module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Geometry.Manifold.HasGroupoid | {
"line": 69,
"column": 82
} | {
"line": 72,
"column": 26
} | {
"line": 74,
"column": 0
} | [
{
"pp": "H : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\n⊢ HasGroupoid M (continuousGroupoid H)",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
... | [] | by
refine ⟨fun _ _ ↦ ?_⟩
rw [continuousGroupoid, mem_groupoid_of_pregroupoid]
simp only [and_self_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 511,
"column": 4
} | {
"line": 511,
"column": 14
} | {
"line": 512,
"column": 6
} | [
{
"pp": "case inr\nH : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : TopologicalSpace M'\ncm : ChartedSpace H M\ncm' : ChartedSpace H M'\ninst✝ : Nonempty H\nx : M'\n⊢ Sum.inr x ∈\n (Sum.elim (fun x ↦ (ChartedSpace.chart... | [] | | inr x => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 521,
"column": 4
} | {
"line": 521,
"column": 14
} | {
"line": 522,
"column": 6
} | [
{
"pp": "case inr\nH : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : TopologicalSpace M'\ncm : ChartedSpace H M\ncm' : ChartedSpace H M'\ninst✝ : Nonempty H\nx : M'\n⊢ Sum.elim (fun x ↦ (ChartedSpace.chartAt x).lift_openEmb... | [] | | inr x => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Geometry.Manifold.HasGroupoid | {
"line": 345,
"column": 73
} | {
"line": 353,
"column": 62
} | {
"line": 355,
"column": 0
} | [
{
"pp": "H : Type u\nM : Type u_2\ninst✝⁴ : TopologicalSpace H\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\ne : OpenPartialHomeomorph M H\nhe : e ∈ atlas H M\ns : Opens M\nhs : Nonempty ↥s\nG : StructureGroupoid H\ninst✝¹ : HasGroupoid M G\ninst✝ : ClosedUnderRestriction G\n⊢ e.subtypeRestr hs ∈ max... | [] | by
intro e' he'
-- `e'` is the restriction of some chart of `M` at `x`,
obtain ⟨x, this⟩ := Opens.chart_eq hs he'
rw [this]
-- The transition functions between the unrestricted charts lie in the groupoid,
-- the transition functions of the restriction are the restriction of the transition function.
exact ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.StructureGroupoid | {
"line": 313,
"column": 6
} | {
"line": 316,
"column": 31
} | {
"line": 317,
"column": 2
} | [
{
"pp": "case right.refine_2\nH : Type u_1\ninst✝ : TopologicalSpace H\nPG : Pregroupoid H\ne : OpenPartialHomeomorph H H\nhe :\n ∀ x ∈ e.source,\n ∃ s, IsOpen[inst✝] s ∧ x ∈ s ∧ e.restr s ∈ {e | PG.property (↑e) e.source ∧ PG.property (↑e.symm) e.target}\nx : H\nxu : x ∈ e.target\ns : Set H\ns_open : IsOpe... | [] | · rw [← inter_assoc, inter_self]
convert! hs.2 using 1
dsimp [OpenPartialHomeomorph.restr]
rw [s_open.interior_eq] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Geometry.Manifold.HasGroupoid | {
"line": 457,
"column": 8
} | {
"line": 460,
"column": 66
} | {
"line": 461,
"column": 8
} | [
{
"pp": "H : Type u\nM : Type u_2\ninst✝⁴ : TopologicalSpace H\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nG : StructureGroupoid H\ne : OpenPartialHomeomorph M H\nhe : e ∈ atlas H M\nhs : Nonempty ↑e.source\ninst✝¹ : HasGroupoid M G\ninst✝ : ClosedUnderRestriction G\ns : Opens M := { carrier := e.s... | [
"H : Type u\nM : Type u_2\ninst✝⁴ : TopologicalSpace H\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nG : StructureGroupoid H\ne : OpenPartialHomeomorph M H\nhe : e ∈ atlas H M\nhs : Nonempty ↑e.source\ninst✝¹ : HasGroupoid M G\ninst✝ : ClosedUnderRestriction G\ns : Opens M := { carrier := e.source, is_op... | simp only [trans_toPartialEquiv, PartialEquiv.trans_source,
Homeomorph.toOpenPartialHomeomorph_source, toFun_eq_coe,
Homeomorph.toOpenPartialHomeomorph_apply, Opens.openPartialHomeomorphSubtypeCoe_source,
preimage_univ, inter_self, subtypeRestr_source, goal, s] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 27
} | {
"line": 350,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : TopologicalSpace H\ninst✝ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ne e' : OpenPartialHomeomorph M H\nx : E\nhx : x ∈ ↑I '' (e.symm ≫... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : TopologicalSpace H\ninst✝ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ne e' : OpenPartialHomeomorph M H\nx : H\nhx : x ∈ (e.symm ≫ₕ e').source\n⊢ ↑I... | obtain ⟨x, hx, rfl⟩ := hx | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 7
} | {
"line": 382,
"column": 0
} | [
{
"pp": "case e_s\nH : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : TopologicalSpace H'\ninst✝¹ : TopologicalSpace M'\ninst✝ : ChartedSpace H' M'\nG : StructureGroupoid H\nG' : StructureGroupoid H'\nP : (H → H... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 449,
"column": 2
} | {
"line": 449,
"column": 12
} | {
"line": 452,
"column": 4
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ :... | [] | | inr x => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 485,
"column": 2
} | {
"line": 485,
"column": 12
} | {
"line": 486,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM' : Type u_16\ninst✝⁸ : TopologicalSpace M'\ninst✝⁷ : ChartedSpace H M'\nn : WithTop ℕ∞\nE' : Type u_17... | [
"𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM' : Type u_16\ninst✝⁸ : TopologicalSpace M'\ninst✝⁷ : ChartedSpace H M'\nn : WithTop ℕ∞\nE' : Type u_17\ninst✝⁶ : N... | inhabit N' | Lean.Elab.Tactic._aux_Mathlib_Tactic_Inhabit___elabRules_Lean_Elab_Tactic_inhabit_1 | Lean.Elab.Tactic.inhabit |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 775,
"column": 2
} | {
"line": 775,
"column": 97
} | {
"line": 776,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nE' : Type u_5\ninst✝⁶ : NormedAddC... | [
"𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nE' : Type u_5\ninst✝⁶ : NormedAddCommGroup E'\... | rcases (contMDiffWithinAt_iff'.1 h).2.contDiffOn le_rfl (by simp [hn]) with ⟨v, hmem, hsub, hv⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Geometry.Manifold.ContMDiff.Atlas | {
