module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Complex.Schwarz | {
"line": 167,
"column": 4
} | {
"line": 167,
"column": 23
} | {
"line": 167,
"column": 24
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc z : E\nR₁ R₂ : ℝ\nn : ℕ\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhn : (fun x ↦ f x - f c) =o[𝓝 c... | [
"E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc z : E\nR₁ R₂ : ℝ\nn : ℕ\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhn : (fun x ↦ f x - f c) =o[𝓝 c] fun w ↦ ‖w... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 98,
"column": 4
} | {
"line": 98,
"column": 62
} | {
"line": 98,
"column": 63
} | [
{
"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+\nf : X → 𝔻\nhfc : ContinuousOn (fun i ↦ ↑(f i)) U\nhf : ∀ (x : X), (fun i ↦ ↑(f i)) x ^ ↑n = (UnitDisc.coe ... | [
"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+\nf : X → 𝔻\nhfc : ContinuousOn (fun i ↦ ↑(f i)) U\nhf : ∀ (x : X), (fun i ↦ ↑(f i)) x ^ ↑n = (UnitDisc.coe ∘ g) x\nx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UnitDisc.Basic | {
"line": 91,
"column": 29
} | {
"line": 91,
"column": 51
} | {
"line": 91,
"column": 52
} | [
{
"pp": "z : 𝔻\n⊢ ‖↑z‖ ≠ ‖-1‖",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Seminorme... | [
"z : 𝔻\n⊢ ¬‖↑z‖ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.IsolatedZeros | {
"line": 123,
"column": 2
} | {
"line": 123,
"column": 64
} | {
"line": 124,
"column": 2
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nhf : MeromorphicOn f U\nhg : MeromorphicOn g U\nhU : Preperfect U\nh : f =ᶠ[codiscreteWithin U] g\n⊢ IsOpen[PseudoMetricSpace.toUniformSpace.toTop... | [
"case h\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nhf : MeromorphicOn f U\nhg : MeromorphicOn g U\nhU : Preperfect U\nh : f =ᶠ[codiscreteWithin U] g\n⊢ IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpac... | simp only [Set.mem_setOf_eq, imp_self, implies_true, and_true] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Complex.Schwarz | {
"line": 177,
"column": 6
} | {
"line": 178,
"column": 13
} | {
"line": 178,
"column": 14
} | [
{
"pp": "case refine_2\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc z : E\nR₁ R₂ : ℝ\nn : ℕ\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhn : (fun x ↦ f x... | [
"case refine_2\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc z : E\nR₁ R₂ : ℝ\nn : ℕ\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhn : (fun x ↦ f x - f ((lineM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 40
} | {
"line": 182,
"column": 41
} | [
{
"pp": "case inr\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc z : E\nR₁ R₂ : ℝ\nn : ℕ\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhn✝ : (fun x ↦ f x - f... | [
"case inr\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc z : E\nR₁ R₂ : ℝ\nn : ℕ\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhn✝ : (fun x ↦ f x - f c) =o[𝓝 c]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 193,
"column": 4
} | {
"line": 193,
"column": 15
} | {
"line": 193,
"column": 16
} | [
{
"pp": "case refine_1\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR₁ R₂ : ℝ\nf : E → F\nc z : E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhz : z ∈ ball c R₁\n⊢ (f... | [
"case refine_1\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR₁ R₂ : ℝ\nf : E → F\nc z : E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nhz : z ∈ ball c R₁\n⊢ Tendsto (fun x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 32
} | {
"line": 208,
"column": 33
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR₁ R₂ : ℝ\nf : E → F\nc : E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh₀ : 0 < R₁\nthis : 0 ≤ R₂\nz : E\nhz : z... | [
"E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR₁ R₂ : ℝ\nf : E → F\nc : E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh₀ : 0 < R₁\nthis : 0 ≤ R₂\nz : E\nhz : z ∈ ball c R₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 218,
"column": 2
} | {
"line": 218,
"column": 45
} | {
"line": 218,
"column": 46
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR : ℝ\nf : E → F\nc z : E\nhd : DifferentiableOn ℂ f (ball c R)\nh_maps : MapsTo f (ball c R) (closedBall (f c) R)\nhz : z ∈ ball c R\n⊢ dist (f z) (f c) ≤ dist z... | [
"E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR : ℝ\nf : E → F\nc z : E\nhd : DifferentiableOn ℂ f (ball c R)\nh_maps : MapsTo f (ball c R) (closedBall (f c) R)\nhz : z ∈ ball c R\n⊢ dist (f z) (f c) ≤ dist z c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 22
} | {
"line": 231,
"column": 23
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR : ℝ\nf : E → F\nc : E\nhd : DifferentiableOn ℂ f (ball c R)\nh_maps : MapsTo f (ball c R) (closedBall (f c) R)\nhR : 0 < R\n⊢ ‖fderiv ℂ f c‖ ≤ 1",
"ppTerm":... | [
"E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR : ℝ\nf : E → F\nc : E\nhd : DifferentiableOn ℂ f (ball c R)\nh_maps : MapsTo f (ball c R) (closedBall (f c) R)\nhR : 0 < R\n⊢ ‖fderiv ℂ f c‖ ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 18
} | {
"line": 240,
"column": 19
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR : ℝ\nf : E → F\nz : E\nhd : DifferentiableOn ℂ f (ball 0 R)\nh_maps : MapsTo f (ball 0 R) (closedBall 0 R)\nh₀ : f 0 = 0\nhz : ‖z‖ < R\n⊢ ‖f z‖ ≤ ‖z‖",
"ppT... | [
"E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nR : ℝ\nf : E → F\nz : E\nhd : DifferentiableOn ℂ f (ball 0 R)\nh_maps : MapsTo f (ball 0 R) (closedBall 0 R)\nh₀ : f 0 = 0\nhz : ‖z‖ < R\n⊢ ‖f z‖ ≤ ‖z‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 282,
"column": 4
} | {
"line": 282,
"column": 15
} | {
"line": 282,
"column": 16
} | [
{
"pp": "case inl\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nz : ℂ\nhd : DifferentiableOn ℂ f (ball z R₁)\nh_maps : MapsTo f (ball z R₁) (closedBall (f z) R₂)\nhz : z ∈ ball z R₁\n⊢ ‖dslope f z z‖ ≤ R₂ / R₁",
"ppTerm": "?inl",
"assigned": true,
"used... | [
"case inl\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nz : ℂ\nhd : DifferentiableOn ℂ f (ball z R₁)\nh_maps : MapsTo f (ball z R₁) (closedBall (f z) R₂)\nhz : z ∈ ball z R₁\n⊢ ‖deriv f z‖ ≤ R₂ / R₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 282,
"column": 63
} | {
"line": 282,
"column": 74
} | {
