module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 270,
"column": 18
} | {
"line": 270,
"column": 91
} | {
"line": 271,
"column": 6
} | [
{
"pp": "case snd\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ni... | [] | simp only [Pi.sub_apply, _root_.id, Prod.fst_sub, sub_zero, Prod.snd_sub] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 424,
"column": 32
} | {
"line": 424,
"column": 47
} | {
"line": 424,
"column": 48
} | [
{
"pp": "G : Type u_1\ninst✝⁶ : TopologicalSpace G\ninst✝⁵ : Group G\ninst✝⁴ : IsTopologicalGroup G\ninst✝³ : MeasurableSpace G\ninst✝² : BorelSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\nH : μ'.haarScalarFactor μ = 0\n⊢ False",
"ppTerm": "?m.36",
"assigned": false,
... | [
"G : Type u_1\ninst✝⁶ : TopologicalSpace G\ninst✝⁵ : Group G\ninst✝⁴ : IsTopologicalGroup G\ninst✝³ : MeasurableSpace G\ninst✝² : BorelSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\nH : μ'.haarScalarFactor μ = 0\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 392,
"column": 6
} | {
"line": 392,
"column": 99
} | {
"line": 393,
"column": 8
} | [
{
"pp": "α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nN : ℕ\nhN : IsEmpty (SatelliteConfig α N p.τ)\ni : Ordinal.{u}\nIH : ∀ y < i, y < p.lastStep → p.color y < N\nhi : i < p.lastStep\nA : Set ℕ :=\n ⋃ j,\n ⋃ (_ :\n (closedBall (p.c (p.index ↑j)) (p.r (p.ind... | [
"α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nN : ℕ\nhN : IsEmpty (SatelliteConfig α N p.τ)\ni : Ordinal.{u}\nIH : ∀ y < i, y < p.lastStep → p.color y < N\nhi : i < p.lastStep\nA : Set ℕ :=\n ⋃ j,\n ⋃ (_ :\n (closedBall (p.c (p.index ↑j)) (p.r (p.index ↑j)) ∩ cl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 500,
"column": 6
} | {
"line": 500,
"column": 17
} | {
"line": 500,
"column": 18
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f :... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f : HasCompactS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 307,
"column": 8
} | {
"line": 307,
"column": 73
} | {
"line": 307,
"column": 73
} | [
{
"pp": "case succ\n𝕜 : Type u𝕜\nE : Type uE\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : RCLike 𝕜\ninst✝¹¹ : NormedSpace 𝕜 E\nG P : Type uP\ninst✝¹⁰ : MeasurableSpace G\nμ : Measure G\ninst✝⁹ : NormedAddCommGroup G\ninst✝⁸ : BorelSpace G\ninst✝⁷ : NormedSpace 𝕜 G\ninst✝⁶ : NormedAddCommGroup P\ninst✝⁵ : Nor... | [
"case succ\n𝕜 : Type u𝕜\nE : Type uE\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : RCLike 𝕜\ninst✝¹¹ : NormedSpace 𝕜 E\nG P : Type uP\ninst✝¹⁰ : MeasurableSpace G\nμ : Measure G\ninst✝⁹ : NormedAddCommGroup G\ninst✝⁸ : BorelSpace G\ninst✝⁷ : NormedSpace 𝕜 G\ninst✝⁶ : NormedAddCommGroup P\ninst✝⁵ : NormedSpace 𝕜 ... | contDiffOn_succ_iff_fderiv_of_isOpen (hs.prod (@isOpen_univ G _)) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 408,
"column": 6
} | {
"line": 408,
"column": 52
} | {
"line": 408,
"column": 53
} | [
{
"pp": "case left\nα : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nN : ℕ\nhN : IsEmpty (SatelliteConfig α N p.τ)\ni : Ordinal.{u}\nIH : ∀ y < i, y < p.lastStep → p.color y < N\nhi : i < p.lastStep\nA : Set ℕ :=\n ⋃ j,\n ⋃ (_ :\n (closedBall (p.c (p.index ↑j)) ... | [
"case left\nα : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nN : ℕ\nhN : IsEmpty (SatelliteConfig α N p.τ)\ni : Ordinal.{u}\nIH : ∀ y < i, y < p.lastStep → p.color y < N\nhi : i < p.lastStep\nA : Set ℕ :=\n ⋃ j,\n ⋃ (_ :\n (closedBall (p.c (p.index ↑j)) (p.r (p.inde... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 509,
"column": 10
} | {
"line": 509,
"column": 59
} | {
"line": 509,
"column": 60
} | [
{
"pp": "case neg.x_out\nG : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[ins... | [
"case neg.x_out\nG : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 522,
"column": 6
} | {
"line": 522,
"column": 17
} | {
"line": 522,
"column": 18
} | [
{
"pp": "case x_out\nG : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷,... | [
"case x_out\nG : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 524,
"column": 2
} | {
"line": 524,
"column": 19
} | {
"line": 525,
"column": 2
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f :... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f : HasCompactS... | simp_rw [M] at I1 | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 47
} | {
"line": 148,
"column": 48
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\ns : Finset E\nhs : ∀ c ∈ s, ‖c‖ ≤ 2\nh : ∀ c ∈ s, ∀ d ∈ s, c ≠ d → 1 ≤ ‖c - d‖\nthis✝¹ : MeasurableSpace E := borel E\nthis✝ : BorelSpace E\nμ : Measure E := Measure.addHaar\nδ : ℝ := 1 / 2\nρ : ℝ := 5... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\ns : Finset E\nhs : ∀ c ∈ s, ‖c‖ ≤ 2\nh : ∀ c ∈ s, ∀ d ∈ s, c ≠ d → 1 ≤ ‖c - d‖\nthis✝¹ : MeasurableSpace E := borel E\nthis✝ : BorelSpace E\nμ : Measure E := Measure.addHaar\nδ : ℝ := 1 / 2\nρ : ℝ := 5 / 2\nρpos :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 535,
