFPowerSeriesAt (cuspFunction h ⇑f) (FormalMultilinearSeries.ofScalars ℂ c) 0\n⊢ HasFPowerSeriesAt (cuspFunction h ... | [
"F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h ⇑f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nh1 : HasFPowerSeriesAt (cuspFunction h ⇑f) (FormalMultilinearSeries.ofScalars ℂ c) 0\n⊢ HasFPowerSeriesAt (cuspFunction h ⇑f)\n (Fo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 725,
"column": 2
} | {
"line": 725,
"column": 48
} | {
"line": 725,
"column": 49
} | [
{
"pp": "F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h ⇑f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nh1 : HasFPowerSeriesAt (cuspFunction h ⇑f) (FormalMultilinearSeries.ofScalars ℂ c) 0\nh2 : HasFPowerSeriesAt (cuspFunction... | [
"F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h ⇑f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nh1 : HasFPowerSeriesAt (cuspFunction h ⇑f) (FormalMultilinearSeries.ofScalars ℂ c) 0\nh2 : HasFPowerSeriesAt (cuspFunction h ⇑f) (qExp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.QExpansion | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 13
} | {
"line": 733,
"column": 14
} | [
{
"pp": "F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h ⇑f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nm : ℕ\nh1 : HasFPowerSeriesAt (cuspFunction h ⇑f) (FormalMultilinearSeries.ofScalars ℂ c) 0\nh2 : HasFPowerSeriesAt (cuspF... | [
"F : Type u_1\ninst✝ : FunLike F ℍ ℂ\nh : ℝ\nf : F\nc : ℕ → ℂ\nhh : 0 < h\nhfanalytic : AnalyticAt ℂ (cuspFunction h ⇑f) 0\nhf : ∀ (τ : ℍ), HasSum (fun m ↦ c m • 𝕢 h ↑τ ^ m) (f τ)\nm : ℕ\nh1 : HasFPowerSeriesAt (cuspFunction h ⇑f) (FormalMultilinearSeries.ofScalars ℂ c) 0\nh2 : HasFPowerSeriesAt (cuspFunction h ⇑f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 492,
"column": 4
} | {
"line": 492,
"column": 57
} | {
"line": 492,
"column": 58
} | [
{
"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 : 0 ≤ ↑g 1 1\n⊢ ↑g 1 1 = 1 ∨ ↑g 1 1 = -1",
"ppTerm": "?m.392",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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 : 0 ≤ ↑g 1 1\n⊢ ↑g 1 1 = 1 ∨ ↑g 1 1 = -1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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