"line": 282,
"column": 75
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nz : ℂ\nhd : DifferentiableOn ℂ f (ball z R₁)\nh_maps : MapsTo f (ball z R₁) (closedBall (f z) R₂)\nhz : z ∈ ball z R₁\n⊢ 0 < R₁",
"ppTerm": "?m.71",
"assigned": false,
"usedConstants": [],
"usedF... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nz : ℂ\nhd : DifferentiableOn ℂ f (ball z R₁)\nh_maps : MapsTo f (ball z R₁) (closedBall (f z) R₂)\nhz : z ∈ ball z R₁\n⊢ 0 < R₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 314,
"column": 21
} | {
"line": 314,
"column": 36
} | {
"line": 314,
"column": 37
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformS... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformSpace.Complet... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 316,
"column": 35
} | {
"line": 316,
"column": 61
} | {
"line": 316,
"column": 62
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformS... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformSpace.Complet... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 321,
"column": 4
} | {
"line": 321,
"column": 24
} | {
"line": 321,
"column": 25
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformS... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformSpace.Complet... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 324,
"column": 4
} | {
"line": 325,
"column": 11
} | {
"line": 325,
"column": 12
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformS... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\nR₁ R₂ : ℝ\nf : ℂ → E\nc z₀ : ℂ\ninst✝ : StrictConvexSpace ℝ E\nhd : DifferentiableOn ℂ f (ball c R₁)\nh_maps : MapsTo f (ball c R₁) (closedBall (f c) R₂)\nh_z₀ : z₀ ∈ ball c R₁\nh_eq : ‖dslope f c z₀‖ = R₂ / R₁\ne : E →L[ℂ] UniformSpace.Complet... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 269,
"column": 6
} | {
"line": 270,
"column": 35
} | {
"line": 272,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\n⊢ (divisor f₁ U)⁻ ⊔ (divisor f₂ U)⁻ ≤ (divisor f₁ U)⁻ + (divisor f₂ U)⁻",
"ppTerm": "?m.112",
... | [] | by_cases h : (divisor f₁ U)⁻ ≤ (divisor f₂ U)⁻
<;> simp_all [negPart_nonneg] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 269,
"column": 6
} | {
"line": 270,
"column": 35
} | {
"line": 272,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\n⊢ (divisor f₁ U)⁻ ⊔ (divisor f₂ U)⁻ ≤ (divisor f₁ U)⁻ + (divisor f₂ U)⁻",
"ppTerm": "?m.112",
... | [] | by_cases h : (divisor f₁ U)⁻ ≤ (divisor f₂ U)⁻
<;> simp_all [negPart_nonneg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 269,
"column": 6
} | {
"line": 270,
"column": 35
} | {
"line": 272,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\n⊢ (divisor f₁ U)⁻ ⊔ (divisor f₂ U)⁻ ≤ (divisor f₁ U)⁻ + (divisor f₂ U)⁻",
"ppTerm": "?m.112",
... | [] | by_cases h : (divisor f₁ U)⁻ ≤ (divisor f₂ U)⁻
<;> simp_all [negPart_nonneg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 340,
"column": 6
} | {
"line": 341,
"column": 13
} | {
"line": 341,
"column": 14
} | [
{
"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... | [
"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, Meromorphi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 439,
"column": 18
} | {
"line": 439,
"column": 29
} | {
"line": 439,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nU : Set 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nhf₁ : MeromorphicOn f₁ U\nhf₂ : AnalyticOnNhd 𝕜 f₂ U\nx : 𝕜\nhx : x ∈ U\nh : ¬0 ≤ meromorphicOrderAt f₁ x\n⊢ meromorphicOrderAt f₁ x < 0",
"ppTerm... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nU : Set 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nhf₁ : MeromorphicOn f₁ U\nhf₂ : AnalyticOnNhd 𝕜 f₂ U\nx : 𝕜\nhx : x ∈ U\nh : ¬0 ≤ meromorphicOrderAt f₁ x\n⊢ meromorphicOrderAt f₁ x < 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 15
} | {
"line": 95,
"column": 8
} | [
{
"pp": "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\nh₁ : MeromorphicAt f x\nh₃ : f x = 0\nn : ℤ\nhn : ↑n = meromorphicOrderAt f x\nmeromorphicNFAt_iff_analyticAt_or : MeromorphicNFAt f x ↔ AnalyticAt 𝕜... | [
"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\nh₁ : MeromorphicAt f x\nh₃ : f x = 0\nn : ℤ\nhn : ↑n = meromorphicOrderAt f x\nmeromorphicNFAt_iff_analyticAt_or : MeromorphicNFAt f x ↔ AnalyticAt 𝕜 f x ∨ Merom... | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 154,
"column": 2
} | {
"line": 167,
"column": 46
} | {
"line": 169,
"column": 0
} | [
{
"pp": "case mpr\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\n⊢ f x ≠ 0 → meromorphicOrderAt f x = 0",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Iff.mpr",... | [] | · intro h
rcases id hf with h₁ | ⟨n, g, h₁g, h₂g, h₃g⟩
· have := h₁.eq_of_nhds
tauto
· have : n = 0 := by
by_contra hContra
have := h₃g.eq_of_nhds
simp only [Pi.smul_apply', Pi.pow_apply, sub_self, zero_zpow n hContra, zero_smul] at this
tauto
simp only [this, zpo... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 224,
"column": 2
} | {
"line": 231,
"column": 20
} | {
"line": 233,
"column": 0
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\ng : 𝕜 → 𝕜\nx : 𝕜\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nn : ℤ\ng_f : 𝕜 → E\nh₁g_f : AnalyticAt 𝕜 g_f x\nh₂g_f : g_f x ≠ 0\nh₃g_f : f =ᶠ[𝓝 x] (fun x_1 ... | [] | · right
use n, g • g_f, h₁g.smul h₁g_f
constructor
· simp [smul_ne_zero h₂g h₂g_f]
· filter_upwards [h₃g_f]
intro y hy
simp only [Pi.smul_apply', hy, Pi.pow_apply]
rw [smul_comm] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 78
} | {
"line": 147,
"column": 79
} | [
{
"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\nh₁ : 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\nh₁ : 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).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 232,
"column": 2
} | {
"line": 232,
"column": 37
} | {
"line": 233,
"column": 2
} | [
{
"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\nh : meromorphicOrderAt f₁ x < meromorphicOrderAt f₂ x\n⊢ meromorphicTrailingCoeffAt (f₁ + f₂) x = meromorphicTrailingCoeffAt f₁ x"... | [
