module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
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 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 286,
"column": 4
} | {
"line": 286,
"column": 9
} | {
"line": 287,
"column": 2
} | [
{
"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": 289,
"column": 84
} | {
"line": 289,
"column": 89
} | {
"line": 289,
"column": 89
} | [
{
"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\nthis... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 289,
"column": 84
} | {
"line": 289,
"column": 89
} | {
"line": 289,
"column": 89
} | [
{
"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\nthis... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 289,
"column": 84
} | {
"line": 289,
"column": 89
} | {
"line": 289,
"column": 89
} | [
{
"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\nthis... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 291,
"column": 4
} | {
"line": 291,
"column": 9
} | {
"line": 293,
"column": 0
} | [
{
"pp": "case neg.h₂g\n𝕜 : 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... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 313,
"column": 35
} | {
"line": 313,
"column": 40
} | {
"line": 313,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\nh₃f : Function.HasFiniteMulSupport f\n⊢ ∀ i ∈ Set.Finite.toFinset h₃f, MeromorphicNFAt (f i) x",
"ppTerm": "?m.44",
"assigned":... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 313,
"column": 35
} | {
"line": 313,
"column": 40
} | {
"line": 313,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\nh₃f : Function.HasFiniteMulSupport f\n⊢ ∀ i ∈ Set.Finite.toFinset h₃f, MeromorphicNFAt (f i) x",
"ppTerm": "?m.44",
"assigned":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 313,
"column": 35
} | {
"line": 313,
"column": 40
} | {
"line": 313,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\nh₃f : Function.HasFiniteMulSupport f\n⊢ ∀ i ∈ Set.Finite.toFinset h₃f, MeromorphicNFAt (f i) x",
"ppTerm": "?m.44",
"assigned":... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 313,
"column": 60
} | {
"line": 313,
"column": 65
} | {
"line": 313,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\nh₃f : Function.HasFiniteMulSupport f\nx✝³ : ι\nx✝² : x✝³ ∈ {σ | σ ∈ Set.Finite.toFinset h₃f ∧ f σ x = 0}\nx✝¹ : ι\nx✝ : x✝¹ ∈ {σ | σ ∈ ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 313,
"column": 60
} | {
"line": 313,
"column": 65
} | {
"line": 313,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\nh₃f : Function.HasFiniteMulSupport f\nx✝³ : ι\nx✝² : x✝³ ∈ {σ | σ ∈ Set.Finite.toFinset h₃f ∧ f σ x = 0}\nx✝¹ : ι\nx✝ : x✝¹ ∈ {σ | σ ∈ ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 313,
"column": 60
} | {
"line": 313,
"column": 65
} | {
"line": 313,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\nh₃f : Function.HasFiniteMulSupport f\nx✝³ : ι\nx✝² : x✝³ ∈ {σ | σ ∈ Set.Finite.toFinset h₃f ∧ f σ x = 0}\nx✝¹ : ι\nx✝ : x✝¹ ∈ {σ | σ ∈ ... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 311,
"column": 2
} | {
"line": 314,
"column": 83
} | {
"line": 316,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\n⊢ MeromorphicNFAt (∏ᶠ (i : ι), f i) x",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulO... | [] | by_cases h₃f : Function.HasFiniteMulSupport f
· simp_rw [finprod_eq_prod f h₃f]
exact meromorphicNFAt_prod (by aesop) (fun _ _ _ _ ↦ by aesop)
· exact finprod_of_not_hasFiniteMulSupport h₃f ▸ analyticAt_const.meromorphicNFAt | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 311,
"column": 2
} | {
"line": 314,
"column": 83
} | {
"line": 316,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nh₁f : ∀ (i : ι), MeromorphicNFAt (f i) x\nh₂f : {σ | f σ x = 0}.Subsingleton\n⊢ MeromorphicNFAt (∏ᶠ (i : ι), f i) x",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulO... | [] | by_cases h₃f : Function.HasFiniteMulSupport f
· simp_rw [finprod_eq_prod f h₃f]
exact meromorphicNFAt_prod (by aesop) (fun _ _ _ _ ↦ by aesop)
· exact finprod_of_not_hasFiniteMulSupport h₃f ▸ analyticAt_const.meromorphicNFAt | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 244,
"column": 46
} | {
"line": 244,
"column": 51
} | {