"line": 278,
"column": 10
} | {
"line": 278,
"column": 41
} | {
"line": 279,
"column": 6
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\nn : ℕ∞ω\nM' : Type u_5... | [] | rw [inter_self]; exact hef.symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.ContMDiff.Atlas | {
"line": 278,
"column": 10
} | {
"line": 278,
"column": 41
} | {
"line": 279,
"column": 6
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\nn : ℕ∞ω\nM' : Type u_5... | [] | rw [inter_self]; exact hef.symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.VectorBundle.Constructions | {
"line": 57,
"column": 8
} | {
"line": 57,
"column": 31
} | {
"line": 57,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_3\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : TopologicalSpace B\ne : Trivialization F TotalSpace.proj\nhe : MemTrivializationAtlas e\n⊢ Trivialization.IsLinear 𝕜 e",
"ppTerm": "?m.28",
"assigne... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_3\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : TopologicalSpace B\ne : Trivialization F TotalSpace.proj\nhe : MemTrivializationAtlas e\n⊢ Trivialization.IsLinear 𝕜 (trivialization B F)"
] | eq_trivialization B F e | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.MFDeriv.Basic | {
"line": 849,
"column": 2
} | {
"line": 849,
"column": 11
} | {
"line": 850,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCom... | [
"𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : NormedAddCommGroup E'\ni... | ext p : 1 | _private.Lean.Elab.Tactic.Ext.0.Lean.Elab.Tactic.Ext.evalExt | Lean.Elab.Tactic.Ext.ext |
Mathlib.Topology.VectorBundle.Constructions | {
"line": 200,
"column": 28
} | {
"line": 202,
"column": 18
} | {
"line": 203,
"column": 2
} | [
{
"pp": "R : Type u_1\n𝕜 : Type u_2\nB : Type u_3\nF : Type u_4\nE : B → Type u_5\nB' : Type u_6\nf✝ : B' → B\ninst✝¹² : TopologicalSpace B'\ninst✝¹¹ : TopologicalSpace (TotalSpace F E)\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : TopologicalSpace B\... | [] | by
rintro _ ⟨e, he, rfl⟩
infer_instance | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.VectorBundle.Basic | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 81
} | {
"line": 219,
"column": 2
} | [
{
"pp": "n : ℕ∞ω\n𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : TopologicalSpace (TotalSpace F E)\ninst✝⁶ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝⁵ : NormedAddCommGroup EB\nins... | [
"n : ℕ∞ω\n𝕜 : Type u_1\nB : Type u_2\nF : Type u_4\nE : B → Type u_6\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup F\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝⁷ : TopologicalSpace (TotalSpace F E)\ninst✝⁶ : (x : B) → TopologicalSpace (E x)\nEB : Type u_7\ninst✝⁵ : NormedAddCommGroup EB\ninst✝⁴ : Normed... | have : ContMDiffAt (IB.prod 𝓘(𝕜, F)) (IB.prod 𝓘(𝕜, F)) n id x := contMDiffAt_id | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 126,
"column": 6
} | {
"line": 127,
"column": 29
} | {
"line": 128,
"column": 2
} | [
{
"pp": "case refine_1.h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\nin... | [] | intro x hx
apply (e.linear 𝕜 hx).2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 126,
"column": 6
} | {
"line": 127,
"column": 29
} | {
"line": 128,
"column": 2
} | [
{
"pp": "case refine_1.h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\nin... | [] | intro x hx
apply (e.linear 𝕜 hx).2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 371,
"column": 2
} | {
"line": 375,
"column": 29
} | {
"line": 377,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : NormedAddC... | [] | rcases z with n | n
· refine (coe_nsmul s n).trans ?_
simp only [Int.ofNat_eq_natCast, natCast_zsmul]
· refine (congr_arg Neg.neg (coe_nsmul s (n + 1))).trans ?_
simp only [negSucc_zsmul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 371,
"column": 2
} | {
"line": 375,
"column": 29
} | {
"line": 377,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : NormedAddC... | [] | rcases z with n | n
· refine (coe_nsmul s n).trans ?_
simp only [Int.ofNat_eq_natCast, natCast_zsmul]
· refine (congr_arg Neg.neg (coe_nsmul s (n + 1))).trans ?_
simp only [negSucc_zsmul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.MFDeriv.Basic | {
"line": 1311,
"column": 2
} | {
"line": 1311,
"column": 11
} | {
"line": 1311,
"column": 11
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\ninst✝⁹ : NormedA... | [
"𝕜 : Type u_1\ninst✝¹⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁴ : NormedAddCommGroup E\ninst✝¹³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹¹ : TopologicalSpace M\ninst✝¹⁰ : ChartedSpace H M\nE' : Type u_5\ninst✝⁹ : NormedAddCommGroup ... | ext p : 1 | _private.Lean.Elab.Tactic.Ext.0.Lean.Elab.Tactic.Ext.evalExt | Lean.Elab.Tactic.Ext.ext |
Mathlib.Topology.PartitionOfUnity | {
"line": 250,
"column": 2
} | {
"line": 250,
"column": 28
} | {
"line": 251,
"column": 2
} | [
{
"pp": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nρ : PartitionOfUnity ι X s\nx₀ : X\ni : ι\nhi : i ∈ ρ.finsupport x₀\n⊢ i ∈ ρ.fintsupport x₀",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Real.instZero",
"congrArg",
"... | [
"ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nρ : PartitionOfUnity ι X s\nx₀ : X\ni : ι\nhi : i ∈ ρ.finsupport x₀\n⊢ x₀ ∈ tsupport ⇑(ρ i)"
] | rw [ρ.mem_fintsupport_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.PartitionOfUnity | {
"line": 351,
"column": 31
} | {
"line": 351,
"column": 79
} | {
"line": 351,
"column": 79
} | [
{
"pp": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns✝ : Set X\nf : BumpCovering ι X s✝\ni : ι\ns : Set X\nx : X\nx✝ : x ∈ s\n⊢ ⇑(Pi.single i 1 i) =ᶠ[𝓝 x] 1",
"ppTerm": "?m.112",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Real.instZero",
"congrArg",
... | [] | by rw [Pi.single_eq_same, ContinuousMap.coe_one] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.PartitionOfUnity | {
