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.Modular | {
"line": 664,
"column": 32
} | {
"line": 664,
"column": 43
} | [
{
"pp": "g✝ : SL(2, ℤ)\nz✝ : ℍ\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhden : z.im ≤ (g • z).im\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ} {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 → g • z ∈ 𝒟 → z.im ≤ (g • z).im → 0 ≤ ↑g 1 0 → (g • z).im = z.im\nhc : ¬0 ≤ ↑g 1 0\n⊢ 0 ≤ ↑(-g) 1 0",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 54
} | [
{
"pp": "n : ℕ\nz : ℂ\nhz : z ∈ ℍₒ\nh : 1 = cexp (2 * ↑π * I * (↑n + 1) * z)\n⊢ 0 < ((n + 1) • z).im",
"usedConstants": [
"Complex.mul_im",
"Real.instIsOrderedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"instHSMul",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 13
} | [
{
"pp": "q : ℂ\nhq : ‖q‖ < 1\n⊢ Summable fun i ↦ ‖-q ^ (i + 1)‖",
"usedConstants": [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 63
} | [
{
"pp": "case h.inl\nK : Set ℂ\nhK : K ⊆ Metric.ball 0 1\nhcK : IsCompact K\nhN : K = ∅\n⊢ HasProdUniformlyOn (fun n q ↦ 1 + -q ^ (n + 1)) (fun q ↦ ∏' (n : ℕ), (1 + -q ^ (n + 1))) K",
"usedConstants": [
"UniformSpace",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"_private.Mathli... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 84,
"column": 10
} | {
"line": 84,
"column": 56
} | [
{
"pp": "K : Set ℂ\nhK : K ⊆ Metric.ball 0 1\nhcK : IsCompact K\nhN : K.Nonempty\nq₀ : ℂ\nhq₀ : q₀ ∈ K\nleft✝ : sSup ((fun q ↦ ‖q‖) '' K) = ‖q₀‖\nHB : ∀ y ∈ K, ‖y‖ ≤ ‖q₀‖\n⊢ ‖?m.238‖ < 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 86,
"column": 4
} | {
"line": 86,
"column": 15
} | [
{
"pp": "case h.inr\nK : Set ℂ\nhK : K ⊆ Metric.ball 0 1\nhcK : IsCompact K\nhN : K.Nonempty\nq₀ : ℂ\nhq₀ : q₀ ∈ K\nleft✝ : sSup ((fun q ↦ ‖q‖) '' K) = ‖q₀‖\nHB : ∀ y ∈ K, ‖y‖ ≤ ‖q₀‖\nn : ℕ\nx : ℂ\nhx : x ∈ K\n⊢ ‖-x ^ (n + 1)‖ ≤ ‖q₀‖ ^ (n + 1)",
"usedConstants": [
"NormedCommRing.toNormedRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 92,
"column": 27
} | {
"line": 92,
"column": 55
} | [
{
"pp": "x✝ : Finset ℕ\n⊢ DifferentiableOn ℂ (fun x2 ↦ ∏ i ∈ x✝, (fun n q ↦ 1 - q ^ (n + 1)) i x2) (Metric.ball 0 1)",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"Real",
"Semiring.toModule",
"Co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 67,
"column": 21
} | {
"line": 67,
"column": 71
} | [
{
"pp": "z : ℍ\nN a : ℕ\n⊢ 0 < ((↑a + 1) * ↑z).im",
"usedConstants": [
"Complex.mul_im",
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"HMul.hMul",
"UpperHalfPlane.coe",
"MulZeroClass.toMul",
"Nat.ble",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 100,
"column": 34
} | {
"line": 100,
"column": 45
} | [
{
"pp": "k : ℕ\nx✝ : ℂ\nhq : x✝ ∈ Metric.ball 0 1\n⊢ ‖x✝‖ < 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 36
} | [
{
"pp": "z : ℍ\n⊢ Summable fun n ↦ ‖-eta_q n ↑z‖",
"usedConstants": [
"summable_geometric_iff_norm_lt_one._simp_1",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 109,
"column": 19
} | {
"line": 109,
"column": 30
} | [
{
"pp": "z : ℂ\nhz : z ∈ ℍₒ\n⊢ 𝕢 1 z ∈ Metric.ball 0 1",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Function.Periodic.qParam",
"congrArg",
"Complex.instZero",
"Real.instLT",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 113,
"column": 21
} | {
"line": 113,
"column": 32
} | [
{
"pp": "z : ℂ\nhz : z ∈ ℍₒ\ni : ℕ\n⊢ 1 + (fun n ↦ -eta_q n z) i ≠ 0",
"usedConstants": [
"NormedCommRing.toNormedRing",
"NormedCommRing.toCommRing",
"ModularForm.eta_q",
"NormedRing.toRing",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"CommCSta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 44
} | [
{
"pp": "case refine_2\nz : ℂ\nhz : z ∈ ℍₒ\n⊢ Summable fun x ↦ ‖(fun n ↦ -eta_q n z) x‖",
"usedConstants": [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 147,
"column": 42
} | {
"line": 147,
"column": 53
} | [
{
"pp": "z : ℂ\nhz : z ∈ ℍₒ\n⊢ 𝕢 1 z ∈ Metric.ball 0 1",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Function.Periodic.qParam",
"congrArg",
"Complex.instZero",
"Real.instLT",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.DedekindEta | {
"line": 155,
"column": 76
} | {
"line": 160,
"column": 21
} | [
{
"pp": "h : ℝ\nz : ℂ\n⊢ logDeriv (𝕢 h) z = 2 * ↑π * I / ↑h",
"usedConstants": [
"logDeriv",
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"logDeriv_comp",
