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.Convex.SpecificFunctions.Deriv | {
"line": 111,
"column": 19
} | {
"line": 111,
"column": 27
} | [
{
"pp": "case hf''.«1»\nx : ℝ\nhx : 0 < x\nhm₀ : (Nat.castEmbedding.trans (addLeftEmbedding 0)) 1 ≠ 0\nhm₁ : (Nat.castEmbedding.trans (addLeftEmbedding 0)) 1 ≠ 1\n⊢ False",
"usedConstants": [
"addLeftEmbedding",
"False",
"Int.instLocallyFiniteOrder._proof_1",
"congrArg",
"False... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Complex.AbsMax | {
"line": 215,
"column": 2
} | {
"line": 218,
"column": 42
} | [
{
"pp": "E : Type u\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℂ E\nF : Type v\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℂ F\nf : E → F\nc : E\nhd : ∀ᶠ (z : E) in 𝓝 c, DifferentiableAt ℂ f z\nhc : IsLocalMax (norm ∘ f) c\nr : ℝ\nhr₀ : 0 < r\nhr : ∀ ⦃x : E⦄, x ∈ closedBall c r → Differentiab... | exact nhds_basis_closedBall.eventually_iff.2
⟨r, hr₀, norm_eqOn_closedBall_of_isMaxOn (DifferentiableOn.diffContOnCl fun x hx =>
(hr <| closure_ball_subset_closedBall hx).1.differentiableWithinAt) fun x hx =>
(hr <| ball_subset_closedBall hx).2⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds | {
"line": 178,
"column": 8
} | {
"line": 178,
"column": 12
} | [
{
"pp": "x : ℝ\nh1 : 0 < x\nh2 : x < π / 2\nU : Set ℝ := Ico 0 (π / 2)\nintU : interior U = Ioo 0 (π / 2)\nhalf_pi_pos : 0 < π / 2\ncos_pos : ∀ {y : ℝ}, y ∈ U → 0 < cos y\ny : ℝ\nhy : y ∈ interior U\n⊢ 0 < sin y",
"usedConstants": [
"Real",
"instHDiv",
"Real.pi",
"Real.instZero",
... | intU | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds | {
"line": 260,
"column": 29
} | {
"line": 260,
"column": 68
} | [
{
"pp": "x : ℝ\n⊢ ↑‖Complex.exp (Complex.I * ↑x) - 1‖₊ ≤ ↑‖x‖₊",
"usedConstants": [
"Real.enorm_exp_I_mul_ofReal_sub_one_le"
]
}
] | exact enorm_exp_I_mul_ofReal_sub_one_le | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Complex.BorelCaratheodory | {
"line": 88,
"column": 57
} | {
"line": 103,
"column": 48
} | [
{
"pp": "f : ℂ → ℂ\nM R : ℝ\nz : ℂ\nhM : 0 < M\nhf : DifferentiableOn ℂ f (ball 0 R)\nhf₁ : Set.MapsTo f (ball 0 R) {z | z.re ≤ M}\nhR : 0 < R\nhz : z ∈ ball 0 R\nhf₂ : f 0 = 0\n⊢ ‖f z‖ ≤ 2 * M * ‖z‖ / (R - ‖z‖)",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"IsRightCancelAdd.add... | by
set w := f z / (2 * M - f z)
have hzR : ‖z‖ < R := mem_ball_zero_iff.mp hz
have hwR := by simpa only [dist_zero_right, div_one, mul_comm (1 / R), mul_one_div]
using schwarz_applied hM hf hf₁ hz hf₂
have h_denom : 2 * M - f z ≠ 0 := sub_ne_zero_of_ne (fun h => by simpa [← h, hM] using hf₁ hz)
calc ‖f z‖... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Meromorphic.IsolatedZeros | {
"line": 90,
"column": 6
} | {
"line": 90,
"column": 27
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nhg : MeromorphicAt g x\n⊢ (∃ᶠ (z : 𝕜) in 𝓝[≠] x, f z = g z) ↔ f =ᶠ[𝓝[≠] x] g",
"usedConstants": [
"Eq.mpr",
"Normed... | eventuallyEq_iff_sub, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 240,
"column": 4
} | {
"line": 240,
"column": 12
} | [
{
"pp": "case h.e'_3.h.mpr\nX : Type u_1\ninst✝² : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝¹ : T1Space X\ninst✝ : Zero Y\nD : locallyFinsuppWithin U Y\nhU : IsClosed[inst✝²] U\nx : X\nhx : x ∈ U \\ {x | (fun x ↦ D x = 0 x) x}\n⊢ x ∈ D.support",
"usedConstants": [
"False",
"Function.loc... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 240,
"column": 4
} | {
"line": 240,
"column": 12
} | [
{
"pp": "case h.e'_3.h.mpr\nX : Type u_1\ninst✝² : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝¹ : T1Space X\ninst✝ : Zero Y\nD : locallyFinsuppWithin U Y\nhU : IsClosed[inst✝²] U\nx : X\nhx : x ∈ U \\ {x | (fun x ↦ D x = 0 x) x}\n⊢ x ∈ D.support",
"usedConstants": [
"False",
"Function.loc... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.LocallyFinsupp | {
"line": 240,
"column": 4
} | {
"line": 240,
"column": 12
} | [
{
"pp": "case h.e'_3.h.mpr\nX : Type u_1\ninst✝² : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝¹ : T1Space X\ninst✝ : Zero Y\nD : locallyFinsuppWithin U Y\nhU : IsClosed[inst✝²] U\nx : X\nhx : x ∈ U \\ {x | (fun x ↦ D x = 0 x) x}\n⊢ x ∈ D.support",
"usedConstants": [
"False",
"Function.loc... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.LocallyFinsupp | {
"line": 285,
"column": 6
} | {
"line": 285,
"column": 14
} | [
{
