module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Analytic.Order | {
"line": 226,
"column": 4
} | {
"line": 226,
"column": 24
} | {
"line": 226,
"column": 25
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg✝ : analyticOrderAt f z₀ ≠ analyticOrderAt g z₀\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt (f + g) z₀ = min (analytic... | [
"case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg✝ : analyticOrderAt f z₀ ≠ analyticOrderAt g z₀\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt (f + g) z₀ = analyticOrderAt f z₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 227,
"column": 4
} | {
"line": 227,
"column": 24
} | {
"line": 227,
"column": 25
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ ≠ analyticOrderAt g z₀\nhgf : analyticOrderAt g z₀ < analyticOrderAt f z₀\n⊢ analyticOrderAt (f + g) z₀ = min (analyticO... | [
"case inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ ≠ analyticOrderAt g z₀\nhgf : analyticOrderAt g z₀ < analyticOrderAt f z₀\n⊢ analyticOrderAt (f + g) z₀ = analyticOrderAt g z₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 272,
"column": 4
} | {
"line": 272,
"column": 15
} | {
"line": 272,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\ninst✝ : CompleteSpace E\ns : Set E\nc : ℝ≥0\nf' : E →L[𝕜] F\nhf : ApproximatesLinearOn f f' s c... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\ninst✝ : CompleteSpace E\ns : Set E\nc : ℝ≥0\nf' : E →L[𝕜] F\nhf : ApproximatesLinearOn f f' s c\nf'symm : f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 237,
"column": 6
} | {
"line": 237,
"column": 87
} | {
"line": 238,
"column": 6
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nx : X.obj (op { obj := ⦋2⦌, property := _proof_14 })\ny : ((truncation 2).obj (nerve C)).obj (op { obj := ⦋2⦌, property := _proof_14 })\nh₂ :\n ComposableArrows.mk₁ (F.map (homMk (Edge.mk' ((C... | [
"X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\ny : ((truncation 2).obj (nerve C)).obj (op { obj := ⦋2⦌, property := _proof_14 })\nh' :\n ∀ {a b : X.obj (op { obj := ⦋0⦌, property := ⋯ })} (e : Edge a b),\n ComposableArrows.mk₁ (F.map (homMk (Edge.m... | obtain ⟨x₀, x₁, x₂, e₀₁, e₁₂, e₀₂, h, rfl⟩ := Edge.CompStruct.exists_of_simplex x | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Analytic.Order | {
"line": 284,
"column": 4
} | {
"line": 284,
"column": 91
} | {
"line": 285,
"column": 4
} | [
{
"pp": "case coe.e_a\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ≠... | [
"case coe.e_a\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ≠ 0\nhfF : ∀ᶠ... | obtain ⟨U, hUf, hUo, hUx⟩ := eventually_nhds_iff.mp (hfF.and hFa.eventually_analyticAt) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Analytic.Order | {
"line": 295,
"column": 10
} | {
"line": 295,
"column": 21
} | {
"line": 295,
"column": 22
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ... | [
"case refine_1\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ≠ 0\nhfF : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 296,
"column": 10
} | {
"line": 296,
"column": 51
} | {
"line": 296,
"column": 52
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ≠ 0\nhfF : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 335,
"column": 4
} | {
"line": 339,
"column": 25
} | {
"line": 340,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\nf' : E ≃L[𝕜] F\nc : ℝ≥0\ninst✝ : CompleteSpace E\nhf : ApproximatesLinearOn f (↑f') univ c\nhc ... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\nf' : E ≃L[𝕜] F\nc : ℝ≥0\ninst✝ : CompleteSpace E\nhf : ApproximatesLinearOn f (↑f') univ c\nhc : c < ‖↑f'.s... | have hp : ∀ᶠ r : ℝ in atTop, p ((N⁻¹ - c) * r) := by
have hr : ∀ᶠ r : ℝ in atTop, 0 ≤ r := eventually_ge_atTop 0
refine hr.mono fun r hr => Subset.trans ?_ (image_subset_range f (closedBall 0 r))
refine hf.surjOn_closedBall_of_nonlinearRightInverse f'.toNonlinearRightInverse hr ?_
exact subset_u... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 102,
"column": 15
} | {
"line": 102,
"column": 44
} | {
"line": 102,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nR : Type u_4\ninst✝³ : NormedRing R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : SMulCommClass 𝕜 R E\nx : 𝕜\nf : 𝕜 → E\nc : R\nm : ℕ\nhf : AnalyticAt 𝕜 (fun z ↦ (... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nR : Type u_4\ninst✝³ : NormedRing R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : SMulCommClass 𝕜 R E\nx : 𝕜\nf : 𝕜 → E\nc : R\nm : ℕ\nhf : AnalyticAt 𝕜 (fun z ↦ (z - x) ^ m •... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 13
} | {
"line": 107,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf g : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nhg : MeromorphicAt g x\n⊢ MeromorphicAt (f * g) x",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": ... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf g : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nhg : MeromorphicAt g x\n⊢ MeromorphicAt (f * g) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 135,
"column": 4
} | {
"line": 135,
"column": 39
} | {
"line": 135,
"column": 40
} | [
{
"pp": "case pos\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhf : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteMulSupport F\n⊢ MeromorphicAt (∏ᶠ (i : ι), F i) x",
... | [
"case pos\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhf : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteMulSupport F\n⊢ MeromorphicAt (∏ i ∈ Finite.toFinset h₂f, F i) x"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 37
} | {
"line": 164,
"column": 38
} | [
{
"pp": "case pos\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhF : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteSupport F\n⊢ MeromorphicAt (∑ᶠ (i : ι), F i) x",
"... | [
"case pos\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhF : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteSupport F\n⊢ MeromorphicAt (∑ i ∈ Finite.toFinset h₂f, F i) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 176,
"column": 14
} | {
"line": 176,
"column": 40
} | {
