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.AbsoluteValue.Equivalence | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x ≤ 1 ↔ w x ≤ 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ 1 ≤ v x ↔ 1 ≤ w x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x = 1 ↔ w x = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 248,
"column": 4
} | {
"line": 248,
"column": 20
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : r < 0\n⊢ IsPreconnected (sphere x r)",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Metric.sphere_eq_empty_of_neg",
"PseudoMetricSpace.toUniformSpace",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 19
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 19
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 185,
"column": 55
} | {
"line": 185,
"column": 66
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 15
} | [
{
"pp": "case refine_2\nR : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 209,
"column": 4
} | {
"line": 209,
"column": 19
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 213,
"column": 4
} | {
"line": 213,
"column": 19
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 216,
"column": 4
} | {
"line": 216,
"column": 19
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 220,
"column": 55
} | {
"line": 220,
"column": 66
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv | {
"line": 188,
"column": 4
} | {
"line": 188,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\nf' : E ≃L[𝕜] F\na : E\ninst✝ : CompleteSpace E\nhf : HasStrictFDerivAt f (↑f') a\n⊢ HasStrictFD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 15
} | [
{
"pp": "case inl\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : w a ≠ 1\nhwa : w a < 1\n⊢ 0 < log (w a) / log (v a)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 15
} | [
{
"pp": "case inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nthis :\n ∀ {a : F},\n a ≠ 0 → v a ≠ 1 → ∀ {b : F}, b ≠ 0 → v b ≠ 1 → log (v b) / log (w b) ≠... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 310,
"column": 4
} | {
"line": 310,
"column": 15
} | [
{
"pp": "case inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nha : 1 < v a\nthis :\n ∀ {a : F},\n a ≠ 0 →\n v a ≠ 1 → ∀ {b : F}, b ≠ 0 → v b ≠ 1 → lo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 386,
"column": 20
} | {
"line": 386,
"column": 51
} | [
{
"pp": "F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nx✝ : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F)) ∧ Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nhi : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F))\nright✝ : Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 387,
"column": 4
} | {
"line": 387,
"column": 35
} | [
{
"pp": "F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nx✝ : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F)) ∧ Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nhi : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F))\nright✝ : Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv | {
"line": 35,
"column": 4
} | {
"line": 35,
"column": 28
} | [
{
"pp": "x : ℂ\nh : x ∈ slitPlane\nh0 : x ≠ 0\n⊢ HasStrictDerivAt (↑expOpenPartialHomeomorph) x (↑expOpenPartialHomeomorph.symm x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 35
} | [
{
"pp": "f : ℝ → ℂ\nx : ℝ\nf' : ℂ\nh₁ : HasStrictDerivAt f f' x\nh₂ : f x ∈ slitPlane\n⊢ HasStrictDerivAt (fun t ↦ log (f t)) (f' / f x) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"Real",
"instHDiv",
"NormedSpace.toIsBoundedSMul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv | {
"line": 86,
"column": 2
} | {
"line": 86,
"column": 35
} | [
{
"pp": "f : ℝ → ℂ\nx : ℝ\nf' : ℂ\nh₁ : HasDerivAt f f' x\nh₂ : f x ∈ slitPlane\n⊢ HasDerivAt (fun t ↦ log (f t)) (f' / f x) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"Real",
"instHDiv",
"NormedSpace.toIsBoundedSMul",
"HM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 35
} | [
{
"pp": "f : ℝ → ℂ\ns : Set ℝ\nx : ℝ\nf' : ℂ\nh₁ : HasDerivWithinAt f f' s x\nh₂ : f x ∈ slitPlane\n⊢ HasDerivWithinAt (fun t ↦ log (f t)) (f' / f x) s x",
"usedConstants": [
"HasDerivWithinAt.congr_simp",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nf' : E →L[𝕜] F\ns : Set E\nc : ℝ≥0\nhf : ApproximatesLinearOn f f' s c\n⊢ LipschitzWith (‖f'‖₊ +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 190,