"pp": "case right\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddMonoid Y\nf g : X → Y\nz : X\nt₁ t₂ : Set X\na : X\nhf : (∀ (x : X), ¬f x = 0 → x ∈ U) ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite\nhg : (∀ (x : X), ¬g x = 0 → x ∈ U) ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Functi... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 298,
"column": 24
} | {
"line": 298,
"column": 32
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddGroup Y\nf : X → Y\nhf : f ∈ {f | Function.support f ⊆ U ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite}\n⊢ -f ∈ {f | Function.support f ⊆ U ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite}",
"usedConstant... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 298,
"column": 24
} | {
"line": 298,
"column": 32
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddGroup Y\nf : X → Y\nhf : f ∈ {f | Function.support f ⊆ U ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite}\n⊢ -f ∈ {f | Function.support f ⊆ U ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite}",
"usedConstant... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.LocallyFinsupp | {
"line": 298,
"column": 24
} | {
"line": 298,
"column": 32
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddGroup Y\nf : X → Y\nhf : f ∈ {f | Function.support f ⊆ U ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite}\n⊢ -f ∈ {f | Function.support f ⊆ U ∧ ∀ z ∈ U, ∃ t ∈ 𝓝 z, (t ∩ Function.support f).Finite}",
"usedConstant... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.LocallyFinsupp | {
"line": 365,
"column": 13
} | {
"line": 365,
"column": 21
} | [
{
"pp": "case empty\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddCommMonoid Y\nι : Type u_3\nF : ι → locallyFinsuppWithin U Y\n⊢ ⇑(∑ n ∈ ∅, F n) = ∑ n ∈ ∅, ⇑(F n)",
"usedConstants": [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.instZero",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 365,
"column": 13
} | {
"line": 365,
"column": 21
} | [
{
"pp": "case empty\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddCommMonoid Y\nι : Type u_3\nF : ι → locallyFinsuppWithin U Y\n⊢ ⇑(∑ n ∈ ∅, F n) = ∑ n ∈ ∅, ⇑(F n)",
"usedConstants": [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.instZero",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.LocallyFinsupp | {
"line": 365,
"column": 13
} | {
"line": 365,
"column": 21
} | [
{
"pp": "case empty\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddCommMonoid Y\nι : Type u_3\nF : ι → locallyFinsuppWithin U Y\n⊢ ⇑(∑ n ∈ ∅, F n) = ∑ n ∈ ∅, ⇑(F n)",
"usedConstants": [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.instZero",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.LocallyFinsupp | {
"line": 366,
"column": 14
} | {
"line": 366,
"column": 22
} | [
{
"pp": "case insert\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddCommMonoid Y\nι : Type u_3\nF : ι → locallyFinsuppWithin U Y\na✝² : ι\ns✝ : Finset ι\na✝¹ : a✝² ∉ s✝\na✝ : ⇑(∑ n ∈ s✝, F n) = ∑ n ∈ s✝, ⇑(F n)\n⊢ ⇑(∑ n ∈ insert a✝² s✝, F n) = ∑ n ∈ insert a✝² s✝, ⇑(F n)",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 366,
"column": 14
} | {
"line": 366,
"column": 22
} | [
{
"pp": "case insert\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddCommMonoid Y\nι : Type u_3\nF : ι → locallyFinsuppWithin U Y\na✝² : ι\ns✝ : Finset ι\na✝¹ : a✝² ∉ s✝\na✝ : ⇑(∑ n ∈ s✝, F n) = ∑ n ∈ s✝, ⇑(F n)\n⊢ ⇑(∑ n ∈ insert a✝² s✝, F n) = ∑ n ∈ insert a✝² s✝, ⇑(F n)",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.LocallyFinsupp | {
"line": 366,
"column": 14
} | {
"line": 366,
"column": 22
} | [
{
"pp": "case insert\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : AddCommMonoid Y\nι : Type u_3\nF : ι → locallyFinsuppWithin U Y\na✝² : ι\ns✝ : Finset ι\na✝¹ : a✝² ∉ s✝\na✝ : ⇑(∑ n ∈ s✝, F n) = ∑ n ∈ s✝, ⇑(F n)\n⊢ ⇑(∑ n ∈ insert a✝² s✝, F n) = ∑ n ∈ insert a✝² s✝, ⇑(F n)",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.LocallyFinsupp | {
"line": 374,
"column": 59
} | {
"line": 374,
"column": 67
} | [
{
"pp": "X : 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⊢ (Function.support fun i ↦ ⇑(F i)).Finite",
"usedConstants": [
"Function.locallyFinsuppWithin.ins... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 432,
"column": 6
} | {
"line": 432,
"column": 14
} | [
{
