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.Analytic.Basic | {
"line": 750,
"column": 2
} | {
"line": 750,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 765,
"column": 2
} | {
"line": 766,
"column": 9
} | [
{
"pp": "case h\n𝕜 : 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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nn : ℕ\nr : ℝ≥0∞\nhf : HasFPowerSeri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 766,
"column": 26
} | {
"line": 766,
"column": 37
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nn : ℕ\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 773,
"column": 2
} | {
"line": 773,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesWithinAt f p univ x\nn : ℕ\n⊢ (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 768,
"column": 8
} | {
"line": 768,
"column": 40
} | [
{
"pp": "case hy\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nq : F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 769,
"column": 8
} | {
"line": 769,
"column": 19
} | [
{
"pp": "case h'y\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nq : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 770,
"column": 4
} | {
"line": 770,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nq : FormalMult... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 813,
"column": 10
} | {
"line": 814,
"column": 71
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 778,
"column": 4
} | {
"line": 778,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nq : FormalMult... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 793,
"column": 64
} | {
"line": 794,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\ng : F → G\nf : E → F\nq : FormalMult... | by
apply ContinuousMultilinearMap.le_opNorm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.Basic | {
"line": 850,
"column": 2
} | {
"line": 850,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr r' : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 873,
"column": 2
} | {
"line": 873,
"column": 59
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr r' : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 895,
"column": 2
} | {
"line": 895,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesWithinAt f p univ x\n⊢ (fun y ↦ f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 922,
"column": 2
} | {
"line": 922,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 939,
"column": 4
} | {
"line": 939,
"column": 34
} | [
{
"pp": "case refine_2\n𝕜 : 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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 948,
"column": 2
} | {
"line": 948,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 969,
"column": 2
} | {
"line": 969,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nr' : ℝ≥0\nhf : HasFPowerSeriesWithinOnBall f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 992,
"column": 2
} | {
"line": 992,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1007,
"column": 2
} | {
"line": 1007,
"column": 13
} | [
{
"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\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinOnBall f p univ x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Composition | {
"line": 1065,
"column": 4
} | {
"line": 1065,
"column": 68
} | [
{
"pp": "case blocks\nn : ℕ\na : Composition n\nb : (i : Fin a.length) → Composition (a.blocksFun i)\na' : Composition n\nb' : (i : Fin a'.length) → Composition (a'.blocksFun i)\nH : (ofFn fun i ↦ (b i).blocks) = ofFn fun i ↦ (b' i).blocks\nthis : (ofFn fun i ↦ (b i).blocks.sum) = ofFn fun i ↦ (b' i).blocks.sum... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1110,
"column": 66
} | {
"line": 1110,
"column": 77
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nx✝¹ : HasFPowerSeriesAt f p z₀\nr : ℝ≥0∞\nr_le✝ : r ≤ p.radius\nr_pos : 0 < r\nh : ∀ {y : 𝕜}, y ∈ Metric.eball 0 r → HasS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1127,
"column": 4
} | {
"line": 1127,
"column": 63
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nr : ℝ\nr_pos : r > 0\nh : ∀ ⦃y : 𝕜⦄, ‖y‖ < r → HasSum (fun n ↦ y ^ n • p.coeff n) (f (z₀ + y))\ny : 𝕜\nx✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Basic | {
