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.Calculus.ContDiffHolder.Pointwise | {
"line": 254,
"column": 4
} | {
"line": 254,
"column": 68
} | [
{
"pp": "case succ\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nk : ℕ\nα : ↑I\nf : E → F\na : E\nhf : ContDiffPointwiseHolderAt k α f a\nm : ℕ\nihm : ∀ {l : ℕ}, l + m ≤ k → ContDiffPointwiseHolderAt l α (iteratedFDe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 15
} | [
{
"pp": "case inl\n⊢ deriv (fun x ↦ |x|) 0 = ↑(SignType.sign 0)",
"usedConstants": [
"SignType.cast",
"Eq.mpr",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.instZero",
"abs",
"congrArg",
"deriv",
"PartialOrder... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 20
} | [
{
"pp": "case inr\nx : ℝ\nhx : x ≠ 0\n⊢ deriv (fun x ↦ |x|) x = ↑(SignType.sign x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Pi | {
"line": 26,
"column": 4
} | {
"line": 26,
"column": 15
} | [
{
"pp": "case inl\n𝕜 : Type u_1\nι : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : NontriviallyNormedField 𝕜\nE : ι → Type u_3\ninst✝¹ : (i : ι) → NormedAddCommGroup (E i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (E i)\nx : (i : ι) → E i\nj : ι\ny : E j\n⊢ HasFDerivAt (fun x_1 ↦ Function.update x j x_1 j) (Pi.single j ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Pi | {
"line": 27,
"column": 4
} | {
"line": 27,
"column": 21
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nι : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : NontriviallyNormedField 𝕜\nE : ι → Type u_3\ninst✝¹ : (i : ι) → NormedAddCommGroup (E i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (E i)\nx : (i : ι) → E i\ni : ι\ny : E i\nj : ι\nhij : j ≠ i\n⊢ HasFDerivAt (fun x_1 ↦ Function.update x i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Pi | {
"line": 27,
"column": 4
} | {
"line": 27,
"column": 43
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nι : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : NontriviallyNormedField 𝕜\nE : ι → Type u_3\ninst✝¹ : (i : ι) → NormedAddCommGroup (E i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (E i)\nx : (i : ι) → E i\ni : ι\ny : E i\nj : ι\nhij : j ≠ i\n⊢ HasFDerivAt (fun x_1 ↦ Function.update x i ... | simpa [hij] using hasFDerivAt_const _ _ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Analysis.Calculus.FDeriv.Pi | {
"line": 27,
"column": 4
} | {
"line": 27,
"column": 43
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nι : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : NontriviallyNormedField 𝕜\nE : ι → Type u_3\ninst✝¹ : (i : ι) → NormedAddCommGroup (E i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (E i)\nx : (i : ι) → E i\ni : ι\ny : E i\nj : ι\nhij : j ≠ i\n⊢ HasFDerivAt (fun x_1 ↦ Function.update x i ... | simpa [hij] using hasFDerivAt_const _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.FDeriv.Pi | {
"line": 27,
"column": 4
} | {
"line": 27,
"column": 43
} | [
{
"pp": "case inr\n𝕜 : Type u_1\nι : Type u_2\ninst✝³ : DecidableEq ι\ninst✝² : NontriviallyNormedField 𝕜\nE : ι → Type u_3\ninst✝¹ : (i : ι) → NormedAddCommGroup (E i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (E i)\nx : (i : ι) → E i\ni : ι\ny : E i\nj : ι\nhij : j ≠ i\n⊢ HasFDerivAt (fun x_1 ↦ Function.update x i ... | simpa [hij] using hasFDerivAt_const _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 875,
"column": 8
} | {
"line": 875,
"column": 86
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : Measure α\ninst✝¹ : SFinite μ\ninst✝ : μ.OuterRegular\nε : ℝ≥0∞\nhε : ε ≠ 0\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 208,
"column": 86
} | {
"line": 211,
"column": 19
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : NontriviallyNormedField 𝕜\nD : Type uD\ninst✝⁷ : NormedAddCommGroup D\ninst✝⁶ : NormedSpace 𝕜 D\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type uF\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type uG\ninst✝¹ : NormedAddCommGro... | by
