module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.SimpleRing.Field | {
"line": 39,
"column": 57
} | {
"line": 39,
"column": 81
} | {
"line": 39,
"column": 82
} | [
{
"pp": "A : Type u_1\ninst✝¹ : Ring A\ninst✝ : IsSimpleRing A\nx : A\nhx1✝ : x ∈ Subring.center A\nhx1 : ∀ (g : A), g * x = x * g\nhx2 : x ≠ 0\nI : TwoSidedIdeal A := mk' (Set.range fun x_1 ↦ x * x_1) ⋯ ⋯ ⋯ ⋯ ⋯\n⊢ x ∈ I",
"ppTerm": "?m.239",
"assigned": true,
"usedConstants": [
"Distrib.leftD... | [
"A : Type u_1\ninst✝¹ : Ring A\ninst✝ : IsSimpleRing A\nx : A\nhx1✝ : x ∈ Subring.center A\nhx1 : ∀ (g : A), g * x = x * g\nhx2 : x ≠ 0\nI : TwoSidedIdeal A := mk' (Set.range fun x_1 ↦ x * x_1) ⋯ ⋯ ⋯ ⋯ ⋯\n⊢ ∃ y, x * y = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 208,
"column": 10
} | {
"line": 208,
"column": 57
} | {
"line": 208,
"column": 58
} | [
{
"pp": "p : ℕ\nw : 1 < p\nh : ↑(sMod p (p - 2)) = 0\n⊢ ?m.28 ∣ sMod p (p - 2)",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : ℕ\nw : 1 < p\nh : ↑(sMod p (p - 2)) = 0\n⊢ ?m.28 ∣ sMod p (p - 2)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 407,
"column": 4
} | {
"line": 407,
"column": 44
} | {
"line": 407,
"column": 45
} | [
{
"pp": "k : ℕ\ninst✝ : Fact (Nat.Prime (2 * k + 1))\nleg3 : legendreSym (2 * k + 1) 3 = -1\nq : ℕ := 2 * k + 1\n⊢ 3 ^ k = -1",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidW... | [
"k : ℕ\ninst✝ : Fact (Nat.Prime (2 * k + 1))\nleg3 : legendreSym (2 * k + 1) 3 = -1\nq : ℕ := 2 * k + 1\n⊢ -1 = 3 ^ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 414,
"column": 36
} | {
"line": 416,
"column": 10
} | {
"line": 418,
"column": 0
} | [
{
"pp": "q : ℕ\ninst✝ : Fact (Nat.Prime q)\nodd : Odd q\nleg3 : legendreSym q 3 = -1\n⊢ (1 + α) ^ (q + 1) = -2",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnitalComm... | [] | by
rw [pow_succ, one_add_α_pow_q odd leg3, mul_comm, ← _root_.sq_sub_sq, α_sq]
norm_num | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Algebra.Valued.LocallyCompact | {
"line": 280,
"column": 6
} | {
"line": 282,
"column": 22
} | {
"line": 284,
"column": 0
} | [
{
"pp": "case neg\nK : Type u_1\nΓ₀ : Type u_2\ninst✝² : Field K\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : Valued K Γ₀\nhc✝ : IsCompact ↑𝒪[K]\nz : (↥(MonoidHom.mrange (MonoidWithZeroHom.ofClass v)))ˣ\na : K\nha : (MonoidWithZeroHom.ofClass v) a = ↑↑z\nhz1 : z ≤ 1\nz0' : 0 < ↑z\nz0 : 0 < ↑↑z\na0 : 0 ... | [] | simp only [Set.mem_setOf_eq] at hj'
rw [dif_neg hcj]
simp [← hj', hc] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.MahlerMeasure | {
"line": 61,
"column": 6
} | {
"line": 61,
"column": 17
} | {
"line": 61,
"column": 18
} | [
{
"pp": "case refine_1\nn : ℕ\nB₁ B₂ : Fin (n + 1) → ℝ\np : ↑(boxPoly n B₁ B₂)\nprop : ∀ (i : Fin (n + 1)), B₁ i ≤ ↑((↑p).coeff ↑i) ∧ ↑((↑p).coeff ↑i) ≤ B₂ i\n⊢ (toFn (n + 1)) ↑p ∈ ↑(Finset.Icc (fun x ↦ ⌈B₁ x⌉) fun x ↦ ⌊B₂ x⌋)",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"case refine_1\nn : ℕ\nB₁ B₂ : Fin (n + 1) → ℝ\np : ↑(boxPoly n B₁ B₂)\nprop : ∀ (i : Fin (n + 1)), B₁ i ≤ ↑((↑p).coeff ↑i) ∧ ↑((↑p).coeff ↑i) ≤ B₂ i\n⊢ (fun x ↦ ⌈B₁ x⌉) ≤ (toFn (n + 1)) ↑p ∧ (toFn (n + 1)) ↑p ≤ fun x ↦ ⌊B₂ x⌋"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.LocallyCompact | {
"line": 280,
"column": 6
} | {
"line": 282,
"column": 22
} | {
"line": 284,
"column": 0
} | [
{