"line": 539,
"column": 2
} | {
"line": 539,
"column": 28
} | {
"line": 540,
"column": 2
} | [
{
"pp": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\nx : X\nU : Set X\nhU : U ∈ 𝓝 x\nhf : {i | ((fun i ↦ support ⇑(f i)) i ∩ U).Nonempty}.Finite\ny : X\nhyU : y ∈ U\n⊢ f.toPOUFun i y = (f i) y * ∏ c ∈ hf.toFinset with WellOrderingRel c i, (1 - f c) y",
"ppT... | [
"ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : BumpCovering ι X s\ni : ι\nx : X\nU : Set X\nhU : U ∈ 𝓝 x\nhf : {i | ((fun i ↦ support ⇑(f i)) i ∩ U).Nonempty}.Finite\ny : X\nhyU : y ∈ U\n⊢ ∀ (j : ι), WellOrderingRel j i → (f j) y ≠ 0 → j ∈ hf.toFinset"
] | apply toPOUFun_eq_mul_prod | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Topology.ShrinkingLemma | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 64
} | {
"line": 374,
"column": 2
} | [
{
"pp": "case h.refine_1\nι : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nu : ι → Set X\ns : Set X\ninst✝¹ : T2Space X\ninst✝ : LocallyCompactSpace X\nhs : IsCompact s\nuo : ∀ (i : ι), IsOpen (u i)\nuf : ∀ x ∈ s, {i | x ∈ u i}.Finite\nus : s ⊆ ⋃ i, u i\nv : ι → Set X\nhsv : s ⊆ iUnion v\nleft✝ : ∀ (i :... | [] | exact Subset.trans hsv (iUnion_mono fun _ => subset_closure) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.ShrinkingLemma | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 64
} | {
"line": 374,
"column": 2
} | [
{
"pp": "case h.refine_1\nι : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nu : ι → Set X\ns : Set X\ninst✝¹ : T2Space X\ninst✝ : LocallyCompactSpace X\nhs : IsCompact s\nuo : ∀ (i : ι), IsOpen (u i)\nuf : ∀ x ∈ s, {i | x ∈ u i}.Finite\nus : s ⊆ ⋃ i, u i\nv : ι → Set X\nhsv : s ⊆ iUnion v\nleft✝ : ∀ (i :... | [] | exact Subset.trans hsv (iUnion_mono fun _ => subset_closure) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ShrinkingLemma | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 64
} | {
"line": 374,
"column": 2
} | [
{
"pp": "case h.refine_1\nι : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nu : ι → Set X\ns : Set X\ninst✝¹ : T2Space X\ninst✝ : LocallyCompactSpace X\nhs : IsCompact s\nuo : ∀ (i : ι), IsOpen (u i)\nuf : ∀ x ∈ s, {i | x ∈ u i}.Finite\nus : s ⊆ ⋃ i, u i\nv : ι → Set X\nhsv : s ⊆ iUnion v\nleft✝ : ∀ (i :... | [] | exact Subset.trans hsv (iUnion_mono fun _ => subset_closure) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Haar.Disintegration | {
"line": 119,
"column": 2
} | {
"line": 124,
"column": 45
} | {
"line": 126,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : CompleteSpace 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : MeasurableSpace E\ninst✝⁸ : BorelSpace E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : MeasurableSpace F\ninst✝⁴ : BorelSpace F\nin... | [] | have : FiniteDimensional 𝕜 E := .of_locallyCompactSpace 𝕜
have : AEMeasurable L μ := L.continuous_of_finiteDimensional.aemeasurable
apply (ae_map_iff this hs).symm.trans
rcases L.exists_map_addHaar_eq_smul_addHaar μ ν h with ⟨c, c_pos, hc⟩
rw [hc]
exact ae_ennreal_smul_measure_iff c_pos.ne' | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Haar.Disintegration | {
"line": 119,
"column": 2
} | {
"line": 124,
"column": 45
} | {
"line": 126,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : CompleteSpace 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : MeasurableSpace E\ninst✝⁸ : BorelSpace E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : MeasurableSpace F\ninst✝⁴ : BorelSpace F\nin... | [] | have : FiniteDimensional 𝕜 E := .of_locallyCompactSpace 𝕜
have : AEMeasurable L μ := L.continuous_of_finiteDimensional.aemeasurable
apply (ae_map_iff this hs).symm.trans
rcases L.exists_map_addHaar_eq_smul_addHaar μ ν h with ⟨c, c_pos, hc⟩
rw [hc]
exact ae_ennreal_smul_measure_iff c_pos.ne' | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Haar.Disintegration | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 71
} | {
"line": 141,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹³ : NontriviallyNormedField 𝕜\ninst✝¹² : CompleteSpace 𝕜\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : MeasurableSpace E\ninst✝⁹ : BorelSpace E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : MeasurableSpace F\ninst✝⁵ : BorelSpace F\ni... | [] | simp [M, ← LinearMap.range_eq_top (f := _), LinearMap.range_coprod] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.Function.AbsolutelyContinuous | {
"line": 353,
"column": 4
} | {
"line": 353,
"column": 55
} | {
"line": 354,
"column": 4
} | [
{
"pp": "case e'_2.e'_4\nF : Type u_2\ninst✝ : SeminormedAddCommGroup F\na✝ b✝ : ℝ\nf : ℝ → F\na b : ℝ\nhf :\n ∀ ε > 0,\n ∃ δ > 0,\n ∀ E ∈ disjWithin a b,\n ∑ i ∈ Finset.range E.1, dist (E.2 i).1 (E.2 i).2 < δ →\n ∑ i ∈ Finset.range E.1, dist (f (E.2 i).1) (f (E.2 i).2) < ε\nhab₀ : a ≤ ... | [
"case e'_3.a.e'_4\nF : Type u_2\ninst✝ : SeminormedAddCommGroup F\na✝¹ b✝ : ℝ\nf : ℝ → F\na b : ℝ\nhf :\n ∀ ε > 0,\n ∃ δ > 0,\n ∀ E ∈ disjWithin a b,\n ∑ i ∈ Finset.range E.1, dist (E.2 i).1 (E.2 i).2 < δ →\n ∑ i ∈ Finset.range E.1, dist (f (E.2 i).1) (f (E.2 i).2) < ε\nhab₀ : a ≤ b\nhab : ... | · simp only [Nat.cast_add, Nat.cast_one, δ']; field | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Calculus.Taylor | {
"line": 251,
"column": 4
} | {
"line": 261,
"column": 65
} | {
"line": 263,
"column": 0
} | [
{
"pp": "case succ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nx₀ : ℝ\ns : Set ℝ\nhs : Convex ℝ s\nhx₀s : x₀ ∈ s\nn : ℕ\nh : ∀ {f : ℝ → E}, ContDiffOn ℝ (↑n) f s → (fun x ↦ f x - taylorWithinEval f n s x₀ x) =o[𝓝[s] x₀] fun x ↦ (x - x₀) ^ n\nf : ℝ → E\nhf : ContDiffOn ℝ (↑(n + 1)) f ... | [] | rcases s.eq_singleton_or_nontrivial hx₀s with rfl | hs'
· simp
replace hs' := uniqueDiffOn_convex hs (hs.nontrivial_iff_nonempty_interior.1 hs')
simp only [Nat.cast_add, Nat.cast_one] at hf
convert!