"line": 244,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf₁ f₂ : 𝕜 → E\nhf₂ : MeromorphicAt f₂ x\nhf₁ : MeromorphicAt f₁ x\nn₂ : ℤ\nhn₂ : ↑n₂ = meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₁ x < ↑n₂\ng₂ : 𝕜 → E\nh₁g₂ : Anal... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 244,
"column": 46
} | {
"line": 244,
"column": 51
} | {
"line": 244,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf₁ f₂ : 𝕜 → E\nhf₂ : MeromorphicAt f₂ x\nhf₁ : MeromorphicAt f₁ x\nn₂ : ℤ\nhn₂ : ↑n₂ = meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₁ x < ↑n₂\ng₂ : 𝕜 → E\nh₁g₂ : Anal... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 244,
"column": 46
} | {
"line": 244,
"column": 51
} | {
"line": 244,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf₁ f₂ : 𝕜 → E\nhf₂ : MeromorphicAt f₂ x\nhf₁ : MeromorphicAt f₁ x\nn₂ : ℤ\nhn₂ : ↑n₂ = meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₁ x < ↑n₂\ng₂ : 𝕜 → E\nh₁g₂ : Anal... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 464,
"column": 6
} | {
"line": 464,
"column": 24
} | {
"line": 465,
"column": 6
} | [
{
"pp": "case right\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : MeromorphicAt f x\nn : ℤ\nhn : ↑n = meromorphicOrderAt f x\ng : 𝕜 → E\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₃g : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f... | [
"case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : MeromorphicAt f x\nn : ℤ\nhn : ↑n = meromorphicOrderAt f x\ng : 𝕜 → E\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₃g : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z = (z - x) ^... | split_ifs with h₃f | Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1 | Mathlib.Tactic.splitIfs |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 420,
"column": 2
} | {
"line": 420,
"column": 26
} | {
"line": 421,
"column": 4
} | [
{
"pp": "case insert\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nι : Type u_3\nf : ι → 𝕜 → 𝕜\nx : 𝕜\nσ : ι\ns₁ : Finset ι\nhσ : σ ∉ s₁\nhind :\n (∀ σ ∈ s₁, MeromorphicAt (f σ) x) →\n meromorphicTrailingCoeffAt (∏ n ∈ s₁, f n) x = ∏ n ∈ s₁, meromorphicTrailingCoeffAt (f n) x\nh : ∀ σ_1 ∈ insert σ ... | [] | | insert σ s₁ hσ hind => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 70,
"column": 6
} | {
"line": 70,
"column": 61
} | {
"line": 71,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nh : HasFiniteSupport d\nx : 𝕜\n⊢ (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ d u) x = ∏ᶠ (u : 𝕜), (x - u) ^ d u",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AddGroupWithOne.toAddGroup",
"congrArg"... | [
"𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nh : HasFiniteSupport d\nx : 𝕜\n⊢ (∏ i ∈ Finite.toFinset h, (fun x ↦ x - i) ^ d i) x = ∏ᶠ (u : 𝕜), (x - u) ^ d u",
"case h\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nh : HasFiniteSupport d\nx : 𝕜\n⊢ (Function.mulSupport fun u ↦... | finprod_eq_prod_of_mulSupport_subset (s := h.toFinset), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 521,
"column": 4
} | {
"line": 521,
"column": 77
} | {
"line": 523,
"column": 0
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : MeromorphicNFAt f x\nz : 𝕜\nhz : ¬z = x\n⊢ toMeromorphicNFAt f x z = f z",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
... | [] | · exact (hf.meromorphicAt.eqOn_compl_singleton_toMeromorphicNFAt hz).symm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Meromorphic.Order | {
"line": 385,
"column": 49
} | {
"line": 385,
"column": 54
} | {
"line": 385,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nn : ℤ\n⊢ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, ((fun x_1 ↦ x_1 - x) ^ n) z = (z - x) ^ n • (fun z ↦ 1) z",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"AddGroupWith... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.Order | {
"line": 385,
"column": 49
} | {
"line": 385,
"column": 54
} | {
"line": 385,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nn : ℤ\n⊢ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, ((fun x_1 ↦ x_1 - x) ^ n) z = (z - x) ^ n • (fun z ↦ 1) z",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"AddGroupWith... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Order | {
"line": 385,
"column": 49
} | {
"line": 385,
"column": 54
} | {
"line": 385,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nn : ℤ\n⊢ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, ((fun x_1 ↦ x_1 - x) ^ n) z = (z - x) ^ n • (fun z ↦ 1) z",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"AddGroupWith... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 408,