"column": 8
} | {
"line": 190,
"column": 35
} | [
{
"pp": "case hbc\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\ninst✝ : CompleteSpace E\ns : Set E\nc : ℝ≥0\nf' : E →L[𝕜] F\nhf : ApproximatesLinearO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 77,
"column": 11
} | {
"line": 77,
"column": 84
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : analyticOrderAt f z₀ = ⊤\n⊢ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0",
"usedConstants": [
"ENat.zero_ne_top._simp_1",
"NormedCommRing.toNormedRing",
... | by unfold analyticOrderAt at hf; split_ifs at hf with h <;> simp [*] at * | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.Order | {
"line": 82,
"column": 2
} | {
"line": 83,
"column": 9
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\n⊢ EventuallyConst f (𝓝 z₀) ↔ analyticOrderAt (fun x ↦ f x - f z₀) z₀ = ⊤",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 15
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh : ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\n⊢ ↑n ≤ ⊤ ↔ ∃ g, AnalyticAt 𝕜 g z₀ ∧ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 54,
"column": 6
} | {
"line": 54,
"column": 32
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 57,
"column": 53
} | {
"line": 57,
"column": 64
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 168,
"column": 8
} | {
"line": 168,
"column": 45
} | [
{
"pp": "case neg.refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh✝ : ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\nm : ℕ := ⋯.choose\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhm : ∀ᶠ (z : 𝕜... | simp [m, Nat.sub_ne_zero_of_lt hg_ne] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Analytic.Order | {
"line": 168,
"column": 8
} | {
"line": 168,
"column": 45
} | [
{
"pp": "case neg.refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh✝ : ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\nm : ℕ := ⋯.choose\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhm : ∀ᶠ (z : 𝕜... | simp [m, Nat.sub_ne_zero_of_lt hg_ne] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Order | {
"line": 168,
"column": 8
} | {
"line": 168,
"column": 45
} | [
{
"pp": "case neg.refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh✝ : ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\nm : ℕ := ⋯.choose\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhm : ∀ᶠ (z : 𝕜... | simp [m, Nat.sub_ne_zero_of_lt hg_ne] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Order | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 54
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : f =ᶠ[𝓝 z₀] g\nhf : AnalyticAt 𝕜 f z₀\n⊢ analyticOrderAt f z₀ = analyticOrderAt g z₀",
"usedConstants": [
"ENat.eq_of_forall_natCa... | refine ENat.eq_of_forall_natCast_le_iff fun n ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Analytic.Order | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 54
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\n⊢ analyticOrderAt (-f) z₀ = analyticOrderAt f z₀",
"usedConstants": [
"NegZeroClass.toNeg",
"Pi.instNeg",
... | refine ENat.eq_of_forall_natCast_le_iff fun n ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Analytic.Order | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\n⊢ min (analyticOrderAt f z₀) (analyticOrderAt g z₀) ≤ analyticOrderAt (f - g) z₀",
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 215,
"column": 18
} | {
"line": 215,
"column": 42
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt (f + g) z₀ ≤ analyticOrderAt f z₀",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 216,
"column": 8
} | {
"line": 216,
"column": 28
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt f z₀ ≤ analyticOrderAt (f + g) z₀",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 227,
"column": 4
} | {
"line": 227,
"column": 24
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg✝ : analyticOrderAt f z₀ ≠ analyticOrderAt g z₀\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt (f + g) z₀ = min (analytic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 228,
"column": 4
} | {
"line": 228,
"column": 24
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ ≠ analyticOrderAt g z₀\nhgf : analyticOrderAt g z₀ < analyticOrderAt f z₀\n⊢ analyticOrderAt (f + g) z₀ = min (analyticO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 80,