"pp": "case neg\nK : Type u_1\nΓ₀ : Type u_2\ninst✝² : Field K\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : Valued K Γ₀\nhc✝ : IsCompact ↑𝒪[K]\nz : (↥(MonoidHom.mrange (MonoidWithZeroHom.ofClass v)))ˣ\na : K\nha : (MonoidWithZeroHom.ofClass v) a = ↑↑z\nhz1 : z ≤ 1\nz0' : 0 < ↑z\nz0 : 0 < ↑↑z\na0 : 0 ... | [] | simp only [Set.mem_setOf_eq] at hj'
rw [dif_neg hcj]
simp [← hj', hc] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LucasLehmer | {
"line": 498,
"column": 6
} | {
"line": 498,
"column": 19
} | {
"line": 498,
"column": 19
} | [
{
"pp": "p' : ℕ\nh : sZMod (p' + 2) (p' + 2 - 2) = 0\n⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1",
"ppTerm": "?m.120",
"assigned": true,
"usedConstants": [
"Int.cast",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
... | [
"p' : ℕ\nh : ↑(s (p' + 2 - 2)) = 0\n⊢ ∃ k, ω ^ 2 ^ (p' + 1) = ↑k * ↑(mersenne (p' + 2)) * ω ^ 2 ^ p' - 1"
] | sZMod_eq_s p' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 499,
"column": 44
} | {
"line": 499,
"column": 91
} | {
"line": 499,
"column": 92
} | [
{
"pp": "p' : ℕ\nh : ↑(s (p' + 2 - 2)) = 0\n⊢ 2 ^ (p' + 2) - 1 ∣ s p'",
"ppTerm": "?m.151",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p' : ℕ\nh : ↑(s (p' + 2 - 2)) = 0\n⊢ 2 ^ (p' + 2) - 1 ∣ s p'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 525,
"column": 2
} | {
"line": 525,
"column": 13
} | {
"line": 525,
"column": 14
} | [
{
"pp": "p' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\nk : ℤ\nw : ω ^ 2 ^ (p' + 1) = ↑k * 0 * ω ^ 2 ^ p' - 1\n⊢ ω ^ 2 ^ (p' + 1) = -1",
"ppTerm": "?m.61",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p' : ℕ\nh : lucasLehmerResidue (p' + 2) = 0\nk : ℤ\nw : ω ^ 2 ^ (p' + 1) = ↑k * 0 * ω ^ 2 ^ p' - 1\n⊢ ω ^ 2 ^ (p' + 1) = -1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.LucasLehmer | {
"line": 667,
"column": 2
} | {
"line": 667,
"column": 39
} | {
"line": 668,
"column": 0
} | [
{
"pp": "q i : ℕ\n⊢ sModNatTR q i = sModNat q i",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"LucasLehmer.norm_num_ext.sModNatAux",
"_private.Mathlib.NumberTheory.LucasL... | [] | rw [sModNatTR, helper, sModNatAux_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.LucasLehmer | {
"line": 667,
"column": 2
} | {
"line": 667,
"column": 39
} | {
"line": 668,
"column": 0
} | [
{
"pp": "q i : ℕ\n⊢ sModNatTR q i = sModNat q i",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"LucasLehmer.norm_num_ext.sModNatAux",
"_private.Mathlib.NumberTheory.LucasL... | [] | rw [sModNatTR, helper, sModNatAux_eq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.LucasLehmer | {
"line": 667,
"column": 2
} | {
"line": 667,
"column": 39
} | {
"line": 668,
"column": 0
} | [
{
"pp": "q i : ℕ\n⊢ sModNatTR q i = sModNat q i",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"LucasLehmer.norm_num_ext.sModNatAux",
"_private.Mathlib.NumberTheory.LucasL... | [] | rw [sModNatTR, helper, sModNatAux_eq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.LucasLehmer | {
"line": 693,
"column": 2
} | {
"line": 693,
"column": 13
} | {
"line": 693,
"column": 14
} | [
{
"pp": "p : ℕ\nhp : 1 < p\nh : sModNatTR (2 ^ p - 1) (p - 2) ≠ 0\n⊢ ¬↑(sModNatTR (2 ^ p - 1) (p - 2)) = 0",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
... | [
"p : ℕ\nhp : 1 < p\nh : sModNatTR (2 ^ p - 1) (p - 2) ≠ 0\n⊢ ¬sModNatTR (2 ^ p - 1) (p - 2) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 29
} | {
"line": 37,
"column": 30