"column": 4
} | {
"line": 408,
"column": 9
} | {
"line": 409,
"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⊢ meromorphicOrderAt f x = meromorphicOrderAt (-f) x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.Order | {
"line": 408,
"column": 4
} | {
"line": 408,
"column": 9
} | {
"line": 409,
"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⊢ meromorphicOrderAt f x = meromorphicOrderAt (-f) x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Order | {
"line": 408,
"column": 4
} | {
"line": 408,
"column": 9
} | {
"line": 409,
"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⊢ meromorphicOrderAt f x = meromorphicOrderAt (-f) x",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 179,
"column": 2
} | {
"line": 180,
"column": 80
} | {
"line": 182,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nU : Set 𝕜\nD : locallyFinsuppWithin U ℤ\nhD : D.support.Finite\nz : 𝕜\n⊢ (MeromorphicOn.divisor (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) U) z = D z",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"NormedCommRing.toSeminormedCo... | [] | by_cases hz : z ∈ U
<;> simp [(meromorphicNFOn D U).meromorphicOn, hz, meromorphicOrderAt_eq D hD] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Analysis.Meromorphic.Order | {
"line": 442,
"column": 6
} | {
"line": 442,
"column": 70
} | {
"line": 443,
"column": 6
} | [
{
"pp": "case right\n𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁶ : NormedRing R\ninst✝⁵ : NoZeroDivisors R\ninst✝⁴ : Module R E\ninst✝³ : IsBoundedSMul R E\ninst✝² : Module.IsTorsionFree R E\nx : 𝕜\ninst✝¹ : No... | [
"𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁶ : NormedRing R\ninst✝⁵ : NoZeroDivisors R\ninst✝⁴ : Module R E\ninst✝³ : IsBoundedSMul R E\ninst✝² : Module.IsTorsionFree R E\nx : 𝕜\ninst✝¹ : NormedAlgebra 𝕜 R\ninst✝ ... | filter_upwards [self_mem_nhdsWithin, h₃F, h₃G] with a ha hfa hga | Mathlib.Tactic._aux_Mathlib_Order_Filter_Defs___elabRules_Mathlib_Tactic_filterUpwards_1 | Mathlib.Tactic.filterUpwards |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 231,
"column": 51
} | {
"line": 231,
"column": 72
} | {
"line": 231,
"column": 72
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh₁ : HasFiniteSupport d\nh₂ : x ∉ support d\nthis : (Function.mulSupport fun u ↦ (x - u) ^ d u) ⊆ ↑(Finite.toFinset h₁)\n⊢ ∏ i ∈ Finite.toFinset h₁, (x - i) ^ update d x 0 i = ∏ i ∈ Finite.toFinset h₁, (x - i) ^ d i",
"ppTerm": ... | [
"𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh₁ : HasFiniteSupport d\nh₂ : x ∉ support d\nthis : (Function.mulSupport fun u ↦ (x - u) ^ d u) ⊆ ↑(Finite.toFinset h₁)\n⊢ (Finite.toFinset h₁).prod ?m.107 = ∏ i ∈ Finite.toFinset h₁, (x - i) ^ d i",
"𝕜 : Type u_1\ninst✝ : NontriviallyNormed... | Finset.prod_congr rfl | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 494,
"column": 2
} | {
"line": 498,
"column": 31
} | {
"line": 499,
"column": 2
} | [
{
"pp": "case zero\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nf : 𝕜 → 𝕜'\nx : 𝕜\nhf : MeromorphicAt f x\n⊢ meromorphicOrderAt (f ^ 0) x = ↑0 * meromorphicOrderAt f x",
"ppTerm": "?zero",
"assigned": true,
... | [
"case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nf : 𝕜 → 𝕜'\nx : 𝕜\nhf : MeromorphicAt f x\nn✝ : ℕ\na✝ : meromorphicOrderAt (f ^ n✝) x = ↑n✝ * meromorphicOrderAt f x\n⊢ meromorphicOrderAt (f ^ (n✝ + 1)) x = ↑(n✝ + ... | case zero =>
simp only [pow_zero, CharP.cast_eq_zero, zero_mul]
rw [← WithTop.coe_zero, meromorphicOrderAt_eq_int_iff]
· exact ⟨1, analyticAt_const, by simp⟩
· apply MeromorphicAt.const | Lean.Elab.Tactic.evalCase | Lean.Parser.Tactic.case |
Mathlib.Analysis.Meromorphic.Order | {
"line": 503,
"column": 6
} | {
"line": 503,
"column": 11
} | {
"line": 504,
"column": 4
} | [
{
"pp": "case top\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nf : 𝕜 → 𝕜'\nx : 𝕜\nhf : MeromorphicAt f x\nn : ℕ\nhn : meromorphicOrderAt (f ^ n) x = ↑n * meromorphicOrderAt f x\n⊢ ↑n * ⊤ + ⊤ = (↑n + 1) * ⊤",
"ppTe... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.Order | {
"line": 503,
"column": 6
} | {
"line": 503,
"column": 11
} | {
"line": 504,
"column": 4
} | [
{