"column": 4
} | {
"line": 536,
"column": 74
} | {
"line": 536,
"column": 75
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f :... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f : HasCompactS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 539,
"column": 2
} | {
"line": 539,
"column": 13
} | {
"line": 539,
"column": 14
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f :... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nf : G → ℝ\nhf : Continuous[inst✝⁷, _] f\nh'f : HasCompactS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 317,
"column": 4
} | {
"line": 317,
"column": 35
} | {
"line": 317,
"column": 36
} | [
{
"pp": "E : Type u_1\ninst✝ : NormedAddCommGroup E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\n⊢ Pairwise fun i j ↦ a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.... | [
"E : Type u_1\ninst✝ : NormedAddCommGroup E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\n⊢ Pairwise fun i j ↦ a.r i ≤ ‖a.c i - a.c j‖ ∧ a.r j ≤ τ * a.r i ∨ a.r j ≤ ‖a.c j - a.c i‖ ∧ a.r i ≤ τ * a.r j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 369,
"column": 6
} | {
"line": 370,
"column": 33
} | {
"line": 370,
"column": 34
} | [
{
"pp": "case refine_3\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ ... | [
"case refine_3\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpac... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 479,
"column": 6
} | {
"line": 479,
"column": 70
} | {
"line": 479,
"column": 71
} | [
{
"pp": "α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i)... | [
"α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i), {p.index k... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 482,
"column": 6
} | {
"line": 482,
"column": 70
} | {
"line": 482,
"column": 71
} | [
{
"pp": "α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i)... | [
"α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i), {p.index k... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 375,
"column": 4
} | {
"line": 376,
"column": 90
} | {
"line": 376,
"column": 91
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpace �... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpace 𝕜 F\ninst✝⁵ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 658,
"column": 6
} | {
"line": 658,
"column": 54
} | {
"line": 659,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : BorelSpace G\ninst✝³ : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\ns : Set G\nh's... | [] | · exact h's.closure_of_subset inter_subset_right | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 667,
"column": 6
} | {
"line": 667,
"column": 54
} | {
"line": 668,
"column": 4
} | [
{
"pp": "G : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : BorelSpace G\ninst✝³ : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝² : μ.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\ns : Set G\nh's... | [] | · exact h's.closure_of_subset inter_subset_right | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 706,
"column": 4
} | {
"line": 706,
"column": 15
} | {
"line": 706,
"column": 16
} | [
{
"pp": "G : Type u_1\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : Group G\ninst✝⁷ : IsTopologicalGroup G\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : BorelSpace G\ninst✝⁴ : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝³ : IsProbabilityMeasure μ\ninst✝² : IsProbabilityMeasure μ'\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaar... | [
"G : Type u_1\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : Group G\ninst✝⁷ : IsTopologicalGroup G\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : BorelSpace G\ninst✝⁴ : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝³ : IsProbabilityMeasure μ\ninst✝² : IsProbabilityMeasure μ'\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\nH :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 706,
"column": 4
} | {
"line": 706,
"column": 52
} | {
"line": 707,
"column": 2
} | [
{
"pp": "G : Type u_1\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : Group G\ninst✝⁷ : IsTopologicalGroup G\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : BorelSpace G\ninst✝⁴ : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝³ : IsProbabilityMeasure μ\ninst✝² : IsProbabilityMeasure μ'\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaar... | [] | simpa using measure_univ_of_isMulLeftInvariant μ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 349,
"column": 4
} | {
"line": 349,
"column": 35
} | {
"line": 349,
"column": 36
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\n⊢ Pairwise fun i j ... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\n⊢ Pairwise fun i j ↦ a.r i ≤ ‖a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 352,