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"Function.Periodic.qPa... | by
have : 𝕢 h = cexp ∘ ((2 * π * I / h) * ·) := by
ext
grind [Periodic.qParam]
rw [this, logDeriv_comp (by fun_prop) (by fun_prop), deriv_const_mul_id]
simp [logDeriv_exp] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 91,
"column": 2
} | {
"line": 92,
"column": 28
} | [
{
"pp": "z : ℍ\n⊢ HasSum (fun x ↦ e2Summand x z)\n (2 * riemannZeta 2 - 8 * ↑π ^ 2 * ∑' (n : ℕ+), ↑((σ 1) ↑n) * cexp (2 * ↑π * I * ↑z) ^ ↑n) (symmetricIcc ℤ)",
"usedConstants": [
"PNat.val",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Nat.instMulZ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 13
} | [
{
"pp": "z : ℍ\n⊢ Tendsto (fun N ↦ -e2Summand (↑N) z) atTop (𝓝 0)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 13
} | [
{
"pp": "z : ℍ\n⊢ Tendsto (fun N ↦ -e2Summand (↑N) z) atTop (𝓝 0)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 15
} | [
{
"pp": "case ha\nz : ℍ\na b m : ℤ\nhm : m ≠ 0 ∨ a ≠ 0 ∧ b ≠ 0\n⊢ ↑m * ↑z + ↑a ≠ 0",
"usedConstants": [
"Int.cast",
"HMul.hMul",
"UpperHalfPlane.coe",
"Complex.instNormedField",
"NormedDivisionRing.toDivisionRing",
"Complex.instMul",
"DivisionRing.toDivisionSemiring... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 15
} | [
{
"pp": "case hb\nz : ℍ\na b m : ℤ\nhm : m ≠ 0 ∨ a ≠ 0 ∧ b ≠ 0\n⊢ ↑m * ↑z + ↑b ≠ 0",
"usedConstants": [
"Int.cast",
"HMul.hMul",
"UpperHalfPlane.coe",
"Complex.instNormedField",
"NormedDivisionRing.toDivisionRing",
"Complex.instMul",
"DivisionRing.toDivisionSemiring... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 99,
"column": 4
} | {
"line": 99,
"column": 49
} | [
{
"pp": "z : ℍ\n⊢ (fun m ↦ ((↑(m 0) * ↑z + ↑(m 1)) ^ 2 * (↑(m 0) * ↑z + ↑(m 1) + 1))⁻¹) =O[cofinite] fun n ↦ (‖n‖ ^ 3)⁻¹",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Int.cast",
"Eq.mpr",
"Real.instPow",
"Semigroup.toMul",
"Real",
"DivInvMo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 35
} | [
{
"pp": "z : ℍ\nm : ℤ\nthis : Summable fun x ↦ ((↑m * ↑z + ↑↑x + 1) * (↑m * ↑z + ↑↑x))⁻¹\nb : { x // x ∉ {0, -1} }\n⊢ ((↑m * ↑z + ↑↑b + 1) * (↑m * ↑z + ↑↑b))⁻¹ = 1 / (↑m * ↑z + ↑↑b) - 1 / (↑m * ↑z + ↑↑b + 1)",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Int.c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 121,
"column": 8
} | {
"line": 121,
"column": 31
} | [
{
"pp": "z : ℍ\nb n : ℤ\nh : b = 0 → ¬n = 0\nhb : ¬b = 0\n⊢ ↑b * ↑z + ↑n + 1 ≠ 0",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"UpperHalfPlane.coe",
"congrArg",
"add_assoc",
"AddGroupWithOne.toAddMonoidWithOne",
"Com... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 137,
"column": 6
} | {
"line": 138,
"column": 13
} | [
{
"pp": "z : ℍ\nt : ℂ := ∑' (m : ℤ) (n : ℤ), G2Term z ![m, n]\n⊢ Summable fun b ↦\n ∑' (n : ℤ), G2Term z ![b, n] + ∑'[symmetricIco ℤ] (n : ℤ), (1 / (↑b * ↑z + ↑n) - 1 / (↑b * ↑z + ↑n + 1))",
"usedConstants": [
"_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform.0.EisensteinSer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 48
} | [
{
"pp": "z : ℍ\nthis :\n Tendsto\n (((fun s ↦ ∑ x ∈ s, (↑z ^ 2)⁻¹ * e2Summand x { coe := (-↑z)⁻¹, coe_im_pos := ⋯ }) ∘ fun N ↦ Ico (-N) N) ∘ Nat.cast)\n atTop\n (𝓝\n (∑'[{ filter := Filter.map (fun N ↦ Ico (-N) N) (Filter.map Nat.cast atTop) }] (x : ℤ),\n (↑z ^ 2)⁻¹ * e2Summand x { coe :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 176,
"column": 22
} | {
"line": 176,
"column": 33
} | [
{
"pp": "z : ℍ\nx : ℕ\ni : ℤ\nhi : i ∈ Ico (-↑x) ↑x\n⊢ Summable fun n ↦ 1 / (↑n * ↑z + ↑i) ^ 2",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 154,
"column": 6
} | {
"line": 154,
"column": 17
} | [
{
"pp": "case hf\nz : ℍ\nN : ℤ\n⊢ Summable fun m ↦ 1 / (↑m * ↑z + ↑N) ^ 2",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"UpperHalfPlane.coe",
"Monoid.toMul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 13
} | [
{
"pp": "case ha\nz : ℍ\nm : ℤ\n⊢ Tendsto (fun N ↦ 1 / (↑m * ↑z - ↑N) - 1 / (↑m * ↑z + ↑N)) atTop (𝓝 0)",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"UpperHalfPlane.coe",
"con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 155,
"column": 6
} | {
"line": 155,
"column": 29
} | [
{
"pp": "case hg\nz : ℍ\nN : ℤ\n⊢ Summable fun m ↦ 1 / (↑m * ↑z + ↑N) - 1 / (↑m * ↑z + ↑N + 1)",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"UpperHa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 15