"pp": "case top\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nf : 𝕜 → 𝕜'\nx : 𝕜\nhf : MeromorphicAt f x\nn : ℕ\nhn : meromorphicOrderAt (f ^ n) x = ↑n * meromorphicOrderAt f x\n⊢ ↑n * ⊤ + ⊤ = (↑n + 1) * ⊤",
"ppTe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Order | {
"line": 503,
"column": 6
} | {
"line": 503,
"column": 11
} | {
"line": 504,
"column": 4
} | [
{
"pp": "case top\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nf : 𝕜 → 𝕜'\nx : 𝕜\nhf : MeromorphicAt f x\nn : ℕ\nhn : meromorphicOrderAt (f ^ n) x = ↑n * meromorphicOrderAt f x\n⊢ ↑n * ⊤ + ⊤ = (↑n + 1) * ⊤",
"ppTe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 303,
"column": 4
} | {
"line": 305,
"column": 62
} | {
"line": 306,
"column": 4
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nh₁f : MeromorphicOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nh₃f : (divisor f U).support.Finite\nφ : 𝕜 → 𝕜 := ∏ᶠ (u : 𝕜), (fun ... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nh₁f : MeromorphicOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nh₃f : (divisor f U).support.Finite\nφ : 𝕜 → 𝕜 := ∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ (divisor f U) ... | rw [← hg.divisor_nonneg_iff_analyticOnNhd, divisor_of_toMeromorphicNFOn (hφ.inv.smul h₁f),
divisor_smul hφ.inv h₁f _ (fun z hz ↦ h₂f ⟨z, hz⟩), divisor_inv,
Function.FactorizedRational.divisor h₃f, neg_add_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 254,
"column": 84
} | {
"line": 254,
"column": 89
} | {
"line": 254,
"column": 89
} | [
{
"pp": "case left\nR : ℝ\nF : locallyFinsuppWithin (ball 0 R) ℤ\nz : ℂ\nhz : z ∈ ball 0 R\na : ℂ\nha : a ∈ {σ | (canonicalFactor R σ ^ F σ) z = 0}\nb : ℂ\nhb : b ∈ {σ | (canonicalFactor R σ ^ F σ) z = 0}\nthis : a ∉ ball 0 R\n⊢ False",
"ppTerm": "?left",
"assigned": true,
"usedConstants": [
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 254,
"column": 84
} | {
"line": 254,
"column": 89
} | {
"line": 254,
"column": 89
} | [
{
"pp": "case right\nR : ℝ\nF : locallyFinsuppWithin (ball 0 R) ℤ\nz : ℂ\nhz : z ∈ ball 0 R\na : ℂ\nha : a ∈ {σ | (canonicalFactor R σ ^ F σ) z = 0}\nb : ℂ\nhb : b ∈ {σ | (canonicalFactor R σ ^ F σ) z = 0}\nthis : b ∉ ball 0 R\n⊢ False",
"ppTerm": "?right",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 267,
"column": 4
} | {
"line": 267,
"column": 9
} | {
"line": 268,
"column": 2
} | [
{
"pp": "case pos\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz : z ∉ U\n⊢ (∑ x ∈ h.toFinset, F x • locallyFinsuppWithin.restrict (single x 1) ⋯) z = F z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstant... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 267,
"column": 4
} | {
"line": 267,
"column": 9
} | {
"line": 268,
"column": 2
} | [
{
"pp": "case pos\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz : z ∉ U\n⊢ (∑ x ∈ h.toFinset, F x • locallyFinsuppWithin.restrict (single x 1) ⋯) z = F z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstant... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 267,
"column": 4
} | {
"line": 267,
"column": 9
} | {
"line": 268,
"column": 2
} | [
{
"pp": "case pos\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz : z ∉ U\n⊢ (∑ x ∈ h.toFinset, F x • locallyFinsuppWithin.restrict (single x 1) ⋯) z = F z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstant... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 271,
"column": 39
} | {
"line": 271,
"column": 44
} | {
"line": 271,
"column": 45
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ z ∈ h.toFinset",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"False",
"Function.locallyFinsuppW... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 271,
"column": 39
} | {
"line": 271,
"column": 44
} | {
"line": 271,
"column": 45
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ z ∈ h.toFinset",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"False",
"Function.locallyFinsuppW... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 271,
"column": 39
} | {
"line": 271,
"column": 44
} | {
"line": 271,
"column": 45
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ z ∈ h.toFinset",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"False",
"Function.locallyFinsuppW... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 271,
"column": 87
} | {
"line": 271,
"column": 92
} | {
"line": 271,
"column": 92
