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.Topology.Metrizable.Urysohn | {
"line": 42,
"column": 2
} | {
"line": 42,
"column": 54
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : RegularSpace X\ninst✝ : SecondCountableTopology X\n⊢ ∃ f, IsInducing f",
"usedConstants": [
"TopologicalSpace.exists_countable_basis"
]
}
] | rcases exists_countable_basis X with ⟨B, hBc, -, hB⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Topology.Metrizable.Urysohn | {
"line": 87,
"column": 52
} | {
"line": 87,
"column": 79
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : RegularSpace X\ninst✝ : SecondCountableTopology X\nB : Set (Set X)\nhBc : B.Countable\nhB : IsTopologicalBasis B\ns : Set (Set X × Set X) := {UV | UV ∈ B ×ˢ B ∧ closure[inst✝²] UV.1 ⊆ UV.2}\nthis✝¹ : Encodable ↑s\nthis✝ : TopologicalSpace ↑s := ⊥\nthi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 110,
"column": 6
} | {
"line": 110,
"column": 51
} | [
{
"pp": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns k : Set α\nhk : IsCompact k\nh'k : k ⊆ s \\ μ.everywherePosSubset s\nx : α\nhx : x ∈ k\n⊢ ∃ u ∈ 𝓝[s] x, μ u = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 172,
"column": 21
} | {
"line": 172,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : μ.IsEverywherePos s\nc : ℝ≥0∞\nhc : c ≠ 0\nx : α\nhx : x ∈ s\nn : Set α\nhn : n ∈ 𝓝[s] x\n⊢ 0 < (c • μ) n",
"usedConstants": [
"ENNReal.instCanonicallyOrderedAdd",
"Eq.mpr",
"inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 176,
"column": 22
} | {
"line": 176,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : μ.IsEverywherePos s\nc : ℝ≥0\nhc : c ≠ 0\n⊢ ↑c ≠ 0",
"usedConstants": [
"Eq.mpr",
"ENNReal.ofNNReal",
"congrArg",
"id",
"NNReal",
"Ne",
"NNReal.instZero",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 250,
"column": 4
} | {
"line": 251,
"column": 74
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | obtain ⟨i, hi, ni⟩ : ∃ i, y i ∈ W n * {z} ∧ n < i :=
((hz.frequently this).and_eventually (eventually_gt_atTop n)).exists | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 252,
"column": 44
} | {
"line": 252,
"column": 55
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 254,
"column": 37
} | {
"line": 254,
"column": 58
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 79,
"column": 4
} | {
"line": 79,
"column": 15
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : Nor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convolution | {
"line": 215,
"column": 6
} | {
"line": 215,
"column": 35
} | [
{
"pp": "case h.refine_1.hy\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup E'\ninst✝⁸ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedSpace 𝕜 E'\ninst... | rwa [neg_sub, sub_add_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 266,
"column": 30
} | {
"line": 266,
"column": 41
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 47
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 288,
"column": 2
} | {
"line": 288,
"column": 52
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nK : Set ... | refine ⟨L, everywherePosSubset_subset μ K, ?_, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Convolution | {
"line": 302,
"column": 2
} | {
"line": 317,
"column": 74
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup E'\ninst✝⁹ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedSpace 𝕜 E'\ninst✝⁵ : NormedSpace 𝕜... | let u := (Homeomorph.neg G).trans (Homeomorph.addRight x₀)
let v := (Homeomorph.neg G).trans (Homeomorph.addLeft x₀)
apply ((u.isCompact_preimage.mpr h).bddAbove_image hg.norm.continuousOn).convolutionExistsAt' L
isClosed_closure.measurableSet subset_closure (hf.integrableOn_isCompact h)
have A : AEStronglyMe... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Convolution | {
"line": 302,
"column": 2
} | {
"line": 317,
"column": 74
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup E'\ninst✝⁹ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedSpace 𝕜 E'\ninst✝⁵ : NormedSpace 𝕜... | let u := (Homeomorph.neg G).trans (Homeomorph.addRight x₀)
let v := (Homeomorph.neg G).trans (Homeomorph.addLeft x₀)
apply ((u.isCompact_preimage.mpr h).bddAbove_image hg.norm.continuousOn).convolutionExistsAt' L
isClosed_closure.measurableSet subset_closure (hf.integrableOn_isCompact h)
have A : AEStronglyMe... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 65
} | [
{
"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\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 59,
"column": 6
} | {
"line": 59,
"column": 70
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\ns : Set E\nx : E\nn : ℕ∞\nhs : s ∈ 𝓝 x\nd : ℝ\nd_pos : 0 < d\nhd : Euclidean.closedBall x d ⊆ s\nc : ContDiffBump (toEuclidean x) := { rIn := d / 2, rOut := d, rIn_pos := ⋯, rIn_lt_rOut := ⋯ }\nf : E ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 51
} | [
{
"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\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convolution | {
"line": 557,
"column": 6
} | {
"line": 557,
"column": 67
} | [
{
"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\nf : G → E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 120,