"case pos\n𝕜 : 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\nh : meromorphicOrderAt f₁ x < meromorphicOrderAt f₂ x\nhf₁ : ¬MeromorphicAt f₁ x\n⊢ meromorphicTrailingCoeffAt (f₁ + f₂) x = meromor... | by_cases! hf₁ : ¬MeromorphicAt f₁ x | Mathlib.Tactic.ByCases._aux_Mathlib_Tactic_ByCases___macroRules_Mathlib_Tactic_ByCases_byCases!_1 | Mathlib.Tactic.ByCases.byCases! |
Mathlib.Analysis.Meromorphic.Order | {
"line": 106,
"column": 22
} | {
"line": 106,
"column": 89
} | {
"line": 106,
"column": 89
} | [
{
"pp": "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\nn : ℤ\nhf : MeromorphicAt f x\nh : ∀ᶠ (z : 𝕜) in 𝓝 x, (z - x) ^ Exists.choose hf • f z = 0\nx✝ : ∃ g, AnalyticAt 𝕜 g x ∧ g x ≠ 0 ∧ ∀ᶠ (z : 𝕜) in �... | [
"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\nn : ℤ\nhf : MeromorphicAt f x\nh : ∀ᶠ (z : 𝕜) in 𝓝 x, (z - x) ^ Exists.choose hf • f z = 0\nx✝ : ∃ g, AnalyticAt 𝕜 g x ∧ g x ≠ 0 ∧ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z ... | ← AnalyticAt.frequently_eq_iff_eventually_eq hg_an analyticAt_const | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 157,
"column": 27
} | {
"line": 157,
"column": 45
} | {
"line": 157,
"column": 46
} | [
{
"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\nho : meromorphicOrderAt f x < 0\nhf : MeromorphicAt f x\nm : ℤ\nhm : ↑m = meromorphicOrderAt f x\n⊢ m < 0",
"ppTerm": "?m.79",
"assigned": false,
"u... | [
"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\nho : meromorphicOrderAt f x < 0\nhf : MeromorphicAt f x\nm : ℤ\nhm : ↑m = meromorphicOrderAt f x\n⊢ m < 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 166,
"column": 8
} | {
"line": 166,
"column": 19
} | {
"line": 166,
"column": 20
} | [
{
"pp": "case refine_1\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\nho : meromorphicOrderAt f x < 0\nhf : MeromorphicAt f x\nm : ℤ\nhm : ↑m = meromorphicOrderAt f x\nm_neg : m < 0\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜... | [
"case refine_1\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\nho : meromorphicOrderAt f x < 0\nhf : MeromorphicAt f x\nm : ℤ\nhm : ↑m = meromorphicOrderAt f x\nm_neg : m < 0\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 168,
"column": 8
} | {
"line": 168,
"column": 33
} | {
"line": 168,
"column": 34
} | [
{
"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\nho : meromorphicOrderAt f x < 0\nhf : MeromorphicAt f x\nm : ℤ\nhm : ↑m = meromorphicOrderAt f x\nm_neg : m < 0\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ... | [
"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\nho : meromorphicOrderAt f x < 0\nhf : MeromorphicAt f x\nm : ℤ\nhm : ↑m = meromorphicOrderAt f x\nm_neg : m < 0\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nhg : ∀ᶠ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 194,
"column": 25
} | {
"line": 194,
"column": 42
} | {
"line": 194,
"column": 43
} | [
{
"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\nho : 0 < meromorphicOrderAt f x\nhf : MeromorphicAt f x\nn : ℤ\nh'o : meromorphicOrderAt f x = ↑n\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nhg : ∀ᶠ (... | [
"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\nho : 0 < meromorphicOrderAt f x\nhf : MeromorphicAt f x\nn : ℤ\nh'o : meromorphicOrderAt f x = ↑n\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nhg : ∀ᶠ (z : 𝕜) in �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 196,
"column": 25
} | {
"line": 196,
"column": 42
} | {
"line": 196,
"column": 43
} | [
{
"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\nho : 0 < meromorphicOrderAt f x\nhf : MeromorphicAt f x\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nn : ℕ\nh'o : meromorphicOrderAt f x = ↑↑n\nhg : ∀ᶠ ... | [
"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\nho : 0 < meromorphicOrderAt f x\nhf : MeromorphicAt f x\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nn : ℕ\nh'o : meromorphicOrderAt f x = ↑↑n\nhg : ∀ᶠ (z : 𝕜) in ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 12
} | {
"line": 193,
"column": 4
} | [
{
"pp": "case coe\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\nho : 0 < meromorphicOrderAt f x\nhf : MeromorphicAt f x\nn : ℤ\nh'o : meromorphicOrderAt f x = ↑n\n⊢ Tendsto f (𝓝[≠] x) (𝓝 0)",
"ppTerm": "?coe"... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 488,
"column": 8
} | {
"line": 489,
"column": 15
} | {
"line": 489,
"column": 16
} | [
{
"pp": "case pos.inl\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx z : 𝕜\nhz : z = x\nh₀f : MeromorphicNFAt f x\nh₁f : f =ᶠ[𝓝 x] 0\n⊢ (if h : True then Function.update f x (if h_1 : meromorphicOrderAt f x = 0 then Cla... | [
"case pos.inl\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx z : 𝕜\nhz : z = x\nh₀f : MeromorphicNFAt f x\nh₁f : f =ᶠ[𝓝 x] 0\n⊢ 0 = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 472,
"column": 6
} | {
"line": 472,
"column": 90
} | {
"line": 473,
"column": 4
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nn : ℤ\nf : 𝕜 → 𝕜\nh₁ : MeromorphicAt f x\nh₂ : meromorphicOrderAt f x = ⊤\nh₃ : n = 0\n⊢ meromorphicTrailingCoeffAt 1 x = 1",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"NonUnital... | [] | apply analyticAt_const.meromorphicTrailingCoeffAt_of_ne_zero (ne_zero_of_eq_one rfl) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Meromorphic.Order | {
"line": 276,
"column": 2
} | {
"line": 276,
"column": 12
} | {
"line": 277,
"column": 4
} | [
{
"pp": "case pos.coe\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₁₂ : f₁ =ᶠ[𝓝[≠] x] f₂\nhf₁ : MeromorphicAt f₁ x\nn : ℤ\nh₁f₁ : meromorphicOrderAt f₁ x = ↑n\n⊢ meromorphicOrderAt f₂ x = ↑n",
"ppTerm":... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 309,
"column": 54
} | {
"line": 309,
"column": 70
} | {
"line": 309,
"column": 71
} | [
{
"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\nhf : MeromorphicAt f x\nnneg : 0 ≤ meromorphicOrderAt f x\nn : ℤ\nh₀ : meromorphicOrderAt f x = ↑n\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g x\nhfg : ∀ᶠ (z : 𝕜) in 𝓝[... | [
"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\nhf : MeromorphicAt f x\nnneg : 0 ≤ meromorphicOrderAt f x\nn : ℤ\nh₀ : meromorphicOrderAt f x = ↑n\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g x\nhfg : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 582,
"column": 18
} | {
"line": 582,
"column": 26
} | {
"line": 583,
"column": 2
} | [
{