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nH K : Subgroup G\nhHK : H ≤ K\n⊢ ∀ (s : Set ↥H),\n (∃ a,\n IsOpen[inst✝] a ∧\n Subtype.val ⁻¹' Subtype.val ⁻¹' a =\n ⇑{ toFun := fun g ↦ ⟨↑↑g, ⋯⟩, invFun := fun g ↦ ⟨⟨↑g, ⋯⟩, ⋯⟩, left_inv := ⋯, right_inv := ⋯,\n ... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nH K : Subgroup G\nhHK : H ≤ K\n⊢ ∀ (s : Set ↥H),\n (∃ a, IsOpen[inst✝] a ∧ ∀ (a_1 : G) (b : a_1 ∈ K) (b_1 : ⟨a_1, b⟩ ∈ H.subgroupOf K), a_1 ∈ a ↔ ⟨a_1, ⋯⟩ ∈ s) ↔\n ∃ t, IsOpen[inst✝] t ∧ ∀ (a : G) (b : a ∈ H), a ∈ t ↔ ⟨a, b⟩ ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.MahlerMeasure | {
"line": 214,
"column": 2
} | {
"line": 214,
"column": 70
} | {
"line": 215,
"column": 2
} | [
{
"pp": "p : ℤ[X]\nh : (map (castRingHom ℂ) p).mahlerMeasure = 1\nz : ℂ\nhz₀ : z ≠ 0\nhz : z ∈ p.aroots ℂ\n⊢ ∃ n, 0 < n ∧ IsPrimitiveRoot z n",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Complex.commRing",
"Exists",
"instOfNatNat",
"Polynomial.pow_eq_one_of_mahl... | [
"p : ℤ[X]\nh : (map (castRingHom ℂ) p).mahlerMeasure = 1\nz : ℂ\nhz₀ : z ≠ 0\nhz : z ∈ p.aroots ℂ\nw✝ : ℕ\nleft✝ : 0 < w✝\nhz_pow : z ^ w✝ = 1\n⊢ ∃ n, 0 < n ∧ IsPrimitiveRoot z n"
] | obtain ⟨_, _, hz_pow⟩ := pow_eq_one_of_mahlerMeasure_eq_one h hz₀ hz | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 48,
"column": 2
} | {
"line": 48,
"column": 69
} | {
"line": 48,
"column": 70
} | [
{
"pp": "n : Type u_1\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq n\nR : Type u_2\ninst✝² : CommRing R\nΓ : Subgroup (GL n R)\ninst✝¹ : LinearOrder R\ninst✝ : IsOrderedRing R\nh : ∀ {g : GL n R}, g ∈ Γ → |↑(GeneralLinearGroup.det g)| = 1\n⊢ ∀ {g : GL n R}, g ∈ Γ → GeneralLinearGroup.det g = 1 ∨ GeneralLinearGroup... | [
"n : Type u_1\ninst✝⁴ : Fintype n\ninst✝³ : DecidableEq n\nR : Type u_2\ninst✝² : CommRing R\nΓ : Subgroup (GL n R)\ninst✝¹ : LinearOrder R\ninst✝ : IsOrderedRing R\nh : ∀ {g : GL n R}, g ∈ Γ → |↑(GeneralLinearGroup.det g)| = 1\n⊢ ∀ {g : GL n R}, g ∈ Γ → GeneralLinearGroup.det g = 1 ∨ GeneralLinearGroup.det g = -1"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 96,
"column": 4
} | {
"line": 97,
"column": 59
} | {
"line": 97,
"column": 60
} | [
{
"pp": "case mp\nΓ : Subgroup SL(2, ℤ)\nx✝ : (map (mapGL ℝ) Γ).IsArithmetic\nh : (map (mapGL ℝ) Γ).Commensurable (mapGL ℝ).range\n⊢ Γ.index ≠ 0",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Matrix.SpecialLinearGroup",
"instDecidableEqFin",
"Matrix.SpecialLinearGroup.ins... | [
"case mp\nΓ : Subgroup SL(2, ℤ)\nx✝ : (map (mapGL ℝ) Γ).IsArithmetic\nh : (map (mapGL ℝ) Γ).Commensurable (mapGL ℝ).range\n⊢ ¬Γ.index = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 96,
"column": 4
} | {
"line": 97,
"column": 59
} | {
"line": 97,
"column": 60
} | [
{
"pp": "case mpr\nΓ : Subgroup SL(2, ℤ)\nx✝ : Γ.FiniteIndex\nh : Γ.index ≠ 0\n⊢ (map (mapGL ℝ) Γ).Commensurable (mapGL ℝ).range",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"False",
"Nat.instMulZeroClass",
"Real.partialOrder",
... | [
"case mpr\nΓ : Subgroup SL(2, ℤ)\nx✝ : Γ.FiniteIndex\nh : Γ.index ≠ 0\n⊢ ¬Γ.index = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 25
} | {
"line": 115,
"column": 2
} | [
{
"pp": "n✝ : Type u_1\ninst✝¹ : Fintype n✝\ninst✝ : DecidableEq n✝\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : Γ.IsArithmetic\ng : GL (Fin 2) ℝ\nhg : g ∈ Γ\nn : ℕ\nhn : 0 < n\nleft✝ : n ≤ (mapGL ℝ).range.relIndex Γ\nhgn : g ^ n ∈ (mapGL ℝ).range ⊓ Γ\n⊢ |↑(GeneralLinearGroup.det g ^ n)| = 1",
"ppTerm": "?m.77",
"... | [
"n✝ : Type u_1\ninst✝¹ : Fintype n✝\ninst✝ : DecidableEq n✝\nΓ : Subgroup (GL (Fin 2) ℝ)\nh : Γ.IsArithmetic\ng : GL (Fin 2) ℝ\nhg : g ∈ Γ\nn : ℕ\nhn : 0 < n\nleft✝ : n ≤ (mapGL ℝ).range.relIndex Γ\nhgn : g ^ n ∈ (mapGL ℝ).range ⊓ Γ\nt : SL(2, ℤ)\nht : (mapGL ℝ) t = g ^ n\n⊢ |↑(GeneralLinearGroup.det g ^ n)| = 1"