simp_rw [← iteratedFDerivWithin_univ]
exact B.norm_iteratedFDerivWithin_le_of_bilinear hf.contDiffOn hg.contDiffOn uniqueDiffOn_univ
(mem_univ x) hn | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nι : Type u_2\nA' : Type u_4\ninst✝³ : NormedCommRing A'\ninst✝² : NormedAlgebra 𝕜 A'\ninst✝¹ : DecidableEq ι\ninst✝ : NormOneClass A'\nu : Finset ι\nf : ι → E → A'\nN : ℕ∞ω\nhf : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 363,
"column": 4
} | {
"line": 364,
"column": 42
} | [
{
"pp": "case hz\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nFu : Type u\ninst✝³ : NormedAddCommGroup Fu\ninst✝² : NormedSpace 𝕜 Fu\nf : E → Fu\ns : Set E\nt : Set Fu\nx : E\nht : UniqueDiffOn 𝕜 t\nhs : UniqueDiffOn 𝕜 s\nhst : Ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 370,
"column": 4
} | {
"line": 370,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nFu : Type u\ninst✝³ : NormedAddCommGroup Fu\ninst✝² : NormedSpace 𝕜 Fu\nf : E → Fu\ns : Set E\nt : Set Fu\nx : E\nht : UniqueDiffOn 𝕜 t\nhs : UniqueDiffOn 𝕜 s\nhst : MapsTo f s ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Star | {
"line": 125,
"column": 8
} | {
"line": 125,
"column": 19
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : StarRing 𝕜\nE : Type u_2\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁸ : NormedAddCommGroup F\ninst✝⁷ : StarAddMonoid F\ninst✝⁶ : NormedSpace 𝕜 F\ninst✝⁵ : StarModule 𝕜 F\ninst✝⁴ : ContinuousStar F\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Star | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 13
} | [
{
"pp": "𝕜 : Type u\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : StarRing 𝕜\nF : Type v\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\ninst✝³ : StarAddMonoid F\ninst✝² : StarModule 𝕜 F\ninst✝¹ : ContinuousStar F\nf : 𝕜 → F\nf' : F\ninst✝ : TrivialStar 𝕜\nL : Filter (𝕜 × 𝕜)\nh : HasDerivAtFi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 954,
"column": 10
} | {
"line": 955,
"column": 76
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : Measure α\ninst✝¹ : SFinite μ\ninst✝ : μ.OuterRegular\nε : ℝ≥0∞\nhε : ε ≠ 0\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 956,
"column": 8
} | {
"line": 956,
"column": 57
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : Measure α\ninst✝¹ : SFinite μ\ninst✝ : μ.OuterRegular\nε : ℝ≥0∞\nhε : ε ≠ 0\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 964,
"column": 8
} | {
"line": 964,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : Measure α\ninst✝¹ : SFinite μ\ninst✝ : μ.OuterRegular\nε : ℝ≥0∞\nhε : ε ≠ 0\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 963,
"column": 6
} | {
"line": 964,
"column": 49
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : Measure α\ninst✝¹ : SFinite μ\ninst✝ : μ.OuterRegular\nε : ℝ≥0∞\nhε : ε ≠ 0\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ ... | obtain ⟨y, yt0, hxy⟩ : ∃ y : α, y ∈ t0 ∧ x ∈ closedBall y (r0 y) := by
simpa [s', hx, -mem_closedBall] using h'x | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 439,
"column": 6
} | {
"line": 439,
"column": 40
} | [
{
"pp": "case h.hbc.ha\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nFu : Type u\ninst✝³ : NormedAddCommGroup Fu\ninst✝² : NormedSpace 𝕜 Fu\nf : E → Fu\ns : Set E\nt : Set Fu\nx : E\nht : UniqueDiffOn 𝕜 t\nhs : UniqueDiffOn 𝕜 s\nhs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 466,
"column": 4
} | {
"line": 466,
"column": 93
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type uF\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type uG\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nn : ℕ\ns : Set E\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DerivativeTest | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 78
} | [
{
"pp": "case refine_2\nf : ℝ → ℝ\na b c : ℝ\nh : ContinuousAt f b\nhd₀ : DifferentiableOn ℝ f (Ioo a b)\nhd₁ : DifferentiableOn ℝ f (Ioo b c)\nh₀ : ∀ x ∈ Ioo a b, deriv f x ≤ 0\nh₁ : ∀ x ∈ Ioo b c, 0 ≤ deriv f x\n⊢ MonotoneOn f (Ico b c)",