"pp": "case right\nX : Type u_1\ninst✝² : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝¹ : SemilatticeSup Y\ninst✝ : Zero Y\nD₁ D₂ : locallyFinsuppWithin U Y\nz : X\nhz : z ∈ U\nt₁ : Set X\nht₁ : t₁ ∈ 𝓝 z ∧ (t₁ ∩ D₁.support).Finite\nt₂ : Set X\nht₂ : t₂ ∈ 𝓝 z ∧ (t₂ ∩ D₂.support).Finite\na : X\nha : (a ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 456,
"column": 6
} | {
"line": 456,
"column": 14
} | [
{
"pp": "case right\nX : Type u_1\ninst✝² : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝¹ : SemilatticeInf Y\ninst✝ : Zero Y\nD₁ D₂ : locallyFinsuppWithin U Y\nz : X\nhz : z ∈ U\nt₁ : Set X\nht₁ : t₁ ∈ 𝓝 z ∧ (t₁ ∩ D₁.support).Finite\nt₂ : Set X\nht₂ : t₂ ∈ 𝓝 z ∧ (t₂ ∩ D₂.support).Finite\na : X\nha : (a ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : 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 : MeromorphicOn f₂ U\nhU : Preperfect U\nh : f₁ =ᶠ[codiscreteWithin U] f₂\nz : 𝕜\nhz : z ∉ U\n⊢ (divisor f₁ U) ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : 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 : MeromorphicOn f₂ U\nhU : Preperfect U\nh : f₁ =ᶠ[codiscreteWithin U] f₂\nz : 𝕜\nhz : z ∉ U\n⊢ (divisor f₁ U) ... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : 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 : MeromorphicOn f₂ U\nhU : Preperfect U\nh : f₁ =ᶠ[codiscreteWithin U] f₂\nz : 𝕜\nhz : z ∉ U\n⊢ (divisor f₁ U) ... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 198,
"column": 4
} | {
"line": 198,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∉ U\n⊢ min ((divisor ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 198,
"column": 4
} | {
"line": 198,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∉ U\n⊢ min ((divisor ... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 198,
"column": 4
} | {
"line": 198,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∉ U\n⊢ min ((divisor ... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∈ U\nh₁ : meromorphic... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∈ U\nh₁ : meromorphic... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 201,
"column": 4
} | {
"line": 201,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∈ U\nh₁ : meromorphic... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∈ U\nh₁ : ¬meromorphi... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∈ U\nh₁ : ¬meromorphi... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₁ f₂ : 𝕜 → E\nz : 𝕜\nU : Set 𝕜\nhf₁ : MeromorphicOn f₁ U\nhf₂ : MeromorphicOn f₂ U\nh₁z : z ∈ U\nh₃ : meromorphicOrderAt (f₁ + f₂) z ≠ ⊤\nhz : z ∈ U\nh₁ : ¬meromorphi... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 105,
"column": 8
} | {
"line": 105,
"column": 33
} | [
{
"pp": "case pos.h.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) ... | eventually_nhdsWithin_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 98,
"column": 2
} | {
"line": 108,
"column": 96
} | [
{
"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 : analyticOrderAt (fun z ↦ (z - x) ^ Exists.choose hf • f z) x = ⊤\n⊢ ENat.map (fun x ↦ ↑x) (analyticOrderAt (fun z ↦... | · rw [h, ENat.map_top, ← WithTop.coe_natCast, top_sub,
eq_false_intro WithTop.top_ne_coe, false_iff]
rw [analyticOrderAt_eq_top] at h
refine fun ⟨g, hg_an, hg_ne, hg_eq⟩ ↦ hg_ne ?_
apply EventuallyEq.eq_of_nhds
rw [EventuallyEq, ← AnalyticAt.frequently_eq_iff_eventually_eq hg_an analyticAt_const]
... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Meromorphic.Order | {
"line": 113,
"column": 10
} | {
"line": 113,
"column": 35
} | [
{
"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\nn : ℤ\nhf : MeromorphicAt f x\nh✝ : ¬analyticOrderAt (fun z ↦ (z - x) ^ Exists.choose hf • f z) x = ⊤\nm : ℕ\nh : ↑m = analyticOrderAt (fun z ↦ (z - x) ^ Exists... | eventually_nhdsWithin_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.LocallyFinsupp | {
"line": 584,
"column": 4
} | {
"line": 584,
"column": 12
} | [
{
"pp": "case right\nX : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : Zero Y\nV : Set X\nD : locallyFinsuppWithin U Y\nh : V ⊆ U\nz : X\nhz : z ∈ V\nt : Set X\nht : t ∈ 𝓝 z ∧ (t ∩ D.support).Finite\na✝¹ : X\na✝ : a✝¹ ∈ t ∩ Function.support fun z ↦ if hz : z ∈ V then D z else 0\n⊢ a✝¹... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.LocallyFinsupp | {
"line": 598,
"column": 2
} | {
"line": 598,
"column": 10