] | obtain ⟨t, ht⟩ := hgn.1 | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 188,
"column": 38
} | {
"line": 188,
"column": 49
} | {
"line": 188,
"column": 50
} | [
{
"pp": "n : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_2\ninst✝ : Ring R\n𝒢 : Subgroup (GL n R)\nhG : -1 ∈ 𝒢\ng : GL n R\nhg : g ∈ 𝒢.adjoinNegOne\nh : -g ∈ 𝒢\n⊢ g ∈ 𝒢",
"ppTerm": "?m.43",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"n : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_2\ninst✝ : Ring R\n𝒢 : Subgroup (GL n R)\nhG : -1 ∈ 𝒢\ng : GL n R\nhg : g ∈ 𝒢.adjoinNegOne\nh : -g ∈ 𝒢\n⊢ g ∈ 𝒢"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | {
"line": 233,
"column": 4
} | {
"line": 233,
"column": 44
} | {
"line": 233,
"column": 45
} | [
{
"pp": "case inr\nn : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_3\ninst✝ : CommRing R\n𝒢 : Subgroup (GL n R)\nhn : Even (Fintype.card n)\nx✝ : 𝒢.HasDetOne\ng : GL n R\nhg : -g ∈ 𝒢\n⊢ GeneralLinearGroup.det g = 1",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
... | [
"case inr\nn : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nR : Type u_3\ninst✝ : CommRing R\n𝒢 : Subgroup (GL n R)\nhn : Even (Fintype.card n)\nx✝ : 𝒢.HasDetOne\ng : GL n R\nhg : -g ∈ 𝒢\n⊢ (↑g).det = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.ArchimedeanDiscrete | {
"line": 72,
"column": 26
} | {
"line": 73,
"column": 90
} | {
"line": 74,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝⁵ : CommGroup G\ninst✝⁴ : LinearOrder G\ninst✝³ : IsOrderedMonoid G\ninst✝² : TopologicalSpace G\ninst✝¹ : OrderTopology G\ninst✝ : MulArchimedean G\nH : Subgroup G\na✝ : Nontrivial G\nthis : Dense ↑H ∨ ∃ a, zpowers a = H\nhA : DiscreteTopology ↥H\nh : Dense ↑H\n⊢ H = ⊤",
"ppTerm... | [] | by
rw [← coe_eq_univ, ← (dense_iff_closure_eq.mp h), H.isClosed_of_discrete.closure_eq] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 86,
"column": 4
} | {
"line": 86,
"column": 32
} | {
"line": 86,
"column": 33
} | [
{
"pp": "N : ℕ\na : SL(2, ℤ)\nha : a ∈ {g | ↑(↑g 1 0) = 0}\n⊢ a⁻¹ ∈ {g | ↑(↑g 1 0) = 0}",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"Matrix.SpecialLinearGroup... | [
"N : ℕ\na : SL(2, ℤ)\nha : a ∈ {g | ↑(↑g 1 0) = 0}\n⊢ ↑(↑a 1 0) = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 121,
"column": 4
} | {
"line": 123,
"column": 21
} | {
"line": 123,
"column": 22
} | [
{
"pp": "case mp\nN : ℕ\nA : ↥(Gamma0 N)\nha : ↑(↑↑A 1 1) = 1\nadet : ↑(↑↑A 0 0) * ↑(↑↑A 1 1) - ↑(↑↑A 0 1) * ↑(↑↑A 1 0) = 1\n⊢ ↑(↑↑A 0 0) = 1 ∧ ↑(↑↑A 1 1) = 1 ∧ ↑(↑↑A 1 0) = 0",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Matrix.SpecialLinearGroup",... | [
"case mp\nN : ℕ\nA : ↥(Gamma0 N)\nha : ↑(↑↑A 1 1) = 1\nadet : ↑(↑↑A 0 0) * ↑(↑↑A 1 1) - ↑(↑↑A 0 1) * ↑(↑↑A 1 0) = 1\n⊢ ↑(↑↑A 0 0) = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.CongruenceSubgroups | {
"line": 244,
"column": 4
} | {
"line": 244,
"column": 55
} | {
"line": 245,
"column": 4
} | [
{
"pp": "g : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nA₁ : Matrix (Fin 2) (Fin 2) ℚ := ↑g\nA₂ : Matrix (Fin 2) (Fin 2) ℚ := ↑g⁻¹\nhA₁₂ : A₁ * A₂ = 1\na₁ : ℕ := A₁.den\na₂ : ℕ := A₂.den\nx✝ : SL(2, ℤ)\ny : Matrix (Fin 2) (Fin 2) ℤ\nhy : y.det = 1\nhy' : y.map Int.cast = 1\n⊢ ∃ k, y = 1 + (a₁ * a₂ * M) • k",
"p... | [