"usedConstants": [
"Real.partialOrder",
"Real",
"... | apply monotoneOn_of_deriv_nonneg (convex_Ico b c) (continuousOn_Ico h hd₁) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Calculus.DerivativeTest | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 53
} | [
{
"pp": "f : ℝ → ℝ\nx₀ : ℝ\nhf : deriv f x₀ < 0\nhx : f x₀ = 0\n⊢ ∀ᶠ (x : ℝ) in 𝓝 x₀, sign (f x) = sign (x₀ - x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DerivativeTest | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 13
} | [
{
"pp": "f : ℝ → ℝ\nx₀ : ℝ\nhf : deriv (deriv f) x₀ < 0\nhd : deriv f x₀ = 0\nhc : ContinuousAt f x₀\n⊢ IsLocalMax f x₀",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin | {
"line": 199,
"column": 2
} | {
"line": 200,
"column": 9
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : E →L[𝕜] E →L[𝕜] E [⋀^Fin n]→L[𝕜] F\nv : Fin (n + 2) → E\n⊢ (alternatizeUncurryFin (alternatize... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 1022,
"column": 39
} | {
"line": 1022,
"column": 57
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MetricSpace α\ninst✝⁵ : SecondCountableTopology α\ninst✝⁴ : MeasurableSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : HasBesicovitchCovering α\nμ : Measure α\ninst✝¹ : SFinite μ\ninst✝ : μ.OuterRegular\nε : ℝ≥0∞\nhε : ε ≠ 0\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f ... | ENNReal.add_halves | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 1041,
"column": 72
} | {
"line": 1041,
"column": 83
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : MetricSpace α\nβ : Type u\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : HasBesicovitchCovering α\nμ : Measure α\ninst✝ : SFinite μ\ns : Set α\nf : α → Set (Set α)\nfsubset : ∀ x ∈ s, f x ⊆ (fun r ↦ closedBall x r) '' Io... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 239,
"column": 4
} | {
"line": 239,
"column": 31
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf : E → F\nf' : E → E →L[ℝ] F\nf'' : E →L[ℝ] E →L[ℝ] F\nhf : ∀ x ∈ interior s, HasFDerivAt f (f' x) x\nx : E\nxs : x ∈ s\nhx : ∀ ⦃... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DifferentialForm.VectorField | {
"line": 177,
"column": 30
} | {
"line": 177,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set E\nx : E\nhsx : UniqueDiffWithinAt 𝕜 s x\nn : ℕ\nω : E → E [⋀^Fin (n + 1)]→L[𝕜] F\nV : Fin (n + 1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 183,
"column": 55
} | {
"line": 183,
"column": 66
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf f₁ : E → F\nf' : F\ns t : Set E\nx v : E\nh : HasLineDerivWithinAt 𝕜 f f' s x v\nht : EqOn f₁ f t\nhx : f₁ x = f x\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 206,
"column": 43
} | {
"line": 206,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf f₁ : E → F\ns : Set E\nx v : E\nhs : EqOn f₁ f s\nhx : f₁ x = f x\n⊢ f₁ (x + 0 • v) = f (x + 0 • v)",
"usedConsta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 306,
"column": 8
} | {
"line": 306,
"column": 73
} | [
{
"pp": "case hbc\nE : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf : E → F\nf' : E → E →L[ℝ] F\nf'' : E →L[ℝ] E →L[ℝ] F\nhf : ∀ x ∈ interior s, HasFDerivAt f (f' x) x\nx : E\nxs : x ∈ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 294,
"column": 58
} | {
"line": 294,
"column": 69
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : E → F\ns : Set E\nx v : E\nh : s ∈ 𝓝 x\n⊢ s ∈ 𝓝 (x + 0 • v)",
"usedConstants": [
"Filter.ins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 342,
"column": 4
} | {
"line": 342,
"column": 15
} | [
{
"pp": "case hx\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf₀ f₁ : E → F\nf' : F\ns : Set E\nx v : E\nh : f₀ =ᶠ[𝓝[s] x] f₁\nhx : f₀ x = f₁ x\n⊢ f₀ (x + 0 • v... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 378,
"column": 30
} | {