} | [
{
"pp": "z : ℍ\nx : ℕ\ni : ℤ\nhi : i ∈ Finset.Ico (-↑x) ↑x\n⊢ Summable fun n ↦ 1 / (↑n * ↑z + ↑i) ^ 2",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 206,
"column": 4
} | {
"line": 206,
"column": 15
} | [
{
"pp": "z : ℍ\nd : ℕ+\n⊢ Summable fun m ↦ 1 / (↑m * ↑z - ↑↑d) - 1 / (↑m * ↑z + ↑↑d)",
"usedConstants": [
"PNat.val",
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"UpperHalfPlane.coe",
"congr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 707,
"column": 4
} | {
"line": 707,
"column": 44
} | [
{
"pp": "case inr\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhim : (g • z).im = z.im\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n (g • z).im = z.im →\n 0 ≤ ↑g 1 0 →\n (g = 1 ∨ g = -1) ∨\n (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 707,
"column": 65
} | {
"line": 707,
"column": 76
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhim : (g • z).im = z.im\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n (g • z).im = z.im →\n 0 ≤ ↑g 1 0 →\n (g = 1 ∨ g = -1) ∨\n (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨\n (g = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Transform | {
"line": 210,
"column": 8
} | {
"line": 210,
"column": 45
} | [
{
"pp": "case mem.inr\nγ g : SL(2, ℤ)\nh2 : g = T\n⊢ G2 ∣[2] g = G2 - D2 g",
"usedConstants": [
"Eq.mpr",
"Matrix.SpecialLinearGroup",
"congrArg",
"sub_zero",
"instDecidableEqFin",
"EisensteinSeries.G2",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 214,
"column": 33
} | {
"line": 214,
"column": 44
} | [
{
"pp": "z : ℍ\nd : ℕ+\n⊢ ?m.161 ∈ integerComplement",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 708,
"column": 10
} | {
"line": 708,
"column": 21
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhim : (g • z).im = z.im\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n (g • z).im = z.im →\n 0 ≤ ↑g 1 0 →\n (g = 1 ∨ g = -1) ∨\n (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨\n (g = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 238,
"column": 10
} | {
"line": 238,
"column": 21
} | [
{
"pp": "z : ℍ\nN : ℕ+\nh2 :\n ↑π * I - 2 * ↑π * I * ∑' (n : ℕ), cexp (2 * ↑π * I * ↑{ coe := -↑↑N / ↑z, coe_im_pos := ⋯ }) ^ n - ↑z / -↑↑N =\n ↑π * I - 2 * ↑π * I * ∑' (n : ℕ), cexp (2 * ↑π * I * ↑{ coe := -↑↑N / ↑z, coe_im_pos := ⋯ }) ^ n - ↑z / -↑↑N\n⊢ Summable (HPow.hPow (cexp (2 * ↑π * I * ↑{ coe := -↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 708,
"column": 31
} | {
"line": 708,
"column": 42
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhim : (g • z).im = z.im\nthis :\n ∀ {g : SL(2, ℤ)} {z : ℍ},\n z ∈ 𝒟 →\n g • z ∈ 𝒟 →\n (g • z).im = z.im →\n 0 ≤ ↑g 1 0 →\n (g = 1 ∨ g = -1) ∨\n (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨\n (g = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 238,
"column": 10
} | {
"line": 238,
"column": 21
} | [
{
"pp": "z : ℍ\nN : ℕ+\nh2 :\n ↑π * I - 2 * ↑π * I * ∑' (n : ℕ), cexp (2 * ↑π * I * ↑{ coe := -↑↑N / ↑z, coe_im_pos := ⋯ }) ^ n - ↑z / -↑↑N =\n ↑π * I - 2 * ↑π * I * ∑' (n : ℕ), cexp (2 * ↑π * I * ↑{ coe := -↑↑N / ↑z, coe_im_pos := ⋯ }) ^ n - ↑z / -↑↑N\n⊢ Summable (HPow.hPow (cexp (2 * ↑π * I * ↑{ coe := -↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Derivative | {
"line": 46,
"column": 4
} | {
"line": 46,
"column": 19
} | [
{
"pp": "F : ℍ → ℂ\nhF : DifferentiableOn ℂ (F ∘ ↑ofComplex) {z | 0 < z.im}\nc : ℂ := (2 * ↑π * I)⁻¹\n⊢ DifferentiableOn ℂ (fun z ↦ c * deriv (F ∘ ↑ofComplex) z) upperHalfPlaneSet",
"usedConstants": [
"UpperHalfPlane.ofComplex",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonUn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 45
} | [
{
"pp": "case hf\nz : ℍ\nthis :\n ∀ (N : ℕ+),\n ∑ n ∈ Ico (-↑↑N) ↑↑N, ∑' (m : ℤ), (1 / (↑m * ↑z + ↑n) - 1 / (↑m * ↑z + ↑n + 1)) =\n -(2 / ↑↑N) +\n ∑' (m : ℕ+), (1 / (↑↑m * ↑z - ↑↑N) + 1 / (-↑↑m * ↑z + -↑↑N) - 1 / (↑↑m * ↑z + ↑↑N) - 1 / (-↑↑m * ↑z + ↑↑N))\n⊢ Tendsto (fun x ↦ -(2 / ↑↑x)) atTop (𝓝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 262,
"column": 4
} | {
"line": 262,
"column": 71
} | [
{
"pp": "case hg\nz : ℍ\nthis :\n ∀ (N : ℕ+),\n ∑ n ∈ Ico (-↑↑N) ↑↑N, ∑' (m : ℤ), (1 / (↑m * ↑z + ↑n) - 1 / (↑m * ↑z + ↑n + 1)) =\n -(2 / ↑↑N) +\n ∑' (m : ℕ+), (1 / (↑↑m * ↑z - ↑↑N) + 1 / (-↑↑m * ↑z + -↑↑N) - 1 / (↑↑m * ↑z + ↑↑N) - 1 / (-↑↑m * ↑z + ↑↑N))\n⊢ Tendsto\n (fun x ↦\n ∑' (m : ℕ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Summable | {