"pp": "case mp\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\n⊢ u ∈ U ∩ f ⁻¹' {0} → u ∈ Function.support ⇑(MeromorphicOn.diviso... | [
"case mp\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\nhu : u ∈ U ∩ f ⁻¹' {0}\n⊢ u ∈ Function.support ⇑(MeromorphicOn.divisor f U)"
... | intro hu | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 582,
"column": 18
} | {
"line": 582,
"column": 26
} | {
"line": 583,
"column": 2
} | [
{
"pp": "case mp\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\n⊢ u ∈ U ∩ f ⁻¹' {0} → u ∈ Function.support ⇑(MeromorphicOn.diviso... | [
"case mp\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\nhu : u ∈ U ∩ f ⁻¹' {0}\n⊢ u ∈ Function.support ⇑(MeromorphicOn.divisor f U)"
... | intro hu | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 582,
"column": 18
} | {
"line": 582,
"column": 26
} | {
"line": 583,
"column": 2
} | [
{
"pp": "case mpr\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\n⊢ u ∈ Function.support ⇑(MeromorphicOn.divisor f U) → u ∈ U ∩ f ... | [
"case mpr\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\nhu : u ∈ Function.support ⇑(MeromorphicOn.divisor f U)\n⊢ u ∈ U ∩ f ⁻¹' {0}"... | intro hu | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 582,
"column": 18
} | {
"line": 582,
"column": 26
} | {
"line": 583,
"column": 2
} | [
{
"pp": "case mpr\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\n⊢ u ∈ Function.support ⇑(MeromorphicOn.divisor f U) → u ∈ U ∩ f ... | [
"case mpr\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\nh₁f : MeromorphicNFOn f U\nh₂f : ∀ (u : ↑U), meromorphicOrderAt f ↑u ≠ ⊤\nu : 𝕜\nhu : u ∈ Function.support ⇑(MeromorphicOn.divisor f U)\n⊢ u ∈ U ∩ f ⁻¹' {0}"... | intro hu | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Analysis.Meromorphic.Order | {
"line": 306,
"column": 4
} | {
"line": 306,
"column": 14
} | {
"line": 307,
"column": 6
} | [
{
"pp": "case refine_1.coe\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\nnneg : 0 ≤ meromorphicOrderAt f x\nn : ℤ\nh₀ : meromorphicOrderAt f x = ↑n\n⊢ ∃ g, AnalyticAt 𝕜 g x ∧ f =ᶠ[𝓝[≠] x] ... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 333,
"column": 25
} | {
"line": 333,
"column": 41
} | {
"line": 333,
"column": 42
} | [
{
"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\nh' : ContinuousAt f x\nn : ℤ\nho : meromorphicOrderAt f x = ↑n\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nhg : ∀ᶠ (z : 𝕜) in �... | [
"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\nh' : ContinuousAt f x\nn : ℤ\nho : meromorphicOrderAt f x = ↑n\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nhg : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 336,
"column": 45
} | {
"line": 336,
"column": 56
} | {
"line": 336,
"column": 57
} | [
{
"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\nh' : ContinuousAt f x\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nthis : 0 ≤ meromorphicOrderAt f x\nn : ℕ\nho : meromorphicOrde... | [
"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\nh' : ContinuousAt f x\ng : 𝕜 → E\ng_an : AnalyticAt 𝕜 g x\ngx : g x ≠ 0\nthis : 0 ≤ meromorphicOrderAt f x\nn : ℕ\nho : meromorphicOrderAt f x = ↑↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 324,
"column": 2
} | {
"line": 324,
"column": 12
} | {
"line": 329,
"column": 4
} | [
{
"pp": "case coe\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\nh : MeromorphicAt f x\nh' : ContinuousAt f x\nn : ℤ\nho : meromorphicOrderAt f x = ↑n\n⊢ AnalyticAt 𝕜 f x",
"ppTerm": "?coe",
"assigned": tru... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.RCLike | {
"line": 31,
"column": 2
} | {
"line": 31,
"column": 13
} | {
"line": 31,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : RCLike 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nhf : Meromorphic f\n⊢ (∃ u, meromorphicOrderAt f u ≠ ⊤) ↔ ∀ (u : 𝕜), meromorphicOrderAt f u ≠ ⊤",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Exists",
... | [
"𝕜 : Type u_1\ninst✝² : RCLike 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nhf : Meromorphic f\n⊢ (∃ u, ¬meromorphicOrderAt f u = ⊤) ↔ ∀ (u : 𝕜), ¬meromorphicOrderAt f u = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 15
} | {
"line": 89,
"column": 16
} | [
{
"pp": "case inl\nw x : ℂ\nhx : x ∈ {w}ᶜ\n⊢ AnalyticAt ℂ (fun z ↦ (↑0 ^ 2 - (starRingEnd ℂ) w * z) / (↑0 * (z - w))) x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"Real",
"instHDiv",
"HMul.hMul",
... | [
"case inl\nw x : ℂ\nhx : x ∈ {w}ᶜ\n⊢ AnalyticAt ℂ (fun z ↦ 0) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 437,
"column": 4
} | {
"line": 437,
"column": 14
} | {
"line": 438,
"column": 6
} | [
{
"pp": "case coe.coe\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 : ... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 122,
"column": 4
} | {
"line": 122,
"column": 54
} | {
"line": 122,
"column": 55
} | [
{
"pp": "case inl\nR : ℝ\nz : ℂ\nhz : z ∈ univ\nh : z ∈ ball 0 R\n⊢ meromorphicOrderAt (canonicalFactor R z) z < 0",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Complex.meromorphicOrderAt_canonicalFactor",
"Eq.mpr",
"Preorder.toLT",
"... | [
"case inl\nR : ℝ\nz : ℂ\nhz : z ∈ univ\nh : z ∈ ball 0 R\n⊢ -1 < 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 487,
"column": 4
} | {
"line": 487,
"column": 80
} | {
"line": 487,
"column": 81
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_5\nF : ι → 𝕜 → 𝕜\nh₁ : ∀ (c : ι), MeromorphicAt (F c) x\nh₂ : ∀ (c : ι), meromorphicOrderAt (F c) x ≠ ⊤\nhF : Function.HasFiniteMulSupport F\n⊢ meromorphicOrderAt (∏ᶠ (c : ι), F c) x ≠ ⊤",
"ppTerm": "?pos✝",
"assi... | [
"case pos\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nι : Type u_5\nF : ι → 𝕜 → 𝕜\nh₁ : ∀ (c : ι), MeromorphicAt (F c) x\nh₂ : ∀ (c : ι), meromorphicOrderAt (F c) x ≠ ⊤\nhF : Function.HasFiniteMulSupport F\n⊢ ∀ (x_1 : ι), ¬F x_1 = 1 → ¬meromorphicOrderAt (F x_1) x = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 165,
"column": 19
} | {
"line": 165,
"column": 57
} | {
"line": 165,
"column": 58
} | [
{
"pp": "R : ℝ\nw z : ℂ\nhw : w ∈ ball 0 R\nhz : z ∈ sphere 0 R\nhR : 0 < R\nhzw : z - w ≠ 0\n⊢ ?m.73",
"ppTerm": "?m.78",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : ℝ\nw z : ℂ\nhw : w ∈ ball 0 R\nhz : z ∈ sphere 0 R\nhR : 0 < R\nhzw : z - w ≠ 0\n⊢ ?m.73"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 530,