"column": 40
} | {
"line": 352,
"column": 88
} | {
"line": 352,
"column": 89
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\nah : Pairwise fun i... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\nah : Pairwise fun i j ↦ a.r i ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 505,
"column": 4
} | {
"line": 505,
"column": 94
} | {
"line": 505,
"column": 95
} | [
{
"pp": "α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i)... | [
"α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i), {p.index k... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 510,
"column": 6
} | {
"line": 511,
"column": 29
} | {
"line": 511,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i)... | [
"α : Type u_1\ninst✝ : MetricSpace α\nβ : Type u\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\nq : BallPackage β α\nh✝ : Nonempty β\np : TauPackage β α := { toBallPackage := q, τ := τ, one_lt_tau := hτ }\ns : Fin N → Set β := fun i ↦ ⋃ k, ⋃ (_ : k < p.lastStep), ⋃ (_ : p.color k = ↑i), {p.index k... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 356,
"column": 6
} | {
"line": 356,
"column": 54
} | {
"line": 356,
"column": 55
} | [
{
"pp": "case inl\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\nah : Pair... | [
"case inl\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\nah : Pairwise fun i j... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 743,
"column": 6
} | {
"line": 746,
"column": 28
} | {
"line": 747,
"column": 4
} | [
{
"pp": "case refine_1\nG : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.Is... | [] | simp only [iUnion_subset_iff]
intro a ac x hx
simp only [A, subset_def, mem_setOf_eq] at cA
exact (cA _ ac).1 x hx | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 743,
"column": 6
} | {
"line": 746,
"column": 28
} | {
"line": 747,
"column": 4
} | [
{
"pp": "case refine_1\nG : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.Is... | [] | simp only [iUnion_subset_iff]
intro a ac x hx
simp only [A, subset_def, mem_setOf_eq] at cA
exact (cA _ ac).1 x hx | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 408,
"column": 2
} | {
"line": 408,
"column": 37
} | {
"line": 408,
"column": 38
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹⁵ : NormedAddCommGroup E\ninst✝¹⁴ : NormedAddCommGroup E'\ninst✝¹³ : NormedAddCommGroup F\ninst✝¹² : RCLike 𝕜\ninst✝¹¹ : NormedSpace 𝕜 E\ninst✝¹⁰ : NormedSpace 𝕜 E'\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : NormedSpace... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹⁵ : NormedAddCommGroup E\ninst✝¹⁴ : NormedAddCommGroup E'\ninst✝¹³ : NormedAddCommGroup F\ninst✝¹² : RCLike 𝕜\ninst✝¹¹ : NormedSpace 𝕜 E\ninst✝¹⁰ : NormedSpace 𝕜 E'\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : NormedSpace 𝕜 F\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 759,
"column": 54
} | {
"line": 759,
"column": 65
} | {
"line": 759,
"column": 66
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.IsEverywherePos s... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.IsEverywherePos s\nν : Measur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 761,
"column": 8
} | {
"line": 761,
"column": 19
} | {
"line": 761,
"column": 20
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.IsEverywherePos s... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.IsEverywherePos s\nν : Measur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 764,
"column": 8
} | {
"line": 765,
"column": 15
} | {
"line": 765,
"column": 16
} | [
{
"pp": "G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.IsEverywherePos s... | [
"G : Type u_1\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\ninst✝² : LocallyCompactSpace G\nμ' μ : Measure G\ninst✝¹ : μ.IsHaarMeasure\ninst✝ : μ'.IsHaarMeasure\ns : Set G\nhs : MeasurableSet s\nh's : μ.IsEverywherePos s\nν : Measur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 574,
"column": 6
} | {
"line": 574,
"column": 44
} | {
"line": 574,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, ... | [
"α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, r x ≤ 1\nhμs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 388,
"column": 43
} | {
"line": 388,
"column": 94
} | {
"line": 388,
"column": 95
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\nah : Pairwise fun i... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\ni j : Fin N.succ\ninej : i ≠ j\nhi : ‖a.c i‖ ≤ 2\nhj : 2 < ‖a.c j‖\nah : Pairwise fun i j ↦ a.r i ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Convolution | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 35
} | {
"line": 131,
"column": 36
} | [
{