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nU : Set X\nY : Type u_2\ninst✝ : Zero Y\nV : Set X\nD : locallyFinsuppWithin U Y\nh : V ⊆ U\nx✝ : X\nhx : x✝ ∈ Vᶜ\n⊢ (D.restrict h) x✝ = 0 x✝",
"usedConstants": [
"False",
"Function.locallyFinsuppWithin.instFunLike",
"eq_false",
"co... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 396,
"column": 53
} | {
"line": 396,
"column": 61
} | [
{
"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\nthis : 0 ≤ meromorphicOrderAt (f₁ + f₂) x\n⊢... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 396,
"column": 53
} | {
"line": 396,
"column": 61
} | [
{
"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\nthis : 0 ≤ meromorphicOrderAt (f₁ + f₂) x\n⊢... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 396,
"column": 53
} | {
"line": 396,
"column": 61
} | [
{
"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\nthis : 0 ≤ meromorphicOrderAt (f₁ + f₂) x\n⊢... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Divisor | {
"line": 404,
"column": 11
} | {
"line": 406,
"column": 73
} | [] | meromorphicOrderAt f₁ x
_ < 0 := by simpa using h
_ ≤ meromorphicOrderAt f₂ x := (hf₂ x hx).meromorphicOrderAt_nonneg | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcSteps |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 155,
"column": 6
} | {
"line": 155,
"column": 27
} | [
{
"pp": "case mpr.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 : 𝕜\nhf : MeromorphicNFAt f x\nh : f x ≠ 0\nh₁ : f =ᶠ[𝓝 x] 0\n⊢ meromorphicOrderAt f x = 0",
"usedConstants": [
"NormedCommRing.toSeminormed... | have := h₁.eq_of_nhds | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 12
} | [
{
"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\ng : 𝕜 → 𝕜\nx : 𝕜\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₁f : f =ᶠ[𝓝 x] 0\n⊢ ∀ (a : 𝕜), f a = 0 a → (g • f) a = 0 a",
"usedConstants": [
"instH... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 124,
"column": 6
} | {
"line": 124,
"column": 14
} | [
{
"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\nh : MeromorphicAt f x\nh₂ : meromorphicOrderAt f x = ⊤\ny : 𝕜\nhy : f y = 0\n⊢ 0 y = f y",
"usedConstants": [
"congrArg",
"SubtractionM... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Order | {
"line": 324,
"column": 24
} | {
"line": 327,
"column": 48
} | [
{
"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 : 0 < meromorphicOrderAt f x\nhf : f x = 0\n⊢ AnalyticAt 𝕜 f x",
"usedConstants": [
"Eq.mpr",
"MeromorphicAt.analyticAt",
"NormedCommRi... | by
refine (meromorphicAt_of_meromorphicOrderAt_ne_zero h.ne').analyticAt ?_
rw [continuousAt_iff_punctured_nhds, hf]
exact tendsto_zero_of_meromorphicOrderAt_pos h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Meromorphic.Order | {
"line": 394,
"column": 8
} | {
"line": 394,
"column": 11
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\nh₁ : MeromorphicAt f x\nh₂ : meromorphicOrderAt f x = ⊤\n⊢ meromorphicOrderAt f x = meromorphicOrderAt (-f) x",
"usedConstants": [
"Eq.mpr",... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 400,
"column": 2
} | {
"line": 400,
"column": 10
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\nh₁ : MeromorphicAt f x\nn : ℤ\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g x ∧ g x ≠ 0 ∧ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z = (z - x) ^ n • g z\n⊢ AnalyticAt 𝕜 (-g) x ∧ ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 348,
"column": 32
} | {
"line": 348,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nn : ℤ\ng : 𝕜 → 𝕜\nh₁ : AnalyticAt 𝕜 g x\nh₂ : g x ≠ 0\nh₃ : f =ᶠ[𝓝 x] (fun x_1 ↦ x_1 - x) ^ n • g\n⊢ g⁻¹ x ≠ 0",
"usedConstants": [
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"False",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 348,
"column": 32
} | {
"line": 348,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nn : ℤ\ng : 𝕜 → 𝕜\nh₁ : AnalyticAt 𝕜 g x\nh₂ : g x ≠ 0\nh₃ : f =ᶠ[𝓝 x] (fun x_1 ↦ x_1 - x) ^ n • g\n⊢ g⁻¹ x ≠ 0",
"usedConstants": [
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"False",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 348,
"column": 32
} | {
"line": 348,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nn : ℤ\ng : 𝕜 → 𝕜\nh₁ : AnalyticAt 𝕜 g x\nh₂ : g x ≠ 0\nh₃ : f =ᶠ[𝓝 x] (fun x_1 ↦ x_1 - x) ^ n • g\n⊢ g⁻¹ x ≠ 0",
"usedConstants": [