"column": 6
} | {
"line": 120,
"column": 48
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ∞ f ∧ range f ⊆ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 161,
"column": 30
} | {
"line": 161,
"column": 68
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn✝ : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ∞ f ∧ range f ⊆... | gcongr; exact (hR i x).trans (IR i hi) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 161,
"column": 30
} | {
"line": 161,
"column": 68
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn✝ : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ∞ f ∧ range f ⊆... | gcongr; exact (hR i x).trans (IR i hi) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Convolution | {
"line": 582,
"column": 21
} | {
"line": 582,
"column": 32
} | [
{
"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\nf : G → E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 192,
"column": 10
} | {
"line": 192,
"column": 80
} | [
{
"pp": "case a.refine_2\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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 167,
"column": 4
} | {
"line": 167,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn✝ : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ∞ f ∧ range f ⊆... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 169,
"column": 4
} | {
"line": 169,
"column": 25
} | [
{
"pp": "case inr.refine_1\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 197,
"column": 6
} | {
"line": 197,
"column": 34
} | [
{
"pp": "case neg\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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 220,
"column": 4
} | {
"line": 220,
"column": 65
} | [
{
"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\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 196,
"column": 4
} | {
"line": 196,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn✝ : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := ⋯\nT : Set ι\nT_count : T.Countable\nhT : ⋃ f ∈ T, support ↑f = s\ng0 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 100,
"column": 6
} | {
"line": 100,
"column": 58
} | [
{
"pp": "case hfs\nG : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : LocallyCompactSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : IsFiniteMeasureOnCompacts μ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 242,
"column": 8
} | {
"line": 242,
"column": 19
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nA : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (ball 0 1)\nf : E → ℝ\nf_support : support f = ball 0 1\nf_smooth : ContDiff ℝ ∞ f\nf_range : range f ⊆ Icc 0 1\nB : ∀ (x : E), f x ∈ Icc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 143,
"column": 26
} | {
"line": 143,
"column": 37
} | [
{
"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\nμ ν : Measure G\ninst✝⁴ : IsFiniteMeasureOnCompacts μ\ninst✝³ : IsFiniteMeasureOnCompacts ν\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : ν.IsMulRightInvariant\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 270,
"column": 18
} | {
"line": 270,
"column": 91
} | [
{
"pp": "case h.fst\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\... | simp only [Pi.sub_apply, _root_.id, Prod.fst_sub, sub_zero, Prod.snd_sub] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 270,
"column": 18
} | {
"line": 270,
"column": 91
} | [
{
"pp": "case h.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\... | simp only [Pi.sub_apply, _root_.id, Prod.fst_sub, sub_zero, Prod.snd_sub] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 307,
"column": 8
} | {
"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... | contDiffOn_succ_iff_fderiv_of_isOpen (hs.prod (@isOpen_univ G _)) | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.BumpFunction.Normed | {
"line": 120,
"column": 4
} | {
"line": 120,
"column": 15
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : HasContDiffBump E\ninst✝³ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : IsLocallyFiniteMeasure μ\nx : E\nhx : x ∉ closedBall c f.rOut\n⊢ f.rOut... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Normed | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 50
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : HasContDiffBump E\ninst✝⁴ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : μ.IsAddHaarMeasure\nK : ℝ\nh : f.rOu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Normed | {
"line": 141,
"column": 4
} | {
"line": 141,
"column": 50
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : HasContDiffBump E\ninst✝⁴ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : μ.IsAddHaarMeasure\nK : ℝ\nh : f.rOu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 301,
"column": 40
} | {
"line": 301,
"column": 57
} | [
{
"pp": "α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nx y : Ordinal.{u}\nhxy : p.index x = p.index y\nx_le_y : x ≤ y\nH : x < y\nh : ∃ x, p.c x ∉ p.iUnionUpTo y ∧ p.R y ≤ p.τ * p.r x\nA : p.c (p.index y) ∉ ball (p.c (p.index x)) (p.r (p.index x))\n⊢ p.r (p.index y) ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 363,
