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.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 234,
"column": 2
} | {
"line": 234,
"column": 24
} | [
{
"pp": "p : ℝ → Prop\na : ℝ\nh : ∀ᶠ (x : ℝ) in 𝓝 a, p x\nl u : ℝ\nhx : a ∈ Ioo l u\nhs : Ioo l u ⊆ {x | p x}\n⊢ 0 < volume (Ioo l u)",
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Eq.mpr",
"sub_pos._simp_1",
"Real.partialOrder",
"Real",
"Me... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 340,
"column": 2
} | {
"line": 340,
"column": 29
} | [
{
"pp": "a : ℝ\nh : a ≠ 0\n⊢ ofReal |a| • Measure.map (fun x ↦ x * a) volume = volume",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 344,
"column": 2
} | {
"line": 344,
"column": 29
} | [
{
"pp": "a : ℝ\nh : a ≠ 0\n⊢ Measure.map (fun x ↦ x * a) volume = ofReal |a⁻¹| • volume",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
"instHSMul",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 382,
"column": 8
} | {
"line": 382,
"column": 35
} | [
{
"pp": "ι : Type u_1\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\nD : ι → ℝ\nh : (Matrix.diagonal D).det ≠ 0\ns : ι → Set ℝ\nhs : ∀ (i : ι), MeasurableSet (s i)\nthis : (⇑(toLin' (Matrix.diagonal D)) ⁻¹' univ.pi fun i ↦ s i) = univ.pi fun i ↦ (fun x ↦ D i * x) ⁻¹' s i\ni : ι\nA : D i ≠ 0\n⊢ ofReal |D i| * volum... | volume_preimage_mul_left A, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 438,
"column": 4
} | {
"line": 438,
"column": 34
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nf : (ι → ℝ) →ₗ[ℝ] ι → ℝ\nhf : LinearMap.det f ≠ 0\n⊢ Measure.map (⇑f) volume = ofReal |(LinearMap.det f)⁻¹| • volume",
"usedConstants": [
"Pi.Function.module",
"Real",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Pi.addCommMonoid",... | let M := LinearMap.toMatrix' f | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 443,
"column": 4
} | {
"line": 443,
"column": 17
} | [
{
"pp": "case hM\nι : Type u_1\ninst✝ : Fintype ι\nf : (ι → ℝ) →ₗ[ℝ] ι → ℝ\nhf : LinearMap.det f ≠ 0\nM : Matrix ι ι ℝ := ⋯\nA : LinearMap.det f = M.det\nB : f = toLin' M\n⊢ M.det ≠ 0",
"usedConstants": [
"Pi.Function.module",
"Real",
"MonoidHom.instFunLike",
"Semiring.toModule",
... | rwa [A] at hf | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 151,
"column": 6
} | {
"line": 151,
"column": 54
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Set E\nu : ℕ → E\nsb : Bornology.IsBounded s\nhu : Bornology.IsBounded (range u)\nhs : Pairwise (Disjo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 79
} | [
{
"pp": "α : Type u_1\nf g : α → ℝ\ns : Set α\n⊢ regionBetween f g s ⊆ s ×ˢ univ",
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"Real",
"SProd.sprod",
"congrArg",
"regionBetween",
"Set.univ",
"setOf",
"Set.prod_univ",
"Membership.mem",
"_pri... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 462,
"column": 43
} | {
"line": 468,
"column": 25
} | [
{
"pp": "α : Type u_1\ninst✝ : MeasurableSpace α\nf g : α → ℝ\ns : Set α\nhf : Measurable f\nhg : Measurable g\nhs : MeasurableSet s\n⊢ MeasurableSet (regionBetween f g s)",
"usedConstants": [
"Real",
"Preorder.toLT",
"Real.lattice",