"line": 176,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\nh : MeromorphicAt (-f) x\n⊢ MeromorphicAt f x",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\nh : MeromorphicAt (-f) x\n⊢ MeromorphicAt f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 191,
"column": 20
} | {
"line": 191,
"column": 31
} | {
"line": 191,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nh : MeromorphicAt (f + g) x\n⊢ MeromorphicAt g x",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nh : MeromorphicAt (f + g) x\n⊢ MeromorphicAt g x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 19
} | {
"line": 331,
"column": 20
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\nhfx : f x = 0\nhf' : deriv f x ≠ 0\n⊢ analyticOrderAt f x = 1",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\nhfx : f x = 0\nhf' : deriv f x ≠ 0\n⊢ analyticOrderAt f x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 224,
"column": 20
} | {
"line": 224,
"column": 31
} | {
"line": 224,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nh : MeromorphicAt (f - g) x\n⊢ MeromorphicAt g x",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nh : MeromorphicAt (f - g) x\n⊢ MeromorphicAt g x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 240,
"column": 20
} | {
"line": 240,
"column": 31
} | {
"line": 240,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhg : MeromorphicAt g x\nh : MeromorphicAt (f - g) x\n⊢ MeromorphicAt f x",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhg : MeromorphicAt g x\nh : MeromorphicAt (f - g) x\n⊢ MeromorphicAt f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 340,
"column": 6
} | {
"line": 340,
"column": 58
} | {
"line": 340,
"column": 59
} | [
{
"pp": "case neg\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nn : ℕ\nIH : ∀ {f : 𝕜 → E}, AnalyticAt 𝕜 f z₀ → (↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0)\... | [
"case neg\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nn : ℕ\nIH : ∀ {f : 𝕜 → E}, AnalyticAt 𝕜 f z₀ → (↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0)\nf : 𝕜 → E\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 342,
"column": 6
} | {
"line": 342,
"column": 23
} | {
"line": 342,
"column": 24
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nn : ℕ\nIH : ∀ {f : 𝕜 → E}, AnalyticAt 𝕜 f z₀ → (↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0)\nf : 𝕜 → ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nn : ℕ\nIH : ∀ {f : 𝕜 → E}, AnalyticAt 𝕜 f z₀ → (↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0)\nf : 𝕜 → E\nhf : Anal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 336,
"column": 2
} | {
"line": 344,
"column": 58
} | {
"line": 346,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nhf : AnalyticAt 𝕜 f z₀\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0",
"ppTerm":... | [] | induction n generalizing f with
| zero => simp
| succ n IH =>
by_cases hfz : f z₀ = 0; swap
· simpa [analyticOrderAt_eq_zero.mpr (.inr hfz)] using ⟨0, by simp, by simpa⟩
have : analyticOrderAt (deriv f) z₀ + 1 = analyticOrderAt f z₀ := by
simpa [hfz] using hf.analyticOrderAt_deriv_add_one
simp... | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Analysis.Analytic.Order | {
"line": 336,
"column": 2
} | {
"line": 344,
"column": 58
} | {
"line": 346,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nhf : AnalyticAt 𝕜 f z₀\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0",
"ppTerm":... | [] | induction n generalizing f with
| zero => simp
| succ n IH =>
by_cases hfz : f z₀ = 0; swap
· simpa [analyticOrderAt_eq_zero.mpr (.inr hfz)] using ⟨0, by simp, by simpa⟩
have : analyticOrderAt (deriv f) z₀ + 1 = analyticOrderAt f z₀ := by
simpa [hfz] using hf.analyticOrderAt_deriv_add_one
simp... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Order | {
"line": 336,
"column": 2
} | {
"line": 344,
"column": 58
} | {
"line": 346,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nhf : AnalyticAt 𝕜 f z₀\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0",
"ppTerm":... | [] | induction n generalizing f with
| zero => simp
| succ n IH =>
by_cases hfz : f z₀ = 0; swap
· simpa [analyticOrderAt_eq_zero.mpr (.inr hfz)] using ⟨0, by simp, by simpa⟩
have : analyticOrderAt (deriv f) z₀ + 1 = analyticOrderAt f z₀ := by
simpa [hfz] using hf.analyticOrderAt_deriv_add_one
simp... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Complex.Analytic | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 15
} | {
"line": 191,
"column": 16
} | [
{
"pp": "r : ENNReal\nhp : HasFPowerSeriesOnBall log (FormalMultilinearSeries.ofScalars ℂ fun n ↦ -(-1) ^ n / ↑n) 1 r\n⊢ HasFPowerSeriesOnBall log\n (FormalMultilinearSeries.restrictScalars ℝ (FormalMultilinearSeries.ofScalars ℂ fun n ↦ -(-1) ^ n / ↑n))\n (ofRealCLM 1) r",
"ppTerm": "?m.99",
"assi... | [
"r : ENNReal\nhp : HasFPowerSeriesOnBall log (FormalMultilinearSeries.ofScalars ℂ fun n ↦ -(-1) ^ n / ↑n) 1 r\n⊢ HasFPowerSeriesOnBall log\n (FormalMultilinearSeries.restrictScalars ℝ (FormalMultilinearSeries.ofScalars ℂ fun n ↦ -(-1) ^ n / ↑n)) 1 r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 352,
"column": 4
} | {
"line": 352,
"column": 47
} | {
"line": 352,
"column": 48
} | [
{
"pp": "𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nhorder : analyticOrderAt f z₀ = ↑n + 1\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhg... | [
"𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nhorder : analyticOrderAt f z₀ = ↑n + 1\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhg₀ : g z₀ ≠ 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 353,
"column": 2
} | {
"line": 353,
"column": 37
} | {
"line": 353,
"column": 38
} | [
{
"pp": "𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nhorder : analyticOrderAt f z₀ = ↑n + 1\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhg... | [
"𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nhorder : analyticOrderAt f z₀ = ↑n + 1\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhg₀ : g z₀ ≠ 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 369,
"column": 4
} | {
"line": 369,
