module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Analysis.Complex.CoveringMap | {
"line": 122,
"column": 54
} | {
"line": 122,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : ProperSpace 𝕜\nn : ℕ\nhn : ↑↑n ≠ 0\nsurj : Function.Surjective fun x ↦ x ^ ↑n\n⊢ Function.Surjective fun x ↦ x ^ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 20
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : LocPathConnectedSpace X\nU : Set X\nhUc : IsSimplyConnected U\nhUo : IsOpen U\ng✝ : X → ℂ\nhgc : ContinuousOn g✝ U\nhU₀ : 0 ∉ g✝ '' U\nthis✝ : SimplyConnectedSpace ↑U\nthis : LocPathConnectedSpace ↑U\nx₀ : { x // x ∈ U }\nhx₀ : g✝ ↑x₀ ≠ 0\nf : C(↑U, ℂ)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 19
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : LocPathConnectedSpace X\nU : Set X\nhUc : IsSimplyConnected U\nhUo : IsOpen U\ng : X → 𝔻\nhgc : ContinuousOn g U\nhU₀ : 0 ∉ g '' U\nn : ℕ+\n⊢ 0 ∉ UnitDisc.coe ∘ g '' U",
"usedConstants": [
"Eq.mpr",
"not_exists._simp_1",
"congrAr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.BranchLogRoot | {
"line": 98,
"column": 4
} | {
"line": 98,
"column": 62
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : LocPathConnectedSpace 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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 163,
"column": 4
} | {
"line": 163,
"column": 47
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 165,
"column": 4
} | {
"line": 165,
"column": 50
} | [
{
"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... | refine MapsTo.comp ?_ (h_maps.comp hmaps_line) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Complex.Schwarz | {
"line": 166,
"column": 4
} | {
"line": 166,
"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\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": 176,
"column": 6
} | {
"line": 177,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 40
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 207,
"column": 2
} | {
"line": 207,
"column": 32
} | [
{
"pp": "case h\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 : 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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 45
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UnitDisc.Basic | {
"line": 84,
"column": 29
} | {
"line": 84,
"column": 51
} | [
{
"pp": "z : 𝔻\n⊢ (fun x ↦ ‖x‖) ↑z ≠ (fun x ↦ ‖x‖) (-1)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Real",
"SeminormedAddGroup.toAddGrou... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 230,
"column": 2
} | {
"line": 230,
"column": 22
} | [
{
"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",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 18
} | [
{
"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‖",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 281,
"column": 4
} | {
"line": 281,
"column": 15
} | [
{
"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",
"usedConstants": [
"Norm.norm",
"Eq.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 281,
"column": 63
} | {
"line": 281,
"column": 74
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 313,
"column": 21
} | {
"line": 313,
"column": 36
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 315,
"column": 35
} | {
"line": 315,
"column": 61
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 320,
"column": 4
} | {
"line": 320,
"column": 24
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Schwarz | {
"line": 323,
"column": 4
} | {
"line": 324,
"column": 11
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.IsolatedZeros | {
"line": 123,
"column": 2
} | {
"line": 123,
"column": 64
} | [
{
"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... | simp only [Set.mem_setOf_eq, imp_self, implies_true, and_true] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.LocallyFinsupp | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 37
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nY : Type u_2\nW : Set X\ninst✝ : Zero Y\nf : X → Y\nh : LocallyFiniteSupport f\nhW : IsCompact W\nthis : {i | ({↑i} ∩ W).Nonempty}.Finite\nlem : ∀ {α : Type u_1} (s t : Set α), Subtype.val '' {i | ({↑i} ∩ t).Nonempty} = t ∩ s\n⊢ (Subtype.val '' {i | ({↑i} ∩ W)... | exact Finite.image Subtype.val this | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.LocallyFinsupp | {
"line": 157,
"column": 28
} | {
"line": 157,
"column": 39
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝¹ : DecidableEq X\ninst✝ : Zero Y\nx : X\ny : Y\nx✝¹ : X\nx✝ : x✝¹ ∈ univ\n⊢ (univ ∩ Function.support (Pi.single x y)).Finite",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.univ",
"Set.Finite",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 374,
"column": 4
} | {
"line": 374,
"column": 67