"column": 6
} | {
"line": 80,
"column": 17
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 285,
"column": 4
} | {
"line": 285,
"column": 91
} | [
{
"pp": "case coe.e_a\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ≠... | obtain ⟨U, hUf, hUo, hUx⟩ := eventually_nhds_iff.mp (hfF.and hFa.eventually_analyticAt) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Analytic.Order | {
"line": 296,
"column": 10
} | {
"line": 296,
"column": 21
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 37
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 297,
"column": 10
} | {
"line": 297,
"column": 51
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\ninst✝¹ : CompleteSpace E\ninst✝ : CharZero 𝕜\ns : ℕ\nhrne : s + 1 ≠ 0\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F x\nhFne : F x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 90,
"column": 8
} | {
"line": 90,
"column": 37
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : E → F\ns : Set E\nx : E\nf' : E →L[ℝ] F\nf_diff : DifferentiableOn ℝ f s\ns_conv : Convex ℝ s\ns_open : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 39
} | [
{
"pp": "case pos\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_4\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhf : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteMulSupport F\n⊢ MeromorphicAt (∏ᶠ (i : ι), F i) x",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 37
} | [
{
"pp": "case pos\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_4\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhF : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteSupport F\n⊢ MeromorphicAt (∑ᶠ (i : ι), F i) x",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 174,
"column": 14
} | {
"line": 174,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf : 𝕜 → E\nh : MeromorphicAt (-f) x\n⊢ MeromorphicAt f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 189,
"column": 20
} | {
"line": 189,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nh : MeromorphicAt (f + g) x\n⊢ MeromorphicAt g x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 222,
"column": 20
} | {
"line": 222,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhf : MeromorphicAt f x\nh : MeromorphicAt (f - g) x\n⊢ MeromorphicAt g x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 272,
"column": 4
} | {
"line": 272,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\ninst✝ : CompleteSpace E\ns : Set E\nc : ℝ≥0\nf' : E →L[𝕜] F\nhf : ApproximatesLinearOn f f' s c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 238,
"column": 20
} | {
"line": 238,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : 𝕜\nf g : 𝕜 → E\nhg : MeromorphicAt g x\nh : MeromorphicAt (f - g) x\n⊢ MeromorphicAt f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 332,
"column": 2
} | {
"line": 332,
"column": 19
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nx : 𝕜\nhf : AnalyticAt 𝕜 f x\nhfx : f x = 0\nhf' : deriv f x ≠ 0\n⊢ analyticOrderAt f x = 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 341,
"column": 6
} | {
"line": 341,
"column": 58
} | [
{
"pp": "case neg\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nn : ℕ\nIH : ∀ {f : 𝕜 → E}, AnalyticAt 𝕜 f z₀ → (↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 23
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nn : ℕ\nIH : ∀ {f : 𝕜 → E}, AnalyticAt 𝕜 f z₀ → (↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0)\nf : 𝕜 → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 337,
"column": 2
} | {
"line": 345,
"column": 58
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nhf : AnalyticAt 𝕜 f z₀\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0",
"usedCons... | induction n generalizing f with
| zero => simp
| succ n IH =>
by_cases hfz : f z₀ = 0; swap
· simpa [analyticOrderAt_eq_zero.mpr (.inr hfz)] using ⟨0, by simp, by simpa⟩
have : analyticOrderAt (deriv f) z₀ + 1 = analyticOrderAt f z₀ := by
simpa [hfz] using hf.analyticOrderAt_deriv_add_one
simp... | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Analysis.Analytic.Order | {
"line": 337,
"column": 2
} | {
"line": 345,
"column": 58
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nhf : AnalyticAt 𝕜 f z₀\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0",