"case h\ng : GL (Fin 2) ℚ\nM : ℕ\ninst✝ : NeZero M\nA₁ : Matrix (Fin 2) (Fin 2) ℚ := ⋯\nA₂ : Matrix (Fin 2) (Fin 2) ℚ := ⋯\nhA₁₂ : A₁ * A₂ = 1\na₁ : ℕ := ⋯\na₂ : ℕ := ⋯\nx✝ : SL(2, ℤ)\ny : Matrix (Fin 2) (Fin 2) ℤ\nhy : y.det = 1\nhy' : y.map Int.cast = 1\n⊢ y = 1 + (a₁ * a₂ * M) • of fun i j ↦ (y - 1) i j / (↑a₁ *... | use Matrix.of fun i j ↦ (y - 1) i j / (a₁ * a₂ * M) | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | {
"line": 135,
"column": 6
} | {
"line": 136,
"column": 13
} | {
"line": 136,
"column": 14
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : DecidableEq K\ng : GL (Fin 2) K\nh : ![↑g 0 0, ↑g 1 0] = 0\n⊢ False",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : DecidableEq K\ng : GL (Fin 2) K\nh : ![↑g 0 0, ↑g 1 0] = 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | {
"line": 204,
"column": 6
} | {
"line": 205,
"column": 13
} | {
"line": 205,
"column": 14
} | [
{
"pp": "case neg\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : DecidableEq K\ng : GL (Fin 2) K\ninst✝ : NeZero 2\nhg : ↑g ∉ Set.range ⇑(Matrix.scalar (Fin 2))\nhdisc : (↑g 0 0 + ↑g 1 1) ^ 2 - 4 * (↑g 0 0 * ↑g 1 1 - ↑g 0 1 * ↑g 1 0) = 0\nc : K\nhc : ¬↑g 1 0 = 0\nthis : discrim (↑g 1 0) (↑g 1 1 - ↑g 0 0) (-↑g 0 1) =... | [
"case neg\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : DecidableEq K\ng : GL (Fin 2) K\ninst✝ : NeZero 2\nhg : ↑g ∉ Set.range ⇑(Matrix.scalar (Fin 2))\nhdisc : (↑g 0 0 + ↑g 1 1) ^ 2 - 4 * (↑g 0 0 * ↑g 1 1 - ↑g 0 1 * ↑g 1 0) = 0\nc : K\nhc : ¬↑g 1 0 = 0\nthis : discrim (↑g 1 0) (↑g 1 1 - ↑g 0 0) (-↑g 0 1) = 0\n⊢ ↑g 1 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 66,
"column": 4
} | {
"line": 66,
"column": 40
} | {
"line": 66,
"column": 41
} | [
{
"pp": "case refine_1\nc : OnePoint ℝ\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ng p : GL (Fin 2) ℝ\nhp𝒢 : p ∈ 𝒢\nhpp : p.IsParabolic\nhpc : p • c = c\n⊢ (ConjAct.toConjAct g • p).IsParabolic",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Matrix.GeneralLinearGroup.isParabolic_conj_iff._... | [
"case refine_1\nc : OnePoint ℝ\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ng p : GL (Fin 2) ℝ\nhp𝒢 : p ∈ 𝒢\nhpp : p.IsParabolic\nhpc : p • c = c\n⊢ p.IsParabolic"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 48
} | {
"line": 69,
"column": 0
} | [
{
"pp": "case refine_2\nc : OnePoint ℝ\n𝒢 : Subgroup (GL (Fin 2) ℝ)\ng p : GL (Fin 2) ℝ\nhp𝒢 : p ∈ 𝒢\nhpp : p.IsParabolic\nhpc : p • c = c\n⊢ (ConjAct.toConjAct g • p) • g • c = g • c",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"OnePoint.instGLAction",
"Semigroup.toM... | [] | · simp [ConjAct.toConjAct_smul, mul_smul, hpc] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Compactification.OnePoint.ProjectiveLine | {
"line": 233,
"column": 8
} | {
"line": 234,
"column": 15
} | {
"line": 234,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : DecidableEq K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\ng : GL (Fin 2) K\nhg : g.IsElliptic\nc : K\nh : g • ↑c = ↑c\n⊢ ↑g 1 0 * (c * c) + (↑g 1 1 + -↑g 0 0) * c + -↑g 0 1 = 0",
"ppTerm": "?m.223",
"assigned": false,
"usedConstants": [],... | [
"K : Type u_1\ninst✝³ : Field K\ninst✝² : DecidableEq K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\ng : GL (Fin 2) K\nhg : g.IsElliptic\nc : K\nh : g • ↑c = ↑c\n⊢ ↑g 1 0 * (c * c) + (↑g 1 1 + -↑g 0 0) * c + -↑g 0 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashActions | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 39
} | {
"line": 78,
"column": 40
} | [
{