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝ : TopologicalSpace X\nU : Set X\nι : Type u_3\nF : ι → locallyFinsuppWithin U ℤ\nthis : Function.support F = Function.support fun i ↦ ⇑(F i)\nh : (Function.support F).Finite\n⊢ ∑ n ∈ h.toFinset, ⇑(F n) = ∑ᶠ (i : ι), ⇑(F i)",
"usedConstants": [
"Function.locallyFi... | have h₂ : (fun i ↦ (F i : X → ℤ)).support.Finite := by simp_all | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.LocallyFinsupp | {
"line": 370,
"column": 2
} | {
"line": 376,
"column": 41
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nU : Set X\nι : Type u_3\nF : ι → locallyFinsuppWithin U ℤ\n⊢ ⇑(∑ᶠ (i : ι), F i) = ∑ᶠ (i : ι), ⇑(F i)",
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"Pi.addCommMonoid",
"Function.locallyFinsuppWithin.instFunLike",
"Func... | have : F.support = (fun i ↦ (F i : X → ℤ)).support := by
simp [Set.ext_iff, DFunLike.ext_iff, funext_iff]
by_cases h : F.support.Finite
· rw [finsum_eq_sum F h, Function.locallyFinsuppWithin.coe_sum]
have h₂ : (fun i ↦ (F i : X → ℤ)).support.Finite := by simp_all
simp_all [finsum_eq_sum _ h₂]
· simp_a... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.LocallyFinsupp | {
"line": 370,
"column": 2
} | {
"line": 376,
"column": 41
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nU : Set X\nι : Type u_3\nF : ι → locallyFinsuppWithin U ℤ\n⊢ ⇑(∑ᶠ (i : ι), F i) = ∑ᶠ (i : ι), ⇑(F i)",
"usedConstants": [
"Eq.mpr",
"Int.instAddCommMonoid",
"Pi.addCommMonoid",
"Function.locallyFinsuppWithin.instFunLike",
"Func... | have : F.support = (fun i ↦ (F i : X → ℤ)).support := by
simp [Set.ext_iff, DFunLike.ext_iff, funext_iff]
by_cases h : F.support.Finite
· rw [finsum_eq_sum F h, Function.locallyFinsuppWithin.coe_sum]
have h₂ : (fun i ↦ (F i : X → ℤ)).support.Finite := by simp_all
simp_all [finsum_eq_sum _ h₂]
· simp_a... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.LocallyFinsupp | {
"line": 532,
"column": 4
} | {
"line": 532,
"column": 38
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝³ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝² : AddCommGroup Y\ninst✝¹ : LinearOrder Y\ninst✝ : IsOrderedAddMonoid Y\nn : ℕ\nf : locallyFinsuppWithin U Y\nx : X\nh : f x < 0\n⊢ max (n • f x) 0 = n • max (f x) 0",
"usedConstants": [
"Eq.mpr",
"instH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 103,
"column": 22
} | {
"line": 103,
"column": 89
} | [
{
"pp": "case pos.h\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... | ← AnalyticAt.frequently_eq_iff_eventually_eq hg_an analyticAt_const | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 533,
"column": 4
} | {
"line": 533,
"column": 28
} | [
{
"pp": "case neg\nX : Type u_1\ninst✝³ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝² : AddCommGroup Y\ninst✝¹ : LinearOrder Y\ninst✝ : IsOrderedAddMonoid Y\nn : ℕ\nf : locallyFinsuppWithin U Y\nx : X\nh : ¬f x < 0\n⊢ max (n • f x) 0 = n • max (f x) 0",
"usedConstants": [
"Eq.mpr",
"inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 545,
"column": 4
} | {
"line": 545,
"column": 38
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝³ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝² : AddCommGroup Y\ninst✝¹ : LinearOrder Y\ninst✝ : IsOrderedAddMonoid Y\nn : ℕ\nf : locallyFinsuppWithin U Y\nx : X\nh : -f x < 0\n⊢ max (-(n • f x)) 0 = n • max (-f x) 0",
"usedConstants": [
"AddGroup.toSubtr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 546,
"column": 4
} | {
"line": 546,
"column": 28
} | [
{
"pp": "case neg\nX : Type u_1\ninst✝³ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝² : AddCommGroup Y\ninst✝¹ : LinearOrder Y\ninst✝ : IsOrderedAddMonoid Y\nn : ℕ\nf : locallyFinsuppWithin U Y\nx : X\nh : ¬-f x < 0\n⊢ max (-(n • f x)) 0 = n • max (-f x) 0",
"usedConstants": [
"AddGroup.toSubt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 553,
"column": 38
} | {
"line": 553,
"column": 61
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nD : locallyFinsupp X ℤ\nh : 0 < D\n⊢ ∃ z, D z ≠ 0",
"usedConstants": [
"Function.locallyFinsuppWithin.instFunLike",
"Function.locallyFinsupp",
"Set.univ",
"Exists",
"id",
"Ne",
"Int",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 556,
"column": 4
} | {
"line": 556,
"column": 30
} | [
{
"pp": "case inl\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nD : locallyFinsupp X ℤ\nh : 0 < D\ne : X\nhz : D e ≠ 0\n⊢ (single e 1) e ≤ D e",
"usedConstants": [
"Eq.mpr",
"Function.locallyFinsuppWithin.instFunLike",
"congrArg",
"Function.locallyFinsuppWithin.s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 557,
"column": 4
} | {
"line": 557,
"column": 34
} | [
{
"pp": "case inr\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : DecidableEq X\nD : locallyFinsupp X ℤ\nh : 0 < D\nz : X\nhz : D z ≠ 0\ne : X\nhe : e ≠ z\n⊢ (single z 1) e ≤ D e",
"usedConstants": [
"Eq.mpr",
"Function.locallyFinsuppWithin.instFunLike",