"MeasurableSet",
"Measurable.comp",
"i... | by
dsimp only [regionBetween, Ioo, mem_setOf_eq, setOf_and]
refine
MeasurableSet.inter ?_
((measurableSet_lt (hf.comp measurable_fst) measurable_snd).inter
(measurableSet_lt measurable_snd (hg.comp measurable_fst)))
exact measurable_fst hs | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 509,
"column": 2
} | {
"line": 509,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : MeasurableSpace α\nf : α → ℝ\nhf : Measurable f\n⊢ MeasurableSet {p | p.2 = f p.1}",
"usedConstants": [
"Eq.mpr",
"Real",
"MeasurableSet",
"measurableSet_setOf._simp_1",
"Measurable",
"setOf",
"id",
"Prod.fst",
"Real.measur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 72
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Submodule ℝ E\nhs : s ≠ ⊤\n⊢ ∃ x, x ∉ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 195,
"column": 4
} | {
"line": 195,
"column": 38
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Submodule ℝ E\nhs : s ≠ ⊤\nx : E\nhx : x ∉ s\nc : ℝ\ncpos : 0 < c\ncone : c < 1\nA✝ : Bornology.IsBoun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 209,
"column": 2
} | {
"line": 210,
"column": 63
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : AffineSubspace ℝ E\nhs : ¬s.direction = ⊤\nx : E\nhx : x ∈ s\n⊢ μ ↑s = 0",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 566,
"column": 4
} | {
"line": 566,
"column": 72
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\nf_mble : AEMeasurable f μ\ng_mble : AEMeasurable g μ\ns : Set α\ns_mble : NullMeasurableSet s μ\n⊢ NullMeasurableSet (fun p ↦ Real.lt✝ p.2 (g p.1)) (μ.prod volume)",
"usedConstants": [
"Real",
"Real.latt... | exact nullMeasurableSet_lt measurable_snd.aemeasurable (by fun_prop) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 566,
"column": 4
} | {
"line": 566,
"column": 72
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\nf_mble : AEMeasurable f μ\ng_mble : AEMeasurable g μ\ns : Set α\ns_mble : NullMeasurableSet s μ\n⊢ NullMeasurableSet (fun p ↦ Real.lt✝ p.2 (g p.1)) (μ.prod volume)",
"usedConstants": [
"Real",
"Real.latt... | exact nullMeasurableSet_lt measurable_snd.aemeasurable (by fun_prop) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 566,
"column": 4
} | {
"line": 566,
"column": 72
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\nf_mble : AEMeasurable f μ\ng_mble : AEMeasurable g μ\ns : Set α\ns_mble : NullMeasurableSet s μ\n⊢ NullMeasurableSet (fun p ↦ Real.lt✝ p.2 (g p.1)) (μ.prod volume)",
"usedConstants": [
"Real",
"Real.latt... | exact nullMeasurableSet_lt measurable_snd.aemeasurable (by fun_prop) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 596,
"column": 4
} | {
"line": 596,
"column": 72
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\nf_mble : AEMeasurable f μ\ng_mble : AEMeasurable g μ\ns : Set α\ns_mble : NullMeasurableSet s μ\n⊢ NullMeasurableSet (fun p ↦ Real.lt✝ p.2 (g p.1)) (μ.prod volume)",
"usedConstants": [
"Real",
"Real.latt... | exact nullMeasurableSet_lt measurable_snd.aemeasurable (by fun_prop) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 596,
"column": 4
} | {
"line": 596,