"pp": "β : Type u_1\nG : Type u_2\nα : Type u_3\ninst✝² : Group G\ninst✝¹ : AddGroup α\ninst✝ : SlashAction β G α\nk : β\ng : G\na : α\nh : (a ∣[k] g) ∣[k] g⁻¹ = 0 ∣[k] g⁻¹\n⊢ a = 0",
"ppTerm": "?m.96",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"β : Type u_1\nG : Type u_2\nα : Type u_3\ninst✝² : Group G\ninst✝¹ : AddGroup α\ninst✝ : SlashAction β G α\nk : β\ng : G\na : α\nh : (a ∣[k] g) ∣[k] g⁻¹ = 0 ∣[k] g⁻¹\n⊢ a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 90,
"column": 4
} | {
"line": 90,
"column": 45
} | {
"line": 90,
"column": 46
} | [
{
"pp": "case h𝒢'\n𝒢 𝒢' : Subgroup (GL (Fin 2) ℝ)\nh𝒢 : 𝒢.Commensurable 𝒢'\nc : OnePoint ℝ\n⊢ (𝒢 ⊓ 𝒢').relIndex 𝒢' ≠ 0",
"ppTerm": "?h𝒢'",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"Matrix",
"instDecidableEqFin",
"CompleteLattice... | [
"case h𝒢'\n𝒢 𝒢' : Subgroup (GL (Fin 2) ℝ)\nh𝒢 : 𝒢.Commensurable 𝒢'\nc : OnePoint ℝ\n⊢ ¬𝒢.relIndex 𝒢' = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 91,
"column": 4
} | {
"line": 91,
"column": 44
} | {
"line": 91,
"column": 45
} | [
{
"pp": "case h𝒢'\n𝒢 𝒢' : Subgroup (GL (Fin 2) ℝ)\nh𝒢 : 𝒢.Commensurable 𝒢'\nc : OnePoint ℝ\n⊢ (𝒢 ⊓ 𝒢').relIndex 𝒢 ≠ 0",
"ppTerm": "?h𝒢'✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Subgroup.inf_relIndex_left",
"Real",
"congrArg",
"Matrix",
"instDec... | [
"case h𝒢'\n𝒢 𝒢' : Subgroup (GL (Fin 2) ℝ)\nh𝒢 : 𝒢.Commensurable 𝒢'\nc : OnePoint ℝ\n⊢ ¬𝒢'.relIndex 𝒢 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 50
} | {
"line": 119,
"column": 51
} | [
{
"pp": "case mp\nc : OnePoint ℝ\ng : SL(2, ℤ)\nhgp : ((mapGL ℝ) g).IsParabolic\nhgc : (mapGL ℝ) g • c = c\n⊢ c ∈ Set.range (OnePoint.map Rat.cast)",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"OnePoint.instGLAction",
"Eq.mpr",
"Real.partialOrder",
"Real",
"i... | [
"case mp\nc : OnePoint ℝ\ng : SL(2, ℤ)\nhgp : ((mapGL ℝ) g).IsParabolic\nhgc : (mapGL ℝ) g • c = c\n⊢ ((mapGL ℝ) g).parabolicFixedPoint ∈ Set.range (OnePoint.map Rat.cast)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.Cusps | {
"line": 125,
"column": 47
} | {
"line": 125,
"column": 75
} | {
"line": 125,
"column": 76
} | [
{
"pp": "a✝ : SL(2, ℤ)\nx✝ : ↑((mapGL ℝ) ModularGroup.T) ∈ Set.range ⇑(Matrix.scalar (Fin 2))\na : ℝ\nha : (Matrix.scalar (Fin 2)) a = ↑((mapGL ℝ) ModularGroup.T)\n⊢ 0 = 1",
"ppTerm": "?m.184",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Real",
"NeZero.one",
... | [
"a✝ : SL(2, ℤ)\nx✝ : ↑((mapGL ℝ) ModularGroup.T) ∈ Set.range ⇑(Matrix.scalar (Fin 2))\na : ℝ\nha : (Matrix.scalar (Fin 2)) a = ↑((mapGL ℝ) ModularGroup.T)\n⊢ False"
] | 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.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.BoundedAtCusp | {
"line": 32,
"column": 2
} | {
"line": 33,
"column": 9
} | {
"line": 33,
"column": 10
} | [
{
"pp": "g : GL (Fin 2) ℝ\nf : ℍ → ℂ\nk : ℤ\nhg : ↑g 1 0 = 0\nhf : Tendsto (fun x ↦ ‖f x‖) atImInfty (nhds 0)\n⊢ Tendsto (fun x ↦ ‖(f ∣[k] g) x‖) atImInfty (nhds 0)",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"UpperHalfPlane.glAction",
"Norm.norm",
"Units.val",
... | [
"g : GL (Fin 2) ℝ\nf : ℍ → ℂ\nk : ℤ\nhg : ↑g 1 0 = 0\nhf : Tendsto (fun x ↦ ‖f x‖) atImInfty (nhds 0)\n⊢ Tendsto (fun x ↦ ‖f (g • x)‖ * (|(↑g).det| ^ (k - 1) * (|↑g 1 1| ^ k)⁻¹)) atImInfty (nhds 0)"
] | 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.SlashActions | {
"line": 258,
"column": 2
} | {
"line": 258,
"column": 36
} | {
"line": 258,
"column": 37