"eq_false",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 235,
"column": 6
} | {
"line": 236,
"column": 35
} | [
{
"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)⁻",
"usedConstants": [
... | 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": 235,
"column": 6
} | {
"line": 236,
"column": 35
} | [
{
"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)⁻",
"usedConstants": [
... | 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": 235,
"column": 6
} | {
"line": 236,
"column": 35
} | [
{
"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)⁻",
"usedConstants": [
... | by_cases h : (divisor f₁ U)⁻ ≤ (divisor f₂ U)⁻
<;> simp_all [negPart_nonneg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 154,
"column": 27
} | {
"line": 154,
"column": 45
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 306,
"column": 6
} | {
"line": 307,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 163,
"column": 8
} | {
"line": 163,
"column": 19
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 165,
"column": 8
} | {
"line": 165,
"column": 33
} | [
{
"pp": "case h\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\ng... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 191,
"column": 25
} | {
"line": 191,
"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\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 (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 93,
"column": 8
} | {
"line": 93,
"column": 15
} | [
{
"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... | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 193,
"column": 25
} | {
"line": 193,
"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\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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 12
} | [
{
"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)",
"usedConstants":... | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 405,
"column": 18
} | {
"line": 405,
"column": 29
} | [
{
"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",
"usedCo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 153,
"column": 2
} | {
"line": 166,
"column": 46
} | [
{
"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",
"usedConstants": [
"Iff.mpr",
"NormedCommRing.toNormedRing",
... | · 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.Order | {
"line": 316,
"column": 25
} | {
"line": 316,
"column": 41
} | [
{
"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 �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 223,
"column": 2
} | {
"line": 230,
"column": 20
} | [
{
"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.Order | {
"line": 319,
"column": 45
} | {
"line": 319,
"column": 56
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 12
} | [
{
"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",
"usedConstants": [
"zpow_natCas... | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 78
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 177,
"column": 37
} | {
"line": 177,
"column": 48
} | [
{
"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✝ : LocPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nuniq :\n ∀ (γ γ' : C(↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 420,
"column": 4
} | {
"line": 420,
"column": 14
} | [
{
"pp": "case coe.coe\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → 𝕜\ng : 𝕜 → E\nhf : MeromorphicAt f x\nhg : MeromorphicAt g x\nm : ℤ\nh₂f : meromorphicOrderAt f x = ↑m\nn : ℤ\nh₂g : meromorphicOrderAt g x = ↑n\n⊢... | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 232,
"column": 2
} | {
"line": 232,
"column": 37
} | [
{
"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"... | 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.NormalForm | {
"line": 446,
"column": 8
} | {
"line": 447,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 196,
"column": 6
} | {
"line": 196,
"column": 36
} | [
{
"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✝ : LocPathConnectedSpace 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... | · apply congr_fun (Γ_lifts ..) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Meromorphic.Order | {
"line": 502,
"column": 4
} | {
"line": 502,
"column": 34
} | [
{
"pp": "case right.left\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 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 ≠ 0\nh₃g : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ (meromorphicOrderAt f x).untop₀ • g z\n⊢ (g ^ ... | simp_all [zpow_eq_zero_iff hn] | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Order | {
"line": 502,
"column": 4
} | {
"line": 502,
"column": 34
} | [
{
"pp": "case right.left\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 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 ≠ 0\nh₃g : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ (meromorphicOrderAt f x).untop₀ • g z\n⊢ (g ^ ... | simp_all [zpow_eq_zero_iff hn] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Order | {