"line": 378,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf f₁ : E → F\ns : Set E\nx v : E\nhs : f₁ =ᶠ[𝓝[s] x] f\nhx : f₁ x = f x\n⊢ f₁ (x + 0 • v) = f (x + 0 • v)",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 399,
"column": 73
} | {
"line": 399,
"column": 84
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nv : E\nf : E → F\nf' : F\nx₀ : E\nhf : HasLineDerivAt 𝕜 f f' x₀ v\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : E) in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.VectorField | {
"line": 273,
"column": 4
} | {
"line": 274,
"column": 43
} | [
{
"pp": "case hf\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nV W : E → E\ns : Set E\nx : E\nm n : ℕ∞ω\nhV : ContDiffWithinAt 𝕜 n V s x\nhW : ContDiffWithinAt 𝕜 n W s x\nhs : UniqueDiffOn 𝕜 s\nhmn : m + 1 ≤ n\nhx : x ∈ s\n⊢ ContDi... | exact ContDiffWithinAt.clm_apply (hW.fderivWithin_right hs hmn hx)
(hV.of_le (le_trans le_self_add hmn)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Calculus.VectorField | {
"line": 273,
"column": 4
} | {
"line": 274,
"column": 43
} | [
{
"pp": "case hf\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nV W : E → E\ns : Set E\nx : E\nm n : ℕ∞ω\nhV : ContDiffWithinAt 𝕜 n V s x\nhW : ContDiffWithinAt 𝕜 n W s x\nhs : UniqueDiffOn 𝕜 s\nhmn : m + 1 ≤ n\nhx : x ∈ s\n⊢ ContDi... | exact ContDiffWithinAt.clm_apply (hW.fderivWithin_right hs hmn hx)
(hV.of_le (le_trans le_self_add hmn)) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.VectorField | {
"line": 273,
"column": 4
} | {
"line": 274,
"column": 43
} | [
{
"pp": "case hf\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nV W : E → E\ns : Set E\nx : E\nm n : ℕ∞ω\nhV : ContDiffWithinAt 𝕜 n V s x\nhW : ContDiffWithinAt 𝕜 n W s x\nhs : UniqueDiffOn 𝕜 s\nhmn : m + 1 ≤ n\nhx : x ∈ s\n⊢ ContDi... | exact ContDiffWithinAt.clm_apply (hW.fderivWithin_right hs hmn hx)
(hV.of_le (le_trans le_self_add hmn)) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 25
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nv : E\nf : E → F\nf' : F\nx₀ : E\nhf : HasLineDerivAt 𝕜 f f' x₀ v\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 434,
"column": 73
} | {
"line": 434,
"column": 84
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nv : E\nf : E → F\nx₀ : E\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : E) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀‖\nA :\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 437,
"column": 2
} | {
"line": 437,
"column": 25
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nv : E\nf : E → F\nx₀ : E\nC : ℝ\nhC₀ : 0 ≤ C\nhlip : ∀ᶠ (x : E) in 𝓝 x₀, ‖f x - f x₀‖ ≤ C * ‖x - x₀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 485,
"column": 2
} | {
"line": 485,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nE : Type u_3\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\nE' : Type u_4\ninst✝¹ : AddCommGroup E'\ninst✝ : Module 𝕜 E'\nf : E → F\nf' : F\nx : E'\nL : E' →ₗ[𝕜] E\nv : E'\nhf ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 502,
"column": 34
} | {
"line": 502,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\ns : Set E\nx v : E\nf' : F\nh : HasDerivWithinAt (fun t ↦ f (x + t • v)) f' ((fun t ↦ x + t • v) ⁻¹' s) 0\nc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 503,
"column": 70
} | {
"line": 503,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\ns : Set E\nx v : E\nf' : F\nh : HasDerivWithinAt (fun t ↦ f (x + t • v)) f' ((fun t ↦ x + t • v) ⁻¹' s) 0\nc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 512,
"column": 14
} | {
"line": 512,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\ns : Set E\nx v : E\nf' : F\nc : 𝕜\nhc : c ≠ 0\nh : HasLineDerivWithinAt 𝕜 f (c • f') s x (c • v)\n⊢ HasLin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 317,
"column": 4
} | {
"line": 317,
"column": 40
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf : E → F\nf' : E → E →L[ℝ] F\nf'' : E →L[ℝ] E →L[ℝ] F\nhf : ∀ x ∈ interior s, HasFDerivAt f (f' x) x\nx : E\nxs : x ∈ s\nhx : ∀ ⦃... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 521,