"column": 15
} | {
"line": 369,
"column": 16
} | [
{
"pp": "case succ\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\ninst✝ : CharZero 𝕜\nn' : ℕ\nhk : ∀ {n : ℕ}, ↑n = analyticOrderAt f z₀ → n ≠ 0 → n' ≤ n → analyt... | [
"case succ\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\ninst✝ : CharZero 𝕜\nn' : ℕ\nhk : ∀ {n : ℕ}, ↑n = analyticOrderAt f z₀ → n ≠ 0 → n' ≤ n → analyticOrderAt (d... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 309,
"column": 14
} | {
"line": 309,
"column": 40
} | {
"line": 309,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nh : MeromorphicAt f⁻¹ x\n⊢ MeromorphicAt f x",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nh : MeromorphicAt f⁻¹ x\n⊢ MeromorphicAt f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 325,
"column": 15
} | {
"line": 325,
"column": 68
} | {
"line": 325,
"column": 69
} | [
{
"pp": "case ofNat\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\n⊢ MeromorphicAt (f ^ Int.ofNat m) x",
"ppTerm": "?ofNat",
"assigned": true,
"usedConstants... | [
"case ofNat\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\n⊢ MeromorphicAt (f ^ m) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 326,
"column": 17
} | {
"line": 326,
"column": 57
} | {
"line": 326,
"column": 58
} | [
{
"pp": "case negSucc\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\n⊢ MeromorphicAt (f ^ Int.negSucc m) x",
"ppTerm": "?negSucc",
"assigned": true,
"usedCon... | [
"case negSucc\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\n⊢ MeromorphicAt (f ^ (m + 1)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 413,
"column": 6
} | {
"line": 413,
"column": 22
} | {
"line": 413,
"column": 23
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nhf : AnalyticAt 𝕜 f 0\nn : ℕ\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F 0\nhF : ∀ᶠ (z : 𝕜) in 𝓝 0, f z = ∑ i ∈ Fins... | [
"case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nhf : AnalyticAt 𝕜 f 0\nn : ℕ\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F 0\nhF : ∀ᶠ (z : 𝕜) in 𝓝 0, f z = ∑ i ∈ Finset.range n, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 54,
"column": 6
} | {
"line": 54,
"column": 32
} | {
"line": 54,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nf_c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 57,
"column": 53
} | {
"line": 57,
"column": 64
} | {
"line": 57,
"column": 65
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nf_c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 402,
"column": 17
} | {
"line": 402,
"column": 79
} | {
"line": 402,
"column": 80
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nh : MeromorphicAt f x\nn : ℕ\nIH : MeromorphicAt (deriv^[n] f) x\n⊢ MeromorphicAt (deriv^[n + 1] f) x",
"ppTerm": "?suc... | [
"case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nh : MeromorphicAt f x\nn : ℕ\nIH : MeromorphicAt (deriv^[n] f) x\n⊢ MeromorphicAt (deriv (deriv^[n] f)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 471,
"column": 51
} | {
"line": 471,
"column": 62
} | {
"line": 471,
"column": 63
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nz₀ : 𝕜\nn : ℕ\nf : 𝕜 → E\nhf : AnalyticAt 𝕜 f z₀\nIH : analyticOrderAt (deriv f) z₀ = ↑n ↔ (∀ k < n, iteratedDeriv (k + 1) f z₀ =... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nz₀ : 𝕜\nn : ℕ\nf : 𝕜 → E\nhf : AnalyticAt 𝕜 f z₀\nIH : analyticOrderAt (deriv f) z₀ = ↑n ↔ (∀ k < n, iteratedDeriv (k + 1) f z₀ = 0) ∧ iterat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 549,
"column": 14
} | {
"line": 549,
"column": 40
} | {
"line": 549,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nU : Set 𝕜\nh : MeromorphicOn (-f) U\n⊢ MeromorphicOn f U",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nU : Set 𝕜\nh : MeromorphicOn (-f) U\n⊢ MeromorphicOn f U"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 602,
"column": 14
} | {
"line": 602,
"column": 40
} | {
"line": 602,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\ns : 𝕜 → 𝕜'\nU : Set 𝕜\nh : MeromorphicOn s⁻¹ U\n⊢ MeromorphicOn s U",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\ns : 𝕜 → 𝕜'\nU : Set 𝕜\nh : MeromorphicOn s⁻¹ U\n⊢ MeromorphicOn s U"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 765,
"column": 2
} | {
"line": 765,
"column": 13
} | {
"line": 765,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\ninst✝¹ : SecondCountableTopology 𝕜\ninst✝ : CompleteSpace E\nh : Meromorphic f\n⊢ {z | AnalyticAt 𝕜 f z}ᶜ.Countable",
"ppTerm": "?m.31",
"assigned": false,
... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\ninst✝¹ : SecondCountableTopology 𝕜\ninst✝ : CompleteSpace E\nh : Meromorphic f\n⊢ {z | AnalyticAt 𝕜 f z}ᶜ.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 779,
"column": 31
} | {
"line": 779,
"column": 42
} | {
"line": 779,
"column": 43
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nf : 𝕜 → E\ninst✝⁵ : MeasurableSpace 𝕜\ninst✝⁴ : SecondCountableTopology 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : MeasurableSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : BorelSpace E\nh... | [
"𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nf : 𝕜 → E\ninst✝⁵ : MeasurableSpace 𝕜\ninst✝⁴ : SecondCountableTopology 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : MeasurableSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : BorelSpace E\nh : Meromorph... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 80,
"column": 6
} | {
"line": 80,
"column": 17
} | {
"line": 80,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nf_c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 37
} | {
"line": 90,
"column": 38
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nf_c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 517,
"column": 12
} | {
"line": 517,
"column": 23
} | {
"line": 517,
"column": 24
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 0 sin x| ≤ 1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"iteratedDeriv_zero",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.lattice",
"Real.denselyNormedField",
"abs",
"congrArg",
"id",
"Real.... | [