Convex.isLittleO_pow_succ_real hs hx₀s ?_ (h (hf.derivWithin hs' le_rfl)) (f := fun x ↦
f x... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.Taylor | {
"line": 251,
"column": 4
} | {
"line": 261,
"column": 65
} | {
"line": 263,
"column": 0
} | [
{
"pp": "case succ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nx₀ : ℝ\ns : Set ℝ\nhs : Convex ℝ s\nhx₀s : x₀ ∈ s\nn : ℕ\nh : ∀ {f : ℝ → E}, ContDiffOn ℝ (↑n) f s → (fun x ↦ f x - taylorWithinEval f n s x₀ x) =o[𝓝[s] x₀] fun x ↦ (x - x₀) ^ n\nf : ℝ → E\nhf : ContDiffOn ℝ (↑(n + 1)) f ... | [] | rcases s.eq_singleton_or_nontrivial hx₀s with rfl | hs'
· simp
replace hs' := uniqueDiffOn_convex hs (hs.nontrivial_iff_nonempty_interior.1 hs')
simp only [Nat.cast_add, Nat.cast_one] at hf
convert!
Convex.isLittleO_pow_succ_real hs hx₀s ?_ (h (hf.derivWithin hs' le_rfl)) (f := fun x ↦
f x... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.Taylor | {
"line": 274,
"column": 4
} | {
"line": 274,
"column": 43
} | {
"line": 275,
"column": 4
} | [
{
"pp": "E : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nx₀ : ℝ\nn : ℕ\ns : Set ℝ\nhs : Convex ℝ s\nhx₀s : x₀ ∈ s\nhf : ContDiffOn ℝ (↑n) f s\nh_isLittleO : Filter.Tendsto (fun x ↦ ‖f x - taylorWithinEval f n s x₀ x‖ / ‖(x - x₀) ^ n‖) (𝓝[s] x₀) (𝓝 0)\n⊢ Filter.Tendsto (fun x ↦... | [
"E : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : ℝ → E\nx₀ : ℝ\nn : ℕ\ns : Set ℝ\nhs : Convex ℝ s\nhx₀s : x₀ ∈ s\nhf : ContDiffOn ℝ (↑n) f s\nh_isLittleO : Filter.Tendsto (fun x ↦ ‖f x - taylorWithinEval f n s x₀ x‖ / ‖(x - x₀) ^ n‖) (𝓝[s] x₀) (𝓝 0)\n⊢ Filter.Tendsto (fun x ↦ ‖((x - x₀) ... | rw [tendsto_zero_iff_norm_tendsto_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Integral.IntervalIntegral.AbsolutelyContinuousFun | {
"line": 195,
"column": 37
} | {
"line": 195,
"column": 50
} | {
"line": 195,
"column": 51
} | [
{
"pp": "F✝ : Type u_2\ninst✝³ : NormedAddCommGroup F✝\ninst✝² : NormedSpace ℝ F✝\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\na b : ℝ\nhf : AbsolutelyContinuousOnInterval f a b\nhab : a ≤ b\nd : ℝ\nhd : a ≤ d ∧ d ≤ b\nr : ℝ\nhr : r > 0\nhad : a ≤ d\nhdb : d < b\nhf₀ : ∀ᵐ (x... | [
"case ha\nF✝ : Type u_2\ninst✝³ : NormedAddCommGroup F✝\ninst✝² : NormedSpace ℝ F✝\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\na b : ℝ\nhf : AbsolutelyContinuousOnInterval f a b\nhab : a ≤ b\nd : ℝ\nhd : a ≤ d ∧ d ≤ b\nr : ℝ\nhr : r > 0\nhad : a ≤ d\nhdb : d < b\nhf₀ : ∀ᵐ (x : ... | apply div_pos | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Calculus.TaylorIntegral | {
"line": 121,
"column": 4
} | {
"line": 130,
"column": 14
} | {
"line": 131,
"column": 4
} | [
{
"pp": "E : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\nf : E → F\nx y : E\nn✝ : ℕ\ninst✝ : CompleteSpace F\nn : ℕ\nih :\n f (x + y) =\n (∑ k ∈ Finset.range (n + 1), (↑k !)⁻¹ • (iteratedFDeriv ℝ k f x) fun x ↦ y) ... | [
"E : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedSpace ℝ F\nf : E → F\nx y : E\nn✝ : ℕ\ninst✝ : CompleteSpace F\nn : ℕ\nih :\n f (x + y) =\n (∑ k ∈ Finset.range (n + 1), (↑k !)⁻¹ • (iteratedFDeriv ℝ k f x) fun x ↦ y) +\n (↑n... | have hv : ∀ (t : ℝ) (ht : t ∈ Set.uIcc 0 1), HasDerivAt (v (n + 1)) (v (n + 1 + 1) t) t := by
intro t ht
unfold v
rw [← (hf t ht).deriv_fderiv_add_smul]
have h_diff : DifferentiableAt ℝ (iteratedFDeriv ℝ (n + 1) f) (x + t • y) := by
apply (hf t ht).differentiableAt_iteratedFDeriv
... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Normed.Module.Ray | {
"line": 43,
"column": 4
} | {
"line": 43,
"column": 35
} | {
"line": 44,
"column": 4
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nu : E\na b : ℝ\nha : 0 ≤ a\nhb : 0 ≤ b\nh : SameRay ℝ (b • u) (a • u)\nH : ∀ (a b : ℝ), 0 ≤ a → 0 ≤ b → SameRay ℝ (a • u) (b • u) → b ≤ a → ‖a • u - b • u‖ = |‖a • u‖ - ‖b • u‖|\nhab : ¬b ≤ a\n⊢ ‖a • u - b • u‖ = |‖a • ... | [
"case inr\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nu : E\na b : ℝ\nha : 0 ≤ a\nhb : 0 ≤ b\nh : SameRay ℝ (b • u) (a • u)\nH : ∀ (a b : ℝ), 0 ≤ a → 0 ≤ b → SameRay ℝ (a • u) (b • u) → b ≤ a → ‖a • u - b • u‖ = |‖a • u‖ - ‖b • u‖|\nhab : ¬b ≤ a\n⊢ ‖b • u - a • u‖ = |‖b • u‖ - ‖a • u‖... | rw [norm_sub_rev, abs_sub_comm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Function.AbsolutelyContinuous | {
"line": 402,
"column": 4
} | {
"line": 402,
"column": 55
} | {
"line": 404,
"column": 0
} | [
{
"pp": "case e'_4\nF : Type u_2\ninst✝ : SeminormedAddCommGroup F\na✝ b✝ : ℝ\nf : ℝ → F\na b : ℝ\nhf :\n ∀ ε > 0,\n ∃ δ > 0,\n ∀ E ∈ disjWithin a b,\n ∑ i ∈ Finset.range E.1, dist (E.2 i).1 (E.2 i).2 < δ →\n ∑ i ∈ Finset.range E.1, dist (f (E.2 i).1) (f (E.2 i).2) < ε\nhab₀ : a ≤ b\nha... | [] | · simp only [Nat.cast_add, Nat.cast_one, δ']; field | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Function.AbsolutelyContinuous | {
"line": 442,
"column": 8
} | {
"line": 444,
"column": 72
} | {
"line": 445,
"column": 8
} | [
{
"pp": "f : ℝ → ℝ\na b c : ℝ\nh : IntervalIntegrable f volume a b\nhc : c ∈ uIcc a b\ns : ℕ × (ℕ → ℝ × ℝ) → Set ℝ := fun E ↦ ⋃ i ∈ Finset.range E.1, uIoc (E.2 i).1 (E.2 i).2\nthis✝¹ :\n Tendsto (fun i ↦ ∫⁻ (x : ℝ) in s i, ‖f x‖ₑ ∂volume.restrict (uIoc a b)) (totalLengthFilter ⊓ 𝓟 (disjWithin a b)) (𝓝 0)\nth... | [
"f : ℝ → ℝ\na b c : ℝ\nh : IntervalIntegrable f volume a b\nhc : c ∈ uIcc a b\ns : ℕ × (ℕ → ℝ × ℝ) → Set ℝ := fun E ↦ ⋃ i ∈ Finset.range E.1, uIoc (E.2 i).1 (E.2 i).2\nthis✝¹ :\n Tendsto (fun i ↦ ∫⁻ (x : ℝ) in s i, ‖f x‖ₑ ∂volume.restrict (uIoc a b)) (totalLengthFilter ⊓ 𝓟 (disjWithin a b)) (𝓝 0)\nthis✝ :\n Ten... | intervalIntegral.integral_interval_sub_left
(by apply IntervalIntegrable.mono_set' h; grind [uIoc, uIcc])
(by apply IntervalIntegrable.mono_set' h; grind [uIoc, uIcc]), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Complex.AbelLimit | {
"line": 166,