"line": 1131,
"column": 6
} | {
"line": 1131,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\np : FormalMultilinearSeries 𝕜 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\n⊢ HasFPowerSeriesAt f p z₀ ↔ ∀ᶠ (z : 𝕜) in 𝓝 z₀, HasSum (fun n ↦ (z - z₀) ^ n • p.coeff n) (f z)",
"usedConstants": ... | ← map_add_left_nhds_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Analytic.CPolynomial | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 35
} | [
{
"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\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nn m : ℕ\nhf : HasFiniteFPowerSeriesOnB... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.CPolynomial | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 35
} | [
{
"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\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nn m : ℕ\nhf : HasFiniteFPowerSeriesAt f pf x n\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.CPolynomial | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 35
} | [
{
"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\nf g : E → F\nx : E\nhf : CPolynomialAt 𝕜 f x\nhg : CPolynomialAt 𝕜 g x\n⊢ CPolynomialAt 𝕜 (f - g) x",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Within | {
"line": 57,
"column": 35
} | {
"line": 57,
"column": 46
} | [
{
"pp": "𝕜 : 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\ns : Set E\nx : E\nh : {x} ∈ 𝓝[s] x\nt : Set E\not : IsOpen[PseudoMetricSpace.toUniformSpace.toTo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 227,
"column": 2
} | {
"line": 228,
"column": 72
} | [
{
"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\nn : ℕ\nhn : 0 < n\np : FormalMultilinearSeries 𝕜 E F\nq : FormalMultilinearSeries 𝕜 F E\nv : Fin n → F\nA ... | simp [FormalMultilinearSeries.comp, A, Finset.sum_union B, C, -Set.toFinset_setOf,
-add_right_inj, -Composition.single_length, -Finset.union_singleton] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.FDeriv.Comp | {
"line": 249,
"column": 2
} | {
"line": 249,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasFDerivAt f f' x\nhx : f x = x\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝 x ×ˢ pure x) (𝓝 x ×ˢ pure x)",
"usedConstants": [
"Pure.pur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Comp | {
"line": 256,
"column": 2
} | {
"line": 256,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\ns : Set E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasFDerivWithinAt f f' s x\nhx : f x = x\nhs : MapsTo f s s\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝[s] x ×ˢ pure x) (𝓝[s] x ×ˢ pure... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Comp | {
"line": 263,
"column": 2
} | {
"line": 263,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nx : E\nf : E → E\nf' : E →L[𝕜] E\nhf : HasStrictFDerivAt f f' x\nhx : f x = x\nn : ℕ\n⊢ Tendsto (Prod.map f f) (𝓝 (x, x)) (𝓝 (x, x))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 398,
"column": 6
} | {
"line": 399,
"column": 62
} | [
{
"pp": "case h\nn : ℕ\np : ℕ → ℝ\nhp : ∀ (k : ℕ), 0 ≤ p k\nr a : ℝ\nhr : 0 ≤ r\nha : 0 ≤ a\nk : ℕ\nc : Composition k\nhd : (2 ≤ k ∧ k < n + 1) ∧ 1 < c.length\nj : Fin c.length\n⊢ c.blocksFun j < n",
"usedConstants": [
"False",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"eq_false... | have : c ≠ Composition.single k (zero_lt_two.trans_le hd.1.1) := by
simp [Composition.eq_single_iff_length, ne_of_gt hd.2] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Analytic.Within | {
"line": 143,
"column": 6
} | {
"line": 143,
"column": 85
} | [
{
"pp": "case mpr.a\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\np : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Within | {
"line": 187,
"column": 6
} | {
"line": 187,
"column": 32
} | [
{
"pp": "case refine_1.refine_1\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\ns : Set E\nx : E\ng : E → F\nhf : f =ᶠ[𝓝[inser... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Within | {
"line": 191,
"column": 8
} | {
"line": 191,
"column": 35