"n : ℕ\nx : ℝ\n⊢ |sin x| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 518,
"column": 12
} | {
"line": 518,
"column": 23
} | {
"line": 518,
"column": 24
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 1 sin x| ≤ 1",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
"... | [
"n : ℕ\nx : ℝ\n⊢ |cos x| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 519,
"column": 16
} | {
"line": 519,
"column": 27
} | {
"line": 519,
"column": 28
} | [
{
"pp": "n✝ : ℕ\nx : ℝ\nn : ℕ\n⊢ |iteratedDeriv (n + 2) sin x| ≤ 1",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"abs_neg",
"Real.instLE",
"Real",
"Pi.instNeg",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
... | [
"n✝ : ℕ\nx : ℝ\nn : ℕ\n⊢ |iteratedDeriv n sin x| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 524,
"column": 12
} | {
"line": 524,
"column": 23
} | {
"line": 524,
"column": 24
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 0 cos x| ≤ 1",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"iteratedDeriv_zero",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
... | [
"n : ℕ\nx : ℝ\n⊢ |cos x| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 525,
"column": 12
} | {
"line": 525,
"column": 23
} | {
"line": 525,
"column": 24
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 1 cos x| ≤ 1",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"abs_neg",
"Real.instLE",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"c... | [
"n : ℕ\nx : ℝ\n⊢ |sin x| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 526,
"column": 16
} | {
"line": 526,
"column": 27
} | {
"line": 526,
"column": 28
} | [
{
"pp": "n✝ : ℕ\nx : ℝ\nn : ℕ\n⊢ |iteratedDeriv (n + 2) cos x| ≤ 1",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"abs_neg",
"Real.instLE",
"Real",
"Pi.instNeg",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
... | [
"n✝ : ℕ\nx : ℝ\nn : ℕ\n⊢ |iteratedDeriv n cos x| ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 37
} | {
"line": 90,
"column": 38
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | [
"E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nf_c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 13
} | {
"line": 193,
"column": 14
} | [
{
"pp": "f g : ℂ → ℂ\nf' g' x : ℂ\nhf : HasStrictDerivAt f f' x\nhg : HasStrictDerivAt g g' x\nh0 : f x ∈ slitPlane\n⊢ HasStrictDerivAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x",
"ppTerm": "?m.64",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"f g : ℂ → ℂ\nf' g' x : ℂ\nhf : HasStrictDerivAt f f' x\nhg : HasStrictDerivAt g g' x\nh0 : f x ∈ slitPlane\n⊢ HasStrictDerivAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 212,
"column": 2
} | {
"line": 212,
"column": 19
} | {
"line": 212,
"column": 20
} | [
{
"pp": "f g : ℂ → ℂ\nf' g' x : ℂ\nhf : HasDerivAt f f' x\nhg : HasDerivAt g g' x\nh0 : f x ∈ slitPlane\n⊢ HasDerivAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x",
"ppTerm": "?m.64",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"f g : ℂ → ℂ\nf' g' x : ℂ\nhf : HasDerivAt f f' x\nhg : HasDerivAt g g' x\nh0 : f x ∈ slitPlane\n⊢ HasDerivAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 19
} | {
"line": 225,
"column": 20
} | [
{
"pp": "f g : ℂ → ℂ\ns : Set ℂ\nf' g' x : ℂ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\nh0 : f x ∈ slitPlane\n⊢ HasDerivWithinAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') s x",
"ppTerm": "?m.64",
"assigned": false,
"usedConstants": []... | [
"f g : ℂ → ℂ\ns : Set ℂ\nf' g' x : ℂ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\nh0 : f x ∈ slitPlane\n⊢ HasDerivWithinAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 619,
"column": 2
} | {
"line": 619,
"column": 70
} | {
"line": 620,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nhf : AnalyticOnNhd 𝕜 f U\nhU : IsConnected U\nthis : ConnectedSpace ↑U\nv : ↑U\n⊢ (∀ (u : ↑U), analyticOrderAt f ↑u ≠ ⊤) ∨ ∀ (u : ↑U), analyticOrderAt f ↑u... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nhf : AnalyticOnNhd 𝕜 f U\nhU : IsConnected U\nthis : ConnectedSpace ↑U\nv : ↑U\n⊢ (∀ a ∈ U, ¬analyticOrderAt f a = ⊤) ∨ ∀ a ∈ U, analyticOrderAt f a = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Binomial | {
"line": 485,
"column": 2
} | {
"line": 485,
"column": 13
} | {
"line": 485,
"column": 14
} | [
{
"pp": "case ha\nR : Type u_1\ninst✝¹ : Field R\ninst✝ : CharZero R\na : R\nn : ℕ\n⊢ ↑n.factorial ≠ 0",
"ppTerm": "?ha",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"DivisionSemiring... | [
"case ha\nR : Type u_1\ninst✝¹ : Field R\ninst✝ : CharZero R\na : R\nn : ℕ\n⊢ ¬n.factorial = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Binomial | {
"line": 530,
"column": 37
} | {
"line": 530,
"column": 65
} | {
"line": 530,
"column": 65
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Ring R\ninst✝ : BinomialRing R\nr s : R\nk : ℕ\nh : Commute r s\nx : ℕ × ℕ\nhx : x ∈ antidiagonal k\n⊢ ↑(k.choose x.1) * ((descPochhammer ℤ x.1).smeval r * (descPochhammer ℤ x.2).smeval s) =\n ↑(k.choose x.1) * ↑x.1.factorial * (choose r x.1 * (↑x.2.factorial * choose s x.2))"... | [
"R : Type u_1\ninst✝¹ : Ring R\ninst✝ : BinomialRing R\nr s : R\nk : ℕ\nh : Commute r s\nx : ℕ × ℕ\nhx : x ∈ antidiagonal k\n⊢ ↑(k.choose x.1) * ((descPochhammer ℤ x.1).smeval r * (descPochhammer ℤ x.2).smeval s) =\n ↑(k.choose x.1) * ↑x.1.factorial * (choose r x.1 * x.2.factorial • choose s x.2)"
] | ← nsmul_eq_mul x.2.factorial | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 52
} | {
"line": 301,
"column": 53
} | [
{
"pp": "x : ℝ\nhx : x ≠ 0\nr : ℂ\nhr : r ≠ 0\nthis : HasDerivAt (fun y ↦ r * (↑y ^ (r - 1 + 1) / (r - 1 + 1))) (r * ↑x ^ (r - 1)) x\n⊢ HasDerivAt (fun y ↦ ↑y ^ r) (r * ↑x ^ (r - 1)) x",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : ℝ\nhx : x ≠ 0\nr : ℂ\nhr : r ≠ 0\nthis : HasDerivAt (fun y ↦ r * (↑y ^ (r - 1 + 1) / (r - 1 + 1))) (r * ↑x ^ (r - 1)) x\n⊢ HasDerivAt (fun y ↦ ↑y ^ r) (r * ↑x ^ (r - 1)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 336,
"column": 24
} | {
"line": 336,
"column": 37
} | {
"line": 336,
"column": 38
} | [
{