"line": 502,
"column": 4
} | {
"line": 502,
"column": 34
} | [
{
"pp": "case right.left\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 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 ≠ 0\nh₃g : f =ᶠ[𝓝[≠] x] fun z ↦ (z - x) ^ (meromorphicOrderAt f x).untop₀ • g z\n⊢ (g ^ ... | simp_all [zpow_eq_zero_iff hn] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Homotopy.Lifting | {
"line": 198,
"column": 4
} | {
"line": 198,
"column": 15
} | [
{
"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✝ : LocPathConnectedSpace 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)) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 540,
"column": 18
} | {
"line": 540,
"column": 26
} | [
{
"pp": "case h.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.divi... | intro hu | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 540,
"column": 18
} | {
"line": 540,
"column": 26
} | [
{
"pp": "case h.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.divi... | intro hu | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Homotopy.Lifting | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 15
} | [
{
"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✝ : LocPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nuniq :\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 540,
"column": 18
} | {
"line": 540,
"column": 26
} | [
{
"pp": "case h.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 ∩ ... | intro hu | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 540,
"column": 18
} | {
"line": 540,
"column": 26
} | [
{
"pp": "case h.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 ∩ ... | intro hu | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Analysis.Meromorphic.Order | {
"line": 515,
"column": 6
} | {
"line": 515,
"column": 17
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nhf : MeromorphicAt f⁻¹ x\n⊢ MeromorphicAt f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 735,
"column": 4
} | {
"line": 735,
"column": 20
} | [
{
"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\nU : Set 𝕜\nhf : ¬MeromorphicOn f U\n⊢ MeromorphicNFOn (toMeromorphicNFOn f U) U",
"usedConstants": [
"Eq.mpr",
"False",
"eq_false",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 472,
"column": 6
} | {
"line": 472,
"column": 90
} | [
{
"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",
"usedConstants": [
"MulOne.toOne",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
... | 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": 604,
"column": 6
} | {
"line": 604,
"column": 17
} | [
{
"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",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 15
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"False",
"Real",
"instHDiv",
"HMul.hMul",
"Complex.instNormedAddCommGroup",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 643,
"column": 4
} | {
"line": 643,
"column": 22
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 54
} | [
{
"pp": "case inl.h\nR : ℝ\nz : ℂ\nhz : z ∈ Set.univ\nh : z ∈ ball 0 R\n⊢ meromorphicOrderAt (canonicalFactor R z) z < 0",
"usedConstants": [
"Int.instAddCommGroup",
"Complex.meromorphicOrderAt_canonicalFactor",
"Eq.mpr",
"Preorder.toLT",
"WithTop.LinearOrderedAddCommGroup.inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 644,
"column": 4
} | {
"line": 644,
"column": 22
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 150,
"column": 19
} | {
"line": 150,
"column": 57
} | [
{
"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.74",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 28,
"column": 55
} | {
"line": 28,
"column": 84
} | [
{
"pp": "R : Type ?u.9\ninst✝ : Field R\na b : R\nhab : a ^ 2 + b ^ 2 ≠ 0\n⊢ !![a, -b; b, a].det ≠ 0",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Equiv.instEquivLike",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 47,
"column": 4
} | {
"line": 47,
"column": 31
} | [
{
"pp": "case mp\nR : 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)\nt : TransvectionStruct n R\n⊢ Commute t.toMatrix ↑g",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 49,
"column": 4
} | {
"line": 49,
"column": 37
} | [
{
"pp": "case mpr\nR : Type u_1\nn : Type u_2\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\ninst✝ : CommRing R\ng : GL n R\nx✝ : ↑g ∈ Set.range ⇑(Matrix.scalar n)\na : R\nha : (Matrix.scalar n) a = ↑g\nh : GL n R\n⊢ h * g = g * h",
"usedConstants": [
"Units.val",
"Eq.mpr",
"Matrix.scalar",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Basic | {
"line": 68,
"column": 8
} | {
"line": 68,
"column": 80
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 280,
"column": 33
} | {
"line": 280,