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : CompleteSpace F\nf : E → F\ns : Set E\nx : E\ng : E → F\nhf : f =ᶠ[𝓝[insert x s] x] g\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 590,
"column": 64
} | {
"line": 591,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeri... | by
apply ContinuousMultilinearMap.le_opNorm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.Inverse | {
"line": 600,
"column": 4
} | {
"line": 600,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 605,
"column": 34
} | {
"line": 605,
"column": 63
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → G\nq : FormalMultilinearSeri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 625,
"column": 6
} | {
"line": 625,
"column": 17
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMult... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 636,
"column": 6
} | {
"line": 636,
"column": 17
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : E → F\ng : F → G\nq : FormalMult... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 155,
"column": 14
} | {
"line": 155,
"column": 25
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nx : E\nhf : AnalyticAt 𝕜 (-f) x\n⊢ AnalyticAt 𝕜 f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesWithinO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nr : ℝ≥0∞\nhf : HasFPowerSeriesOnBall f pf x r\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\ns : Set E\nx : E\nhf : HasFPowerSeriesWithinAt f pf s x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 180,
"column": 2
} | {
"line": 180,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\npf pg : FormalMultilinearSeries 𝕜 E F\nx : E\nhf : HasFPowerSeriesAt f pf x\nhg : HasFPowerSer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\ns : Set E\nx : E\nhf : AnalyticWithinAt 𝕜 f s x\nhg : AnalyticWithinAt 𝕜 g s x\n⊢ AnalyticWit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 35
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\nF : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf g : E → F\nx : E\nhf : AnalyticAt 𝕜 f x\nhg : AnalyticAt 𝕜 g x\n⊢ AnalyticAt 𝕜 (f - g) x",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 241,
"column": 2
} | {
"line": 241,
"column": 30
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\ns : Set E\nx : E\nf : E → 𝕝\nhf : AnalyticWithinAt 𝕜 f s x\nc : 𝕝\n⊢ AnalyticWithinAt 𝕜 (fun x ↦ f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 246,
"column": 2
} | {
"line": 246,
"column": 30
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nx : E\nf : E → 𝕝\nhf : AnalyticAt 𝕜 f x\nc : 𝕝\n⊢ AnalyticAt 𝕜 (fun x ↦ f x / c) x",
"usedConst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 250,
"column": 2
} | {
"line": 250,
"column": 30
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\ns : Set E\nf : E → 𝕝\nhf : AnalyticOn 𝕜 f s\nc : 𝕝\n⊢ AnalyticOn 𝕜 (fun x ↦ f x / c) s",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 254,
"column": 2
} | {
"line": 254,
"column": 30
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\ns : Set E\nf : E → 𝕝\nhf : AnalyticOnNhd 𝕜 f s\nc : 𝕝\n⊢ AnalyticOnNhd 𝕜 (fun x ↦ f x / c) s",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 668,
"column": 4
} | {
"line": 668,
"column": 15
} | [
{
"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 : OpenPartialHomeomorph E F\na : E\ni : E ≃L[𝕜] F\nh0 : a ∈ f.source\np : FormalMultilinearSeries 𝕜 E F\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 673,
"column": 4
} | {
"line": 673,
"column": 15
} | [
{
"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 : OpenPartialHomeomorph E F\na : E\ni : E ≃L[𝕜] F\nh0 : a ∈ f.source\np : FormalMultilinearSeries 𝕜 E F\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 678,
"column": 4
} | {
"line": 678,
"column": 21
} | [
{
"pp": "case h\n𝕜 : 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 : OpenPartialHomeomorph E F\na : E\ni : E ≃L[𝕜] F\nh0 : a ∈ f.source\np : FormalMultilinearSeries... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 685,
"column": 4
} | {
"line": 685,
"column": 20
} | [
{
"pp": "case h\n𝕜 : 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 : OpenPartialHomeomorph E✝ F\na : E✝\ni : E✝ ≃L[𝕜] F\nh0 : a ∈ f.source\np : FormalMultilinear... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Inverse | {