"column": 32
} | {
"line": 166,
"column": 49
} | {
"line": 166,
"column": 50
} | [
{
"pp": "case inl\nf : ℕ → ℂ\nl : ℂ\nh : Tendsto (fun n ↦ ∑ i ∈ range n, f i) atTop (𝓝 l)\nM : ℝ\nhM : M ≤ 1\n⊢ Tendsto (fun z ↦ ∑' (n : ℕ), f n * z ^ n) (𝓝[∅] 1) (𝓝 l)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"HMu... | [
"case inl\nf : ℕ → ℂ\nl : ℂ\nh : Tendsto (fun n ↦ ∑ i ∈ range n, f i) atTop (𝓝 l)\nM : ℝ\nhM : M ≤ 1\n⊢ Tendsto (fun z ↦ ∑' (n : ℕ), f n * z ^ n) ⊥ (𝓝 l)"
] | nhdsWithin_empty, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.Convex.SpecificFunctions.Deriv | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 63
} | {
"line": 93,
"column": 2
} | [
{
"pp": "m : ℤ\nn : ℕ\nhn : Even n\nhm : m ∉ Ico 0 ↑n\n⊢ 0 < ∏ k ∈ Finset.range n, (m - ↑k)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Int.instCommMonoid",
"HSub.hSub",
"Int.instConditionallyCompleteLinearOrder",
"Int",
"ConditionallyCompleteLinearOrder.... | [
"m : ℤ\nn : ℕ\nhn : Even n\nhm : m ∉ Ico 0 ↑n\nh : 0 = ∏ k ∈ Finset.range n, (m - ↑k)\n⊢ m ∈ Ico 0 ↑n"
] | refine (int_prod_range_nonneg m n hn).lt_of_ne fun h => hm ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Complex.AbelLimit | {
"line": 200,
"column": 21
} | {
"line": 200,
"column": 64
} | {
"line": 200,
"column": 64
} | [
{
"pp": "f : ℕ → ℂ\nl : ℂ\nh : Tendsto (fun n ↦ ∑ i ∈ range n, f i) atTop (𝓝 l)\nM : ℝ\nhM : 1 < M\ns : ℕ → ℂ := fun n ↦ ∑ i ∈ range n, f i\ng : ℂ → ℂ := fun z ↦ ∑' (n : ℕ), f n * z ^ n\nε : ℝ\nεpos : ε > 0\nB₁ : ℕ\nhB₁ : ∀ n ≥ B₁, ‖∑ i ∈ range n, f i - l‖ < ε / 4 / M\nF : ℝ := ∑ i ∈ range B₁, ‖l - s (i + 1)‖\... | [
"f : ℕ → ℂ\nl : ℂ\nh : Tendsto (fun n ↦ ∑ i ∈ range n, f i) atTop (𝓝 l)\nM : ℝ\nhM : 1 < M\ns : ℕ → ℂ := fun n ↦ ∑ i ∈ range n, f i\ng : ℂ → ℂ := fun z ↦ ∑' (n : ℕ), f n * z ^ n\nε : ℝ\nεpos : ε > 0\nB₁ : ℕ\nhB₁ : ∀ n ≥ B₁, ‖∑ i ∈ range n, f i - l‖ < ε / 4 / M\nF : ℝ := ∑ i ∈ range B₁, ‖l - s (i + 1)‖\nz : ℂ\nzn :... | sum_range_add_sum_Ico _ (le_max_left B₁ B₂) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Convex.Deriv | {
"line": 80,
"column": 56
} | {
"line": 107,
"column": 12
} | {
"line": 109,
"column": 0
} | [
{
"pp": "x y : ℝ\nf : ℝ → ℝ\nhf : ContinuousOn f (Icc x y)\nhxy : x < y\nhf'_mono : StrictMonoOn (deriv f) (Ioo x y)\n⊢ ∃ a ∈ Ioo x y, (f y - f x) / (y - x) < deriv f a",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_forall_eq",
"Mathlib.Tactic.Ring.Com... | [] | by
by_cases! h : ∀ w ∈ Ioo x y, deriv f w ≠ 0
· apply StrictMonoOn.exists_slope_lt_deriv_aux hf hxy hf'_mono h
· rcases h with ⟨w, ⟨hxw, hwy⟩, hw⟩
obtain ⟨a, ⟨hxa, haw⟩, ha⟩ : ∃ a ∈ Ioo x w, (f w - f x) / (w - x) < deriv f a := by
apply StrictMonoOn.exists_slope_lt_deriv_aux _ hxw _ _
· exact hf.m... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv | {
"line": 29,
"column": 45
} | {
"line": 29,
"column": 61
} | {
"line": 29,
"column": 61
} | [
{
"pp": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Real",
"Complex.cos",
"Real.instZero",
"Real.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.ins... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv | {
"line": 29,
"column": 45
} | {
"line": 29,
"column": 61
} | {
"line": 29,
"column": 61
} | [
{
"pp": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Real",
"Complex.cos",
"Real.instZero",
"Real.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.ins... | [] | exact mod_cast h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv | {
"line": 29,
"column": 45
} | {
"line": 29,
"column": 61
} | {
"line": 29,
"column": 61
} | [
{
"pp": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Real",
"Complex.cos",
"Real.instZero",
"Real.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.ins... | [] | exact mod_cast h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv | {
"line": 32,
"column": 39
} | {
"line": 32,
"column": 55
} | {
"line": 32,
"column": 55
} | [
{
"pp": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Real",
"Complex.cos",
"Real.instZero",
"Real.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.ins... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv | {
"line": 32,
"column": 39
} | {
"line": 32,
"column": 55
} | {
"line": 32,
"column": 55
} | [
{
"pp": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Real",
"Complex.cos",
"Real.instZero",
"Real.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.ins... | [] | exact mod_cast h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv | {
"line": 32,
"column": 39
} | {
"line": 32,
"column": 55
} | {
"line": 32,
"column": 55
} | [
{
"pp": "x : ℝ\nh : cos x ≠ 0\n⊢ Complex.cos ↑x ≠ 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Real",
"Complex.cos",
"Real.instZero",
"Real.cos",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Complex.ins... | [] | exact mod_cast h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan | {
"line": 260,
"column": 2
} | {
"line": 261,
"column": 39
} | {
"line": 263,
"column": 0
} | [
{
"pp": "case hx₂\nx : ℝ\nh : 0 < x\n⊢ π / 2 - arctan x < π / 2",
"ppTerm": "?hx₂",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"Real.pi",
"Real.arctan",
"... | [] | · rw [sub_lt_self_iff, ← arctan_zero]
exact tanOrderIso.symm.strictMono h | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Convex.Deriv | {
"line": 513,
"column": 4
} | {
"line": 513,
"column": 51
} | {
"line": 513,
"column": 51
} | [
{
"pp": "case inr\nS : Set ℝ\nf : ℝ → ℝ\nhfc : ConvexOn ℝ S f\nx : ℝ\nhxs : x ∈ interior S\ny : ℝ\nhys : y ∈ interior S\nhxy✝ : x ≤ y\nhxy : x < y\n⊢ sSup (slope f x '' {y | y ∈ S ∧ y < x}) ≤ derivWithin f (Iio y) y",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Norm... | [
"case inr\nS : Set ℝ\nf : ℝ → ℝ\nhfc : ConvexOn ℝ S f\nx : ℝ\nhxs : x ∈ interior S\ny : ℝ\nhys : y ∈ interior S\nhxy✝ : x ≤ y\nhxy : x < y\n⊢ sSup (slope f x '' {y | y ∈ S ∧ y < x}) ≤ sSup (slope f y '' {y_1 | y_1 ∈ S ∧ y_1 < y})"