"pp": "case inl\n⊢ (deriv fun x ↦ 1) =O[atTop] fun x ↦ x ^ (re 0 - 1)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real",
"Complex.instNormedAddCommGroup",
"deriv_const'",
"Real.... | [
"case inl\n⊢ (fun x ↦ 0) =O[atTop] fun x ↦ x ^ (re 0 - 1)"
] | deriv_const', | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 112,
"column": 6
} | {
"line": 112,
"column": 17
} | {
"line": 112,
"column": 18
} | [
{
"pp": "case convert_7\na : ℂ\nthis : binomialSeries ℂ a = FormalMultilinearSeries.ofScalars ℂ fun n ↦ iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 / ↑n !\nz : ℂ\nhz : z ∈ Metric.ball 0 1\n⊢ ‖(fun x ↦ x) z‖ < 1",
"ppTerm": "?convert_7",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Real... | [
"case convert_7\na : ℂ\nthis : binomialSeries ℂ a = FormalMultilinearSeries.ofScalars ℂ fun n ↦ iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 / ↑n !\nz : ℂ\nhz : z ∈ Metric.ball 0 1\n⊢ ‖z‖ < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 402,
"column": 4
} | {
"line": 402,
"column": 15
} | {
"line": 402,
"column": 16
} | [
{
"pp": "case inr\nx : ℝ\nhx✝ : x ≠ 0\np : ℝ\nhx : 0 < x\n⊢ HasStrictDerivAt (fun x ↦ x ^ p) (p * x ^ (p - 1)) x",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nx : ℝ\nhx✝ : x ≠ 0\np : ℝ\nhx : 0 < x\n⊢ HasStrictDerivAt (fun x ↦ x ^ p) (p * x ^ (p - 1)) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 13
} | {
"line": 406,
"column": 14
} | [
{
"pp": "a : ℝ\nha : 0 < a\nx : ℝ\n⊢ HasStrictDerivAt (fun x ↦ a ^ x) (a ^ x * log a) x",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a : ℝ\nha : 0 < a\nx : ℝ\n⊢ HasStrictDerivAt (fun x ↦ a ^ x) (a ^ x * log a) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 15
} | {
"line": 125,
"column": 16
} | [
{
"pp": "a : ℂ\nn : ℕ\nB : Set ℂ := ⋯\nthis : iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (fun x ↦ (descPochhammer ℤ n).smeval a * (1 + x) ^ (a - ↑n)) 0\n⊢ iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (descPochhammer ℤ n).smeval a",
"ppTerm": "?m.756",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"a : ℂ\nn : ℕ\nB : Set ℂ := ⋯\nthis : iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (fun x ↦ (descPochhammer ℤ n).smeval a * (1 + x) ^ (a - ↑n)) 0\n⊢ iteratedDeriv n (fun x ↦ (1 + x) ^ a) 0 = (descPochhammer ℤ n).smeval a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 476,
"column": 82
} | {
"line": 476,
"column": 93
} | {
"line": 476,
"column": 94
} | [
{
"pp": "p : ℝ\nh : ↑0 ≤ p\nx : ℝ\n⊢ 0 ≤ p",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : ℝ\nh : ↑0 ≤ p\nx : ℝ\n⊢ 0 ≤ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.IteratedFDeriv | {
"line": 141,
"column": 4
} | {
"line": 141,
"column": 19
} | {
"line": 141,
"column": 20
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nh : HasFPowerSeriesWithinOnBall f p s x r\nh'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 654,
"column": 2
} | {
"line": 654,
"column": 64
} | {
"line": 656,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nx : E\np : ℝ\nm : ℕ\nhf : ContDiffAt ℝ (↑m) f x\nh : ↑m ≤ p\n⊢ ContDiffAt ℝ (↑m) (fun x ↦ f x ^ p) x",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"ContDiffAt",
"Eq.mpr",
"Real.ins... | [] | rw [← contDiffWithinAt_univ] at *; exact hf.rpow_const_of_le h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 654,
"column": 2
} | {
"line": 654,
"column": 64
} | {
"line": 656,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nx : E\np : ℝ\nm : ℕ\nhf : ContDiffAt ℝ (↑m) f x\nh : ↑m ≤ p\n⊢ ContDiffAt ℝ (↑m) (fun x ↦ f x ^ p) x",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"ContDiffAt",
"Eq.mpr",
"Real.ins... | [] | rw [← contDiffWithinAt_univ] at *; exact hf.rpow_const_of_le h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Binomial | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 21
} | {
"line": 147,
"column": 22
} | [
{
"pp": "case succ\na : ℂ\nB : Set ℂ := ⋯\nn : ℕ\nih :\n Set.EqOn (iteratedDerivWithin n (fun x ↦ (1 + x) ^ a) B) (fun x ↦ (descPochhammer ℤ n).smeval a * (1 + x) ^ (a - ↑n))\n B\nthis✝ :\n iteratedDerivWithin (n + 1) (fun x ↦ (1 + x) ^ a) B = derivWithin (iteratedDerivWithin n (fun x ↦ (1 + x) ^ a) B) B\n... | [
"case succ\na : ℂ\nB : Set ℂ := ⋯\nn : ℕ\nih :\n Set.EqOn (iteratedDerivWithin n (fun x ↦ (1 + x) ^ a) B) (fun x ↦ (descPochhammer ℤ n).smeval a * (1 + x) ^ (a - ↑n))\n B\nthis✝ :\n iteratedDerivWithin (n + 1) (fun x ↦ (1 + x) ^ a) B = derivWithin (iteratedDerivWithin n (fun x ↦ (1 + x) ^ a) B) B\nthis :\n Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 167,
"column": 4
} | {
"line": 167,
"column": 15
} | {
"line": 167,
"column": 16
} | [
{
"pp": "a : ℂ\nH :\n (binomialSeries ℂ (-a)).compContinuousLinearMap (-1) =\n FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (a + ↑n - 1) n\n⊢ HasFPowerSeriesOnBall (fun x ↦ (1 + x) ^ (-a)) (binomialSeries ℂ (-a)) (-0) 1",
"ppTerm": "?m.210",
"assigned": true,
"usedConstants": [
... | [
"a : ℂ\nH :\n (binomialSeries ℂ (-a)).compContinuousLinearMap (-1) =\n FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (a + ↑n - 1) n\n⊢ HasFPowerSeriesOnBall (fun x ↦ (1 + x) ^ (-a)) (binomialSeries ℂ (-a)) 0 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 64
} | {
"line": 169,
"column": 4
} | [
{
"pp": "a : ℂ\nH :\n (binomialSeries ℂ (-a)).compContinuousLinearMap (-1) =\n FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (a + ↑n - 1) n\nthis : HasFPowerSeriesOnBall (fun x ↦ (1 + x) ^ (-a)) (binomialSeries ℂ (-a)) (-0) 1\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ a)\n (FormalMultiline... | [
"a : ℂ\nH :\n (binomialSeries ℂ (-a)).compContinuousLinearMap (-1) =\n FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (a + ↑n - 1) n\nthis : HasFPowerSeriesOnBall (fun x ↦ (1 + x) ^ (-a)) (binomialSeries ℂ (-a)) (-0) 1\n⊢ HasFPowerSeriesOnBall (fun x ↦ ((1 - x) ^ a)⁻¹)\n (FormalMultilinearSeries.ofS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Polynomial | {
"line": 33,
"column": 23
} | {
"line": 33,
"column": 51
} | {
"line": 34,
"column": 2