"line": 270,
"column": 2
} | {
"line": 271,
"column": 9
} | [
{
"pp": "case ha\nz : ℍ\n⊢ HasSum (fun b ↦ ∑' (m : ℤ), (1 / (↑m * ↑z + ↑b) - 1 / (↑m * ↑z + ↑b + 1))) (-2 * ↑π * I / ↑z) (symmetricIco ℤ)",
"usedConstants": [
"PNat.val",
"Int.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"_private.Mathlib.NumberTheory.ModularForms.Ei... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 715,
"column": 4
} | {
"line": 718,
"column": 53
} | [
{
"pp": "case inr\ng✝ : SL(2, ℤ)\nz✝ : ℍ\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhim : ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) g)) ↑z‖ = 1\nhc✝ : 0 ≤ ↑g 1 0\nhc : ↑g 1 0 = 1\n⊢ (g = 1 ∨ g = -1) ∨\n (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨\n (g = T⁻¹ ∨ g = -T⁻¹) ∧ z.re = 1 / 2 ∨\... | rcases Int.abs_le_one_iff.mp (cases_d_of_c_eq_one hz him.le hc) with hd | hd | hd
· grind [cases_c_one_d_zero hz hg him.le hc hd] -- ± S, T⁻¹S, TS
· grind [case_c_one_d_one hz hg him.le hc hd] -- ± ST, TST
· grind [case_c_one_d_neg_one hz hg him.le hc hd] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Modular | {
"line": 715,
"column": 4
} | {
"line": 718,
"column": 53
} | [
{
"pp": "case inr\ng✝ : SL(2, ℤ)\nz✝ : ℍ\ng : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟\nhg : g • z ∈ 𝒟\nhim : ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) g)) ↑z‖ = 1\nhc✝ : 0 ≤ ↑g 1 0\nhc : ↑g 1 0 = 1\n⊢ (g = 1 ∨ g = -1) ∨\n (g = T ∨ g = -T) ∧ z.re = -1 / 2 ∨\n (g = T⁻¹ ∨ g = -T⁻¹) ∧ z.re = 1 / 2 ∨\... | rcases Int.abs_le_one_iff.mp (cases_d_of_c_eq_one hz him.le hc) with hd | hd | hd
· grind [cases_c_one_d_zero hz hg him.le hc hd] -- ± S, T⁻¹S, TS
· grind [case_c_one_d_one hz hg him.le hc hd] -- ± ST, TST
· grind [case_c_one_d_neg_one hz hg him.le hc hd] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Modular | {
"line": 744,
"column": 4
} | {
"line": 744,
"column": 47
} | [
{
"pp": "case mpr\ng : SL(2, ℤ)\n⊢ S • I = I",
"usedConstants": [
"Eq.mpr",
"Real",
"instHSMul",
"Matrix.SpecialLinearGroup",
"UpperHalfPlane.SLAction",
"UpperHalfPlane.coe",
"congrArg",
"UpperHalfPlane.ext_iff",
"instDecidableEqFin",
"UpperHalfPla... | rw [modular_S_smul, UpperHalfPlane.ext_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.Modular | {
"line": 784,
"column": 4
} | {
"line": 784,
"column": 15
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\nhz : z ∈ 𝒟ᵒ\nhg : g • z ∈ 𝒟\nthis✝ : ρ ∉ 𝒟ᵒ\nh : 1 +ᵥ ρ ∈ 𝒟ᵒ\nthis : (1 +ᵥ ρ).re = 1 / 2\n⊢ False",
"usedConstants": [
"_private.Mathlib.NumberTheory.Modular.0.ModularGroup.eq_one_or_neg_one_of_mem_fdo_mem_fd._proof_1_3"
]
}
] | grind [h.2] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.NumberTheory.Modular | {
"line": 867,
"column": 8
} | {
"line": 867,
"column": 31
} | [
{
"pp": "x : ℍ\nhxnorm : 1 < ‖↑x‖\nhxre : |x.re| ≤ 1 / 2\n⊢ ↑1 * ↑x ∈ ofComplex.source",
"usedConstants": [
"UpperHalfPlane.ofComplex",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"UpperHalfPlane.isOpenEmbedding_coe",
"Real",
"HMul.hMul",
"UpperHalfPlane.coe",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 868,
"column": 6
} | {
"line": 868,
"column": 58
} | [
{
"pp": "case h.h.refine_1\nx : ℍ\nhxnorm : 1 < ‖↑x‖\nhxre : |x.re| ≤ 1 / 2\nthis : ContinuousAt (fun a ↦ ↑(↑ofComplex (↑a * ↑x))) 1\n⊢ Filter.Tendsto (fun x_1 ↦ ‖↑(↑ofComplex (↑x_1 * ↑x))‖) (𝓝 1) (𝓝 ‖↑x‖)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 871,
"column": 50
} | {
"line": 871,
"column": 61
} | [
{
"pp": "x : ℍ\nhxnorm : 1 < ‖↑x‖\nhxre : |x.re| ≤ 1 / 2\na : ℝ\nha : 0 < a\nha' : a ∈ Set.Iio 1\n⊢ 0 < (↑a * ↑x).im",
"usedConstants": [
"Complex.mul_im",
"Eq.mpr",
"Real",
"HMul.hMul",
"UpperHalfPlane.coe",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 881,
"column": 38
} | {
"line": 881,
"column": 49
} | [
{
"pp": "x : ℍ\nhxnorm : 1 < ‖↑x‖\nhxre : |x.re| ≤ 1 / 2\nthis : Filter.Tendsto (fun t ↦ ↑t * ↑x) (𝓝 1) (𝓝 ↑x)\na : ℝ\nha : 0 < a\n⊢ 0 < (↑a * ↑x).im",
"usedConstants": [
"Complex.mul_im",
"Eq.mpr",
"Real",
"HMul.hMul",
"UpperHalfPlane.coe",
"Real.instZero",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 893,
"column": 6
} | {
"line": 893,
"column": 17
} | [
{
"pp": "x : ℍ\nhxnorm : ‖↑x‖ = 1\nhxre : |x.re| ≤ 1 / 2\nt : ℝ≥0\n⊢ 0 < (↑x + ↑↑t * Complex.I).im",
"usedConstants": [
"Complex.mul_im",
"Eq.mpr",