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"False",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 235,
"column": 4
} | {
"line": 235,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf₁ f₂ : 𝕜 → E\nhf₂ : MeromorphicAt f₂ x\nh : meromorphicOrderAt f₁ x < meromorphicOrderAt f₂ x\nhf₁ : ¬MeromorphicAt f₁ x\nthis : ¬MeromorphicAt (f₁ + f₂) x\n⊢ m... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.NormalForm | {
"line": 428,
"column": 8
} | {
"line": 428,
"column": 16
} | [
{
"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\nhf : MeromorphicAt f x\nn : ℤ\nhn : ↑n = meromorphicOrderAt f x\ng : 𝕜 → E\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₃g : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z =... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Homotopy.Lifting | {
"line": 180,
"column": 4
} | {
"line": 198,
"column": 20
} | [
{
"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\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... | obtain ⟨p, hep, rfl⟩ := homeo (F a)
have hfap : f a ∈ p.target := by rw [← this]; exact p.map_source hep
refine ContinuousAt.congr (f := p.symm ∘ f)
((p.continuousAt_symm hfap).comp f.2.continuousAt) ?_
have ⟨U, ⟨haU, U_conn⟩, hUp⟩ := (path_connected_basis a).mem_iff.mp
((p.open_target.preimage ... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Homotopy.Lifting | {
"line": 180,
"column": 4
} | {
"line": 198,
"column": 20
} | [
{
"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\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... | obtain ⟨p, hep, rfl⟩ := homeo (F a)
have hfap : f a ∈ p.target := by rw [← this]; exact p.map_source hep
refine ContinuousAt.congr (f := p.symm ∘ f)
((p.continuousAt_symm hfap).comp f.2.continuousAt) ?_
have ⟨U, ⟨haU, U_conn⟩, hUp⟩ := (path_connected_basis a).mem_iff.mp
((p.open_target.preimage ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 526,
"column": 6
} | {
"line": 526,
"column": 31
} | [
{
"pp": "case right\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nhf : MeromorphicAt f x\na : ℤ\nha : ↑a = meromorphicOrderAt f x\ng : 𝕜 → 𝕜\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh₃g : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z = (z - x) ^ a • g z\n⊢ ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f⁻¹ z = (z - x) ^ (f... | eventually_nhdsWithin_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.Order | {
"line": 549,
"column": 2
} | {
"line": 549,
"column": 10
} | [
{
"pp": "case h\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 : meromorphicOrderAt f₁ x = ⊤\nz : 𝕜\nhz : f₁ z = 0\n⊢ (f₁ + f₂) z = f₂ z",
"usedConstants": [
"congrArg",
"AddCommGroup.toAddC... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.Order | {
"line": 567,
"column": 4
} | {
"line": 567,
"column": 53
} | [
{
"pp": "case pos\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\nh₂f₁ : meromorphicOrderAt f₁ x = ⊤\n⊢ min (meromorphicOrderAt f₁ x) (meromorphicOrderAt f₂ x) ... | rw [h₂f₁, min_top_left, meromorphicOrderAt_congr] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 317,
"column": 4
} | {
"line": 317,
"column": 12
} | [
{
"pp": "case h\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\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nn₁ : ℤ\nhn₁ : ↑n₁ = meromorphicOrderAt f₁ x\nh₁f₁ : ¬↑n₁ = ⊤\ng₁ : 𝕜 → E\nh₁g₁ : AnalyticAt 𝕜 ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 319,
"column": 8
} | {
"line": 319,
"column": 16
} | [
{
"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\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nn₁ : ℤ\nhn₁ : ↑n₁ = meromorphicOrderAt f₁ x\nh₁f₁ : ¬↑n₁ = ⊤\ng₁ : 𝕜 → E\nh₁g₁ : AnalyticAt 𝕜 g₁ x\nh₂... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 319,
"column": 8
} | {
"line": 319,
"column": 16
} | [
{
"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\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nn₁ : ℤ\nhn₁ : ↑n₁ = meromorphicOrderAt f₁ x\nh₁f₁ : ¬↑n₁ = ⊤\ng₁ : 𝕜 → E\nh₁g₁ : AnalyticAt 𝕜 g₁ x\nh₂... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 319,
"column": 8
} | {
"line": 319,
"column": 16
} | [
{
"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\nhf₁ : MeromorphicAt f₁ x\nhf₂ : MeromorphicAt f₂ x\nn₁ : ℤ\nhn₁ : ↑n₁ = meromorphicOrderAt f₁ x\nh₁f₁ : ¬↑n₁ = ⊤\ng₁ : 𝕜 → E\nh₁g₁ : AnalyticAt 𝕜 g₁ x\nh₂... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 448,