] | hfc.leftDeriv_eq_sSup_slope_of_mem_interior hys | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 39
} | {
"line": 160,
"column": 2
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ cos (angle x y) * (‖x‖ * ‖y‖) = ⟪x, y⟫",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Real",
"instHDiv",
... | [
"V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\n⊢ ‖x‖ * ‖y‖ = 0 → ⟪x, y⟫ = 0"
] | rw [cos_angle, div_mul_cancel_of_imp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 36
} | {
"line": 179,
"column": 2
} | [
{
"pp": "V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ sin (angle x y) = √(⟪x, x⟫ * ⟪y, y⟫ - ⟪x, y⟫ * ⟪x, y⟫) / (‖x‖ * ‖y‖)",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real",
... | [
"V : Type u_1\ninst✝¹ : NormedAddCommGroup V\ninst✝ : InnerProductSpace ℝ V\nx y : V\nhx : x ≠ 0\nhy : y ≠ 0\n⊢ sin (angle x y) = sin (angle x y) * (‖x‖ * ‖y‖) / (‖x‖ * ‖y‖)"
] | rw [← sin_angle_mul_norm_mul_norm] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Complex.BorelCaratheodory | {
"line": 74,
"column": 4
} | {
"line": 74,
"column": 9
} | {
"line": 75,
"column": 2
} | [
{
"pp": "f : ℂ → ℂ\nM R : ℝ\nz : ℂ\nhM : 0 < M\nhf : DifferentiableOn ℂ f (ball 0 R)\nhf₁ : Set.MapsTo f (ball 0 R) {z | z.re ≤ M}\nhz : z ∈ ball 0 R\nhf₂ : f 0 = 0\nx : ℂ\nhx : x ∈ ball 0 R\nh : 2 * ↑M - f x = 0\nthis : 2 * ↑M ∈ {z | z.re ≤ M}\n⊢ False",
"ppTerm": "?m.138",
"assigned": true,
"usedC... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.BorelCaratheodory | {
"line": 119,
"column": 2
} | {
"line": 121,
"column": 86
} | {
"line": 123,
"column": 0
} | [
{
"pp": "f : ℂ → ℂ\nM R : ℝ\nz : ℂ\nhM : 0 < M\nhf : DifferentiableOn ℂ f (ball 0 R)\nhf₁ : Set.MapsTo f (ball 0 R) {z | z.re ≤ M}\nhR : 0 < R\nhz : z ∈ ball 0 R\nhfz : ‖f z - f 0‖ ≤ 2 * (M + ‖f 0‖) * ‖z‖ / (R - ‖z‖)\nh_denom_ne : R - ‖z‖ ≠ 0\n⊢ ‖f z‖ ≤ 2 * M * ‖z‖ / (R - ‖z‖) + ‖f 0‖ * (R + ‖z‖) / (R - ‖z‖)",
... | [] | calc ‖f z‖ ≤ ‖f z - f 0‖ + ‖f 0‖ := norm_le_norm_sub_add _ _
_ ≤ 2 * (M + ‖f 0‖) * ‖z‖ / (R - ‖z‖) + ‖f 0‖ := by gcongr
_ = 2 * M * ‖z‖ / (R - ‖z‖) + ‖f 0‖ * (R + ‖z‖) / (R - ‖z‖) := by field_simp; ring | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 68,
"column": 47
} | {
"line": 68,
"column": 52
} | {
"line": 68,
"column": 52
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nx' : 𝕜\nh : x' ∈ {0}ᶜ\n⊢ n ≠ 0",
"ppTerm": "?m.221",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"AddGroupWi... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 68,
"column": 47
} | {
"line": 68,
"column": 52
} | {
"line": 68,
"column": 52
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nx' : 𝕜\nh : x' ∈ {0}ᶜ\n⊢ n ≠ 0",
"ppTerm": "?m.221",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"AddGroupWi... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 68,
"column": 47
} | {
"line": 68,
"column": 52
} | {
"line": 68,
"column": 52
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nx' : 𝕜\nh : x' ∈ {0}ᶜ\n⊢ n ≠ 0",
"ppTerm": "?m.221",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"AddGroupWi... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 76,
"column": 27
} | {
"line": 76,
"column": 32
} | {
"line": 76,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nx✝ : 𝕜\n⊢ n ≠ 0",
"ppTerm": "?m.313",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMono... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 76,
"column": 27
} | {
"line": 76,
"column": 32
} | {
"line": 76,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nx✝ : 𝕜\n⊢ n ≠ 0",
"ppTerm": "?m.313",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMono... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 76,
"column": 27
} | {
"line": 76,
"column": 32
} | {
"line": 76,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nx✝ : 𝕜\n⊢ n ≠ 0",
"ppTerm": "?m.313",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"False.elim",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMono... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 82,
"column": 40
} | {
"line": 82,
"column": 45
} | {
"line": 83,
"column": 2
} | [
{
"pp": "case e'_5\n𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\nx✝ : { x // x ≠ 0 }\n⊢ ↑x✝ ^ ↑n = ↑x✝ ^ n",
"ppTerm": "?e'_5",
"assigned": true,
"usedConstants": [
"zpow_natCast",
"congrArg",
"DivInvMonoid.toZPow",
"NormedF... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 82,
"column": 40
} | {
"line": 82,
"column": 45
} | {
"line": 83,
"column": 2
} | [
{
"pp": "case inl.convert_3\n𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\n⊢ ProperSpace 𝕜",
"ppTerm": "?inl.convert_3",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"inst✝"
],
"usedGoals": []
}
] | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 82,
"column": 40
} | {
"line": 82,
"column": 45
} | {
"line": 83,
"column": 2
} | [
{
"pp": "case inl.convert_4\n𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\n⊢ ↑n ≠ 0",
"ppTerm": "?inl.convert_4",
"assigned": true,
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"False",
"eq_false",
"congrArg",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 89,
"column": 59
} | {
"line": 89,
"column": 64
} | {
"line": 89,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nx : 𝕜\n⊢ n ≠ 0",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"False",
"AddGroupWithOne.toAddGroup",
"congrAr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 89,
"column": 59
} | {
"line": 89,
"column": 64
} | {
"line": 89,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nx : 𝕜\n⊢ n ≠ 0",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"False",
"AddGroupWithOne.toAddGroup",
"congrAr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 89,
"column": 59
} | {