"column": 6
} | {
"line": 363,
"column": 72
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 93
} | [
{
"pp": "case pos\nG : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : BorelSpace G\nμ' μ ν : Measure G\ninst✝³ : μ.IsHaarMeasure\ninst✝² : ν.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nhG : Loc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 369,
"column": 6
} | {
"line": 370,
"column": 33
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 375,
"column": 4
} | {
"line": 376,
"column": 90
} | [
{
"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 �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 392,
"column": 6
} | {
"line": 392,
"column": 99
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 418,
"column": 32
} | {
"line": 418,
"column": 47
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 408,
"column": 6
} | {
"line": 408,
"column": 52
} | [
{
"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)) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 494,
"column": 6
} | {
"line": 494,
"column": 17
} | [
{
"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 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 408,
"column": 2
} | {
"line": 408,
"column": 37
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 503,
"column": 10
} | {
"line": 503,
"column": 59
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 47
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Convolution | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 35
} | [
{
"pp": "case h.g_supp.h\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✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 516,
"column": 6
} | {
"line": 516,
"column": 17
} | [
{
"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,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 518,
"column": 2
} | {
"line": 518,
"column": 19
} | [
{
"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 :... | simp_rw [M] at I1 | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 529,
"column": 4
} | {
"line": 530,
"column": 74
} | [
{
"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 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 479,
"column": 6
} | {
"line": 479,
"column": 70
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 482,
"column": 6
} | {
"line": 482,
"column": 70
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 533,
"column": 2
} | {
"line": 533,
"column": 13
} | [
{
"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 :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 505,
"column": 4
} | {
"line": 505,
"column": 94
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 510,
"column": 6
} | {
"line": 511,
"column": 29
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 574,
"column": 6
} | {
"line": 574,
"column": 44
} | [
{
"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, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 318,
"column": 4
} | {
"line": 318,
"column": 35
} | [
{
"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.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 350,
"column": 4
} | {
"line": 350,
"column": 35
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 652,
"column": 6
} | {
"line": 652,
"column": 54
} | [
{
"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.Covering.BesicovitchVectorSpace | {
"line": 353,
"column": 40
} | {
"line": 353,
"column": 88
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 357,
"column": 6
} | {
"line": 357,
"column": 54
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 661,
"column": 6
} | {
"line": 661,
"column": 54
} | [
{
"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": 697,
"column": 4
} | {
"line": 697,
"column": 15
} | [
{
"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 | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 697,
"column": 4
} | {
"line": 697,
"column": 52
} | [
{
"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.Measure.Haar.Unique | {
"line": 734,
"column": 6
} | {
"line": 737,
"column": 28
} | [
{
"pp": "case h.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.... | 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": 734,
"column": 6
} | {
"line": 737,
"column": 28
} | [
{
"pp": "case h.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.... | 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.MeasureTheory.Measure.Haar.Unique | {
"line": 750,
"column": 54
} | {
"line": 750,
"column": 65
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 752,
"column": 8
} | {
"line": 752,
"column": 19
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 755,
"column": 8
} | {
"line": 756,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 389,
"column": 43
} | {
"line": 389,
"column": 94
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 403,
"column": 4
} | {
"line": 403,
"column": 35
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 405,
"column": 40
} | {
"line": 405,
"column": 88
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 638,
"column": 54
} | {
"line": 638,
"column": 68
} | [
{