"Real",
"HMul.hMul",
"UpperHalfPlane.coe",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"Complex.im"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 896,
"column": 45
} | {
"line": 896,
"column": 56
} | [
{
"pp": "x : ℍ\nhxnorm : ‖↑x‖ = 1\nhxre : |x.re| ≤ 1 / 2\na : ℝ≥0\nha : 0 < a\n⊢ |{ coe := ↑x + ↑↑a * Complex.I, coe_im_pos := ⋯ }.re| ≤ 1 / 2",
"usedConstants": [
"Complex.mul_im",
"Eq.mpr",
"Real.instLE",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"Complex.mul_re",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 905,
"column": 4
} | {
"line": 906,
"column": 49
} | [
{
"pp": "case hf\nx : ℍ\nhxnorm : ‖↑x‖ = 1\nhxre : |x.re| ≤ 1 / 2\n⊢ Filter.Tendsto (fun t ↦ { coe := ↑x + ↑↑t * Complex.I, coe_im_pos := ⋯ }) (𝓝 0) (𝓝 x)",
"usedConstants": [
"NNReal.instTopologicalSpace",
"Complex.mul_im",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 927,
"column": 4
} | {
"line": 927,
"column": 66
} | [
{
"pp": "ho1 : interior 𝒟 ⊆ UpperHalfPlane.re ⁻¹' interior (UpperHalfPlane.re '' 𝒟)\nho2 : interior 𝒟 ⊆ (fun τ ↦ ‖↑τ‖) ⁻¹' interior ((fun τ ↦ ‖↑τ‖) '' 𝒟)\nx : ℍ\nhx : x ∈ interior 𝒟\nξ : ℍ\nhξ : ξ ∈ 𝒟\n⊢ ξ ∈ (fun τ ↦ ‖↑τ‖) ⁻¹' Set.Ici 1",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 932,
"column": 4
} | {
"line": 932,
"column": 55
} | [
{
"pp": "ho1 : interior 𝒟 ⊆ UpperHalfPlane.re ⁻¹' interior (UpperHalfPlane.re '' 𝒟)\nho2 : interior 𝒟 ⊆ (fun τ ↦ ‖↑τ‖) ⁻¹' interior ((fun τ ↦ ‖↑τ‖) '' 𝒟)\nx : ℍ\nhx : x ∈ interior 𝒟\nξ : ℍ\nhξ : ξ ∈ 𝒟\n⊢ ξ ∈ UpperHalfPlane.re ⁻¹' Set.Icc (-(1 / 2)) (1 / 2)",
"usedConstants": [
"AddGroup.toSubtra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 949,
"column": 33
} | {
"line": 949,
"column": 72
} | [
{
"pp": "y : ℝ\nz : ℂ\nhz : 0 < z.im\nh : { coe := z, coe_im_pos := hz } ∈ truncatedFundamentalDomain y\n⊢ 1 ≤ ‖↑{ coe := z, coe_im_pos := hz }‖",
"usedConstants": [
"Norm.norm",
"Real.instLE",
"Real",
"UpperHalfPlane.coe",
"Complex.instNorm",
"UpperHalfPlane.mk",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 954,
"column": 6
} | {
"line": 955,
"column": 25
} | [
{
"pp": "y : ℝ\nz : ℂ\nhz : 0 ≤ z.im\nh1 : z.im ≤ y\nh2 : |z.re| ≤ 1 / 2\nh3 : 0 = z.im\n⊢ ‖z‖ < 1",
"usedConstants": [
"sq_lt_one_iff₀",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Complex.normSq._proof_2",
"MulOne.to... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Modular | {
"line": 995,
"column": 4
} | {
"line": 996,
"column": 56
} | [
{
"pp": "case inl\nτ : ℍ\nh : 1 / 2 ≤ τ.im\n⊢ ∃ γ, 1 / 2 ≤ (γ • τ).im ∧ ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ≤ 1",
"usedConstants": [
"Norm.norm",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"Real.instLE",
"Real",
"instHSMul",
"Matr... | exact ⟨1, (one_smul SL(2, ℤ) τ).symm ▸ h, by
simp only [map_one, denom_one, norm_one, le_refl]⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.Modular | {
"line": 995,
"column": 4
} | {
"line": 996,
"column": 56
} | [
{
"pp": "case inl\nτ : ℍ\nh : 1 / 2 ≤ τ.im\n⊢ ∃ γ, 1 / 2 ≤ (γ • τ).im ∧ ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ≤ 1",
"usedConstants": [
"Norm.norm",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"Real.instLE",
"Real",
"instHSMul",
"Matr... | exact ⟨1, (one_smul SL(2, ℤ) τ).symm ▸ h, by
simp only [map_one, denom_one, norm_one, le_refl]⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Modular | {
"line": 995,
"column": 4
} | {
"line": 996,
"column": 56
} | [
{
"pp": "case inl\nτ : ℍ\nh : 1 / 2 ≤ τ.im\n⊢ ∃ γ, 1 / 2 ≤ (γ • τ).im ∧ ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ≤ 1",
"usedConstants": [
"Norm.norm",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"Real.instLE",
"Real",
"instHSMul",
"Matr... | exact ⟨1, (one_smul SL(2, ℤ) τ).symm ▸ h, by
simp only [map_one, denom_one, norm_one, le_refl]⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Modular | {
"line": 1001,
"column": 4
} | {
"line": 1001,
"column": 57
} | [
{
"pp": "case inr\nτ : ℍ\nh : τ.im ≤ 1 / 2\nγ : SL(2, ℤ)\nhγ : 1 / 2 ≤ (γ • τ).im\nh1 : τ.im * ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ^ 2 ≤ τ.im\n⊢ ‖denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) γ)) ↑τ‖ ≤ 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 20
} | [
{
"pp": "k l : ℕ\np : ℝ\nf : ℕ → ℂ\nhf : f =O[atTop] fun n ↦ ↑n ^ l\nh1 : (fun n ↦ (2 * ↑π * I * ↑n / ↑p) ^ k) = fun n ↦ (2 * ↑π * I / ↑p) ^ k * ↑n ^ k\n⊢ (fun n ↦ (2 * ↑π * I * ↑n / ↑p) ^ k) =O[atTop] fun n ↦ ↑n ^ k",