"line": 89,
"column": 64
} | {
"line": 89,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nx : 𝕜\n⊢ n ≠ 0",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"False",
"AddGroupWithOne.toAddGroup",
"congrAr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 101,
"column": 2
} | {
"line": 101,
"column": 28
} | {
"line": 102,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\n⊢ IsQuotientCoveringMap (fun x ↦ x ^ n) ↥(powMonoidHom n).ker",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedComm... | [
"𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\n⊢ IsQuotientCoveringMap (fun x ↦ x ^ n) ↥(rootsOfUnity n 𝕜)"
] | rw [← rootsOfUnity_eq_ker] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 102,
"column": 25
} | {
"line": 102,
"column": 30
} | {
"line": 102,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\n⊢ n ≠ 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"congrArg",
"False.elim",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 102,
"column": 25
} | {
"line": 102,
"column": 30
} | {
"line": 102,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\n⊢ n ≠ 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"congrArg",
"False.elim",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 102,
"column": 25
} | {
"line": 102,
"column": 30
} | {
"line": 102,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\n⊢ n ≠ 0",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"congrArg",
"False.elim",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 92
} | {
"line": 108,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\nthis✝ : NeZero n\nthis : IsQuotientMap ({0}ᶜ.restrictPreimage fun x ↦ x ^ n)\ne : 𝕜ˣ ≃ₜ { g // g ≠ 0 } := unitsHomeomorphNeZero\n⊢ IsQuotientMap fun x ↦ x ^ n",
... | [
"𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ n\nthis✝ : NeZero n\nthis : IsQuotientMap ({0}ᶜ.restrictPreimage fun x ↦ x ^ n)\ne : 𝕜ˣ ≃ₜ { g // g ≠ 0 } := unitsHomeomorphNeZero\nx✝ : 𝕜ˣ\n⊢ x✝ ^ n = ((⇑e.symm ∘ {0}ᶜ.restrictP... | convert! (e.symm.isQuotientMap.comp this).comp (e.trans (.ofEqSubtypes _)).isQuotientMap | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 122,
"column": 43
} | {
"line": 122,
"column": 48
} | {
"line": 122,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ ↑n\n⊢ ↑n ≠ 0",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"False",
"eq_false",
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 122,
"column": 43
} | {
"line": 122,
"column": 48
} | {
"line": 122,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ ↑n\n⊢ ↑n ≠ 0",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"False",
"eq_false",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 122,
"column": 43
} | {
"line": 122,
"column": 48
} | {
"line": 122,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ ↑n\n⊢ ↑n ≠ 0",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Int.cast",
"Int.cast_natCast",
"False",
"eq_false",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 124,
"column": 44
} | {
"line": 124,
"column": 49
} | {
"line": 124,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑(-↑n) ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ (-↑n)\n⊢ ↑n ≠ 0",
"ppTerm": "?m.110",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 124,
"column": 44
} | {
"line": 124,
"column": 49
} | {
"line": 124,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑(-↑n) ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ (-↑n)\n⊢ ↑n ≠ 0",
"ppTerm": "?m.110",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CoveringMap | {
"line": 124,
"column": 44
} | {
"line": 124,
"column": 49
} | {
"line": 124,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑(-↑n) ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ (-↑n)\n⊢ ↑n ≠ 0",
"ppTerm": "?m.110",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast_neg",
"Int.cast",... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 23
} | {
"line": 94,
"column": 23
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : LocallyPathConnectedSpace X\nU : Set X\nhUc : IsSimplyConnected U\nhUo : IsOpen U\ng : X → 𝔻\nhgc : ContinuousOn g U\nhU₀ : 0 ∉ g '' U\nn : ℕ+\n⊢ 0 ∉ UnitDisc.coe ∘ g '' U",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq... | [] | simpa using hU₀ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 23
} | {
"line": 94,
"column": 23
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : LocallyPathConnectedSpace X\nU : Set X\nhUc : IsSimplyConnected U\nhUo : IsOpen U\ng : X → 𝔻\nhgc : ContinuousOn g U\nhU₀ : 0 ∉ g '' U\nn : ℕ+\n⊢ 0 ∉ UnitDisc.coe ∘ g '' U",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq... | [] | simpa using hU₀ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 23
} | {
"line": 94,
"column": 23
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : LocallyPathConnectedSpace X\nU : Set X\nhUc : IsSimplyConnected U\nhUo : IsOpen U\ng : X → 𝔻\nhgc : ContinuousOn g U\nhU₀ : 0 ∉ g '' U\nn : ℕ+\n⊢ 0 ∉ UnitDisc.coe ∘ g '' U",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq... | [] | simpa using hU₀ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.UnitDisc.Basic | {
"line": 182,
"column": 30
} | {
"line": 182,
"column": 76
} | {
"line": 182,
"column": 76
} | [
{
"pp": "z : 𝔻\nn : ℕ+\n⊢ ↑z ^ ↑n ∈ Subsemigroup.unitBall ℂ",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"PNat.val",
"PNat.ne_zero._simp_1",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Semin... | [] | simp [pow_lt_one_iff_of_nonneg, z.norm_lt_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Complex.UnitDisc.Basic | {
"line": 182,
"column": 30
} | {
"line": 182,
"column": 76
} | {
"line": 182,
"column": 76
} | [
{
"pp": "z : 𝔻\nn : ℕ+\n⊢ ↑z ^ ↑n ∈ Subsemigroup.unitBall ℂ",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"PNat.val",