"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, ... | inter_iUnion₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 649,
"column": 6
} | {
"line": 649,
"column": 68
} | [
{
"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, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 651,
"column": 6
} | {
"line": 651,
"column": 68
} | [
{
"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, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 470,
"column": 41
} | {
"line": 470,
"column": 77
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | {
"line": 476,
"column": 43
} | {
"line": 476,
"column": 79
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Polynomial | {
"line": 25,
"column": 21
} | {
"line": 25,
"column": 32
} | [
{
"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)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Polynomial | {
"line": 26,
"column": 20
} | {
"line": 26,
"column": 31
} | [
{
"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)",
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"HMul.hMul",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 734,
"column": 6
} | {
"line": 738,
"column": 35
} | [
{
"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": 734,
"column": 6
} | {
"line": 738,
"column": 35
} | [
{
"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.ContDiffHolder.Pointwise | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 13
} | [
{
"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",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 126,
"column": 4
} | {
"line": 127,
"column": 11
} | [
{
"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\nα : ↑I\nf : E → F\na : E\ns : Set E\nC : ℝ≥0\nhf : ContDiffOn ℝ (↑k) f s\nhs : s ∈ 𝓝 a\nhd : HolderOnWith C ⟨↑α, ⋯⟩ (iteratedFDeriv ℝ k f) s\nx : E\nhx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Holder | {
"line": 191,
"column": 4
} | {
"line": 191,
"column": 15
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.Holder | {
"line": 196,
"column": 38
} | {
"line": 196,
"column": 49
} | [
{
"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",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Darboux | {
"line": 38,
"column": 4
} | {
"line": 38,
"column": 15
} | [
{
"pp": "a b : ℝ\nf f' : ℝ → ℝ\nhab : a ≤ b\nhf : ∀ x ∈ Icc a b, HasDerivWithinAt f (f' x) (Icc a b) x\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\nhab' : a < b\ng : ℝ → ℝ := fun x ↦ f x - m * x\nx : ℝ\nhx : x ∈ Icc a b\n⊢ HasDerivWithinAt g (f' x - m) (Icc a b) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Darboux | {
"line": 48,
"column": 6
} | {
"line": 49,
"column": 13
} | [
{
"pp": "case inl\na b : ℝ\nf f' : ℝ → ℝ\nhab : a ≤ b\nhf : ∀ x ∈ Icc a b, HasDerivWithinAt f (f' x) (Icc a b) x\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\nhab' : a < b\ng : ℝ → ℝ := fun x ↦ f x - m * x\nhg : ∀ x ∈ Icc a b, HasDerivWithinAt g (f' x - m) (Icc a b) x\ncmem : a ∈ Icc a b\nhc : IsMinOn g (Icc a b) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Darboux | {
"line": 56,
"column": 6
} | {
"line": 57,
"column": 13
} | [
{
"pp": "case inr.inl\na b : ℝ\nf f' : ℝ → ℝ\nhab : a ≤ b\nhf : ∀ x ∈ Icc a b, HasDerivWithinAt f (f' x) (Icc a b) x\nm : ℝ\nhma : f' a < m\nhmb : m < f' b\nhab' : a < b\ng : ℝ → ℝ := fun x ↦ f x - m * x\nhg : ∀ x ∈ Icc a b, HasDerivWithinAt g (f' x - m) (Icc a b) x\ncmem : b ∈ Icc a b\nhc : IsMinOn g (Icc a b)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Darboux | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 36
} | [
{
"pp": "case hs\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\n⊢ m ∈ f' '' s",
"usedConstants": [
"Real",
"le_total",
"Real.linearOrder"
]
}
] | 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
} | [
{
"pp": "case hs.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",
"usedConstants": [
"Real",
"Set.OrdConnected.out",
"HasSubset.Subset",
... | 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.ContDiff.Bounds | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 85
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 20
} | [
{
"pp": "case inl\nx : ℝ\nhx✝ : x ≠ 0\nhx : x < 0\n⊢ HasStrictDerivAt (fun x ↦ |x|) (↑(SignType.sign x)) x",
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"SignType.cast",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonU... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.Abs | {
"line": 71,
"column": 4
} | {
"line": 71,
"column": 20
} | [
{
"pp": "case inr\nx : ℝ\nhx✝ : x ≠ 0\nhx : 0 < x\n⊢ HasStrictDerivAt (fun x ↦ |x|) (↑(SignType.sign x)) x",
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"SignType.cast",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 224,
"column": 14
} | {
"line": 224,
"column": 45
} | [
{
"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) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 243,
"column": 4
} | {
"line": 244,
"column": 11
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 63
} | [
{
"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) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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