"column": 6
} | {
"line": 448,
"column": 14
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nh₁ : MeromorphicAt f x\nh₂ : ¬meromorphicOrderAt f x = ⊤\n⊢ ∀ (a : 𝕜), f a ≠ 0 → (f⁻¹ * f) a = 1 a",
"usedConstants": [
"NormedCommRing.toNormedRing",
"GroupWithZero.toMonoidWithZero",
"MulOne.toOne",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 455,
"column": 4
} | {
"line": 455,
"column": 12
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nh₁ : ¬MeromorphicAt f x\n⊢ meromorphicTrailingCoeffAt f⁻¹ x = (meromorphicTrailingCoeffAt f x)⁻¹",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"False",... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 455,
"column": 4
} | {
"line": 455,
"column": 12
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nh₁ : ¬MeromorphicAt f x\n⊢ meromorphicTrailingCoeffAt f⁻¹ x = (meromorphicTrailingCoeffAt f x)⁻¹",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"False",... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.TrailingCoefficient | {
"line": 455,
"column": 4
} | {
"line": 455,
"column": 12
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nf : 𝕜 → 𝕜\nh₁ : ¬MeromorphicAt f x\n⊢ meromorphicTrailingCoeffAt f⁻¹ x = (meromorphicTrailingCoeffAt f x)⁻¹",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"False",... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 75,
"column": 4
} | {
"line": 75,
"column": 12
} | [
{
"pp": "case h.h\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nh : HasFiniteSupport d\nx u : 𝕜\n⊢ u ∉ ↑(Finite.toFinset h) → u ∉ Function.mulSupport fun u ↦ (x - u) ^ d u",
"usedConstants": [
"NormedCommRing.toNormedRing",
"MulOne.toOne",
"False",
"Function.mem_mu... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 114,
"column": 34
} | {
"line": 114,
"column": 42
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nu₀ : 𝕜\nhd : HasFiniteSupport d\nh₁d : ¬d u₀ = 0\nthis : (Function.mulSupport fun u ↦ (fun x ↦ x - u) ^ d u) ⊆ ↑(Finite.toFinset hd)\n⊢ u₀ ∈ Finite.toFinset hd",
"usedConstants": [
"False",
"eq_false",
"Function.mem_s... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 120,
"column": 32
} | {
"line": 120,
"column": 40
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nu₀ : 𝕜\nhd : HasFiniteSupport d\nh₁d : ¬d u₀ = 0\nthis✝ : (Function.mulSupport fun u ↦ (fun x ↦ x - u) ^ d u) ⊆ ↑(Finite.toFinset hd)\nthis : u₀ ∈ Finite.toFinset hd\nx : 𝕜\nhx : x ∈ support (update d u₀ 0)\nh₁x : x = u₀\n⊢ x ∈ ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 120,
"column": 32
} | {
"line": 120,
"column": 40
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nu₀ : 𝕜\nhd : HasFiniteSupport d\nh₁d : ¬d u₀ = 0\nthis✝ : (Function.mulSupport fun u ↦ (fun x ↦ x - u) ^ d u) ⊆ ↑(Finite.toFinset hd)\nthis : u₀ ∈ Finite.toFinset hd\nx : 𝕜\nhx : x ∈ support (update d u₀ 0)\nh₁x : ¬x = u₀\n⊢ x ∈... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Complex.CanonicalDecomposition | {
"line": 151,
"column": 20
} | {
"line": 151,
"column": 40
} | [
{
"pp": "w z : ℂ\nhzw : z - w ≠ 0\nhw : w ∈ ball 0 ‖z‖\nhz : z ∈ sphere 0 ‖z‖\nhR : 0 < ‖z‖\n⊢ ‖↑(‖z‖ ^ 2) - (starRingEnd ℂ) w * z‖ = ‖↑‖z‖ * (z - w)‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"HMul.hMul",
"congrArg",
... | ← normSq_eq_norm_sq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 127,
"column": 50
} | {
"line": 137,
"column": 59
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\n⊢ MeromorphicNFOn (∏ᶠ (u : 𝕜), (fun x ↦ x - u) ^ d u) univ",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"False",
"instHSMul",
... | by
classical
by_cases hd : d.support.Finite
· intro z hz
rw [extractFactor z hd]
right
use d z, (∏ᶠ u, (· - u) ^ update d z 0 u)
simp [analyticAt, ne_zero]
· rw [← mulSupport d] at hd
rw [finprod_of_infinite_mulSupport hd]
exact AnalyticOnNhd.meromorphicNFOn analyticOnNhd_const | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 12
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh : (support d).Finite\nu : 𝕜\nh₁ : ¬u = x\n⊢ u ∉ ↑h.toFinset → (x - u) ^ update d x 0 u = 1",
"usedConstants": [
"NormedCommRing.toNormedRing",
"MulOne.toOne",
"False",
"Function.update",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 12
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh : (support d).Finite\nu : 𝕜\nh₁ : ¬u = x\n⊢ u ∉ ↑h.toFinset → (x - u) ^ update d x 0 u = 1",