"pp": "case g_supp\nG : Type uG\nE' : Type uE'\ninst✝⁸ : NormedAddCommGroup E'\ng : G → E'\ninst✝⁷ : MeasurableSpace G\nμ : Measure G\ninst✝⁶ : NormedSpace ℝ E'\ninst✝⁵ : NormedAddCommGroup G\ninst✝⁴ : NormedSpace ℝ G\ninst✝³ : CompleteSpace E'\ninst✝² : BorelSpace G\ninst✝¹ : FiniteDimensional ℝ G\ninst✝ : μ... | [
"case g_supp\nG : Type uG\nE' : Type uE'\ninst✝⁸ : NormedAddCommGroup E'\ng : G → E'\ninst✝⁷ : MeasurableSpace G\nμ : Measure G\ninst✝⁶ : NormedSpace ℝ E'\ninst✝⁵ : NormedAddCommGroup G\ninst✝⁴ : NormedSpace ℝ G\ninst✝³ : CompleteSpace E'\ninst✝² : BorelSpace G\ninst✝¹ : FiniteDimensional ℝ G\ninst✝ : μ.IsAddHaarMe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 402,
"column": 4
} | {
"line": 402,
"column": 35
} | {
"line": 402,
"column": 36
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\ni j : Fin N.succ\ninej : i ≠ j\nhi : 2 < ‖a.c i‖\nhij : ‖a.c i‖ ≤ ‖a.c j‖\n⊢ Pairwise fun i j ↦ a.r ... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\ni j : Fin N.succ\ninej : i ≠ j\nhi : 2 < ‖a.c i‖\nhij : ‖a.c i‖ ≤ ‖a.c j‖\n⊢ Pairwise fun i j ↦ a.r i ≤ ‖a.c i -... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 404,
"column": 40
} | {
"line": 404,
"column": 88
} | {
"line": 404,
"column": 89
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\ni j : Fin N.succ\ninej : i ≠ j\nhi : 2 < ‖a.c i‖\nhij : ‖a.c i‖ ≤ ‖a.c j‖\nah : Pairwise fun i j ↦ a... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\ni j : Fin N.succ\ninej : i ≠ j\nhi : 2 < ‖a.c i‖\nhij : ‖a.c i‖ ≤ ‖a.c j‖\nah : Pairwise fun i j ↦ a.r i ≤ ‖a.c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 469,
"column": 41
} | {
"line": 469,
"column": 77
} | {
"line": 469,
"column": 78
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\nc' : Fin N.succ → E := fun i ↦ if ‖a.c i‖ ≤ 2 then a.c i else (2 / ‖a.c i‖) • a.c i\nno... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\nc' : Fin N.succ → E := fun i ↦ if ‖a.c i‖ ≤ 2 then a.c i else (2 / ‖a.c i‖) • a.c i\nnorm_c'_le : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 475,
"column": 43
} | {
"line": 475,
"column": 79
} | {
"line": 475,
"column": 80
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\nc' : Fin N.succ → E := fun i ↦ if ‖a.c i‖ ≤ 2 then a.c i else (2 / ‖a.c i‖) • a.c i\nno... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nN : ℕ\nτ : ℝ\na : SatelliteConfig E N τ\nlastc : a.c (last N) = 0\nlastr : a.r (last N) = 1\nhτ : 1 ≤ τ\nδ : ℝ\nhδ1 : τ ≤ 1 + δ / 4\nhδ2 : δ ≤ 1\nc' : Fin N.succ → E := fun i ↦ if ‖a.c i‖ ≤ 2 then a.c i else (2 / ‖a.c i‖) • a.c i\nnorm_c'_le : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Polynomial | {
"line": 25,
"column": 21
} | {
"line": 25,
"column": 32
} | {
"line": 25,
"column": 33
} | [
{
"pp": "case add\nR : Type u_1\n𝕜 : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : Algebra R 𝕜\nn : WithTop ℕ∞\nf g : R[X]\nfc : ContDiff 𝕜 n fun x ↦ (aeval x) f\ngc : ContDiff 𝕜 n fun x ↦ (aeval x) g\n⊢ ContDiff 𝕜 n fun x ↦ (aeval x) (f + g)",
"ppTerm": "?add",
"a... | [
"case add\nR : Type u_1\n𝕜 : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : Algebra R 𝕜\nn : WithTop ℕ∞\nf g : R[X]\nfc : ContDiff 𝕜 n fun x ↦ (aeval x) f\ngc : ContDiff 𝕜 n fun x ↦ (aeval x) g\n⊢ ContDiff 𝕜 n fun x ↦ (aeval x) f + (aeval x) g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Polynomial | {
"line": 26,
"column": 20
} | {
"line": 26,
"column": 31
} | {
"line": 26,
"column": 32
} | [
{
"pp": "case monomial\nR : Type u_1\n𝕜 : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : Algebra R 𝕜\nn✝ : WithTop ℕ∞\nn : ℕ\na : R\n⊢ ContDiff 𝕜 n✝ fun x ↦ (aeval x) ((monomial n) a)",
"ppTerm": "?monomial",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"case monomial\nR : Type u_1\n𝕜 : Type u_2\ninst✝² : CommSemiring R\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : Algebra R 𝕜\nn✝ : WithTop ℕ∞\nn : ℕ\na : R\n⊢ ContDiff 𝕜 n✝ fun x ↦ (algebraMap R 𝕜) a * x ^ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 634,
"column": 54
} | {
"line": 634,
"column": 68
} | {
"line": 634,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, ... | [
"α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, r x ≤ 1\nhμs... | inter_iUnion₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 645,
"column": 6
} | {
"line": 645,
"column": 68
} | {
"line": 645,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, ... | [
"α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, r x ≤ 1\nhμs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 647,
"column": 6
} | {
"line": 647,
"column": 68
} | {
"line": 647,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, ... | [
"α : Type u_1\ninst✝⁴ : MetricSpace α\ninst✝³ : SecondCountableTopology α\ninst✝² : MeasurableSpace α\ninst✝¹ : OpensMeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nN : ℕ\nτ : ℝ\nhτ : 1 < τ\nhN : IsEmpty (SatelliteConfig α N τ)\ns : Set α\nr : α → ℝ\nrpos : ∀ x ∈ s, 0 < r x\nrle : ∀ x ∈ s, r x ≤ 1\nhμs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Holder | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 15