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ ∀ x ∈ h.toFinset.erase z, (F x * if z ∈ U then (single x 1) z else 0) = 0",
"ppTerm": "?m.99",
"assigned": true,
"usedC... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 271,
"column": 87
} | {
"line": 271,
"column": 92
} | {
"line": 271,
"column": 92
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ ∀ x ∈ h.toFinset.erase z, (F x * if z ∈ U then (single x 1) z else 0) = 0",
"ppTerm": "?m.99",
"assigned": true,
"usedC... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 271,
"column": 87
} | {
"line": 271,
"column": 92
} | {
"line": 271,
"column": 92
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ ∀ x ∈ h.toFinset.erase z, (F x * if z ∈ U then (single x 1) z else 0) = 0",
"ppTerm": "?m.99",
"assigned": true,
"usedC... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 272,
"column": 4
} | {
"line": 272,
"column": 9
} | {
"line": 273,
"column": 2
} | [
{
"pp": "case pos\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∈ F.support\n⊢ (F z * if z ∈ U then (single z 1) z else 0) + 0 = F z",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants":... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 9
} | {
"line": 277,
"column": 0
} | [
{
"pp": "case neg\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∉ F.support\n⊢ (∑ x ∈ h.toFinset, F x * if z ∈ U then (single x 1) z else 0) = F z",
"ppTerm": "?neg✝",
"assigned": true,
"u... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 9
} | {
"line": 277,
"column": 0
} | [
{
"pp": "case neg\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∉ F.support\n⊢ (∑ x ∈ h.toFinset, F x * if z ∈ U then (single x 1) z else 0) = F z",
"ppTerm": "?neg✝",
"assigned": true,
"u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 273,
"column": 4
} | {
"line": 273,
"column": 9
} | {
"line": 277,
"column": 0
} | [
{
"pp": "case neg\nX : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nU : Set X\nF : locallyFinsuppWithin U ℤ\nh : F.support.Finite\nz : X\nhz✝ : ¬z ∉ U\nhz : z ∉ F.support\n⊢ (∑ x ∈ h.toFinset, F x * if z ∈ U then (single x 1) z else 0) = F z",
"ppTerm": "?neg✝",
"assigned": true,
"u... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 281,
"column": 59
} | {
"line": 281,
"column": 64
} | {
"line": 281,
"column": 64
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nη₀ : (-divisor f (ball 0 R)).support.Finite\n⊢ (mulSupport fun u ↦ canonicalFactor R u ^ (divisor f (ball 0 R)) u) ⊆ (-divisor f (ball 0 R)).support",
"ppTerm": "?m.77",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 281,
"column": 59
} | {
"line": 281,
"column": 64
} | {
"line": 281,
"column": 64
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nη₀ : (-divisor f (ball 0 R)).support.Finite\n⊢ (mulSupport fun u ↦ canonicalFactor R u ^ (divisor f (ball 0 R)) u) ⊆ (-divisor f (ball 0 R)).support",
"ppTerm": "?m.77",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 281,
"column": 59
} | {
"line": 281,
"column": 64
} | {
"line": 281,
"column": 64
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nη₀ : (-divisor f (ball 0 R)).support.Finite\n⊢ (mulSupport fun u ↦ canonicalFactor R u ^ (divisor f (ball 0 R)) u) ⊆ (-divisor f (ball 0 R)).support",
"ppTerm": "?m.77",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 327,
"column": 8
} | {
"line": 327,
"column": 13
} | {
"line": 328,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : R ≤ 0\na : ℂ\nha : a ∈ closedBall 0 R\nthis : R = 0\n⊢ f a = ((∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor ... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 368,
"column": 65
} | {
"line": 368,
"column": 70
} | {
"line": 368,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 368,
"column": 65
} | {
"line": 368,
"column": 70
} | {
"line": 368,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 368,
"column": 65
} | {
"line": 368,
"column": 70
} | {
"line": 368,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 693,
"column": 6
} | {
"line": 693,
"column": 92
} | {
"line": 694,
"column": 6
} | [
{
"pp": "case left.inr\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nU : Set 𝕜\nhf : MeromorphicOn f U\nz : ↑U\nhz : z ∈ {u | meromorphicOrderAt f ↑u = ⊤}ᶜ\nh : ∀ᶠ (z : 𝕜) in 𝓝[≠] ↑z, f z ≠ 0\n⊢ ∃ t ⊆ {u | meromorphicOr... | [