"usedConstants": [
"NormedCommRing.toNormedRing",
"MulOne.toOne",
"False",
"Function.update",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 192,
"column": 4
} | {
"line": 192,
"column": 12
} | [
{
"pp": "case neg\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh : (support d).Finite\nu : 𝕜\nh₁ : ¬u = x\n⊢ u ∉ ↑h.toFinset → (x - u) ^ update d x 0 u = 1",
"usedConstants": [
"NormedCommRing.toNormedRing",
"MulOne.toOne",
"False",
"Function.update",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 214,
"column": 4
} | {
"line": 214,
"column": 12
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh : HasFiniteSupport d\nthis : (Function.mulSupport fun u ↦ (fun x ↦ x - u) ^ d u) ⊆ ↑(Finite.toFinset h)\ny : 𝕜\nhy : y ∈ Finite.toFinset h\nhxy : x = y\n⊢ (if y = y then 1 else y - y) ^ d y = (y - y) ^ update d y 0 y",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 230,
"column": 4
} | {
"line": 230,
"column": 12
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh₁ : HasFiniteSupport d\nh₂ : x ∉ support d\nu : 𝕜\n⊢ u ∉ ↑(Finite.toFinset h₁) → u ∉ Function.mulSupport fun u ↦ (x - u) ^ d u",
"usedConstants": [
"NormedCommRing.toNormedRing",
"MulOne.toOne",
"False",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 236,
"column": 2
} | {
"line": 236,
"column": 10
} | [
{
"pp": "case e_a.h\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh₁ : HasFiniteSupport d\nh₂ : x ∉ support d\nthis : (Function.mulSupport fun u ↦ (x - u) ^ d u) ⊆ ↑(Finite.toFinset h₁)\ny : 𝕜\nhy : y ∈ Finite.toFinset h₁\nhCon : y = x\n⊢ False",
"usedConstants": [
"False",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 252,
"column": 6
} | {
"line": 252,
"column": 14
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh✝ : HasFiniteSupport d\ny : 𝕜\na✝ : y ∈ Finite.toFinset h✝\nh : x = y\n⊢ ‖(y - y) ^ update d y 0 y‖ ≠ 0",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Norm.norm",
"MulOne.toOne",
"False"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 258,
"column": 4
} | {
"line": 258,
"column": 12
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nd : 𝕜 → ℤ\nx : 𝕜\nh : HasFiniteSupport d\nthis : ∀ y ∈ Finite.toFinset h, ‖(x - y) ^ update d x 0 y‖ ≠ 0\nu : 𝕜\n⊢ u ∉ ↑(Finite.toFinset h) → u ∉ support fun u ↦ ↑(d u) * log ‖x - u‖",
"usedConstants": [
"NormedCommRing.toNormedRing",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Complex.Isometry | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 7
} | [
{
"pp": "f : ℂ →ₗᵢ[ℝ] ℂ\nh₂ : ∀ (z : ℂ), (f z).re = z.re\nz : ℂ\nh₁ : (f z).re * (f z).re + (f z).im * (f z).im = z.re * z.re + z.im * z.im\n⊢ (f z).im = z.im ∨ (f z).im = -z.im",
"usedConstants": [
"LinearIsometry",
"NormedCommRing.toSeminormedCommRing",
"Real",
"HMul.hMul",
"... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 363,
"column": 6
} | {
"line": 363,
"column": 19
} | [
{
"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 ... | Pi.zero_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 366,
"column": 62
} | {
"line": 366,
"column": 70
} | [
{
"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 ↦ ↑(... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 366,
"column": 62
} | {
"line": 366,
"column": 70
} | [
{
"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 ↦ ↑(... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 366,
"column": 62
} | {
"line": 366,
"column": 70
} | [
{
"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 ↦ ↑(... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 374,
"column": 51
} | {
"line": 374,
"column": 69
} | [
{
"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 ↦ ↑(... | simp [hg ⟨z, h₃z⟩] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 374,
"column": 51
} | {
"line": 374,
"column": 69
} | [
{
"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 ↦ ↑(... | simp [hg ⟨z, h₃z⟩] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 374,
"column": 51
} | {
"line": 374,
"column": 69
} | [
{
"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 ↦ ↑(... | simp [hg ⟨z, h₃z⟩] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 415,
"column": 4
} | {
"line": 415,
"column": 12
} | [
{
"pp": "case hy\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nx : 𝕜\nf g : 𝕜 → E\nD : 𝕜 → ℤ\nhD : HasFiniteSupport D\nh₁x : x ∈ U\nh₂x : AccPt x (𝓟 U)\nhf : MeromorphicAt f x\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 415,