"column": 4
} | {
"line": 530,
"column": 34
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case right.left\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 : ℤ\nhn : ¬n = 0\nh : ¬meromorphicOrderAt f x = ⊤\ng : 𝕜 → 𝕜'\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ ... | [] | simp_all [zpow_eq_zero_iff hn] | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Order | {
"line": 530,
"column": 4
} | {
"line": 530,
"column": 34
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case right.left\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 : ℤ\nhn : ¬n = 0\nh : ¬meromorphicOrderAt f x = ⊤\ng : 𝕜 → 𝕜'\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ ... | [] | simp_all [zpow_eq_zero_iff hn] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Order | {
"line": 530,
"column": 4
} | {
"line": 530,
"column": 34
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case right.left\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 : ℤ\nhn : ¬n = 0\nh : ¬meromorphicOrderAt f x = ⊤\ng : 𝕜 → 𝕜'\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ ... | [] | simp_all [zpow_eq_zero_iff hn] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 543,
"column": 6
} | {
"line": 543,
"column": 17
} | {
"line": 543,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f⁻¹ x\n⊢ MeromorphicAt f x",
"ppTerm": "?m.59",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\n𝕜' : Type u_4\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f⁻¹ x\n⊢ MeromorphicAt f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 40
} | {
"line": 307,
"column": 41
} | [
{
"pp": "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) ^ (d... | [
"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) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 631,
"column": 6
} | {
"line": 631,
"column": 17
} | {
"line": 631,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₂ : MeromorphicAt f₂ x\nh : meromorphicOrderAt f₁ x < meromorphicOrderAt f₂ x\nhf₁ : MeromorphicAt (f₁ + f₂) x\n⊢ MeromorphicAt f₁ x",
"ppTerm": "?m.7... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₂ : MeromorphicAt f₂ x\nh : meromorphicOrderAt f₁ x < meromorphicOrderAt f₂ x\nhf₁ : MeromorphicAt (f₁ + f₂) x\n⊢ MeromorphicAt f₁ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 288,
"column": 4
} | {
"line": 289,
"column": 61
} | {
"line": 290,
"column": 2
} | [
{
"pp": "case h₁f\nE : 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⊢ ∀ i ∈ η₀.toFinset, MeromorphicOn (canonicalFactor R i ^ (divisor f (ball 0 R)) i) (ball 0 R)",
"ppTerm": "?h₁f",
... | [] | intro z hz
apply zpow (fun x hx ↦ meromorphic_canonicalFactor R z x) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 288,
"column": 4
} | {
"line": 289,
"column": 61
} | {
"line": 290,
"column": 2
} | [
{
"pp": "case h₁f\nE : 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⊢ ∀ i ∈ η₀.toFinset, MeromorphicOn (canonicalFactor R i ^ (divisor f (ball 0 R)) i) (ball 0 R)",
"ppTerm": "?h₁f",
... | [] | intro z hz
apply zpow (fun x hx ↦ meromorphic_canonicalFactor R z x) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 300,
"column": 2
} | {
"line": 306,
"column": 26
} | {
"line": 308,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nz : ℂ\nhR : 0 < R\n⊢ meromorphicOrderAt (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) z ≠ ⊤",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.... | [] | apply meromorphicOrderAt_finprod_ne_top
(fun _ ↦ MeromorphicAt.zpow (meromorphic_canonicalFactor _ _ _) _)
intro c
rw [meromorphicOrderAt_zpow (meromorphic_canonicalFactor R c z)]
lift meromorphicOrderAt (canonicalFactor R c) z to ℤ using
(meromorphicOrderAt_canonicalFactor_ne_top c hR) with ℓ
simp [← W... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 300,
"column": 2
} | {
"line": 306,
"column": 26
} | {
"line": 308,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nR : ℝ\nf : ℂ → E\nz : ℂ\nhR : 0 < R\n⊢ meromorphicOrderAt (∏ᶠ (c : ℂ), canonicalFactor R c ^ (divisor f (ball 0 R)) c) z ≠ ⊤",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.... | [] | apply meromorphicOrderAt_finprod_ne_top
(fun _ ↦ MeromorphicAt.zpow (meromorphic_canonicalFactor _ _ _) _)
intro c
rw [meromorphicOrderAt_zpow (meromorphic_canonicalFactor R c z)]
lift meromorphicOrderAt (canonicalFactor R c) z to ℤ using
(meromorphicOrderAt_canonicalFactor_ne_top c hR) with ℓ
simp [← W... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 357,
"column": 39
} | {
"line": 357,
"column": 55
} | {
"line": 357,
"column": 56
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nD : locallyFinsuppWithin U ℤ\nhg : ∀ (u : ↑U), g ↑u ≠ 0\nh : f =ᶠ[codiscreteWithin U] (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) • g\nt₁ : (support fun u x ↦ ↑(... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nD : locallyFinsuppWithin U ℤ\nhg : ∀ (u : ↑U), g ↑u ≠ 0\nh : f =ᶠ[codiscreteWithin U] (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) • g\nt₁ : (support fun u x ↦ ↑(D u) * log ‖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 358,
"column": 43
} | {
"line": 358,
"column": 86
} | {
"line": 358,
"column": 87
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nD : locallyFinsuppWithin U ℤ\nhg : ∀ (u : ↑U), g ↑u ≠ 0\nh : f =ᶠ[codiscreteWithin U] (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) • g\nt₁ : (support fun u x ↦ ↑(... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nD : locallyFinsuppWithin U ℤ\nhg : ∀ (u : ↑U), g ↑u ≠ 0\nh : f =ᶠ[codiscreteWithin U] (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) • g\nt₁ : (support fun u x ↦ ↑(D u) * log ‖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 670,
"column": 4
} | {
"line": 670,
"column": 22
} | {
"line": 670,
"column": 23
} | [
{
"pp": "case inl\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nh✝ : meromorphicOrderAt f₁ x ≠ meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₁ x < meromorp... | [
"case inl\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nh✝ : meromorphicOrderAt f₁ x ≠ meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₁ x < meromorphicOrderAt f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 671,