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : Nonempty ι\nk : ℤ\ng : GL (Fin 2) ℝ\nf : ι → ℍ → ℂ\nthis : 0 < Fintype.card ι\n⊢ (∏ i, f i) ∣[k * ↑(Fintype.card ι)] g = |↑(Matrix.GeneralLinearGroup.det g)| ^ (Fintype.card ι - 1) • ∏ i, f i ∣[k] g",
"ppTerm": "?m.72",
"assigned": true,
"usedConsta... | [
"ι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : Nonempty ι\nk : ℤ\ng : GL (Fin 2) ℝ\nf : ι → ℍ → ℂ\nthis : 0 < Fintype.card ι\n⊢ (∏ i, f i) ∣[k * ↑(Fintype.card ι)] g = |(↑g).det| ^ (↑(Fintype.card ι) - 1) • ∏ i, f i ∣[k] g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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.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.BoundedAtCusp | {
"line": 75,
"column": 14
} | {
"line": 75,
"column": 25
} | {
"line": 75,
"column": 26
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nh : ∞.IsBoundedAt f k\n⊢ IsBoundedAtImInfty f",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℍ → ℂ\nk : ℤ\nh : ∞.IsBoundedAt f k\n⊢ IsBoundedAtImInfty f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.BoundedAtCusp | {
"line": 78,
"column": 14
} | {
"line": 78,
"column": 25
} | {
"line": 78,
"column": 26
} | [
{
"pp": "f : ℍ → ℂ\nk : ℤ\nh : ∞.IsZeroAt f k\n⊢ IsZeroAtImInfty f",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℍ → ℂ\nk : ℤ\nh : ∞.IsZeroAt f k\n⊢ IsZeroAtImInfty f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.ModularForms.SlashInvariantForms | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 41
} | {
"line": 304,
"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.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.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.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.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.Cusps | {
"line": 459,
"column": 26
} | {
"line": 459,
"column": 37
} | {
"line": 459,
"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": 245,
"column": 25
} | {
"line": 245,
"column": 36
} | {
"line": 245,
"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": 250,
"column": 16
} | {
"line": 250,
"column": 27
} | {
"line": 250,
"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",
"InnerProductSpa... | [
"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": 252,
"column": 6
} | {
"line": 254,
"column": 13
} | {
"line": 254,
"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.Basic | {
"line": 273,
"column": 16
} | {
"line": 273,
"column": 27
} | {
"line": 273,
"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",
"InnerProduct... | [
"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.Identities | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 78
} | {
"line": 60,
"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.Basic | {
"line": 410,
"column": 36
} | {
"line": 410,
"column": 47
} | {
"line": 410,
"column": 48
} | [
{
"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": 439,
"column": 25
} | {
"line": 439,
"column": 36
} | {
"line": 439,
"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": 443,
"column": 16
} | {
"line": 443,
"column": 27
} | {
"line": 443,
"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",
"Inne... | [
"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": 466,
"column": 16
} | {
"line": 466,
"column": 27
} | {
"line": 466,
"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",
"I... | [
"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.Basic | {
"line": 641,
"column": 4
} | {
"line": 641,
"column": 63
} | {
"line": 642,