} | {
"line": 191,
"column": 16
} | [
{
"pp": "case inl\nX : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nr : ℝ≥0\nf : X → Y\nC D : ℝ≥0\nA : Set X\nhA : ∀ x ∈ A, ∀ y ∈ A, edist x y ≤ ↑D\nhf : HolderOnWith C r f A\nhsr : 0 ≤ r\n⊢ HolderOnWith (C * D ^ (↑r - ↑0)) 0 f A",
"ppTerm": "?inl",
"assigned": tr... | [
"case inl\nX : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nr : ℝ≥0\nf : X → Y\nC D : ℝ≥0\nA : Set X\nhA : ∀ x ∈ A, ∀ y ∈ A, edist x y ≤ ↑D\nhf : HolderOnWith C r f A\nhsr : 0 ≤ r\n⊢ HolderOnWith (C * D ^ ↑r) 0 f A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Holder | {
"line": 196,
"column": 38
} | {
"line": 196,
"column": 49
} | {
"line": 196,
"column": 50
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nr : ℝ≥0\nf : X → Y\nC D s : ℝ≥0\nA : Set X\nhA : ∀ x ∈ A, ∀ y ∈ A, edist x y ≤ ↑D\nhf : HolderOnWith C r f A\nhsr : ↑s ≤ ↑r\nht : 0 < s\nhr : 0 < ↑r\nθ₁ : ℝ≥0 := NNReal.mk (↑s / ↑r) ⋯\n⊢ 0 ≤ 1 - ↑s / ↑r",
"ppTe... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nr : ℝ≥0\nf : X → Y\nC D s : ℝ≥0\nA : Set X\nhA : ∀ x ∈ A, ∀ y ∈ A, edist x y ≤ ↑D\nhf : HolderOnWith C r f A\nhsr : ↑s ≤ ↑r\nht : 0 < s\nhr : 0 < ↑r\nθ₁ : ℝ≥0 := NNReal.mk (↑s / ↑r) ⋯\n⊢ ↑s / ↑r ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 13
} | {
"line": 84,
"column": 14
} | [
{
"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\nk : ℕ\nf : E → F\na : E\nh : ContDiffAt ℝ (↑k) f a\n⊢ (fun x ↦ iteratedFDeriv ℝ k f x - iteratedFDeriv ℝ k f a) =O[𝓝 a] fun x ↦ ‖x - a‖ ^ ↑0",
"ppTerm": "?m.... | [
"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\nk : ℕ\nf : E → F\na : E\nh : ContDiffAt ℝ (↑k) f a\n⊢ IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) (𝓝 a) fun x ↦ ‖iteratedFDeriv ℝ k f x - iteratedFDeriv ℝ k f a‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Darboux | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 36
} | {
"line": 81,
"column": 2
} | [
{
"pp": "f f' : ℝ → ℝ\ns : Set ℝ\nhs : s.OrdConnected\nhf : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\na : ℝ\nha : a ∈ s\nb : ℝ\nhb : b ∈ s\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\n⊢ m ∈ f' '' s",
"ppTerm": "?m.84",
"assigned": true,
"usedConstants": [
"Real",
"PartialOrder.toPreorder",
... | [
"case inl\nf f' : ℝ → ℝ\ns : Set ℝ\nhs : s.OrdConnected\nhf : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\na : ℝ\nha : a ∈ s\nb : ℝ\nhb : b ∈ s\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\nhab : a ≤ b\n⊢ m ∈ f' '' s",
"case inr\nf f' : ℝ → ℝ\ns : Set ℝ\nhs : s.OrdConnected\nhf : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\na : ... | rcases le_total a b with hab | hab | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.Calculus.Darboux | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 38
} | {
"line": 82,
"column": 4
} | [
{
"pp": "case inl\nf f' : ℝ → ℝ\ns : Set ℝ\nhs : s.OrdConnected\nhf : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\na : ℝ\nha : a ∈ s\nb : ℝ\nhb : b ∈ s\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\nhab : a ≤ b\n⊢ m ∈ f' '' s",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Real",
"Set.OrdC... | [
"case inl\nf f' : ℝ → ℝ\ns : Set ℝ\nhs : s.OrdConnected\nhf : ∀ x ∈ s, HasDerivWithinAt f (f' x) s x\na : ℝ\nha : a ∈ s\nb : ℝ\nhb : b ∈ s\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\nhab : a ≤ b\nthis : Icc a b ⊆ s\n⊢ m ∈ f' '' s"
] | have : Icc a b ⊆ s := hs.out ha hb | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 20
} | {
"line": 70,
"column": 21
} | [
{
"pp": "case inl\nx : ℝ\nhx✝ : x ≠ 0\nhx : x < 0\n⊢ HasStrictDerivAt (fun x ↦ |x|) (↑(SignType.sign x)) x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"SignType.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSe... | [
"case inl\nx : ℝ\nhx✝ : x ≠ 0\nhx : x < 0\n⊢ HasStrictDerivAt (fun x ↦ |x|) (-1) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 20
} | {
"line": 71,
"column": 21
} | [
{
"pp": "case inr\nx : ℝ\nhx✝ : x ≠ 0\nhx : 0 < x\n⊢ HasStrictDerivAt (fun x ↦ |x|) (↑(SignType.sign x)) x",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"SignType.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Re... | [
"case inr\nx : ℝ\nhx✝ : x ≠ 0\nhx : 0 < x\n⊢ HasStrictDerivAt (fun x ↦ |x|) 1 x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 224,
"column": 14
} | {
"line": 224,
"column": 45
} | {
"line": 224,
"column": 46
} | [
{
"pp": "E : Type u_1\nF : Type u_2\nG : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G\nk : ℕ\nα : ↑I\nf : E → F\na : E\ng : F ≃L[ℝ] G\nh : ContDiffPointwiseHolderAt k α (⇑g ∘ f) ... | [