"column": 4
} | {
"line": 671,
"column": 22
} | {
"line": 671,
"column": 23
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nh✝ : meromorphicOrderAt f₁ x ≠ meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₂ x < meromorp... | [
"case inr\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nx : 𝕜\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nh✝ : meromorphicOrderAt f₁ x ≠ meromorphicOrderAt f₂ x\nh : meromorphicOrderAt f₂ x < meromorphicOrderAt f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 351,
"column": 6
} | {
"line": 351,
"column": 31
} | {
"line": 351,
"column": 32
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 363,
"column": 2
} | {
"line": 363,
"column": 27
} | {
"line": 364,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nD : locallyFinsuppWithin U ℤ\nhg : ∀ (u : ↑U), g ↑u ≠ 0\nh : f =ᶠ[codiscreteWithin U] (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) • g\nt₁ : (support fun u x ↦ ↑(... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf g : 𝕜 → E\nD : locallyFinsuppWithin U ℤ\nhg : ∀ (u : ↑U), g ↑u ≠ 0\nh : f =ᶠ[codiscreteWithin U] (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ D u) • g\nt₁ : (support fun u x ↦ ↑(D u) * log ‖... | rw [Pi.zero_apply] at h₂z | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 364,
"column": 6
} | {
"line": 364,
"column": 51
} | {
"line": 364,
"column": 52
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 28,
"column": 55
} | {
"line": 28,
"column": 84
} | {
"line": 28,
"column": 85
} | [
{
"pp": "R : Type ?u.3\ninst✝ : Field R\na b : R\nhab : a ^ 2 + b ^ 2 ≠ 0\n⊢ !![a, -b; b, a].det ≠ 0",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Equiv.instEquivLike",
"HMul.h... | [
"R : Type ?u.3\ninst✝ : Field R\na b : R\nhab : a ^ 2 + b ^ 2 ≠ 0\n⊢ ¬a * a + b * b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 68,
"column": 8
} | {
"line": 68,
"column": 80
} | {
"line": 68,
"column": 81
} | [
{
"pp": "R : Type u_1\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : GL n R\nhg : g ∈ Subgroup.center (GL n R)\nhn : Nonempty n\na : R\nha : (Matrix.scalar n) a = ↑g\nb : R\nhb : (Matrix.scalar n) b = ↑g⁻¹\n⊢ a * b = 1",
"ppTerm": "?m.109",
"assigned": false,
"use... | [
"R : Type u_1\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : GL n R\nhg : g ∈ Subgroup.center (GL n R)\nhn : Nonempty n\na : R\nha : (Matrix.scalar n) a = ↑g\nb : R\nhb : (Matrix.scalar n) b = ↑g⁻¹\n⊢ a * b = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 92,
"column": 32
} | {
"line": 92,
"column": 43
} | {
"line": 92,
"column": 44
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\nhn : ¬IsEmpty n\n⊢ Nonempty n",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\nhn : ¬IsEmpty n\n⊢ Nonempty n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 96,
"column": 31
} | {
"line": 96,
"column": 58
} | {
"line": 96,
"column": 59
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ x, (GeneralLinearGroup.scalar n) x = toGL g\nr : Rˣ\nhr : (GeneralLinearGroup.scalar n) r = toGL g\n⊢ ↑r ^ Fintype.card n = 1",
"ppTerm": "?m.67",
"assigned": fa... | [
"n : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ x, (GeneralLinearGroup.scalar n) x = toGL g\nr : Rˣ\nhr : (GeneralLinearGroup.scalar n) r = toGL g\n⊢ ↑r ^ Fintype.card n = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 97,
"column": 7
} | {
"line": 97,
"column": 34
} | {
"line": 97,
"column": 35
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ x, (GeneralLinearGroup.scalar n) x = toGL g\nr : Rˣ\nhr : (GeneralLinearGroup.scalar n) r = toGL g\n⊢ (diagonal fun x ↦ ↑r) = ↑g",
"ppTerm": "?m.68",
"assigned":... | [
"n : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ x, (GeneralLinearGroup.scalar n) x = toGL g\nr : Rˣ\nhr : (GeneralLinearGroup.scalar n) r = toGL g\n⊢ (diagonal fun x ↦ ↑r) = ↑g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 179,
"column": 37
} | {
"line": 179,
"column": 48
} | {
"line": 179,
"column": 49
} | [
{
"pp": "E : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\np : E → X\nhomeo : IsLocalHomeomorph p\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nuniq :\n ∀ (γ γ' :... | [
"E : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\np : E → X\nhomeo : IsLocalHomeomorph p\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nuniq :\n ∀ (γ γ' : C(↑I, A)) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 99,
"column": 4
} | {
"line": 100,
"column": 57
} | {
"line": 101,
"column": 8
} | [
{
"pp": "case refine_1\nn : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ r, r ^ Fintype.card n = 1 ∧ (diagonal fun x ↦ r) = ↑g\nr : R\nhr1 : r ^ Fintype.card n = 1\nhr : (diagonal fun x ↦ r) = ↑g\n⊢ r * ↑g⁻¹ i i = 1",
"ppTe... | [
"case refine_1\nn : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ r, r ^ Fintype.card n = 1 ∧ (diagonal fun x ↦ r) = ↑g\nr : R\nhr1 : r ^ Fintype.card n = 1\nhr : (diagonal fun x ↦ r) = ↑g\n⊢ r ^ (Fintype.card n - 1 + 1) = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 102,
"column": 4
} | {
"line": 102,
"column": 39
} | {
"line": 102,
"column": 40
} | [
{
"pp": "case refine_2\nn : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ r, r ^ Fintype.card n = 1 ∧ (diagonal fun x ↦ r) = ↑g\nr : R\nhr1 : r ^ Fintype.card n = 1\nhr : (diagonal fun x ↦ r) = ↑g\n⊢ ↑g⁻¹ i i * r = 1",
"ppTe... | [
"case refine_2\nn : Type u_1\nR : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : SpecialLinearGroup n R\ni : n\nx✝ : ∃ r, r ^ Fintype.card n = 1 ∧ (diagonal fun x ↦ r) = ↑g\nr : R\nhr1 : r ^ Fintype.card n = 1\nhr : (diagonal fun x ↦ r) = ↑g\n⊢ r ^ (Fintype.card n - 1) * r = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Isometry | {
"line": 92,
"column": 2
} | {
"line": 93,
"column": 35
} | {
"line": 93,
"column": 36
} | [
{
"pp": "f : ℂ →ₗᵢ[ℝ] ℂ\nh₃ : ∀ (z : ℂ), z + (starRingEnd ℂ) z = f z + (starRingEnd ℂ) (f z)\nz : ℂ\n⊢ (f z).re = z.re",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℂ →ₗᵢ[ℝ] ℂ\nh₃ : ∀ (z : ℂ), z + (starRingEnd ℂ) z = f z + (starRingEnd ℂ) (f z)\nz : ℂ\n⊢ (f z).re = z.re"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 692,
"column": 4
} | {
"line": 705,
"column": 41
} | {
"line": 706,
"column": 2
} | [
{