"case left.inr\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nU : Set 𝕜\nhf : MeromorphicOn f U\nz : ↑U\nhz : z ∈ {u | meromorphicOrderAt f ↑u = ⊤}ᶜ\nh : ∀ᶠ (z : 𝕜) in 𝓝[≠] ↑z, f z ≠ 0\nt' : Set 𝕜\nh₁t' : ∀ y ∈ t', y ∈ {↑z}... | obtain ⟨t', h₁t', h₂t', h₃t'⟩ := eventually_nhds_iff.1 (eventually_nhdsWithin_iff.1 h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 374,
"column": 10
} | {
"line": 374,
"column": 66
} | {
"line": 375,
"column": 10
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (closedBall 0... | rw [smul_eq_mul, ← zpow_add', neg_add_cancel, zpow_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 382,
"column": 65
} | {
"line": 382,
"column": 70
} | {
"line": 382,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 382,
"column": 65
} | {
"line": 382,
"column": 70
} | {
"line": 382,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 382,
"column": 65
} | {
"line": 382,
"column": 70
} | {
"line": 382,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nh₁f : MeromorphicOn f (closedBall 0 R)\nh₂f : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt f ↑u ≠ ⊤\nhR : 0 < R\nφ : ℂ → E := (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) • f\nhφ : MeromorphicOn φ (... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 397,
"column": 38
} | {
"line": 397,
"column": 43
} | {
"line": 398,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ < R\n⊢ x ∉ sphere 0 R",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminorm... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 399,
"column": 23
} | {
"line": 399,
"column": 28
} | {
"line": 399,
"column": 28
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ < R\nthis : x ∉ sphere 0 R\n⊢ x ∈ ball 0 R",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 399,
"column": 23
} | {
"line": 399,
"column": 28
} | {
"line": 399,
"column": 28
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ < R\nthis : x ∉ sphere 0 R\n⊢ x ∈ ball 0 R",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 399,
"column": 23
} | {
"line": 399,
"column": 28
} | {
"line": 399,
"column": 28
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ < R\nthis : x ∉ sphere 0 R\n⊢ x ∈ ball 0 R",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 407,
"column": 55
} | {
"line": 407,
"column": 60
} | {
"line": 407,
"column": 60
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ∈ {a}ᶜ",
"ppTerm": "?m.202",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.t... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 407,
"column": 55
} | {
"line": 407,
"column": 60
} | {
"line": 407,
"column": 60
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ∈ {a}ᶜ",
"ppTerm": "?m.202",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.t... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 407,
"column": 55
} | {
"line": 407,
"column": 60
} | {
"line": 407,
"column": 60
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ∈ {a}ᶜ",
"ppTerm": "?m.202",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.t... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 408,
"column": 42
} | {
"line": 408,
"column": 47
} | {
"line": 408,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.217",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Seminormed... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 408,
"column": 42
} | {
"line": 408,
"column": 47
} | {
"line": 408,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.217",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Seminormed... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 408,
"column": 42
} | {
"line": 408,
"column": 47
} | {
"line": 408,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.217",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Seminormed... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 408,
"column": 53
} | {
"line": 408,
"column": 58
} | {
"line": 408,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ≠ a",
"ppTerm": "?m.218",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNo... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 408,
"column": 53
} | {
"line": 408,
"column": 58
} | {
"line": 408,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ≠ a",
"ppTerm": "?m.218",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 408,
"column": 53
} | {
"line": 408,
"column": 58
} | {