"usedConstants": [
"Eq.mpr",
"Real",
"instHDiv",
"Real.pi",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 15
} | [
{
"pp": "k l : ℕ\nf : ℕ → ℂ\np : ℝ\nhp : 0 < p\nhf : f =O[atTop] fun n ↦ ↑n ^ l\nK : Set ℂ\nhK : K ⊆ ℍₒ\nhKc : IsCompact K\nthis : CompactSpace ↑K\nc : C(↑K, ℂ) := { toFun := fun r ↦ cexp (2 * ↑π * I * ↑r / ↑p), continuous_toFun := ⋯ }\nr : ℝ := ‖mkOfCompact c‖\nx : ↑K\nh1 : cexp (2 * ↑π * I * (↑x / ↑p)) = cexp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 96,
"column": 16
} | {
"line": 96,
"column": 27
} | [
{
"pp": "k l : ℕ\nf : ℕ → ℂ\np : ℝ\nhp : 0 < p\nhf : f =O[atTop] fun n ↦ ↑n ^ l\nK : Set ℂ\nhK : K ⊆ ℍₒ\nhKc : IsCompact K\nthis : CompactSpace ↑K\nc : C(↑K, ℂ) := { toFun := fun r ↦ cexp (2 * ↑π * I * ↑r / ↑p), continuous_toFun := ⋯ }\nr : ℝ := ‖mkOfCompact c‖\nhr : ‖r‖ < 1\n⊢ Summable ?m.229",
"usedConsta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 13
} | [
{
"pp": "k : ℕ\nh0 : (fun n ↦ 1) =O[atTop] fun n ↦ ↑n ^ 1\n⊢ SummableLocallyUniformlyOn (fun n ↦ iteratedDerivWithin k (fun z ↦ cexp (2 * ↑π * I * z) ^ n) ℍₒ) ℍₒ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 131,
"column": 62
} | {
"line": 131,
"column": 73
} | [
{
"pp": "k : ℕ\nz : ℍ\n⊢ ↑z ∈ ℍₒ",
"usedConstants": [
"UpperHalfPlane.coe",
"Membership.mem",
"id",
"UpperHalfPlane.upperHalfPlaneSet",
"Complex",
"Set.instMembership",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 154,
"column": 40
} | {
"line": 154,
"column": 51
} | [
{
"pp": "k : ℕ\nhk : 1 ≤ k\nz : ℍ\n⊢ ↑z ∈ ℍₒ",
"usedConstants": [
"UpperHalfPlane.coe",
"Membership.mem",
"id",
"UpperHalfPlane.upperHalfPlaneSet",
"Complex",
"Set.instMembership",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 156,
"column": 58
} | {
"line": 156,
"column": 69
} | [
{
"pp": "k : ℕ\nhk : 1 ≤ k\nz : ℍ\n⊢ ↑z ∈ ℍₒ",
"usedConstants": [
"UpperHalfPlane.coe",
"Membership.mem",
"id",
"UpperHalfPlane.upperHalfPlaneSet",
"Complex",
"Set.instMembership",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable | {
"line": 101,
"column": 4
} | {
"line": 101,
"column": 49
} | [
{
"pp": "τ : ℂ\nhτ : 0 < τ.im\nn : ℕ\n⊢ ‖cexp (↑π * I * (↑n + 1) ^ 2 * τ)‖ ≤ rexp (-π * τ.im) ^ (n + 1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 124,
"column": 2
} | {
"line": 124,
"column": 28
} | [
{
"pp": "z : ℍ\n⊢ Δ z ≠ 0",
"usedConstants": [
"Eq.mpr",
"False",
"UpperHalfPlane.coe",
"congrArg",
"NormedDivisionRing.toNormMulClass",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instNormedField",
"Complex.instZero",
"CStarAlgebra.toNormedRing",
"Nat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 169,
"column": 2
} | {
"line": 169,
"column": 40
} | [
{
"pp": "case e_f.h\nk : ℕ\nhk : 1 ≤ k\nz : ℍ\nthis✝ :\n iteratedDerivWithin k (fun z ↦ ↑π * I - 2 * ↑π * I * ∑' (n : ℕ), cexp (2 * ↑π * I * z) ^ n) ℍₒ ↑z =\n -(2 * ↑π * I) * ∑' (n : ℕ), iteratedDerivWithin k (fun s ↦ cexp (2 * ↑π * I * s) ^ n) ℍₒ ↑z\nh :\n -(2 * ↑π * I * (2 * ↑π * I) ^ k) * ∑' (n : ℕ), ↑n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 181,
"column": 66
} | {
"line": 181,
"column": 77
} | [
{
"pp": "k : ℕ\nhk : 1 ≤ k\nz : ℍ\n⊢ ↑z ∈ ℍₒ",
"usedConstants": [
"UpperHalfPlane.coe",
"Membership.mem",
"id",
"UpperHalfPlane.upperHalfPlaneSet",
"Complex",
"Set.instMembership",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 182,
"column": 52
} | {
"line": 182,
"column": 63
} | [
{
"pp": "k : ℕ\nhk : 1 ≤ k\nz : ℍ\nx : ℂ\nhx : x ∈ ℍₒ\n⊢ ↑π * (↑π * x).cot = ↑π * I - 2 * ↑π * I * ∑' (n : ℕ), cexp (2 * ↑π * I * x) ^ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 183,
"column": 10
} | {
"line": 183,
"column": 21
} | [
{
"pp": "k : ℕ\nhk : 1 ≤ k\nz : ℍ\n⊢ ↑z ∈ ℍₒ",
"usedConstants": [
"UpperHalfPlane.coe",
"Membership.mem",
"id",
"UpperHalfPlane.upperHalfPlaneSet",
"Complex",
"Set.instMembership",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 177,
"column": 50
} | {
"line": 190,
"column": 20
} | [
{
"pp": "k : ℕ\nhk : 1 ≤ k\nz : ℍ\n⊢ ∑' (n : ℤ), 1 / (↑z + ↑n) ^ (k + 1) = (-2 * ↑π * I) ^ (k + 1) / ↑k ! * ∑' (n : ℕ), ↑n ^ k * cexp (2 * ↑π * I * ↑z) ^ n",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"one_pow",
"Mathlib.Tactic.FieldSimp.zpow'_one",
... | by
have : (-1) ^ k * k ! * ∑' n : ℤ, 1 / ((z : ℂ) + n) ^ (k + 1) =
-(2 * π * I) ^ (k + 1) * ∑' n : ℕ, n ^ k * cexp (2 * π * I * z) ^ n := by