"usedCons... | induction n generalizing f with
| zero => simp
| succ n IH =>
by_cases hfz : f z₀ = 0; swap
· simpa [analyticOrderAt_eq_zero.mpr (.inr hfz)] using ⟨0, by simp, by simpa⟩
have : analyticOrderAt (deriv f) z₀ + 1 = analyticOrderAt f z₀ := by
simpa [hfz] using hf.analyticOrderAt_deriv_add_one
simp... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Order | {
"line": 337,
"column": 2
} | {
"line": 345,
"column": 58
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nn : ℕ\nz₀ : 𝕜\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nhf : AnalyticAt 𝕜 f z₀\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ∀ i < n, iteratedDeriv i f z₀ = 0",
"usedCons... | induction n generalizing f with
| zero => simp
| succ n IH =>
by_cases hfz : f z₀ = 0; swap
· simpa [analyticOrderAt_eq_zero.mpr (.inr hfz)] using ⟨0, by simp, by simpa⟩
have : analyticOrderAt (deriv f) z₀ + 1 = analyticOrderAt f z₀ := by
simpa [hfz] using hf.analyticOrderAt_deriv_add_one
simp... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Order | {
"line": 353,
"column": 4
} | {
"line": 353,
"column": 47
} | [
{
"pp": "𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nhorder : analyticOrderAt f z₀ = ↑n + 1\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 37
} | [
{
"pp": "𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CharZero 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nhorder : analyticOrderAt f z₀ = ↑n + 1\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 370,
"column": 4
} | {
"line": 370,
"column": 15
} | [
{
"pp": "case succ\n𝕜 : Type u_3\nE : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CompleteSpace E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\ninst✝ : CharZero 𝕜\nn' : ℕ\nhk : ∀ {n : ℕ}, ↑n = analyticOrderAt f z₀ → n ≠ 0 → n' ≤ n → analyt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 307,
"column": 14
} | {
"line": 307,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nh : MeromorphicAt f⁻¹ x\n⊢ MeromorphicAt f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 317,
"column": 12
} | {
"line": 317,
"column": 39
} | [
{
"pp": "case zero\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\n⊢ MeromorphicAt (f ^ 0) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 318,
"column": 17
} | {
"line": 318,
"column": 44
} | [
{
"pp": "case succ\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\nhm : MeromorphicAt (f ^ m) x\n⊢ MeromorphicAt (f ^ (m + 1)) x",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 323,
"column": 15
} | {
"line": 323,
"column": 68
} | [
{
"pp": "case ofNat\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\n⊢ MeromorphicAt (f ^ Int.ofNat m) x",
"usedConstants": [
"zpow_natCast",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 324,
"column": 17
} | {
"line": 324,
"column": 57
} | [
{
"pp": "case negSucc\n𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nx : 𝕜\nf : 𝕜 → 𝕜'\nhf : MeromorphicAt f x\nm : ℕ\n⊢ MeromorphicAt (f ^ Int.negSucc m) x",
"usedConstants": [
"Eq.mpr",
"NormedCommRing... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 414,
"column": 6
} | {
"line": 414,
"column": 22
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : CharZero 𝕜\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nhf : AnalyticAt 𝕜 f 0\nn : ℕ\nF : 𝕜 → E\nhFa : AnalyticAt 𝕜 F 0\nhF : ∀ᶠ (z : 𝕜) in 𝓝 0, f z = ∑ i ∈ Fins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 335,
"column": 4
} | {
"line": 339,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\nf' : E ≃L[𝕜] F\nc : ℝ≥0\ninst✝ : CompleteSpace E\nhf : ApproximatesLinearOn f (↑f') univ c\nhc ... | have hp : ∀ᶠ r : ℝ in atTop, p ((N⁻¹ - c) * r) := by
have hr : ∀ᶠ r : ℝ in atTop, 0 ≤ r := eventually_ge_atTop 0
refine hr.mono fun r hr => Subset.trans ?_ (image_subset_range f (closedBall 0 r))
refine hf.surjOn_closedBall_of_nonlinearRightInverse f'.toNonlinearRightInverse hr ?_
exact subset_u... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 400,
"column": 17
} | {
"line": 400,
"column": 79
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nh : MeromorphicAt f x\nn : ℕ\nIH : MeromorphicAt (deriv^[n] f) x\n⊢ MeromorphicAt (deriv^[n + 1] f) x",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Extend | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nx : ℝ\nf_diff : ∀ (y : ℝ), y ≠ x → HasDerivAt f (g y) y\nhf : ContinuousAt f x\nhg : ContinuousAt g x\nA : HasDerivWithinAt f (g x) (Ici x) x\nB : HasDerivWithinAt f (g x) (Iic x) x\n⊢ HasDerivAt f (g x) x",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 49,