"column": 4
} | {
"line": 415,
"column": 12
} | [
{
"pp": "case hy\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nx : 𝕜\nf g : 𝕜 → E\nD : 𝕜 → ℤ\nhD : HasFiniteSupport D\nh₁x : x ∈ U\nh₂x : AccPt x (𝓟 U)\nhf : MeromorphicAt f x\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.FactorizedRational | {
"line": 415,
"column": 4
} | {
"line": 415,
"column": 12
} | [
{
"pp": "case hy\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nx : 𝕜\nf g : 𝕜 → E\nD : 𝕜 → ℤ\nhD : HasFiniteSupport D\nh₁x : x ∈ U\nh₂x : AccPt x (𝓟 U)\nhf : MeromorphicAt f x\nh₁g : AnalyticAt 𝕜 g x\nh₂g : g x ≠ 0\nh... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Order | {
"line": 844,
"column": 8
} | {
"line": 844,
"column": 38
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\ng : 𝕜 → 𝕜\nhg : AnalyticAt 𝕜 g x\nhg' : deriv g x ≠ 0\ninst✝¹ : CompleteSpace 𝕜\ninst✝ : CharZero 𝕜\nhf : MeromorphicAt f (g x)\nhgo : analyticO... | hf.meromorphicOrderAt_comp hg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Complex.Hadamard | {
"line": 137,
"column": 2
} | {
"line": 138,
"column": 53
} | [
{
"pp": "case refine_1\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℂ → E\nz : ℂ\nhD : z ∈ verticalClosedStrip 0 1\nhB : BddAbove (norm ∘ f '' verticalClosedStrip 0 1)\n⊢ BddAbove (norm ∘ f '' re ⁻¹' {z.re})",
"usedConstants": [
"Iff.mpr",
"Set.singleton_subset_iff",
"Norm.norm",
... | · revert hB; gcongr
exact preimage_mono (singleton_subset_iff.mpr hD) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Complex.ExponentialBounds | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 59
} | [
{
"pp": "t : |2⁻¹| = 2⁻¹\nz : |log 2 - ∑ x ∈ range 34, 2⁻¹ ^ (x + 1) / (↑x + 1)| ≤ 1 / 17179869184\n⊢ |log 2 - 287209 / 414355| ≤ 1 / 17179869184 + (1 / 10 ^ 10 - 1 / 2 ^ 34)",
"usedConstants": [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
... | apply le_trans (_root_.abs_sub_le _ _ _) (add_le_add z _) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Complex.ExponentialBounds | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 59
} | [
{
"pp": "t : |2 / 3| = 2 / 3\nz : |log 3 - ∑ i ∈ range 70, (2 / 3) ^ (i + 1) / (↑i + 1)| ≤ (2 / 3) ^ (70 + 1) / 3⁻¹\n⊢ |log 3 - 109861228867 / 100000000000| ≤ (2 / 3) ^ 71 / 3⁻¹ + (1 / 10 ^ 10 - (2 / 3) ^ 71 / 3⁻¹)",
"usedConstants": [
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"abs",... | apply le_trans (_root_.abs_sub_le _ _ _) (add_le_add z _) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Complex.ExponentialBounds | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 59
} | [
{
"pp": "t : |4 / 5| = 4 / 5\nz : |log 5 - ∑ i ∈ range 130, (4 / 5) ^ (i + 1) / (↑i + 1)| ≤ (4 / 5) ^ (130 + 1) / 5⁻¹\n⊢ |log 5 - 160943791243 / 100000000000| ≤ (4 / 5) ^ 131 / 5⁻¹ + (1 / 10 ^ 10 - (4 / 5) ^ 131 / 5⁻¹)",
"usedConstants": [
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"a... | apply le_trans (_root_.abs_sub_le _ _ _) (add_le_add z _) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Complex.Hadamard | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 42
} | [
{
"pp": "l u : ℝ\nhul : l < u\nz : ℂ\n⊢ z.re / (u - l) + z.im * 0 / ((u - l) * (u - l)) - l / (u - l) = (z.re - l) / (u - l)",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Real",
"instHDiv",
"HMul.hMul",
"Real.instZero",
"Real.instAddMonoid",
... | simp only [mul_zero, zero_div, add_zero] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.InnerProductSpace.Harmonic.Basic | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 12
} | [
{
"pp": "case h\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace ℝ E\ninst✝² : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf₁ f₂ : E → F\nx : E\nh₁ : HarmonicAt f₁ x\nh₂ : HarmonicAt f₂ x\n⊢ ∀ (a : E), Δ (f₁ + f₂) a = (Δ f₁ + Δ f₂) a → Δ f... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Analysis.InnerProductSpace.Harmonic.Basic | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 12
} | [
{
"pp": "case h\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace ℝ E\ninst✝² : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf₁ f₂ : E → F\nx : E\nh₁ : HarmonicAt f₁ x\nh₂ : HarmonicAt f₂ x\n⊢ ∀ (a : E), Δ (f₁ - f₂) a = (Δ f₁ - Δ f₂) a → Δ f... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
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