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\nA : Type u_3\nB : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : CommSemiring A\nz : E\ns : Set E\ninst✝² : NormedRing B\ninst✝¹ : NormedAlgebra 𝕜 B\ninst✝ : Algebra A B\nf : E → B\nhf : Anal... | [] | apply analyticWithinAt_const | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 13
} | {
"line": 206,
"column": 14
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nx : ℝ\nf_diff : ∀ (y : ℝ), y ≠ x → HasDerivAt f (g y) y\nhf : ContinuousAt f x\nhg : ContinuousAt g x\nA : HasDerivWithinAt f (g x) (Ici x) x\nB : HasDerivWithinAt f (g x) (Iic x) x\n⊢ HasDerivAt f (g x) x",
"ppTerm"... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nx : ℝ\nf_diff : ∀ (y : ℝ), y ≠ x → HasDerivAt f (g y) y\nhf : ContinuousAt f x\nhg : ContinuousAt g x\nA : HasDerivWithinAt f (g x) (Ici x) x\nB : HasDerivWithinAt f (g x) (Iic x) x\n⊢ HasDerivAt f (g x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 197,
"column": 2
} | {
"line": 197,
"column": 13
} | {
"line": 197,
"column": 14
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (z - x)) (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (z ^ (n + 1))⁻¹) 0 ‖z‖ₑ",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing... | [
"z : ℂ\nhz : z ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ (z - x)⁻¹) (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (z ^ (n + 1))⁻¹) 0 ‖z‖ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 26
} | {
"line": 202,
"column": 27
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (z - x) ^ 2)\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (z ^ (n + 2))⁻¹ * (↑n + 1)) 0 ‖z‖ₑ",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.... | [
"z : ℂ\nhz : z ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ ((z - x) ^ 2)⁻¹)\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (z ^ (n + 2))⁻¹ * (↑n + 1)) 0 ‖z‖ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.MetricSeparated | {
"line": 122,
"column": 50
} | {
"line": 122,
"column": 61
} | {
"line": 122,
"column": 62
} | [
{
"pp": "X : Type u_1\ninst✝ : PseudoEMetricSpace X\ns t : Set X\nh : AreSeparated s t\nr : ℝ≥0∞\nr0 : r ≠ 0\nhr : ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y\nx : X\nhx1 : x ∈ s\nhx2 : x ∈ t\n⊢ r = 0",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u_1\ninst✝ : PseudoEMetricSpace X\ns t : Set X\nh : AreSeparated s t\nr : ℝ≥0∞\nr0 : r ≠ 0\nhr : ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y\nx : X\nhx1 : x ∈ s\nhx2 : x ∈ t\n⊢ r = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 13
} | {
"line": 210,
"column": 14
} | [
{
"pp": "⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ 2) (FormalMultilinearSeries.ofScalars ℂ fun n ↦ ↑n + 1) 0 1",
"ppTerm": "?m.62",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
... | [
"⊢ HasFPowerSeriesOnBall (fun x ↦ ((1 - x) ^ 2)⁻¹) (FormalMultilinearSeries.ofScalars ℂ fun n ↦ ↑n + 1) 0 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 227,
"column": 4
} | {
"line": 228,
"column": 11
} | {
"line": 228,
"column": 12
} | [
{
"pp": "case refine_1\nw x : ℂ\nhw : w ≠ x\n⊢ HasFPowerSeriesOnBall (fun z ↦ 1 / (z - w) ^ 2)\n (FormalMultilinearSeries.ofScalars ℂ fun i ↦ (↑i + 1) * (w - x) ^ (-↑(i + 2))) x ‖w - x‖ₑ",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
"Inn... | [
"case refine_1\nw x : ℂ\nhw : w ≠ x\n⊢ HasFPowerSeriesOnBall (fun z ↦ 1 / (z - w) ^ 2)\n (FormalMultilinearSeries.ofScalars ℂ fun i ↦ (↑i + 1) * ((w - x) ^ (i + 2))⁻¹) x ‖w - x‖ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.RadiusLiminf | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 15
} | {
"line": 62,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nthis : ∀ (r : ℝ≥0) {n : ℕ}, 0 < n → (↑r ≤ 1 / ↑(‖p n‖₊ ^ (1 / ↑n)) ↔ ‖p ... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\nthis : ∀ (r : ℝ≥0) {n : ℕ}, 0 < n → (↑r ≤ 1 / ↑(‖p n‖₊ ^ (1 / ↑n)) ↔ ‖p n‖₊ * r ^ n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.MetricSeparated | {
"line": 172,
"column": 2
} | {
"line": 172,
"column": 32
} | {
"line": 172,
"column": 33
} | [
{
"pp": "X : Type u_1\ninst✝ : PseudoEMetricSpace X\nι : Type u_3\nI : Set ι\nhI : I.Finite\ns : Set X\nt : ι → Set X\n⊢ AreSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, AreSeparated s (t i)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
... | [
"X : Type u_1\ninst✝ : PseudoEMetricSpace X\nι : Type u_3\nI : Set ι\nhI : I.Finite\ns : Set X\nt : ι → Set X\n⊢ AreSeparated (⋃ i ∈ I, t i) s ↔ ∀ i ∈ I, AreSeparated (t i) s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.RadiusLiminf | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 34
} | {
"line": 68,
"column": 35
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\n⊢ p.radius⁻¹ = limsup (fun n ↦ ↑(‖p n‖₊ ^ (1 / ↑n))) atTop",
"ppTerm... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\np : FormalMultilinearSeries 𝕜 E F\n⊢ p.radius⁻¹ = limsup (fun n ↦ ↑(‖p n‖₊ ^ (↑n)⁻¹)) atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 264,
"column": 2
} | {
"line": 264,
"column": 43
} | {
"line": 265,
"column": 2
} | [
{
"pp": "a : ℝ\nthis :\n HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ ↑a)\n (FormalMultilinearSeries.restrictScalars ℝ\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (↑a + ↑n - 1) n))\n 0 1\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ a)\n (FormalMultilinearSeries.ofScalars ℝ fun n... | [
"a : ℝ\nthis :\n HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ ↑a)\n (FormalMultilinearSeries.restrictScalars ℝ\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ Ring.choose (↑a + ↑n - 1) n))\n (Complex.ofRealCLM 0) 1\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ a)\n (FormalMultilinearSeries.ofScalars... | rw [← Complex.ofRealCLM.map_zero] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Analytic.Binomial | {
"line": 283,
"column": 2
} | {
"line": 283,
"column": 43
} | {
"line": 284,
"column": 2
} | [
{
"pp": "a : ℕ\nr : ℝ\nhr : r ≠ 0\nthis :\n HasFPowerSeriesOnBall (fun x ↦ 1 / (↑r - x) ^ (a + 1))\n (FormalMultilinearSeries.restrictScalars ℝ\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (↑r ^ (n + a + 1))⁻¹ * ↑((a + n).choose a)))\n 0 ‖↑r‖ₑ\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (r - x) ^ (a + 1... | [