"line": 693,
"column": 2
} | {
"line": 693,
"column": 24
} | [
{
"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 : OpenPartialHomeomorph E✝ F✝\na : E✝\ni : E✝ ≃L[𝕜] F✝\nh0 : a ∈ f.source\np : FormalMultilinearSer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 479,
"column": 4
} | {
"line": 479,
"column": 18
} | [
{
"pp": "case inr\n𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nr : ℝ≥0∞\np : (i : ι) → Form... | simp only [pi] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Analytic.Constructions | {
"line": 529,
"column": 2
} | {
"line": 529,
"column": 52
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nι : Type u_9\ninst✝² : Fintype ι\ne : E\nFm : ι → Type u_10\ninst✝¹ : (i : ι) → NormedAddCommGroup (Fm i)\ninst✝ : (i : ι) → NormedSpace 𝕜 (Fm i)\nf : (i : ι) → E → Fm i\ns : Set... | exact ⟨r, HasFPowerSeriesWithinOnBall.pi hr r_pos⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Analytic.Constructions | {
"line": 663,
"column": 4
} | {
"line": 663,
"column": 32
} | [
{
"pp": "case zero\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nA : Type u_7\ninst✝¹ : NormedRing A\ninst✝ : NormedAlgebra 𝕜 A\nf : E → A\nz : E\ns : Set E\nhf : AnalyticWithinAt 𝕜 f s z\n⊢ AnalyticWithinAt 𝕜 1 s z",
"usedCon... | apply analyticWithinAt_const | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Analytic.Constructions | {
"line": 693,
"column": 2
} | {
"line": 693,
"column": 34
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\nz : E\ns : Set E\nn : ℤ\nhf : AnalyticWithinAt 𝕜 f s z\nhn : 0 ≤ n\n⊢ AnalyticWithinAt 𝕜 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 700,
"column": 2
} | {
"line": 700,
"column": 34
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\nz : E\nn : ℤ\nhf : AnalyticAt 𝕜 f z\nhn : 0 ≤ n\n⊢ AnalyticAt 𝕜 (f ^ n) z",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Constructions | {
"line": 708,
"column": 2
} | {
"line": 708,
"column": 34
} | [
{
"pp": "𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\n𝕝 : Type u_8\ninst✝¹ : NormedDivisionRing 𝕝\ninst✝ : NormedAlgebra 𝕜 𝕝\nf : E → 𝕝\ns : Set E\nn : ℤ\nhf : AnalyticOn 𝕜 f s\nhn : 0 ≤ n\n⊢ AnalyticOn 𝕜 (f ^ n) s",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 104,
"column": 2
} | {
"line": 105,
"column": 9
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\niso : E ≃L[𝕜] F\nf : G → E\ns : Set... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 53
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\niso : E ≃L[𝕜] F\nf : F → G\ns : Set... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 51
} | [
{
"pp": "case a\n𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\niso : E ≃L[𝕜] F\nf : F → G\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 F\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\niso : E ≃L[𝕜] F\nf : F → G\ns : Set... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 327,
"column": 25
} | {
"line": 327,
"column": 36
} | [
{
"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\nx✝ : E\ns : Set E\nh : HasFDerivWithinAt f f' s x✝\nC : ℝ≥0\nhC : AntilipschitzW... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 332,
"column": 4
} | {
"line": 332,
"column": 42
} | [
{
"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\nx : E\ns : Set E\nh : HasFDerivWithinAt f f' s x\nhf' : ∃ C, ∀ (z : E), ‖z‖ ≤ C ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 353,
"column": 2
} | {
"line": 353,
"column": 39
} | [
{
"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\nx : E\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\n⊢ Tendsto f (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 357,
"column": 2
} | {
"line": 357,
"column": 39
} | [
{
"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\nx : E\nc : F\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\n⊢ ∀ᶠ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 39
} | [
{
"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\nx : E\nh : HasFDerivAt f f' x\nhf' : ∃ C, AntilipschitzWith C ⇑f'\nt : Set F\nht... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 409,
"column": 4
} | {
"line": 409,