"E : Type u_1\nF : Type u_2\nG : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace ℝ G\nk : ℕ\nα : ↑I\nf : E → F\na : E\ng : F ≃L[ℝ] G\nh : ContDiffPointwiseHolderAt k α (⇑g ∘ f) a\n⊢ ContDif... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 15
} | {
"line": 203,
"column": 16
} | [
{
"pp": "case inl\n⊢ deriv (fun x ↦ |x|) 0 = ↑(SignType.sign 0)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"SignType.cast",
"Eq.mpr",
"Real",
"Semiring.toModule",
"Real.lattice",
"Real.denselyNormedField",
"Real.instZero",
"abs",
"c... | [
"case inl\n⊢ deriv (fun x ↦ |x|) 0 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 20
} | {
"line": 204,
"column": 21
} | [
{
"pp": "case inr\nx : ℝ\nhx : x ≠ 0\n⊢ deriv (fun x ↦ |x|) x = ↑(SignType.sign x)",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nx : ℝ\nhx : x ≠ 0\n⊢ deriv (fun x ↦ |x|) x = ↑(SignType.sign x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 243,
"column": 4
} | {
"line": 244,
"column": 11
} | {
"line": 244,
"column": 12
} | [
{
"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\nk l : ℕ\nα : ↑I\nf : E → F\na : E\nhf : ContDiffPointwiseHolderAt k α f a\nhl : l < k\n⊢ (fun x ↦ ‖iteratedFDeriv ℝ l (fderiv ℝ f) x - iteratedFDeriv ℝ l (fderiv ... | [
"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\nk l : ℕ\nα : ↑I\nf : E → F\na : E\nhf : ContDiffPointwiseHolderAt k α f a\nhl : l < k\n⊢ (fun x ↦ dist (iteratedFDeriv ℝ l (fderiv ℝ f) x) (iteratedFDeriv ℝ l (fderiv ℝ f) a)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 63
} | {
"line": 251,
"column": 64
} | [
{
"pp": "case zero\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\nl : ℕ\nhl : l + 0 ≤ k\n⊢ ContDiffPointwiseHolderAt l α (iteratedFDeriv ℝ 0 f) ... | [
"case zero\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\nl : ℕ\nhl : l + 0 ≤ k\n⊢ ContDiffPointwiseHolderAt l α f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 254,
"column": 4
} | {
"line": 254,
"column": 68
} | {
"line": 254,
"column": 69
} | [
{
"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... | [
"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 (iteratedFDeriv ℝ m f) a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Star | {
"line": 125,
"column": 8
} | {
"line": 125,
"column": 19
} | {
"line": 125,
"column": 20
} | [
{
"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... | [
"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\ninst✝³ : StarAd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Star | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 13
} | {
"line": 39,
"column": 14
} | [
{
"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... | [
"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 : HasDerivAtFilter f f' L\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 731,
"column": 6
} | {
"line": 735,
"column": 35
} | {
"line": 736,
"column": 4
} | [
{
"pp": "case refine_3\nα : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : HasBesicovitchCovering α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f x ∩ Ioo 0 δ).Nonempty\nN... | [] | intro p hp
rcases Finset.mem_union.1 hp with (h'p | h'p)
· exact ht.2.2 p h'p
· rcases Finset.mem_image.1 h'p with ⟨p', p'v, rfl⟩
exact (hr p' (vs' p'v)).1.1 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 731,
"column": 6
} | {
"line": 735,
"column": 35
} | {
"line": 736,
"column": 4
} | [
{
"pp": "case refine_3\nα : Type u_1\ninst✝⁵ : MetricSpace α\ninst✝⁴ : SecondCountableTopology α\ninst✝³ : MeasurableSpace α\ninst✝² : OpensMeasurableSpace α\ninst✝¹ : HasBesicovitchCovering α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\nf : α → Set ℝ\ns : Set α\nhf : ∀ x ∈ s, ∀ δ > 0, (f x ∩ Ioo 0 δ).Nonempty\nN... | [] | intro p hp
rcases Finset.mem_union.1 hp with (h'p | h'p)
· exact ht.2.2 p h'p
· rcases Finset.mem_image.1 h'p with ⟨p', p'v, rfl⟩
exact (hr p' (vs' p'v)).1.1 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 167,
"column": 4
} | {
"line": 167,
"column": 85
} | {
"line": 167,
"column": 86
} | [
{
"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... | [
"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 : NormedAddCommGroup G\ninst✝ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 207,
"column": 86
} | {
"line": 210,
"column": 19
} | {
"line": 212,
"column": 0
} | [
{
"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.DerivativeTest | {
"line": 200,
"column": 4
} | {
"line": 200,
"column": 78
} | {
"line": 200,
"column": 79
} | [
{
"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)",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [... | [
"case refine_2.hf'\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⊢ DifferentiableOn ℝ f (interior (Ico b c))",
"case refine_2.hf'_nonneg\nf : ℝ → ℝ\na b c : ℝ\nh : Conti... | apply monotoneOn_of_deriv_nonneg (convex_Ico b c) (continuousOn_Ico h hd₁) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 336,
"column": 2