"column": 44
} | [
{
"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 ⋯... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 286,
"column": 4
} | {
"line": 286,
"column": 15
} | [
{
"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)",
"usedConstants": [
"Real.instIsO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Isometry | {
"line": 92,
"column": 2
} | {
"line": 93,
"column": 35
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 40
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 665,
"column": 4
} | {
"line": 678,
"column": 41
} | [
{
"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": 140,
"column": 49
} | {
"line": 140,
"column": 64
} | [
{
"pp": "f : ℂ ≃ₗᵢ[ℝ] ℂ\na : Circle := ⟨f 1, ⋯⟩\n⊢ (f.trans (rotation a).symm) 1 = 1",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MonoidHom.instMonoidHomClass",
"Real",
"DivInvMonoid.toInv",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Isometry | {
"line": 142,
"column": 4
} | {
"line": 142,
"column": 15
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 397,
"column": 28
} | {
"line": 397,
"column": 39
} | [
{
"pp": "case h.toFun.h\nE : 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\nH : C(↑I × A, X)\nf : C(A, E)\nH_0 : ∀ (a : A), H (0, a) = p (f a)\nf₀ f₁ : C(A, X)\nS : Set A\nF : f₀.HomotopyRel f₁ S\nx✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 398,
"column": 30
} | {
"line": 398,
"column": 41
} | [
{
"pp": "case h.toFun.h\nE : 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\nH : C(↑I × A, X)\nf : C(A, E)\nH_0 : ∀ (a : A), H (0, a) = p (f a)\nf₀ f₁ : C(A, X)\nS : Set A\nF : f₀.HomotopyRel f₁ S\nX✝ Y... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 426,
"column": 4
} | {
"line": 426,
"column": 26
} | [
{
"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\np : E → X\ncov : IsCoveringMap p\ninst✝¹ : SimplyConnectedSpace A\ninst✝ : LocPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nγ : C(↑I, A)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 357,
"column": 39
} | {
"line": 357,
"column": 55
} | [
{
"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 ↦ ↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homotopy.Lifting | {
"line": 449,
"column": 4
} | {
"line": 449,
"column": 26
} | [
{
"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\np : E → X\ncov : IsCoveringMap p\ninst✝¹ : PathConnectedSpace A\ninst✝ : LocPathConnectedSpace A\nf : C(A, X)\na₀ : A\ne₀ : E\nhe : p e₀ = f a₀\nle : (Fundamen... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 358,
"column": 43
} | {
"line": 358,
"column": 86
} | [
{
"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 ↦ ↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 363,
"column": 2
} | {
"line": 363,
"column": 27
} | [
{
"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\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 ... | rw [Pi.zero_apply] at h₂z | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 815,
"column": 2
} | {
"line": 815,
"column": 63
} | [
{
"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 (... | 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
} | [
{
"pp": "case h.hb.h\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℂ → E\nε : ℝ\nhε : ε > 0\n⊢ ε + sSupNormIm f 1 ≠ 0",
"usedConstants": [
"Real",
"Real.instZero",
"ne_of_gt",
"Complex.HadamardThreeLines.sSupNormIm_eps_pos",
"Real.instAdd",
"Real.instOne",
"instH... | 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
} | [
{
"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",
"usedConstants": [
"Norm.norm",
"E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Hadamard | {
"line": 230,
"column": 2
} | {
"line": 230,
"column": 13
} | [
{
"pp": "case h.hp\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℂ → E\nε : ℝ\nhε : 0 < ε\nz : ℂ\nhd : DiffContOnCl ℂ f (verticalStrip 0 1)\nhB : BddAbove (norm ∘ f '' verticalClosedStrip 0 1)\nhz : z ∈ verticalClosedStrip 0 1\nBF : ℝ\nhBF : ∀ a ∈ verticalClosedStrip 0 1, ‖F f ε a‖ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.Hadamard | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 46
} | [
{
"pp": "E : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℂ → E\nl u a : ℝ\nha : ∀ z ∈ re ⁻¹' {l}, ‖f z‖ ≤ a\nz : ℂ\nhz : z.re = 0\n⊢ ‖f (↑l + z * (↑u - ↑l))‖ ≤ a",
"usedConstants": [
"Real",
"Complex.mul_re",
"HMul.hMul",
"sub_self",
"Real.instZero",
"Real.instAddMonoid",... | exact ha (↑l + z * (↑u - ↑l)) (by simp [hz]) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Complex.Conformal | {
"line": 74,
"column": 4
} | {
"line": 74,
"column": 73
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : NormedSpace ℂ E\nmap : ℂ →L[ℂ] E\nnonzero : map ≠ 0\n⊢ ‖map 1‖ ≠ 0",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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