"line": 408,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\na : ℂ\nha : a ∈ ball 0 R\n⊢ x ≠ a",
"ppTerm": "?m.218",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNo... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 414,
"column": 53
} | {
"line": 414,
"column": 58
} | {
"line": 414,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.288",
"assigned": true,
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 414,
"column": 53
} | {
"line": 414,
"column": 58
} | {
"line": 414,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.288",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 414,
"column": 53
} | {
"line": 414,
"column": 58
} | {
"line": 414,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.288",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 415,
"column": 70
} | {
"line": 415,
"column": 75
} | {
"line": 415,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.323",
"assigned": true,
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 415,
"column": 70
} | {
"line": 415,
"column": 75
} | {
"line": 415,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.323",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 415,
"column": 70
} | {
"line": 415,
"column": 75
} | {
"line": 415,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.323",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 415,
"column": 83
} | {
"line": 415,
"column": 88
} | {
"line": 415,
"column": 88
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.324",
"assigned": true,
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 415,
"column": 83
} | {
"line": 415,
"column": 88
} | {
"line": 415,
"column": 88
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.324",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 415,
"column": 83
} | {
"line": 415,
"column": 88
} | {
"line": 415,
"column": 88
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\n⊢ x ∈ closedBall 0 R",
"ppTerm": "?m.324",
"assigned": true,
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 422,
"column": 61
} | {
"line": 422,
"column": 66
} | {
"line": 422,
"column": 66
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 422,
"column": 61
} | {
"line": 422,
"column": 66
} | {
"line": 422,
"column": 66
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 422,
"column": 61
} | {
"line": 422,
"column": 66
} | {
"line": 422,
"column": 66
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 422,
"column": 72
} | {
"line": 422,
"column": 77
} | {
"line": 422,
"column": 77
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 422,
"column": 72
} | {
"line": 422,
"column": 77
} | {
"line": 422,
"column": 77
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 422,
"column": 72
} | {
"line": 422,
"column": 77
} | {
"line": 422,
"column": 77
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 424,
"column": 78
} | {
"line": 424,
"column": 83
} | {
"line": 424,
"column": 83
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 424,
"column": 78
} | {
"line": 424,
"column": 83
} | {
"line": 424,
"column": 83
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 424,
"column": 78
} | {
"line": 424,
"column": 83
} | {
"line": 424,
"column": 83
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 425,
"column": 56
} | {
"line": 425,
"column": 61
} | {
"line": 425,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 425,
"column": 56
} | {
"line": 425,
"column": 61
} | {
"line": 425,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 425,
"column": 56
} | {
"line": 425,
"column": 61
} | {
"line": 425,
"column": 61
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 426,
"column": 70
} | {
"line": 426,
"column": 75
} | {
"line": 426,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 426,
"column": 70
} | {
"line": 426,
"column": 75
} | {
"line": 426,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 426,
"column": 70
} | {
"line": 426,
"column": 75
} | {
"line": 426,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf g : ℂ → E\nx : ℂ\nD : CanonicalDecomp f g R\nhR : 0 < R\nh : ‖x‖ = R\nη₁ : AnalyticAt ℂ (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (ball 0 R)) u)) x\nη₀ : f =ᶠ[𝓝[≠] x] (∏ᶠ (u : ℂ), canonicalFactor R u ^ (-(divisor f (b... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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