"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": 643,
"column": 4
} | {
"line": 644,
"column": 35
} | {
"line": 646,
"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.Basic | {
"line": 697,
"column": 4
} | {
"line": 697,
"column": 30
} | {
"line": 697,
"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.Basic | {
"line": 715,
"column": 4
} | {
"line": 715,
"column": 30
} | {
"line": 715,
"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": 731,
"column": 6
} | {
"line": 732,
"column": 9
} | {
"line": 732,
"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.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.QExpansion | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 28
} | {
"line": 81,
"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.QExpansion | {
"line": 105,
"column": 8
} | {
"line": 105,
"column": 34
} | {
"line": 105,
"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": 113,
"column": 4
} | {
"line": 113,
"column": 15
} | {
"line": 113,
"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": 114,
"column": 2
} | {
"line": 114,
"column": 20
} | {
"line": 114,
"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.QExpansion | {
"line": 129,
"column": 32
} | {
"line": 129,
"column": 43
} | {
"line": 129,
"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.QExpansion | {
"line": 185,
"column": 10
} | {
"line": 185,
"column": 21
} | {
"line": 185,
"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.Modular | {
"line": 238,
"column": 65
} | {
"line": 238,
"column": 76
} | {
"line": 238,
"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.ModularForms.QExpansion | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 46
} | {
"line": 194,
"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.Modular | {
"line": 239,
"column": 45
} | {
"line": 239,
"column": 56
} | {
"line": 239,
"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.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": 227,
"column": 8
} | {
"line": 227,
"column": 19
} | {
"line": 227,
"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.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.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.QExpansion | {
"line": 249,
"column": 6
} | {
"line": 249,
"column": 77
} | {
"line": 250,
"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": 250,
"column": 68
} | {
"line": 250,
"column": 79
} | {
"line": 250,
"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.QExpansion | {
"line": 256,
"column": 6
} | {
"line": 256,
"column": 43
} | {
"line": 256,
"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": 257,
"column": 6
} | {
"line": 258,
"column": 13
} | {
"line": 258,
"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.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.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.QExpansion | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 48
} | {
"line": 274,
"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": 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.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.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": 293,
"column": 4
} | {
"line": 293,
"column": 29
} | {
"line": 293,
"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": 117,
"column": 2
} | {
"line": 117,
"column": 33
} | {
"line": 117,
"column": 34
} | [
{
"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 |
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