rw [← iteratedDerivWithin_tsum_exp_aux_eq hk z,
← iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow hk (by simpa using z.2)]
exact iteratedDerivWithin_congr (... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 195,
"column": 4
} | {
"line": 195,
"column": 15
} | [
{
"pp": "k : ℕ\ne : ℕ+\nz : ℍ\n⊢ 0 < (↑↑e * ↑z).im",
"usedConstants": [
"PNat.val",
"Complex.mul_im",
"Real.instIsOrderedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"HMul.hMul",
"UpperHa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 138,
"column": 41
} | {
"line": 138,
"column": 66
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\nh : Set.EqOn (η ∘ fun z ↦ -1 / z) (z • (sqrt * η)) upperHalfPlaneSet\n⊢ η I = z * I.sqrt * η I",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 136,
"column": 48
} | {
"line": 139,
"column": 51
} | [
{
"pp": "⊢ Set.EqOn (η ∘ fun x ↦ -1 / x) (I.sqrt⁻¹ • (sqrt * η)) upperHalfPlaneSet",
"usedConstants": [
"Real.partialOrder",
"Semigroup.toMul",
"Real",
"instHSMul",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
... | by
obtain ⟨z, hz, h⟩ := eta_comp_eqOn_const_mul_csqrt_eta
have h3 : η I = z * sqrt I * η I := by simpa [← mul_assoc] using h (show I ∈ _ by simp)
grind [sqrt, eta_ne_zero (show 0 < I.im by simp)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 227,
"column": 10
} | {
"line": 227,
"column": 21
} | [
{
"pp": "k : ℕ\nhk : 3 ≤ k\nhk2 : Even k\nz : ℍ\n⊢ Summable fun b ↦ ∑' (c : ℤ), eisSummand ↑k ![(b, c).1, (b, c).2] z",
"usedConstants": [
"NormedCommRing.toSeminormedCommRing",
"AddCommGroup.toAddCommMonoid",
"PseudoMetricSpace.toUniformSpace",
"CommCStarAlgebra.toNormedCommRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 25
} | [
{
"pp": "z : ℍ\n⊢ η (-(↑z)⁻¹) = I.sqrt⁻¹ * ((↑z).sqrt * η ↑z)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 231,
"column": 81
} | {
"line": 231,
"column": 92
} | [
{
"pp": "k : ℕ\nhk : 3 ≤ k\nhk2 : Even k\nz : ℍ\nb : ℕ+\n⊢ 0 < (↑↑b * ↑z).im",
"usedConstants": [
"PNat.val",
"Complex.mul_im",
"Real.instIsOrderedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 161,
"column": 10
} | {
"line": 161,
"column": 38
} | [
{
"pp": "this :\n (Summable fun n ↦ (1 / 2) ^ (n + 1)) →\n (∀ (k : ℕ), Tendsto (fun x ↦ -x ^ (k + 1)) (𝓝 0) (𝓝 0)) →\n (∀ᶠ (n : ℂ) in 𝓝 0, ∀ (k : ℕ), ‖n‖ ^ (k + 1) ≤ (1 / 2) ^ (k + 1)) →\n Tendsto (fun n ↦ ∏' (k : ℕ), (1 + -n ^ (k + 1))) (𝓝 0) (𝓝 1)\n⊢ Summable fun n ↦ (1 / 2) ^ (n + 1)",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 162,
"column": 18
} | {
"line": 162,
"column": 29
} | [
{
"pp": "this :\n (Summable fun n ↦ (1 / 2) ^ (n + 1)) →\n (∀ (k : ℕ), Tendsto (fun x ↦ -x ^ (k + 1)) (𝓝 0) (𝓝 0)) →\n (∀ᶠ (n : ℂ) in 𝓝 0, ∀ (k : ℕ), ‖n‖ ^ (k + 1) ≤ (1 / 2) ^ (k + 1)) →\n Tendsto (fun n ↦ ∏' (k : ℕ), (1 + -n ^ (k + 1))) (𝓝 0) (𝓝 1)\nk : ℕ\n⊢ Tendsto (fun x ↦ -x ^ (k + 1)) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 21
} | [
{
"pp": "case pos\nq : ℂ\nhq : q ∈ Metric.ball 0 1\nhq0 : q = 0\n⊢ cuspFunction 1 Δ q = (fun q ↦ q * ∏' (i : ℕ), (1 - q ^ (i + 1)) ^ 24) q",
"usedConstants": [
"one_pow",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 204,
"column": 10
} | {
"line": 204,
"column": 39
} | [
{
"pp": "q : ℂ\nhq : q ∈ Metric.ball 0 1\nhq0 : ¬q = 0\n⊢ ‖q‖ < 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 267,
"column": 4
} | {
"line": 267,
"column": 15
} | [
{
"pp": "k : ℕ\nhk : 3 ≤ k\nz : ℍ\nhk1 : 1 < k\nhk2 : 3 ≤ ↑k\nb : ℕ\n⊢ Summable fun c ↦ (↑(b, c).1 ^ k)⁻¹ * eisSummand (↑k) (↑(b, c).2) z",
"usedConstants": [
"DivInvMonoid.toInv",
"NormedRing.toRing",
"HMul.hMul",
"ZMod.commRing",
"Ring.toNonAssocRing",
"CommSemiring.toS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 272,
"column": 4
} | {
"line": 273,
"column": 11
} | [
{
"pp": "case inr\nk : ℕ\nhk : 3 ≤ k\nz : ℍ\nhk1 : 1 < k\nhk2 : 3 ≤ ↑k\nb : ℕ\nhb : b ≠ 0\nthis : NeZero b\n⊢ ∑' (c : ↑(gammaSet 1 b 0)), eisSummand (↑k) (↑c) z =\n ∑' (c : { x // x ∈ gammaSet 1 1 0 }), (↑(b, c).1 ^ k)⁻¹ * eisSummand (↑k) (↑(b, c).2) z",
"usedConstants": [
"zpow_natCast",
"on... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Discriminant | {
"line": 261,
"column": 8
} | {
"line": 261,
"column": 19
} | [
{
"pp": "k : ℤ\nf : CuspForm (Matrix.SpecialLinearGroup.mapGL ℝ).range k\n⊢ (fun τ ↦ rexp (-2 * π * τ.im / 1)) =O[atImInfty] Δ",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.GradedRing | {