} | {
"line": 336,
"column": 41
} | {
"line": 337,
"column": 4
} | [
{
"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 : ... | [
"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 : ∀ i ∈ u, Con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 370,
"column": 4
} | {
"line": 370,
"column": 15
} | {
"line": 370,
"column": 16
} | [
{
"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 ... | [
"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 t\nhx : x ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin | {
"line": 199,
"column": 2
} | {
"line": 200,
"column": 9
} | {
"line": 200,
"column": 10
} | [
{
"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... | [
"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⊢ ∑ x, (-1) ^ ↑x • ∑ i, (-1) ^ ↑i • ((f (v x)) (x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DerivativeTest | {
"line": 354,
"column": 2
} | {
"line": 354,
"column": 53
} | {
"line": 355,
"column": 4
} | [
{
"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)",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DerivativeTest | {
"line": 411,
"column": 2
} | {
"line": 411,
"column": 13
} | {
"line": 411,
"column": 14
} | [
{
"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",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℝ → ℝ\nx₀ : ℝ\nhf : deriv (deriv f) x₀ < 0\nhd : deriv f x₀ = 0\nhc : ContinuousAt f x₀\n⊢ IsLocalMax f x₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 873,
"column": 8
} | {
"line": 873,
"column": 86
} | {
"line": 873,
"column": 87
} | [
{
"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 ... | [
"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 x ∩ Ioo 0 δ)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 239,
"column": 4
} | {
"line": 239,
"column": 31
} | {
"line": 239,
"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 : ∀ ⦃... | [
"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 : ∀ ⦃c : ℝ⦄, 0 < ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Bounds | {
"line": 466,
"column": 4
} | {
"line": 466,
"column": 93
} | {
"line": 466,
"column": 94
} | [
{
"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\... | [
"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\nt : Set F\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 305,
"column": 8
} | {
"line": 305,
"column": 73
} | {
"line": 305,
"column": 74
} | [
{
"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... | [
"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\nhx : ∀ ⦃c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 947,
"column": 10
} | {
"line": 948,
"column": 81
} | {
"line": 948,
"column": 82
} | [
{
"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 ... | [
"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 x ∩ Ioo 0 δ)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 949,
"column": 8
} | {
"line": 949,
"column": 57
} | {
"line": 949,
"column": 58
} | [
{
"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 ... | [
"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 x ∩ Ioo 0 δ)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.DifferentialForm.VectorField | {
"line": 177,
"column": 30
} | {
"line": 177,
"column": 41
} | {
"line": 177,
"column": 42
} | [
{
"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 ... | [
"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 + 1) → E → E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 316,
"column": 4
} | {
"line": 316,
"column": 40
} | {
"line": 317,
"column": 6
} | [
{
"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 : ∀ ⦃... | [
"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 : ∀ ⦃c : ℝ⦄, 0 < ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 183,
"column": 55
} | {
"line": 183,
"column": 66
} | {
"line": 183,
"column": 67
} | [
{
"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... | [
"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\nh₁ : t ⊆ s\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 206,
"column": 43
} | {
"line": 206,
"column": 54
} | {
"line": 206,
"column": 55
} | [
{
"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)",
"ppTerm": "... | [
"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 = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 294,
"column": 58
} | {
"line": 294,
"column": 69
} | {
"line": 294,
"column": 70
} | [
{
"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)",
"ppTerm": "?m.60",
"assigned": t... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 957,
"column": 8
} | {
"line": 957,
"column": 45
} | {
"line": 957,
"column": 46
} | [
{
"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 ... | [
"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 x ∩ Ioo 0 δ)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 342,
"column": 4
} | {
"line": 342,