"column": 72
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\nf_mble : AEMeasurable f μ\ng_mble : AEMeasurable g μ\ns : Set α\ns_mble : NullMeasurableSet s μ\n⊢ NullMeasurableSet (fun p ↦ Real.lt✝ p.2 (g p.1)) (μ.prod volume)",
"usedConstants": [
"Real",
"Real.latt... | exact nullMeasurableSet_lt measurable_snd.aemeasurable (by fun_prop) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 596,
"column": 4
} | {
"line": 596,
"column": 72
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝ : MeasurableSpace α\nμ : Measure α\nf g : α → ℝ\nf_mble : AEMeasurable f μ\ng_mble : AEMeasurable g μ\ns : Set α\ns_mble : NullMeasurableSet s μ\n⊢ NullMeasurableSet (fun p ↦ Real.lt✝ p.2 (g p.1)) (μ.prod volume)",
"usedConstants": [
"Real",
"Real.latt... | exact nullMeasurableSet_lt measurable_snd.aemeasurable (by fun_prop) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 20
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E →ₗ[ℝ] E\ns : Set E\nhf : LinearMap.det f = 0\n⊢ μ (⇑f '' s) = ENNReal.ofReal |LinearMap.de... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 1255,
"column": 4
} | {
"line": 1255,
"column": 44
} | [
{
"pp": "case refine_1\np : ℝ≥0∞\nι : Type u_2\nα : ι → Type u_3\ninst✝⁵ : Fact (1 ≤ p)\ninst✝⁴ : Fintype ι\ninst✝³ : (i : ι) → SeminormedAddCommGroup (α i)\nR : Type u_5\ninst✝² : SeminormedRing R\ninst✝¹ : (i : ι) → Module R (α i)\ninst✝ : ∀ (i : ι), IsBoundedSMul R (α i)\nthis : PseudoMetricSpace ((i : ι) → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.PiLp | {
"line": 1256,
"column": 4
} | {
"line": 1256,
"column": 44
} | [
{
"pp": "case refine_2\np : ℝ≥0∞\nι : Type u_2\nα : ι → Type u_3\ninst✝⁵ : Fact (1 ≤ p)\ninst✝⁴ : Fintype ι\ninst✝³ : (i : ι) → SeminormedAddCommGroup (α i)\nR : Type u_5\ninst✝² : SeminormedRing R\ninst✝¹ : (i : ι) → Module R (α i)\ninst✝ : ∀ (i : ι), IsBoundedSMul R (α i)\nthis : PseudoMetricSpace ((i : ι) → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 638,
"column": 8
} | {
"line": 638,
"column": 83
} | [
{
"pp": "μ : Measure ℝ\ninst✝ : NoAtoms μ\ns : Set ℝ\np : ℝ → Prop\nh : ∀ (a b : ℝ), a ∈ s → b ∈ s → a < b → ∀ᵐ (x : ℝ) ∂μ.restrict (s ∩ Ioo a b), p x\nT : ↑s × ↑s → Set ℝ := fun p ↦ Ioo ↑p.1 ↑p.2\nu : Set ℝ := ⋃ i, T i\nhfinite : (s \\ u).Finite\nA : Set (↑s × ↑s)\nA_count : A.Countable\nhA : ⋃ i ∈ A, T i = ⋃ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 398,
"column": 4
} | {
"line": 398,
"column": 35
} | [
{
"pp": "case inr.inl\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Set E\nhs : NullMeasurableSet s μ\nhs' : s.Nonempty\n⊢ NullMeasurableSet (0 • s) μ",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 513,
"column": 41
} | {
"line": 516,
"column": 51
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : MeasurableSpace E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\nμ : Measure E\ninst✝¹ : μ.IsAddHaarMeasure\ninst✝ : Nontrivial E\nx : E\nr : ℝ\n⊢ μ (closedBall x r) = μ (ball x r)",
"usedConstants": [
"I... | by
by_cases! h : r < 0
· rw [Metric.closedBall_eq_empty.mpr h, Metric.ball_eq_empty.mpr h.le]