"a : ℕ\nr : ℝ\nhr : r ≠ 0\nthis :\n HasFPowerSeriesOnBall (fun x ↦ 1 / (↑r - x) ^ (a + 1))\n (FormalMultilinearSeries.restrictScalars ℝ\n (FormalMultilinearSeries.ofScalars ℂ fun n ↦ (↑r ^ (n + a + 1))⁻¹ * ↑((a + n).choose a)))\n (Complex.ofRealCLM 0) ‖↑r‖ₑ\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (r - x) ... | rw [← Complex.ofRealCLM.map_zero] at this | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Analytic.Binomial | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 13
} | {
"line": 295,
"column": 14
} | [
{
"pp": "r : ℝ\nhr : r ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (r - x)) (FormalMultilinearSeries.ofScalars ℝ fun n ↦ (r ^ (n + 1))⁻¹) 0 ‖r‖ₑ",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing... | [
"r : ℝ\nhr : r ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ (r - x)⁻¹) (FormalMultilinearSeries.ofScalars ℝ fun n ↦ (r ^ (n + 1))⁻¹) 0 ‖r‖ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 300,
"column": 2
} | {
"line": 300,
"column": 26
} | {
"line": 300,
"column": 27
} | [
{
"pp": "r : ℝ\nhr : r ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (r - x) ^ 2)\n (FormalMultilinearSeries.ofScalars ℝ fun n ↦ (r ^ (n + 2))⁻¹ * (↑n + 1)) 0 ‖r‖ₑ",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.... | [
"r : ℝ\nhr : r ≠ 0\n⊢ HasFPowerSeriesOnBall (fun x ↦ ((r - x) ^ 2)⁻¹)\n (FormalMultilinearSeries.ofScalars ℝ fun n ↦ (r ^ (n + 2))⁻¹ * (↑n + 1)) 0 ‖r‖ₑ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Binomial | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 13
} | {
"line": 308,
"column": 14
} | [
{
"pp": "⊢ HasFPowerSeriesOnBall (fun x ↦ 1 / (1 - x) ^ 2) (FormalMultilinearSeries.ofScalars ℝ fun n ↦ ↑n + 1) 0 1",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
... | [
"⊢ HasFPowerSeriesOnBall (fun x ↦ ((1 - x) ^ 2)⁻¹) (FormalMultilinearSeries.ofScalars ℝ fun n ↦ ↑n + 1) 0 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Cover | {
"line": 82,
"column": 38
} | {
"line": 82,
"column": 49
} | {
"line": 82,
"column": 50
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nε : ℝ≥0\ns : Set X\nf : X → Y\nhf : Isometry f\nC : Set X\nh : IsCover ε s C\n⊢ IsCover ε (f '' s) (f '' C)",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoa... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nε : ℝ≥0\ns : Set X\nf : X → Y\nhf : Isometry f\nC : Set X\nh : IsCover ε s C\n⊢ IsCover ε (f '' s) (f '' C)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Cover | {
"line": 103,
"column": 32
} | {
"line": 103,
"column": 79
} | {
"line": 103,
"column": 80
} | [
{
"pp": "X : Type u_1\ninst✝ : PseudoEMetricSpace X\nε : ℝ≥0\ns N : Set X\nhN : Maximal (fun N ↦ N ⊆ s ∧ IsSeparated (↑ε) N) N\n⊢ Maximal (fun N ↦ N ⊆ s ∧ SetRel.IsSeparated {(x, y) | edist x y ≤ ↑ε} N) N",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"PseudoEMetricSpace.toWeakPseud... | [
"X : Type u_1\ninst✝ : PseudoEMetricSpace X\nε : ℝ≥0\ns N : Set X\nhN : Maximal (fun N ↦ N ⊆ s ∧ IsSeparated (↑ε) N) N\n⊢ Maximal (fun N ↦ N ⊆ s ∧ SetRel.IsSeparated {x | edist x.1 x.2 ≤ ↑ε} N) N"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Cover | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 49
} | {
"line": 151,
"column": 50
} | [
{
"pp": "X : Type u_1\ninst✝¹ : PseudoMetricSpace X\nε : ℝ≥0\ns N : Set X\ninst✝ : ProperSpace X\nhN : IsClosed N\n⊢ IsCover ε (closure s) N ↔ IsCover ε s N",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Metric.isCover_iff_subset_cthickening",
... | [
"X : Type u_1\ninst✝¹ : PseudoMetricSpace X\nε : ℝ≥0\ns N : Set X\ninst✝ : ProperSpace X\nhN : IsClosed N\n⊢ closure s ⊆ cthickening (↑ε) N ↔ s ⊆ cthickening (↑ε) N"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AperiodicOrder.Delone.Basic | {
"line": 106,
"column": 26
} | {
"line": 106,
"column": 49
} | {
"line": 106,
"column": 50
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ 0 < packingRadius",
"ppTer... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ 0 < D.packingRadius"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AperiodicOrder.Delone.Basic | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 38
} | {
"line": 108,
"column": 39
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ IsSeparated (↑packingRadius) c... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ IsSeparated (↑D.packingRadius) D.carrier"
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AperiodicOrder.Delone.Basic | {
"line": 110,
"column": 27
} | {
"line": 110,
"column": 51
} | {
"line": 110,
"column": 52
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ 0 < coveringRadius",
"ppTe... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ 0 < D.coveringRadius"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AperiodicOrder.Delone.Basic | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 39
} | {
"line": 112,
"column": 40
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ IsCover coveringRadius Set.uni... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : MetricSpace X\ninst✝ : MetricSpace Y\nD : DeloneSet X\ncarrier : Set X\npackingRadius coveringRadius : ℝ≥0\nh_carrier : carrier = D.carrier\nh_packing : packingRadius = D.packingRadius\nh_covering : coveringRadius = D.coveringRadius\n⊢ IsCover D.coveringRadius Set.univ D.carrie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AperiodicOrder.Delone.Basic | {
"line": 123,
"column": 4
} | {
"line": 123,
"column": 28
} | {
"line": 123,
"column": 29
} | [
{
"pp": "X : Type u_1\ninst✝ : MetricSpace X\nD : DeloneSet X\nx y : X\nhx : x ∈ D\nhy : y ∈ D\nhne : x ≠ y\n⊢ ENNReal.ofReal ↑D.packingRadius < ENNReal.ofReal (dist x y)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"ENNReal.ofNNReal",
"Preorder... | [
"X : Type u_1\ninst✝ : MetricSpace X\nD : DeloneSet X\nx y : X\nhx : x ∈ D\nhy : y ∈ D\nhne : x ≠ y\n⊢ ↑D.packingRadius < dist x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AperiodicOrder.Delone.Basic | {
"line": 129,
"column": 19
} | {
"line": 129,
"column": 43