"column": 15
} | {
"line": 342,
"column": 16
} | [
{
"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... | [
"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 = f₁ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 378,
"column": 30
} | {
"line": 378,
"column": 41
} | {
"line": 378,
"column": 42
} | [
{
"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)",... | [
"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 = f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.VectorField | {
"line": 273,
"column": 4
} | {
"line": 274,
"column": 43
} | {
"line": 275,
"column": 2
} | [
{
"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
} | {
"line": 275,
"column": 2
} | [
{
"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
} | {
"line": 275,
"column": 2
} | [
{
"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.MeasureTheory.Covering.Besicovitch | {
"line": 956,
"column": 6
} | {
"line": 957,
"column": 49
} | {
"line": 958,
"column": 6
} | [
{
"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, ∀ ... | [
"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, ∀ δ > 0, (f x ... | 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.LineDeriv.Basic | {
"line": 399,
"column": 73
} | {
"line": 399,
"column": 84
} | {
"line": 399,
"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 : 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... | [
"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 𝓝 x₀, ‖f x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 25
} | {
"line": 402,
"column": 26
} | [
{
"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... | [
"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 𝓝 x₀, ‖f x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 434,
"column": 73
} | {
"line": 434,
"column": 84
} | {
"line": 434,
"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 : 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... | [
"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 Continuous... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 437,
"column": 2
} | {
"line": 437,
"column": 25
} | {
"line": 437,
"column": 26
} | [
{
"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... | [
"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 Continuous... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 485,
"column": 2
} | {
"line": 485,
"column": 30
} | {
"line": 485,
"column": 31
} | [
{
"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 ... | [
"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 : HasLineDer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 512,
"column": 14
} | {
"line": 512,
"column": 57
} | {
"line": 512,
"column": 58
} | [
{
"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... | [
"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⊢ HasLineDerivWithin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 521,
"column": 14
} | {
"line": 521,
"column": 57
} | {
"line": 521,
"column": 58
} | [
{
"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 ... | [
"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 v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 529,
"column": 14
} | {
"line": 529,
"column": 57
} | {
"line": 529,
"column": 58
} | [
{
"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... | [
"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⊢ LineDifferentiableWithinAt 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.LineDeriv.Basic | {
"line": 537,
"column": 14
} | {
"line": 537,
"column": 57
} | {
"line": 537,
"column": 58
} | [
{
"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",
... | [
"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
} | {
"line": 545,
"column": 53
} | [
{
"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)",
... | [
"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 v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Norm | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 18
} | {
"line": 107,
"column": 19
} | [
{
"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)",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Norm | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 18
} | {
"line": 112,
"column": 19
} | [
{
"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)",
"ppTerm": "?m.44",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"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)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Symmetric | {
"line": 389,
"column": 2
} | {
"line": 389,
"column": 32
} | {
"line": 389,
"column": 33
} | [
{
"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... | [
"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 : HasFDerivWithin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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