"column": 47
} | {
"line": 49,
"column": 58
} | [
{
"pp": "⊢ sin ~[𝓝 0] id",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 547,
"column": 14
} | {
"line": 547,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nU : Set 𝕜\nh : MeromorphicOn (-f) U\n⊢ MeromorphicOn f U",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 594,
"column": 14
} | {
"line": 594,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\ns : 𝕜 → 𝕜'\nU : Set 𝕜\nh : MeromorphicOn s⁻¹ U\n⊢ MeromorphicOn s U",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 323,
"column": 47
} | {
"line": 323,
"column": 58
} | [
{
"pp": "⊢ sin ~[𝓝 0] id",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 43,
"column": 2
} | {
"line": 43,
"column": 88
} | [
{
"pp": "p : ℂ × ℂ\nhp : p.1 ∈ slitPlane\nA : p.1 ≠ 0\nthis : (fun x ↦ x.1 ^ x.2) =ᶠ[𝓝 p] fun x ↦ cexp (log x.1 * x.2)\n⊢ HasStrictFDerivAt (fun x ↦ cexp (log x.1 * x.2))\n (p.1 ^ p.2 • (p.2 / p.1) • ContinuousLinearMap.fst ℂ ℂ ℂ + p.1 ^ p.2 • log p.1 • ContinuousLinearMap.snd ℂ ℂ ℂ) p",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 649,
"column": 2
} | {
"line": 649,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\nU : Set 𝕜\ninst✝¹ : SecondCountableTopology 𝕜\ninst✝ : CompleteSpace E\nh : MeromorphicOn f U\n⊢ {z | AnalyticAt 𝕜 f z}ᶜᶜ ∈ codiscreteWithin U",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 752,
"column": 2
} | {
"line": 752,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nf : 𝕜 → E\ninst✝¹ : SecondCountableTopology 𝕜\ninst✝ : CompleteSpace E\nh : Meromorphic f\n⊢ {z | AnalyticAt 𝕜 f z}ᶜ.Countable",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 766,
"column": 31
} | {
"line": 766,
"column": 42
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nf : 𝕜 → E\ninst✝⁵ : MeasurableSpace 𝕜\ninst✝⁴ : SecondCountableTopology 𝕜\ninst✝³ : BorelSpace 𝕜\ninst✝² : MeasurableSpace E\ninst✝¹ : CompleteSpace E\ninst✝ : BorelSpace E\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 54
} | [
{
"pp": "case inr\nx y : ℂ\nh : x ≠ 0 ∨ y ≠ 0\nhx : ¬x = 0\n⊢ HasStrictDerivAt (fun y ↦ x ^ y) (x ^ y * log x) y",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 193,
"column": 2
} | {
"line": 193,
"column": 13
} | [
{
"pp": "f g : ℂ → ℂ\nf' g' x : ℂ\nhf : HasStrictDerivAt f f' x\nhg : HasStrictDerivAt g g' x\nh0 : f x ∈ slitPlane\n⊢ HasStrictDerivAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 201,
"column": 2
} | {
"line": 201,
"column": 48
} | [
{
"pp": "x c : ℂ\nh : x ∈ slitPlane\n⊢ HasStrictDerivAt (fun z ↦ z ^ c) (c * x ^ (c - 1)) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 212,
"column": 2
} | {
"line": 212,
"column": 19
} | [
{
"pp": "f g : ℂ → ℂ\nf' g' x : ℂ\nhf : HasDerivAt f f' x\nhg : HasDerivAt g g' x\nh0 : f x ∈ slitPlane\n⊢ HasDerivAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 225,
"column": 2
} | {
"line": 225,
"column": 19
} | [
{
"pp": "f g : ℂ → ℂ\ns : Set ℂ\nf' g' x : ℂ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\nh0 : f x ∈ slitPlane\n⊢ HasDerivWithinAt (fun x ↦ f x ^ g x) (g x * f x ^ (g x - 1) * f' + f x ^ g x * Complex.log (f x) * g') s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 517,
"column": 12
} | {
"line": 517,
"column": 23
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 0 sin x| ≤ 1",
"usedConstants": [
"iteratedDeriv_zero",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.lattice",
"Real.denselyNormedField",
"abs",
"congrArg",
"id",
"Real.normedAddCommGroup",
"Real.instAddGroup... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 518,
"column": 12
} | {
"line": 518,
"column": 23
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 1 sin x| ≤ 1",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
"deriv",
"NormedSpace.toModule",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 519,
"column": 16
} | {
"line": 519,
"column": 27
} | [
{
"pp": "n✝ : ℕ\nx : ℝ\nn : ℕ\n⊢ |iteratedDeriv (n + 2) sin x| ≤ 1",
"usedConstants": [
"Eq.mpr",
"abs_neg",
"Real.instLE",
"Real",
"Pi.instNeg",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
"id",
"Real.iter... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 524,