"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: f is locally nonzero in a punctured neighborhood of z
obtain ⟨t', h₁t', h₂t', h₃t'⟩ := eventually_nhds_iff.1 (eventually_nhdsWithin_iff.1 h)
use Subtype.val ⁻¹' t'
constructor
· intro w hw
push _ ∈ _
by_cases h₁w : w = z
· rwa [h₁w]
· rw [meromorphicOrd... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Complex.Isometry | {
"line": 104,
"column": 47
} | {
"line": 104,
"column": 62
} | {
"line": 104,
"column": 63
} | [
{
"pp": "f : ℂ →ₗᵢ[ℝ] ℂ\nh : f 1 = 1\nz : ℂ\n⊢ ‖f z - 1‖ ^ 2 = ‖z - 1‖ ^ 2",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"LinearIsometry",
"Real.instIsOrderedRing",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRin... | [
"f : ℂ →ₗᵢ[ℝ] ℂ\nh : f 1 = 1\nz : ℂ\n⊢ ‖f z - 1‖ = ‖z - 1‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Isometry | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 76
} | {
"line": 106,
"column": 77
} | [
{
"pp": "f : ℂ →ₗᵢ[ℝ] ℂ\nh : f 1 = 1\nz : ℂ\nhsq : normSq (f z) + normSq 1 - 2 * (f z * (starRingEnd ℂ) 1).re = normSq z + normSq 1 - 2 * (z * (starRingEnd ℂ) 1).re\n⊢ z + (starRingEnd ℂ) z = f z + (starRingEnd ℂ) (f z)",
"ppTerm": "?m.113",
"assigned": true,
"usedConstants": [
"LinearIsometry... | [
"f : ℂ →ₗᵢ[ℝ] ℂ\nh : f 1 = 1\nz : ℂ\nhsq : normSq (f z) + normSq 1 - 2 * (f z * (starRingEnd ℂ) 1).re = normSq z + normSq 1 - 2 * (z * (starRingEnd ℂ) 1).re\n⊢ z.re = (f z).re"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Isometry | {
"line": 132,
"column": 49
} | {
"line": 132,
"column": 64
} | {
"line": 132,
"column": 65
} | [
{
"pp": "f : ℂ ≃ₗᵢ[ℝ] ℂ\na : Circle := ⟨f 1, ⋯⟩\n⊢ (f.trans (rotation a).symm) 1 = 1",
"ppTerm": "?m.112",
"assigned": true,
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MonoidHom.instMonoidHomCla... | [
"f : ℂ ≃ₗᵢ[ℝ] ℂ\na : Circle := ⟨f 1, ⋯⟩\n⊢ (rotation ⟨f 1, ⋯⟩).symm (f 1) = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Isometry | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 15
} | {
"line": 134,
"column": 16
} | [
{
"pp": "case h.refine_1\nf : ℂ ≃ₗᵢ[ℝ] ℂ\na : Circle := ⟨f 1, ⋯⟩\nthis : (f.trans (rotation a).symm) 1 = 1\nh₁ : f.trans (rotation a).symm = LinearIsometryEquiv.refl ℝ ℂ\n⊢ f = rotation a",
"ppTerm": "?h.refine_1",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
... | [
"case h.refine_1\nf : ℂ ≃ₗᵢ[ℝ] ℂ\na : Circle := ⟨f 1, ⋯⟩\nthis : (f.trans (rotation a).symm) 1 = 1\nh₁ : f.trans (rotation a).symm = LinearIsometryEquiv.refl ℝ ℂ\n⊢ f = rotation a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Conformal | {
"line": 80,
"column": 8
} | {
"line": 80,
"column": 37
} | {
"line": 80,
"column": 37
} | [
{
"pp": "case refine_1\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace ℂ E\nmap : ℂ →L[ℂ] E\nnonzero : map ≠ 0\nminor₁ : ‖map 1‖ ≠ 0\nx : ℂ\nthis : x = x • 1\n⊢ ‖‖map 1‖⁻¹ • (↑ℝ ↑map) (x • 1)‖ = ‖x‖",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants... | [
"case refine_1\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace ℂ E\nmap : ℂ →L[ℂ] E\nnonzero : map ≠ 0\nminor₁ : ‖map 1‖ ≠ 0\nx : ℂ\nthis : x = x • 1\n⊢ ‖‖map 1‖⁻¹ • ↑map (x • 1)‖ = ‖x‖"
] | LinearMap.coe_restrictScalars | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 198,
"column": 6
} | {
"line": 198,
"column": 36
} | {
"line": 199,
"column": 6
} | [
{
"pp": "case pos\nE : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nΓ : (γ : C(↑I, A)) → γ 0 = a₀ → C(↑I, E)\nΓ_0 : ∀ (γ : C(↑I, A)) (a... | [
"case neg\nE : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nΓ : (γ : C(↑I, A)) → γ 0 = a₀ → C(↑I, E)\nΓ_0 : ∀ (γ : C(↑I, A)) (a : γ 0 = a₀)... | · apply congr_fun (Γ_lifts ..) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 503,
"column": 2
} | {
"line": 504,
"column": 74
} | {
"line": 505,
"column": 2
} | [
{
"pp": "case inr.inr\nE : 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\ng : ℂ → E\nD : CanonicalDecomp f g R\nh₄g : ∀ (u : ↑(closedBall 0 R)), meromorphicOrder... | [
"case inr.inr\nE : 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\ng : ℂ → E\nD : CanonicalDecomp f g R\nh₄g : ∀ (u : ↑(closedBall 0 R)), meromorphicOrderAt g ↑u ≠ ⊤\... | obtain ⟨h, h₁h, h₂h, h₃h⟩ := D.meromorphicNFOn.meromorphicOn.extract_zeros_poles h₄g <|
(divisor g (closedBall 0 R)).finiteSupport <| isCompact_closedBall 0 R | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.Homotopy.Lifting | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 15
} | {
"line": 200,
"column": 16
} | [
{
"pp": "case refine_1\nE : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nΓ : (γ : C(↑I, A)) → γ 0 = a₀ → C(↑I, E)\nΓ_0 : ∀ (γ : C(↑I, A... | [
"case refine_1\nE : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nΓ : (γ : C(↑I, A)) → γ 0 = a₀ → C(↑I, E)\nΓ_0 : ∀ (γ : C(↑I, A)) (a : γ 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 15
} | {
"line": 204,
"column": 16
} | [
{
"pp": "case refine_3\nE : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\np : E → X\nhomeo : IsLocalHomeomorph p\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nuniq... | [
"case refine_3\nE : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝⁴ : TopologicalSpace E\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace A\np : E → X\nhomeo : IsLocalHomeomorph p\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocallyPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nuniq :\n ∀ (γ γ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 858,
"column": 2
} | {
"line": 858,
"column": 63
} | {
"line": 859,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\ng : 𝕜 → 𝕜\nhf : MeromorphicAt f (g x)\nhg : AnalyticAt 𝕜 g x\nhg_nc : ¬EventuallyConst g (𝓝 x)\n⊢ meromorphicOrderAt (f ∘ g) x =\n meromorphicOrderAt f (... | [
"case inl\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\ng : 𝕜 → 𝕜\nhf : MeromorphicAt f (g x)\nhg : AnalyticAt 𝕜 g x\nhg_nc : ¬EventuallyConst g (𝓝 x)\nhf' : meromorphicOrderAt f (g x) = ⊤\n⊢ meromorphicOrderAt (f ... | rcases eq_or_ne (meromorphicOrderAt f (g x)) ⊤ with hf' | hf' | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Complex.Hadamard | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 48
} | {
"line": 132,
"column": 0
} | [
{
"pp": "case hb\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℂ → E\nε : ℝ\nhε : ε > 0\n⊢ ε + sSupNormIm f 1 ≠ 0",
"ppTerm": "?hb",