"column": 15
} | [
{
"pp": "case hd₀\n𝕜 : 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\ns : Set E\nf' : E →L[𝕜] F\nx : E\nh : HasFDerivWithinAt f f' s x\ny : E\nhy : y ∈ tang... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 460,
"column": 14
} | {
"line": 460,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\ns : Set E\nx : E\nG : Type u_4\ninst✝³ : GroupWithZero G\ninst✝² : DistribMulAction G E\ninst✝¹ : ContinuousConstSMul G E\ninst✝ : SMulCommClass G 𝕜 E\nc : G\nhc : c ≠ 0\nh : Uni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Equiv | {
"line": 471,
"column": 92
} | {
"line": 479,
"column": 86
} | [
{
"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\ns : Set E\nf' : E →L[𝕜] F\nx : E\nc : 𝕜\n⊢ HasFDerivWithinAt (fun x ↦ f (c • x)) (c • f') s x ↔... | by
rcases eq_or_ne c 0 with rfl | hc
· simp [hasFDerivWithinAt_const, HasFDerivWithinAt.of_subsingleton (subsingleton_zero_smul_set _)]
· lift c to 𝕜ˣ using IsUnit.mk0 c hc
have A : f'.comp ((ContinuousLinearEquiv.smulLeft c : E ≃L[𝕜] E) : E →L[𝕜] E) = c • f' := by
ext; simp
rw [← Units.smul_def ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.MetricSpace.Completion | {
"line": 129,
"column": 12
} | {
"line": 129,
"column": 85
} | [
{
"pp": "α : Type u\ninst✝ : PseudoMetricSpace α\ns : Set (Completion α × Completion α)\nε : ℝ\nεpos : ε > 0\nhε : ∀ {a b : Completion α}, dist a b < ε → (a, b) ∈ s\nr : Set (ℝ × ℝ) := {p | dist p.1 p.2 < ε}\nthis✝ : r ∈ 𝓤 ℝ\nt1 : Set (Completion α × Completion α)\nht1 : t1 ∈ 𝓤 (Completion α)\nt2 : Set (Compl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Completion | {
"line": 143,
"column": 2
} | {
"line": 143,
"column": 28
} | [
{
"pp": "α : Type u\ninst✝ : PseudoMetricSpace α\n⊢ 𝓤 (Completion α) = ⨅ ε, ⨅ (_ : ε > 0), 𝓟 {p | dist p.1 p.2 < ε}",
"usedConstants": [
"Eq.mpr",
"Real",
"iInf",
"Real.instZero",
"Iff.of_eq",
"congrArg",
"Filter.instInfSet",
"uniformity",
"setOf",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Completion | {
"line": 186,
"column": 6
} | {
"line": 186,
"column": 78
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝² : PseudoMetricSpace α\ninst✝¹ : MetricSpace β\ninst✝ : CompleteSpace β\nf : α → β\nK : ℝ≥0\nh : LipschitzWith K f\nx y : Completion α\n⊢ ∀ (a b : α), dist (Completion.extension f ↑a) (Completion.extension f ↑b) ≤ ↑K * dist ↑a ↑b",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Completion | {
"line": 81,
"column": 16
} | {
"line": 81,
"column": 54
} | [
{
"pp": "case ih\n𝕜 : Type u_1\nE : Type u_2\nA : Type u_3\ninst✝ : SeminormedRing A\nx y : A\n⊢ ‖↑x * ↑y‖ ≤ ‖↑x‖ * ‖↑y‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"UniformSpace.Completion.coe'",
"Real.instLE",
"Semigroup.toMul",
"Real",
"HMul.hMul",
"congrA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\ns : Set 𝕜\nf : 𝕜 → F\nx : 𝕜\n⊢ fderivWithin 𝕜 (-f) s x = -fderivWithin 𝕜 f s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 324,
"column": 2
} | {
"line": 324,
"column": 29
} | [
{
"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\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ c + f x) f' L ↔ HasFDeri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 29
} | [
{
"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\nx : E\nc : F\n⊢ HasStrictFDerivAt (fun x ↦ c + f x) f' x ↔ HasStrictFDerivAt f f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 386,
"column": 2
} | {
"line": 386,
"column": 29
} | [
{
"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\nx : E\ns : Set E\nc : F\n⊢ fderivWithin 𝕜 (fun y ↦ c + f y) s x = fderivWithin 𝕜 f s x",
"u... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 536,
"column": 15
} | {
"line": 536,
"column": 41
} | [
{
"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\nx : E\ns : Set E\nh : DifferentiableWithinAt 𝕜 (fun y ↦ -f y) s x\n⊢ DifferentiableWithinAt 𝕜 f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 541,
"column": 15
} | {
"line": 541,
"column": 41
} | [
{
"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\nx : E\ns : Set E\nh : DifferentiableWithinAt 𝕜 (-f) s x\n⊢ DifferentiableWithinAt 𝕜 f s x",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 550,