"PNat.ne_zero._simp_1",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Semin... | [] | simp [pow_lt_one_iff_of_nonneg, z.norm_lt_one] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.UnitDisc.Basic | {
"line": 182,
"column": 30
} | {
"line": 182,
"column": 76
} | {
"line": 182,
"column": 76
} | [
{
"pp": "z : 𝔻\nn : ℕ+\n⊢ ↑z ^ ↑n ∈ Subsemigroup.unitBall ℂ",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"PNat.val",
"PNat.ne_zero._simp_1",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"Semin... | [] | simp [pow_lt_one_iff_of_nonneg, z.norm_lt_one] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 342,
"column": 55
} | {
"line": 342,
"column": 60
} | {
"line": 342,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nU : Set 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\na : ι\ns : Finset ι\nha : a ∉ s\nhs :\n (∀ i ∈ s, MeromorphicOn (f i) U) →\n (∀ i ∈ s, ∀ z ∈ U, meromorphicOrderAt (f i) z ≠ ⊤) → divisor (∏ i ∈ s, f i) U = ∑ i ∈ s, divisor (f i) U\nh₁f : ∀ i ∈ insert a s... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 342,
"column": 55
} | {
"line": 342,
"column": 60
} | {
"line": 342,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nU : Set 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\na : ι\ns : Finset ι\nha : a ∉ s\nhs :\n (∀ i ∈ s, MeromorphicOn (f i) U) →\n (∀ i ∈ s, ∀ z ∈ U, meromorphicOrderAt (f i) z ≠ ⊤) → divisor (∏ i ∈ s, f i) U = ∑ i ∈ s, divisor (f i) U\nh₁f : ∀ i ∈ insert a s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 342,
"column": 55
} | {
"line": 342,
"column": 60
} | {
"line": 342,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nU : Set 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\na : ι\ns : Finset ι\nha : a ∉ s\nhs :\n (∀ i ∈ s, MeromorphicOn (f i) U) →\n (∀ i ∈ s, ∀ z ∈ U, meromorphicOrderAt (f i) z ≠ ⊤) → divisor (∏ i ∈ s, f i) U = ∑ i ∈ s, divisor (f i) U\nh₁f : ∀ i ∈ insert a s... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 74,
"column": 4
} | {
"line": 74,
"column": 93
} | {
"line": 75,
"column": 4
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nx : 𝕜\nh₁g : AnalyticAt 𝕜 g x\nh₁f : MeromorphicAt f x\nh₃ : meromorphicOrderAt f x = ⊤\nh : f =ᶠ[𝓝[≠] x] fun z ↦ g z\n⊢ 0 =ᶠ[𝓝 x] g",
"ppTerm": "?p... | [
"case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nx : 𝕜\nh₁g : AnalyticAt 𝕜 g x\nh₁f : MeromorphicAt f x\nh₃ : meromorphicOrderAt f x = ⊤\nh : f =ᶠ[𝓝[≠] x] fun z ↦ g z\n⊢ 0 =ᶠ[𝓝[≠] x] g"
] | rw [← ContinuousAt.eventuallyEq_nhds_iff_eventuallyEq_nhdsNE (by fun_prop) (by fun_prop)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 129,
"column": 8
} | {
"line": 129,
"column": 17
} | {
"line": 129,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nh : MeromorphicAt f x\nh₂ : ¬meromorphicOrderAt f x = ⊤\ng : 𝕜 → E\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₃g : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ (meromorphicO... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nh : MeromorphicAt f x\nh₂ : ¬meromorphicOrderAt f x = ⊤\ng : 𝕜 → E\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₃g : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ (meromorphicOrderAt f x).... | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 279,
"column": 59
} | {
"line": 279,
"column": 64
} | {
"line": 279,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nh₄f : {σ ∈ s | f σ x = 0} = ∅\nσ : ι\nhσ ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 279,
"column": 59
} | {
"line": 279,
"column": 64
} | {
"line": 279,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nh₄f : {σ ∈ s | f σ x = 0} = ∅\nσ : ι\nhσ ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 279,
"column": 59
} | {
"line": 279,
"column": 64
} | {
"line": 279,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nh₄f : {σ ∈ s | f σ x = 0} = ∅\nσ : ι\nhσ ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 285,
"column": 28
} | {
"line": 285,
"column": 33
} | {
"line": 285,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nτ : ι\nh₁τ : τ ∈ s\nh₂τ : f τ x = 0\nμ : ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 285,
"column": 28
} | {
"line": 285,
"column": 33
} | {
"line": 285,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nτ : ι\nh₁τ : τ ∈ s\nh₂τ : f τ x = 0\nμ : ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 285,
"column": 28
} | {
"line": 285,
"column": 33
} | {
"line": 285,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nτ : ι\nh₁τ : τ ∈ s\nh₂τ : f τ x = 0\nμ : ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 285,
"column": 39
} | {
"line": 285,
"column": 44
} | {
"line": 285,
"column": 44
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nτ : ι\nh₁τ : τ ∈ s\nh₂τ : f τ x = 0\nμ : ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 285,
"column": 39
} | {
"line": 285,
"column": 44
} | {
"line": 285,
"column": 44
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nτ : ι\nh₁τ : τ ∈ s\nh₂τ : f τ x = 0\nμ : ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 285,
"column": 39
} | {
"line": 285,
"column": 44
} | {
"line": 285,
"column": 44
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\ns : Finset ι\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ i ∈ s, MeromorphicNFAt (f i) x\nh₂f : {σ | σ ∈ s ∧ f σ x = 0}.Subsingleton\nh₃f : ∀ {τ : ι}, τ ∈ s → τ ∉ {σ ∈ s | f σ x = 0} → AnalyticAt 𝕜 (f τ) x\nτ : ι\nh₁τ : τ ∈ s\nh₂τ : f τ x = 0\nμ : ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 205,
"column": 4
} | {
"line": 205,
"column": 9
} | {
"line": 206,
"column": 2
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\nh₁ : ¬MeromorphicAt f x\n⊢ meromorphicTrailingCoeffAt (-f) x = -meromorphicTrailingCoeffAt f x",
"ppTerm": "?pos✝",
"assigned": true,
"use... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.