"assigned": true,
"usedConstants": [
"Real",
"Real.instZero",
"ne_of_gt",
"Complex.HadamardThreeLines.sSupNormIm_eps_pos",
"Real.instA... | [] | exact (ne_of_gt (sSupNormIm_eps_pos f hε 1)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Complex.Hadamard | {
"line": 162,
"column": 28
} | {
"line": 162,
"column": 76
} | {
"line": 162,
"column": 77
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nε : ℝ\nhε : ε > 0\nB : ℝ\nhB : ∀ y ∈ norm ∘ f '' verticalClosedStrip 0 1, y ≤ B\nz : ℂ\nhset : z ∈ verticalClosedStrip 0 1\n⊢ ‖f z‖ ∈ norm ∘ f '' verticalClosedStrip 0 1",
"ppTerm": "?m.118",
"assigned": true,
... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nε : ℝ\nhε : ε > 0\nB : ℝ\nhB : ∀ y ∈ norm ∘ f '' verticalClosedStrip 0 1, y ≤ B\nz : ℂ\nhset : z ∈ verticalClosedStrip 0 1\n⊢ ∃ x ∈ verticalClosedStrip 0 1, ‖f x‖ = ‖f z‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 928,
"column": 71
} | {
"line": 928,
"column": 82
} | {
"line": 928,
"column": 83
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nhmero : MeromorphicAt f x\ng : 𝕜 → E\nhga : AnalyticAt 𝕜 g x\nhg0 : g x ≠ 0\nhg : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nhmero : MeromorphicAt f x\ng : 𝕜 → E\nhga : AnalyticAt 𝕜 g x\nhg0 : g x ≠ 0\nhg : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ n • g z\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 931,
"column": 29
} | {
"line": 931,
"column": 54
} | {
"line": 931,
"column": 55
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nhmero : MeromorphicAt f x\ng : 𝕜 → E\nhga : AnalyticAt 𝕜 g x\nhg0 : g x ≠ 0\nhg : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\nhn : ↑n ≠ 0\nhmero : MeromorphicAt f x\ng : 𝕜 → E\nhga : AnalyticAt 𝕜 g x\nhg0 : g x ≠ 0\nhg : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ n • g z\nz... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 948,
"column": 2
} | {
"line": 948,
"column": 13
} | {
"line": 948,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\nhn : ↑(n + 1) ≠ 0\nhf : meromorphicOrderAt f x = ↑(n + 1)\n⊢ meromorphicOrderAt (deriv f) x = ↑n",
"ppTerm": "?m.55",
"... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\nhn : ↑(n + 1) ≠ 0\nhf : meromorphicOrderAt f x = ↑(n + 1)\n⊢ meromorphicOrderAt (deriv f) x = ↑n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 282,
"column": 33
} | {
"line": 282,
"column": 44
} | {
"line": 282,
"column": 45
} | [
{
"pp": "E : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace A\np : E → X\ncov : IsCoveringMap p\nγ✝ : C(↑I, X)\ne✝ : E\nγ_0 : γ✝ 0 = p e✝\nx y z : X\ne : E\nhpe : x = p e\nγ : Path x y\nγ' : Path y z\nΓ : C(↑I, E) := cov.liftPath (↑γ) e ⋯... | [
"E : Type u_1\nX : Type u_2\nA : Type u_3\ninst✝² : TopologicalSpace E\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace A\np : E → X\ncov : IsCoveringMap p\nγ✝ : C(↑I, X)\ne✝ : E\nγ_0 : γ✝ 0 = p e✝\nx y z : X\ne : E\nhpe : x = p e\nγ : Path x y\nγ' : Path y z\nΓ : C(↑I, E) := cov.liftPath (↑γ) e ⋯\n⊢ y = p (Γ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.HasPrimitives | {
"line": 86,
"column": 4
} | {
"line": 86,
"column": 15
} | {
"line": 86,
"column": 16
} | [
{
"pp": "case hb₂\nc z : ℂ\nr : ℝ\nw : ℂ\nhw : w ∈ ball z (r - dist z c)\n⊢ ↑w.re + ↑w.im * I ∈ ball z (r - dist z c)",
"ppTerm": "?hb₂",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"HMul.hMul",
"congrArg",
"Comple... | [
"case hb₂\nc z : ℂ\nr : ℝ\nw : ℂ\nhw : w ∈ ball z (r - dist z c)\n⊢ dist w z < r - dist z c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 288,
"column": 4
} | {
"line": 288,
"column": 15
} | {
"line": 288,
"column": 16
} | [
{
"pp": "case neg\nE : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace E\ninst✝ : TopologicalSpace X\np : E → X\ncov : IsCoveringMap p\nx y z : X\ne : E\nhpe : x = p e\nγ : Path x y\nγ' : Path y z\nx✝ : ↑I\nh✝ : ¬↑x✝ ≤ 1 / 2\n⊢ ↑γ' 0 = p ((cov.liftPath (↑γ) e ⋯) 1)",
"ppTerm": "?neg✝",
"assigned": tru... | [
"case neg\nE : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace E\ninst✝ : TopologicalSpace X\np : E → X\ncov : IsCoveringMap p\nx y z : X\ne : E\nhpe : x = p e\nγ : Path x y\nγ' : Path y z\nx✝ : ↑I\nh✝ : ¬↑x✝ ≤ 1 / 2\n⊢ y = p ((cov.liftPath (↑γ) e ⋯) 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.HasPrimitives | {
"line": 121,
"column": 42
} | {
"line": 121,
"column": 53
} | {
"line": 121,
"column": 54
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\ns : Set ℂ\nx₀ : ℂ\ny : E\nη : ℂ → E\nhη : ∀ z ∈ s, HasDerivAt η (f z) z\n⊢ ∀ x ∈ s, HasDerivAt (fun z ↦ η z - η x₀ + y) (f x) x",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"N... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\ns : Set ℂ\nx₀ : ℂ\ny : E\nη : ℂ → E\nhη : ∀ z ∈ s, HasDerivAt η (f z) z\n⊢ ∀ x ∈ s, HasDerivAt η (f x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.PhragmenLindelof | {
"line": 133,
"column": 24
} | {
"line": 133,
"column": 95
} | {
"line": 133,
"column": 96
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nC✝ : ℝ\nf : ℂ → E\nz : ℂ\nC : ℝ\nhC₀ : 0 < C\na b : ℝ\nhza : a - b < z.im\nhle_a : ∀ (z : ℂ), z.im = a - b → ‖f z‖ ≤ C\nhzb : z.im < a + b\nhle_b : ∀ (z : ℂ), z.im = a + b → ‖f z‖ ≤ C\nhfd : DiffContOnCl ℂ f (im ⁻¹' Ioo (a - b) (a + ... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nC✝ : ℝ\nf : ℂ → E\nz : ℂ\nC : ℝ\nhC₀ : 0 < C\na b : ℝ\nhza : a - b < z.im\nhle_a : ∀ (z : ℂ), z.im = a - b → ‖f z‖ ≤ C\nhzb : z.im < a + b\nhle_b : ∀ (z : ℂ), z.im = a + b → ‖f z‖ ≤ C\nhfd : DiffContOnCl ℂ f (im ⁻¹' Ioo (a - b) (a + b))\nhB :\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.HasPrimitives | {
"line": 155,
"column": 56
} | {
"line": 155,
"column": 67
} | {
"line": 155,
"column": 68
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nc : ℂ\nr : ℝ\nf : ℂ → E\nf_cont : ContinuousOn f (ball c r)\nz : ℂ\nhz : z ∈ ball c r\nhf : IsConservativeOn f (ball c r)\n⊢ r - dist z c > 0",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"IsRightCancelA... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nc : ℂ\nr : ℝ\nf : ℂ → E\nf_cont : ContinuousOn f (ball c r)\nz : ℂ\nhz : z ∈ ball c r\nhf : IsConservativeOn f (ball c r)\n⊢ dist z c < r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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