"column": 14
} | {
"line": 521,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\nx v : E\nf' : F\nc : 𝕜\nhc : c ≠ 0\nh : HasLineDerivAt 𝕜 f (c • f') x (c • v)\n⊢ HasLineDerivAt 𝕜 f f' x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 529,
"column": 14
} | {
"line": 529,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\ns : Set E\nx v : E\nc : 𝕜\nhc : c ≠ 0\nh : LineDifferentiableWithinAt 𝕜 f s x (c • v)\n⊢ LineDifferentiabl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 537,
"column": 14
} | {
"line": 537,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\nx v : E\nc : 𝕜\nhc : c ≠ 0\nh : LineDifferentiableAt 𝕜 f x (c • v)\n⊢ LineDifferentiableAt 𝕜 f x v",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 545,
"column": 6
} | {
"line": 545,
"column": 52
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nE : Type u_3\ninst✝¹ : AddCommGroup E\ninst✝ : Module 𝕜 E\nf : E → F\nx v : E\nc : 𝕜\nhc : c ≠ 0\nH : ¬LineDifferentiableAt 𝕜 f x v\n⊢ ¬LineDifferentiableAt 𝕜 f x (c • v)",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Norm | {
"line": 108,
"column": 2
} | {
"line": 108,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : StrongDual ℝ E\nx : E\nt : ℝ\nht : t < 0\nh : HasStrictFDerivAt (fun x ↦ ‖x‖) f x\n⊢ HasStrictFDerivAt (fun x ↦ ‖x‖) (-f) (t • x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Norm | {
"line": 113,
"column": 2
} | {
"line": 113,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : StrongDual ℝ E\nx : E\nt : ℝ\nht : 0 < t\nh : HasStrictFDerivAt (fun x ↦ ‖x‖) f x\n⊢ HasStrictFDerivAt (fun x ↦ ‖x‖) f (t • x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.VectorField | {
"line": 512,
"column": 2
} | {
"line": 513,
"column": 33
} | [
{
"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\nV : F → F\n⊢ pullbackWithin 𝕜 f V univ = pullback 𝕜 f V",
"usedConstants": [
"congrAr... | ext x
simp [pullbackWithin, pullback] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.VectorField | {
"line": 512,
"column": 2
} | {
"line": 513,
"column": 33
} | [
{
"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\nV : F → F\n⊢ pullbackWithin 𝕜 f V univ = pullback 𝕜 f V",
"usedConstants": [
"congrAr... | ext x
simp [pullbackWithin, pullback] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.FDeriv.Norm | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : StrongDual ℝ E\nx : E\nt : ℝ\nht : t < 0\nh : HasFDerivAt (fun x ↦ ‖x‖) f x\n⊢ HasFDerivAt (fun x ↦ ‖x‖) (-f) (t • x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Norm | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : StrongDual ℝ E\nx : E\nt : ℝ\nht : 0 < t\nh : HasFDerivAt (fun x ↦ ‖x‖) f x\n⊢ HasFDerivAt (fun x ↦ ‖x‖) f (t • x)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.VectorField | {
"line": 556,
"column": 4
} | {
"line": 556,
"column": 41
} | [
{
"pp": "case h\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\ninst✝ : CompleteSpace E\nf : E → F\ns : Set E\nx : E\nh'f : ContDiffWithinAt 𝕜 2 f s x\nhs : Uniqu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.VectorField | {
"line": 577,
"column": 4
} | {
"line": 577,
"column": 40
} | [
{
"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\ninst✝ : CompleteSpace E\nf : E → F\ns : Set E\nx : E\nh'f : ContDiffWithinAt 𝕜 2 f s x\nhs : UniqueDiffOn ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Partial | {
"line": 86,
"column": 14
} | {
"line": 86,
"column": 25
} | [
{
"pp": "case df'\n𝕜 : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\nF : Type u_4\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E₁\ninst✝⁵ : NormedSpace 𝕜 E₁\ninst✝⁴ : NormedAddCommGroup E₂\ninst✝³ : NormedSpace 𝕜 E₂\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : IsRCLikeNor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 390,
"column": 2
} | {
"line": 390,