} | {
"line": 129,
"column": 44
} | [
{
"pp": "X : Type u_1\ninst✝ : MetricSpace X\nD : DeloneSet X\nx y : X\nhy : y ∈ D.carrier\nhdist : (x, y) ∈ {(x, y) | edist x y ≤ ↑D.coveringRadius}\n⊢ dist x y ≤ ↑D.coveringRadius",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NNDist.nndist",
"Real.instLE",
... | [
"X : Type u_1\ninst✝ : MetricSpace X\nD : DeloneSet X\nx y : X\nhy : y ∈ D.carrier\nhdist : (x, y) ∈ {(x, y) | edist x y ≤ ↑D.coveringRadius}\n⊢ nndist x y ≤ D.coveringRadius"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.LinearGrowth | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 38
} | {
"line": 111,
"column": 2
} | [
{
"pp": "u : ℕ → EReal\na : EReal\n⊢ linearGrowthSup u ≤ a ↔ ∀ b > a, ∀ᶠ (n : ℕ) in atTop, u n ≤ b * ↑n",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"instAddCommMonoidWithOneEReal",
"Eq.mpr",
"EReal.instDivInvMonoid",
"Preorder.toLT",
"instHDiv",
"HMu... | [
"u : ℕ → EReal\na : EReal\n⊢ (∀ y > a, ∀ᶠ (a : ℕ) in atTop, u a / ↑a ≤ y) ↔ ∀ b > a, ∀ᶠ (n : ℕ) in atTop, u n ≤ b * ↑n"
] | rw [linearGrowthSup, limsup_le_iff'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 78,
"column": 14
} | {
"line": 78,
"column": 56
} | {
"line": 78,
"column": 57
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nl : Filter α\nk : α → β\nz : ℕ\n⊢ Tendsto (fun a ↦ k a ^ z * 0 a) l (𝓝 0)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nl : Filter α\nk : α → β\nz : ℕ\n⊢ Tendsto (fun a ↦ 0) l (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 52
} | {
"line": 82,
"column": 53
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f g : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : CommSemiring β\ninst✝ : ContinuousAdd β\nhf : SuperpolynomialDecay l k f\nhg : SuperpolynomialDecay l k g\nz : ℕ\n⊢ Tendsto (fun a ↦ k a ^ z * (f + g) a) l (𝓝 0)",
"ppTerm": "?m.20",
"assigned": true... | [
"α : Type u_1\nβ : Type u_2\nl : Filter α\nk f g : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : CommSemiring β\ninst✝ : ContinuousAdd β\nhf : SuperpolynomialDecay l k f\nhg : SuperpolynomialDecay l k g\nz : ℕ\n⊢ Tendsto (fun a ↦ k a ^ z * f a + k a ^ z * g a) l (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 42
} | {
"line": 90,
"column": 43
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : CommSemiring β\ninst✝ : ContinuousMul β\nhf : SuperpolynomialDecay l k f\nc : β\nz : ℕ\n⊢ Tendsto (fun a ↦ k a ^ z * (fun n ↦ f n * c) a) l (𝓝 0)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstan... | [
"α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : CommSemiring β\ninst✝ : ContinuousMul β\nhf : SuperpolynomialDecay l k f\nc : β\nz : ℕ\n⊢ Tendsto (fun a ↦ k a ^ z * f a * c) l (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 100,
"column": 6
} | {
"line": 100,
"column": 80
} | {
"line": 100,
"column": 81
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\nz : ℕ\ns : Set β\nhs : IsOpen[inst✝¹] s\nhs0 : 0 ∈ s\nx : α\nhx : x ∈ (fun a ↦ k a ^ (z + 1) * f a) ⁻¹' s\n⊢ x ∈ (fun a ↦ k a ^ z * (k * f) a) ⁻¹' s",
"ppTerm... | [
"α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\nz : ℕ\ns : Set β\nhs : IsOpen[inst✝¹] s\nhs0 : 0 ∈ s\nx : α\nhx : x ∈ (fun a ↦ k a ^ (z + 1) * f a) ⁻¹' s\n⊢ k x ^ (z + 1) * f x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 109,
"column": 12
} | {
"line": 109,
"column": 48
} | {
"line": 109,
"column": 49
} | [
{
"pp": "case zero\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\n⊢ SuperpolynomialDecay l k (k ^ 0 * f)",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
... | [
"case zero\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\n⊢ SuperpolynomialDecay l k f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 110,
"column": 17
} | {
"line": 110,
"column": 56
} | {
"line": 110,
"column": 57
} | [
{
"pp": "case succ\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\nn : ℕ\nhn : SuperpolynomialDecay l k (k ^ n * f)\n⊢ SuperpolynomialDecay l k (k ^ (n + 1) * f)",
"ppTerm": "?succ",
"assigned": true,
"used... | [
"case succ\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝¹ : TopologicalSpace β\ninst✝ : CommSemiring β\nhf : SuperpolynomialDecay l k f\nn : ℕ\nhn : SuperpolynomialDecay l k (k ^ n * f)\n⊢ SuperpolynomialDecay l k (k * (k ^ n * f))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 182,
"column": 45
} | {
"line": 182,
"column": 85
} | {
"line": 182,
"column": 85
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝² : TopologicalSpace β\ninst✝¹ : Field β\ninst✝ : ContinuousMul β\nc : β\nhc0 : c ≠ 0\nh : SuperpolynomialDecay l k fun n ↦ f n * c\nx : α\n⊢ f x * c * c⁻¹ = f x",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Grou... | [] | by simp [mul_assoc, mul_inv_cancel₀ hc0] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 259,
"column": 2
} | {
"line": 259,
"column": 26
} | {
"line": 259,
"column": 27
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : Field β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\n⊢ SuperpolynomialDecay l k (f * k) ↔ SuperpolynomialDecay l k f",
"ppTerm": "?m.21",
"as... | [
"α : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : Field β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\n⊢ SuperpolynomialDecay l k (f * k) ↔ SuperpolynomialDecay l k f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Asymptotics.SuperpolynomialDecay | {
"line": 266,
"column": 4
} | {
"line": 267,
"column": 62
} | {
"line": 267,
"column": 63
} | [
{
"pp": "case succ\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : Field β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\nn : ℕ\nhn : SuperpolynomialDecay l k (k ^ n * f) ↔ SuperpolynomialDecay l k f\n⊢ Supe... | [
"case succ\nα : Type u_1\nβ : Type u_2\nl : Filter α\nk f : α → β\ninst✝⁴ : TopologicalSpace β\ninst✝³ : Field β\ninst✝² : LinearOrder β\ninst✝¹ : IsStrictOrderedRing β\ninst✝ : OrderTopology β\nhk : Tendsto k l atTop\nn : ℕ\nhn : SuperpolynomialDecay l k (k ^ n * f) ↔ SuperpolynomialDecay l k f\n⊢ SuperpolynomialD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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