"column": 15
} | {
"line": 550,
"column": 41
} | [
{
"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\nx : E\nh : DifferentiableAt 𝕜 (fun y ↦ -f y) x\n⊢ DifferentiableAt 𝕜 f x",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 554,
"column": 15
} | {
"line": 554,
"column": 41
} | [
{
"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\nx : E\nh : DifferentiableAt 𝕜 (-f) x\n⊢ DifferentiableAt 𝕜 f x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 563,
"column": 15
} | {
"line": 563,
"column": 41
} | [
{
"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\ns : Set E\nh : DifferentiableOn 𝕜 (fun y ↦ -f y) s\n⊢ DifferentiableOn 𝕜 f s",
"usedConstan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 567,
"column": 15
} | {
"line": 567,
"column": 41
} | [
{
"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\ns : Set E\nh : DifferentiableOn 𝕜 (-f) s\n⊢ DifferentiableOn 𝕜 f s",
"usedConstants": []
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 575,
"column": 15
} | {
"line": 575,
"column": 41
} | [
{
"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\nh : Differentiable 𝕜 fun y ↦ -f y\n⊢ Differentiable 𝕜 f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 579,
"column": 15
} | {
"line": 579,
"column": 41
} | [
{
"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\nh : Differentiable 𝕜 (-f)\n⊢ Differentiable 𝕜 f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 614,
"column": 2
} | {
"line": 614,
"column": 35
} | [
{
"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 g : E → F\nf' g' : E →L[𝕜] F\nL : Filter (E × E)\nhf : HasFDerivAtFilter f f' L\nhg : HasFDerivAtFilter g... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 645,
"column": 2
} | {
"line": 645,
"column": 41
} | [
{
"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 g : E → F\nx : E\nhg : DifferentiableAt 𝕜 g x\nh : DifferentiableAt 𝕜 (f + g) x\n⊢ DifferentiableAt 𝕜 f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 670,
"column": 2
} | {
"line": 670,
"column": 41
} | [
{
"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 g : E → F\ns : Set E\nhg : DifferentiableOn 𝕜 g s\nh : DifferentiableOn 𝕜 (f + g) s\n⊢ DifferentiableOn ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 695,
"column": 2
} | {
"line": 695,
"column": 41
} | [
{
"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 g : E → F\nhg : Differentiable 𝕜 g\nh : Differentiable 𝕜 (f + g)\n⊢ Differentiable 𝕜 f",
"usedConst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 61
} | [
{
"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\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ f x - c) f' L ↔ HasFDeri... | simp only [sub_eq_add_neg, hasFDerivAtFilter_add_const_iff] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 61
} | [
{
"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\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ f x - c) f' L ↔ HasFDeri... | simp only [sub_eq_add_neg, hasFDerivAtFilter_add_const_iff] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 733,
"column": 2
} | {
"line": 733,
"column": 61
} | [
{
"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\nL : Filter (E × E)\nc : F\n⊢ HasFDerivAtFilter (fun x ↦ f x - c) f' L ↔ HasFDeri... | simp only [sub_eq_add_neg, hasFDerivAtFilter_add_const_iff] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 800,
"column": 2
} | {
"line": 800,
"column": 35
} | [
{
"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\nL : Filter (E × E)\nhf : HasFDerivAtFilter f f' L\nc : F\n⊢ HasFDerivAtFilter (f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 874,
"column": 2
} | {
"line": 874,
"column": 31
} | [
{
"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\nx : E\ns : Set E\na : E\n⊢ HasFDerivWithinAt (fun x ↦ f (x + a)) f' s x ↔ HasFDe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Add | {
"line": 899,
"column": 2
} | {
"line": 899,
"column": 26
} | [
{
"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\nx a : E\n⊢ HasFDerivAt (fun x ↦ f (a + x)) f' x ↔ HasFDerivAt f f' (a + x)",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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