"column": 32
} | [
{
"pp": "E : Type u_1\nF : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ns : Set E\ns_conv : Convex ℝ s\nf : E → F\nf' : E → E →L[ℝ] F\nf'' : E →L[ℝ] E →L[ℝ] F\nhf : ∀ x ∈ interior s, HasFDerivAt f (f' x) x\nx : E\nxs : x ∈ s\nhx : Has... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Partial | {
"line": 87,
"column": 14
} | {
"line": 87,
"column": 25
} | [
{
"pp": "case cf'\n𝕜 : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\nF : Type u_4\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E₁\ninst✝⁵ : NormedSpace 𝕜 E₁\ninst✝⁴ : NormedAddCommGroup E₂\ninst✝³ : NormedSpace 𝕜 E₂\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : IsRCLikeNor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Partial | {
"line": 98,
"column": 14
} | {
"line": 98,
"column": 25
} | [
{
"pp": "case df'\n𝕜 : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\nF : Type u_4\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E₁\ninst✝⁵ : NormedSpace 𝕜 E₁\ninst✝⁴ : NormedAddCommGroup E₂\ninst✝³ : NormedSpace 𝕜 E₂\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : IsRCLikeNor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Partial | {
"line": 99,
"column": 14
} | {
"line": 99,
"column": 25
} | [
{
"pp": "case cf'\n𝕜 : Type u_1\nE₁ : Type u_2\nE₂ : Type u_3\nF : Type u_4\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup E₁\ninst✝⁵ : NormedSpace 𝕜 E₁\ninst✝⁴ : NormedAddCommGroup E₂\ninst✝³ : NormedSpace 𝕜 E₂\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : IsRCLikeNor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 556,
"column": 4
} | {
"line": 556,
"column": 20
} | [
{
"pp": "case neg.hf\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nn : ℕ∞ω\nhf : ContDiffAt 𝕜 n f x\nh : ¬IsRCLikeNormedField 𝕜\nhn : n = ω\n⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Gradient.Basic | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : RCLike 𝕜\ng : 𝕜 → 𝕜\ng' u : 𝕜\nh : HasDerivAt g (((toDual 𝕜 𝕜) g') 1) u\n⊢ HasDerivAt g ((starRingEnd 𝕜) g') u",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain | {
"line": 65,
"column": 6
} | {
"line": 65,
"column": 17
} | [
{
"pp": "case disjoint\n𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAdd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain | {
"line": 61,
"column": 17
} | {
"line": 70,
"column": 11
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\nin... | by
constructor
· rw [LinearMap.disjoint_ker]
intro (_, y) h rfl
simpa using (injective_iff_map_eq_zero _).mp if₂u.injective y h
· rw [Submodule.codisjoint_iff_exists_add_eq]
intro v
have ⟨y, hy⟩ := if₂u.surjective (f'u v)
use v - (0, y), (0, y)
aesop | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 51,
"column": 59
} | {
"line": 51,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain | {
"line": 111,
"column": 2
} | {
"line": 116,
"column": 22
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\nin... | suffices f'u ∘L (.prod (.id ..) (-(f'u ∘L .inr ..).inverse ∘L (f'u ∘L .inl ..))) = 0 from
((dfu.implicitFunctionDataOfProdDomain if₂u).hasStrictFDerivAt_implicitFunction _
(ContinuousLinearMap.fst_comp_prod _ _) this).snd
ext
rw [f'u.comp_apply, ← f'u.comp_inl_add_comp_inr]
simp [map_neg, if₂u] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 56,
"column": 63
} | {
"line": 56,
"column": 74
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain | {
"line": 111,
"column": 2
} | {
"line": 116,
"column": 22
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\nin... | suffices f'u ∘L (.prod (.id ..) (-(f'u ∘L .inr ..).inverse ∘L (f'u ∘L .inl ..))) = 0 from
((dfu.implicitFunctionDataOfProdDomain if₂u).hasStrictFDerivAt_implicitFunction _
(ContinuousLinearMap.fst_comp_prod _ _) this).snd
ext
rw [f'u.comp_apply, ← f'u.comp_inl_add_comp_inr]
simp [map_neg, if₂u] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 58