"line": 69,
"column": 4
} | {
"line": 70,
"column": 51
} | [
{
"pp": "z : ℍ\ng : CuspForm (Matrix.SpecialLinearGroup.mapGL ℝ).range 12\nhg : CuspForm.toModularFormₗ g = E₄CubeSubE₆SqForm\nc : ℂ\nhc : c • CuspForm.discriminant = g\nhgE : ⇑g = ⇑E₄CubeSubE₆SqForm\nhcΔ : c • ⇑CuspForm.discriminant = ⇑g\nhgΔ : qExpansion 1 ⇑E₄CubeSubE₆SqForm = c • qExpansion 1 ⇑CuspForm.discr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.LevelOne.GradedRing | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 72
} | [
{
"pp": "⊢ (DirectSum.of (ModularForm (Matrix.SpecialLinearGroup.mapGL ℝ).range) 12) (modularForm CuspForm.discriminant) =\n (1 / 1728) •\n ((DirectSum.of (ModularForm (Matrix.SpecialLinearGroup.mapGL ℝ).range) 12) (E₄.pow 3) -\n (DirectSum.of (ModularForm (Matrix.SpecialLinearGroup.mapGL ℝ).rang... | rw [← map_sub (DirectSum.of (ModularForm 𝒮ℒ) 12), ← DirectSum.of_smul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | {
"line": 350,
"column": 2
} | {
"line": 350,
"column": 13
} | [
{
"pp": "k : ℕ\nhk : 3 ≤ k\nhk2 : Even k\n⊢ (PowerSeries.coeff 0) (qExpansion 1 ⇑(E hk)) = 1",
"usedConstants": [
"ModularForm",
"Eq.mpr",
"MonoidHom.range",
"Real",
"Matrix.SpecialLinearGroup",
"Semiring.toModule",
"UpperHalfPlane.qExpansion",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Multiplicity | {
"line": 47,
"column": 53
} | {
"line": 47,
"column": 64
} | [
{
"pp": "R : Type u_1\nn : ℕ\ninst✝ : CommRing R\nx y p : R\nh : p ∣ x - y\n⊢ p ∣ y - x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 58,
"column": 4
} | {
"line": 59,
"column": 11
} | [
{
"pp": "𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝² : FunLike F ℍ ℂ\nk : ℤ\ninst✝¹ : SlashInvariantFormClass F 𝒢 k\ninst✝ : 𝒢.IsFiniteRelIndex ℋ\nh : GL (Fin 2) ℝ\nhh : h ∈ ℋ\nthis : Fintype (↥ℋ ⧸ 𝒢.subgroupOf ℋ) := Fintype.ofFinite (↥ℋ ⧸ 𝒢.subgroupOf ℋ)\n⊢ (let this := Fintype.ofFinite (↥ℋ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 67,
"column": 4
} | {
"line": 69,
"column": 53
} | [
{
"pp": "𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝³ : FunLike F ℍ ℂ\nk : ℤ\ninst✝² : SlashInvariantFormClass F 𝒢 k\ninst✝¹ : 𝒢.IsFiniteRelIndex ℋ\ninst✝ : ℋ.HasDetPlusMinusOne\nh : GL (Fin 2) ℝ\nhh : h ∈ ℋ\nthis : Fintype (↥ℋ ⧸ 𝒢.subgroupOf ℋ) := Fintype.ofFinite (↥ℋ ⧸ 𝒢.subgroupOf ℋ)\n⊢ (l... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 15
} | [
{
"pp": "𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝² : FunLike F ℍ ℂ\nk : ℤ\ninst✝¹ : 𝒢.IsFiniteRelIndex ℋ\ninst✝ : ModularFormClass F 𝒢 k\nγ : GL (Fin 2) ℝ\nh : IsCusp (γ • OnePoint.infty) ℋ\nx✝¹ : ↥ℋ\nr : GL (Fin 2) ℝ\nhr : r ∈ ℋ\nx✝ : ⟦⟨r, hr⟩⟧ ∈ Finset.univ\n⊢ IsCusp (γ • OnePoint.infty) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 15
} | [
{
"pp": "𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝² : FunLike F ℍ ℂ\nk : ℤ\ninst✝¹ : 𝒢.IsFiniteRelIndex ℋ\ninst✝ : CuspFormClass F 𝒢 k\nγ : GL (Fin 2) ℝ\nh : IsCusp (γ • OnePoint.infty) ℋ\nthis : Fintype (↥ℋ ⧸ 𝒢.subgroupOf ℋ) := Fintype.ofFinite (↥ℋ ⧸ 𝒢.subgroupOf ℋ)\nx✝¹ : ↥ℋ\nr : GL (Fin ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 15
} | [
{
"pp": "case h\n𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝³ : FunLike F ℍ ℂ\nk : ℤ\ninst✝² : 𝒢.IsFiniteRelIndex ℋ\ninst✝¹ : ℋ.HasDetPlusMinusOne\ninst✝ : ModularFormClass F 𝒢 k\nγ : GL (Fin 2) ℝ\nh : IsCusp (γ • OnePoint.infty) ℋ\nthis : Fintype (↥ℋ ⧸ 𝒢.subgroupOf ℋ) := Fintype.ofFinite (↥ℋ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 126,
"column": 4
} | {
"line": 126,
"column": 41
} | [
{
"pp": "𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝³ : FunLike F ℍ ℂ\nk : ℤ\ninst✝² : 𝒢.IsFiniteRelIndex ℋ\ninst✝¹ : ℋ.HasDetPlusMinusOne\ninst✝ : ModularFormClass F 𝒢 k\nhf : ∃ i ∈ Finset.univ, quotientFunc f i = 0\n⊢ ⇑f = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.NormTrace | {
"line": 135,
"column": 4
} | {
"line": 136,
"column": 11
} | [
{
"pp": "case refine_2.h\n𝒢 ℋ : Subgroup (GL (Fin 2) ℝ)\nF : Type u_1\nf : F\ninst✝³ : FunLike F ℍ ℂ\nk : ℤ\ninst✝² : 𝒢.IsFiniteRelIndex ℋ\ninst✝¹ : ℋ.HasDetPlusMinusOne\ninst✝ : ModularFormClass F 𝒢 k\nhf : ⇑f = 0\nτ : ℍ\n⊢ (ModularForm.norm ℋ f) τ = 0 τ",
"usedConstants": [
"NormedCommRing.toNorm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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