"column": 12
} | {
"line": 524,
"column": 23
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 0 cos x| ≤ 1",
"usedConstants": [
"iteratedDeriv_zero",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
"id",
"Real.normedAddCommGroup",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 525,
"column": 12
} | {
"line": 525,
"column": 23
} | [
{
"pp": "n : ℕ\nx : ℝ\n⊢ |iteratedDeriv 1 cos x| ≤ 1",
"usedConstants": [
"Eq.mpr",
"abs_neg",
"Real.instLE",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
"deriv",
"NormedSpace.t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | {
"line": 526,
"column": 16
} | {
"line": 526,
"column": 27
} | [
{
"pp": "n✝ : ℕ\nx : ℝ\nn : ℕ\n⊢ |iteratedDeriv (n + 2) cos x| ≤ 1",
"usedConstants": [
"Eq.mpr",
"abs_neg",
"Real.instLE",
"Real",
"Pi.instNeg",
"Real.lattice",
"Real.denselyNormedField",
"Real.cos",
"abs",
"congrArg",
"id",
"Real.iter... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 52
} | [
{
"pp": "x : ℝ\nhx : x ≠ 0\nr : ℂ\nhr : r ≠ 0\nthis : HasDerivAt (fun y ↦ r * (↑y ^ (r - 1 + 1) / (r - 1 + 1))) (r * ↑x ^ (r - 1)) x\n⊢ HasDerivAt (fun y ↦ ↑y ^ r) (r * ↑x ^ (r - 1)) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 336,
"column": 24
} | {
"line": 336,
"column": 37
} | [
{
"pp": "case inl\n⊢ (deriv fun x ↦ 1) =O[atTop] fun x ↦ x ^ (re 0 - 1)",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real",
"Complex.instNormedAddCommGroup",
"deriv_const'",
"Real.denselyNormedField",
"congrArg",
... | deriv_const', | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.Binomial | {
"line": 485,
"column": 2
} | {
"line": 485,
"column": 13
} | [
{
"pp": "case ha\nR : Type u_1\ninst✝¹ : Field R\ninst✝ : CharZero R\na : R\nn : ℕ\n⊢ ↑n.factorial ≠ 0",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"DivisionSemiring.toGroupWithZero",
"Field.toDivisionR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 566,
"column": 2
} | {
"line": 566,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nhf : AnalyticOnNhd 𝕜 f U\nhU : IsConnected U\nthis : ConnectedSpace ↑U\nv : ↑U\n⊢ (∀ (u : ↑U), analyticOrderAt f ↑u ≠ ⊤) ∨ ∀ (u : ↑U), analyticOrderAt f ↑u... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 402,
"column": 4
} | {
"line": 402,
"column": 15
} | [
{
"pp": "case inr\nx : ℝ\nhx✝ : x ≠ 0\np : ℝ\nhx : 0 < x\n⊢ HasStrictDerivAt (fun x ↦ x ^ p) (p * x ^ (p - 1)) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 13
} | [
{
"pp": "a : ℝ\nha : 0 < a\nx : ℝ\n⊢ HasStrictDerivAt (fun x ↦ a ^ x) (a ^ x * log a) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 435,
"column": 2
} | {
"line": 435,
"column": 13
} | [
{
"pp": "a x : ℝ\nha : a < 0\n⊢ HasStrictDerivAt (fun x ↦ a ^ x) (a ^ x * log a - rexp (log a * x) * sin (x * π) * π) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 476,
"column": 82
} | {
"line": 476,
"column": 93
} | [
{
"pp": "p : ℝ\nh : ↑0 ≤ p\nx : ℝ\n⊢ 0 ≤ p",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 654,
"column": 2
} | {
"line": 654,
"column": 64
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nx : E\np : ℝ\nm : ℕ\nhf : ContDiffAt ℝ (↑m) f x\nh : ↑m ≤ p\n⊢ ContDiffAt ℝ (↑m) (fun x ↦ f x ^ p) x",
"usedConstants": [
"ContDiffAt",
"Eq.mpr",
"Real.instPow",
"Real",
"ENat.instNatCast"... | rw [← contDiffWithinAt_univ] at *; exact hf.rpow_const_of_le h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 654,
"column": 2
} | {
"line": 654,
"column": 64
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\nx : E\np : ℝ\nm : ℕ\nhf : ContDiffAt ℝ (↑m) f x\nh : ↑m ≤ p\n⊢ ContDiffAt ℝ (↑m) (fun x ↦ f x ^ p) x",
"usedConstants": [
"ContDiffAt",
"Eq.mpr",
"Real.instPow",
"Real",
"ENat.instNatCast"... | rw [← contDiffWithinAt_univ] at *; exact hf.rpow_const_of_le h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Binomial | {
"line": 530,
"column": 37
} | {
"line": 530,
"column": 65
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Ring R\ninst✝ : BinomialRing R\nr s : R\nk : ℕ\nh : Commute r s\nx : ℕ × ℕ\nhx : x ∈ antidiagonal k\n⊢ ↑(k.choose x.1) * ((descPochhammer ℤ x.1).smeval r * (descPochhammer ℤ x.2).smeval s) =\n ↑(k.choose x.1) * ↑x.1.factorial * (choose r x.1 * (↑x.2.factorial * choose s x.2))"... | ← nsmul_eq_mul x.2.factorial | Lean.Elab.Tactic.evalRewriteSeq | null |
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