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\nin... | have hψ := dfu.tendsto_implicitFunctionOfProdDomain if₂u | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Calculus.ImplicitFunction.ProdDomain | {
"line": 129,
"column": 58
} | {
"line": 129,
"column": 69
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : NontriviallyNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 62,
"column": 59
} | {
"line": 62,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 67,
"column": 59
} | {
"line": 67,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitContDiff | {
"line": 44,
"column": 52
} | {
"line": 44,
"column": 88
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : RCLike 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpac... | ← HasStrictFDerivAt.localInverse_def | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 73,
"column": 59
} | {
"line": 73,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitContDiff | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 19
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : RCLike 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitContDiff | {
"line": 97,
"column": 10
} | {
"line": 97,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : RCLike 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitFunction.Bivariate | {
"line": 79,
"column": 59
} | {
"line": 79,
"column": 70
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : IsRCLikeNormedField 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ImplicitContDiff | {
"line": 97,
"column": 35
} | {
"line": 97,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁹ : RCLike 𝕜\nE₁ : Type u_2\ninst✝⁸ : NormedAddCommGroup E₁\ninst✝⁷ : NormedSpace 𝕜 E₁\ninst✝⁶ : CompleteSpace E₁\nE₂ : Type u_3\ninst✝⁵ : NormedAddCommGroup E₂\ninst✝⁴ : NormedSpace 𝕜 E₂\ninst✝³ : CompleteSpace E₂\nF : Type u_4\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno | {
"line": 61,
"column": 2
} | {
"line": 63,
"column": 55
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ng : E → F\nf : 𝕜 → E\nx : 𝕜\nn : ℕ∞ω\ni : ℕ\nhg : ContDiffAt 𝕜 n g (f x)\nhf : ContDiffAt 𝕜 n f x\nhi : ... | simp only [← iteratedDerivWithin_univ, ← iteratedFDerivWithin_univ]
exact iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition hg hf uniqueDiffOn_univ
uniqueDiffOn_univ (mem_univ x) (mapsTo_univ f _) hi | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.IteratedDeriv.FaaDiBruno | {
"line": 61,
"column": 2
} | {
"line": 63,
"column": 55
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ng : E → F\nf : 𝕜 → E\nx : 𝕜\nn : ℕ∞ω\ni : ℕ\nhg : ContDiffAt 𝕜 n g (f x)\nhf : ContDiffAt 𝕜 n f x\nhi : ... | simp only [← iteratedDerivWithin_univ, ← iteratedFDerivWithin_univ]
exact iteratedDerivWithin_vcomp_eq_sum_orderedFinpartition hg hf uniqueDiffOn_univ
uniqueDiffOn_univ (mem_univ x) (mapsTo_univ f _) hi | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.Implicit | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : CompleteSpace E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nf' : E →L[𝕜] F\na : E\nhf : HasStrictFDerivA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Implicit | {
"line": 393,
"column": 2
} | {
"line": 395,
"column": 74
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : CompleteSpace E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nf' : E →L[𝕜] F\na : E\nhf : HasStrictFDerivA... | simpa only [implicitToOpenPartialHomeomorphOfComplemented_self] using
(hf.implicitToOpenPartialHomeomorphOfComplemented f f' hf' hker).map_source <|
hf.mem_implicitToOpenPartialHomeomorphOfComplemented_source hf' hker | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Analysis.Calculus.Implicit | {
"line": 393,
"column": 2
} | {
"line": 395,
"column": 74
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : CompleteSpace E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nf' : E →L[𝕜] F\na : E\nhf : HasStrictFDerivA... | simpa only [implicitToOpenPartialHomeomorphOfComplemented_self] using
(hf.implicitToOpenPartialHomeomorphOfComplemented f f' hf' hker).map_source <|
hf.mem_implicitToOpenPartialHomeomorphOfComplemented_source hf' hker | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.Implicit | {
"line": 393,
"column": 2
} | {
"line": 395,
"column": 74
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : CompleteSpace E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nf' : E →L[𝕜] F\na : E\nhf : HasStrictFDerivA... | simpa only [implicitToOpenPartialHomeomorphOfComplemented_self] using
(hf.implicitToOpenPartialHomeomorphOfComplemented f f' hf' hker).map_source <|
hf.mem_implicitToOpenPartialHomeomorphOfComplemented_source hf' hker | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.Implicit | {
"line": 418,
"column": 2
} | {
"line": 418,
"column": 71
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : CompleteSpace E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\nf' : E →L[𝕜] F\na : E\nhf : HasStrictFDerivA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LagrangeMultipliers | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 22
} | [
{
"pp": "case refine_1\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nφ : E → ℝ\nx₀ : E\nφ' : StrongDual ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\nhextr : IsLocalExtrOn φ {x | f x = f x₀} x₀\nhf' : HasStrictFDerivAt f f' x₀\nhφ' : HasStrictFDerivAt φ φ' x₀\nΛ : Modul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LagrangeMultipliers | {
"line": 98,
"column": 6
} | {
"line": 98,
"column": 45
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nφ : E → ℝ\nx₀ : E\nφ' : StrongDual ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\nhextr : IsLocalExtrOn φ {x | f x = f x₀} x₀\nhf' : HasStrictFDerivAt f f' x₀\nhφ' : HasStrictFDerivAt φ φ' x₀\nΛ : Module.Dual ℝ ℝ\nΛ₀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LagrangeMultipliers | {
"line": 99,
"column": 47
} | {
"line": 99,
"column": 81
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nφ : E → ℝ\nx₀ : E\nφ' : StrongDual ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\nhextr : IsLocalExtrOn φ {x | f x = f x₀} x₀\nhf' : HasStrictFDerivAt f f' x₀\nhφ' : HasStrictFDerivAt φ φ' x₀\nΛ : Module.Dual ℝ ℝ\nΛ₀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LagrangeMultipliers | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 26
} | [
{
"pp": "case refine_2.h\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nφ : E → ℝ\nx₀ : E\nφ' : StrongDual ℝ E\nf : E → ℝ\nf' : StrongDual ℝ E\nhextr : IsLocalExtrOn φ {x | f x = f x₀} x₀\nhf' : HasStrictFDerivAt f f' x₀\nhφ' : HasStrictFDerivAt φ φ' x₀\nΛ : Mod... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LagrangeMultipliers | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nφ : E → ℝ\nx₀ : E\nφ' : StrongDual ℝ E\nι : Type u_3\ninst✝ : Fintype ι\nf : ι → E → ℝ\nf' : ι → StrongDual ℝ E\nhextr : IsLocalExtrOn φ {x | ∀ (i : ι), f i x = f i x₀} x₀\nhf' : ∀ (i : ι), HasStrictFDerivA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LagrangeMultipliers | {
"line": 122,
"column": 4
} | {
"line": 122,
"column": 83
} | [
{
"pp": "case refine_1\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nφ : E → ℝ\nx₀ : E\nφ' : StrongDual ℝ E\nι : Type u_3\ninst✝ : Fintype ι\nf : ι → E → ℝ\nf' : ι → StrongDual ℝ E\nhf' : ∀ (i : ι), HasStrictFDerivAt (f i) (f' i) x₀\nhφ' : HasStrictFDerivAt φ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LHopital | {
"line": 174,
"column": 8
} | {
"line": 174,
"column": 19
} | [
{
"pp": "a : ℝ\nl : Filter ℝ\nf f' g g' : ℝ → ℝ\nhff' : ∀ x ∈ Iio a, HasDerivAt f (f' x) x\nhgg' : ∀ x ∈ Iio a, HasDerivAt g (g' x) x\nhg' : ∀ x ∈ Iio a, g' x ≠ 0\nhfbot : Tendsto f atBot (𝓝 0)\nhgbot : Tendsto g atBot (𝓝 0)\nhdiv : Tendsto (fun x ↦ f' x / g' x) atBot l\nhdnf : ∀ x ∈ Ioi (-a), HasDerivAt (f ∘... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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