rw [addHaar_closedBall μ x h, addHaar_ball μ x h] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 546,
"column": 8
} | {
"line": 546,
"column": 89
} | [
{
"pp": "case ha\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nr : ℝ\nhr : r ≠ 0\nx y : E\ns t : Set E\n⊢ ENNReal.ofReal (|r| ^ finrank ℝ E) ≠ 0 ∨ μ t ≠ ∞",
... | simp only [pow_pos (abs_pos.mpr hr), ENNReal.ofReal_eq_zero, not_le, Ne, true_or] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 546,
"column": 8
} | {
"line": 546,
"column": 89
} | [
{
"pp": "case ha\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nr : ℝ\nhr : r ≠ 0\nx y : E\ns t : Set E\n⊢ ENNReal.ofReal (|r| ^ finrank ℝ E) ≠ 0 ∨ μ t ≠ ∞",
... | simp only [pow_pos (abs_pos.mpr hr), ENNReal.ofReal_eq_zero, not_le, Ne, true_or] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 546,
"column": 8
} | {
"line": 546,
"column": 89
} | [
{
"pp": "case ha\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nr : ℝ\nhr : r ≠ 0\nx y : E\ns t : Set E\n⊢ ENNReal.ofReal (|r| ^ finrank ℝ E) ≠ 0 ∨ μ t ≠ ∞",
... | simp only [pow_pos (abs_pos.mpr hr), ENNReal.ofReal_eq_zero, not_le, Ne, true_or] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Lebesgue.Basic | {
"line": 681,
"column": 6
} | {
"line": 681,
"column": 81
} | [
{
"pp": "μ : Measure ℝ\ninst✝ : NoAtoms μ\ns : Set ℝ\np : ℝ → Prop\nh : ∀ (a b : ℝ), a ∈ s → b ∈ s → a < b → ∀ᵐ (x : ℝ) ∂μ, x ∈ s ∩ Ioo a b → p x\nT : ↑s × ↑s → Set ℝ := fun p ↦ Ioo ↑p.1 ↑p.2\nu : Set ℝ := ⋃ i, T i\nhfinite : (s \\ u).Finite\nA : Set (↑s × ↑s)\nA_count : A.Countable\nhA : ⋃ i ∈ A, T i = ⋃ i, T ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.Basic | {
"line": 149,
"column": 12
} | {
"line": 149,
"column": 67
} | [
{
"pp": "ι : Type u_1\nI J : Box ι\ntfae_1_iff_2 : I ≤ J ↔ ↑I ⊆ ↑J\nx✝ : ↑I ⊆ ↑J\nh : ↑I ⊆ ↑J := x✝\n⊢ Icc I.lower I.upper ⊆ Icc J.lower J.upper",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.Basic | {
"line": 289,
"column": 23
} | {
"line": 289,
"column": 34
} | [
{
"pp": "case pos\nι : Type u_1\nl u : ι → ℝ\nh : ∀ (i : ι), l i < u i\n⊢ ↑{ lower := l, upper := u, lower_lt_upper := h } = ⊥ ↔ ∃ i, u i ≤ l i",
"usedConstants": [
"Eq.mpr",
"not_exists._simp_1",
"False",
"Real.instLE",
"Real",
"WithBot.some",
"WithBot",
"Pre... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.Basic | {
"line": 289,
"column": 23
} | {
"line": 289,
"column": 34
} | [
{
"pp": "case neg\nι : Type u_1\nl u : ι → ℝ\nh : ¬∀ (i : ι), l i < u i\n⊢ ⊥ = ⊥ ↔ ∃ i, u i ≤ l i",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"WithBot",
"congrArg",
"true_iff",
"Exists",
"id",
"Bot.bot",
"LE.le",
"Iff",
"True"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.Basic | {
"line": 471,
"column": 2
} | {
"line": 472,
"column": 18
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nI : Box ι\ni : ι\nA : I.lower i - I.upper i < 0\n⊢ dist I.lower I.upper ≤ ↑I.distortion * (I.upper i - I.lower i)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.SubboxInduction | {
"line": 130,
"column": 39
} | {
"line": 130,
"column": 59
} | [
{
"pp": "ι : Type u_1\np : Box ι → Prop\nI : Box ι\nH_nhds :\n ∀ z ∈ Box.Icc I,\n ∃ U ∈ 𝓝[Box.Icc I] z,\n ∀ J ≤ I,\n ∀ (m : ℕ),\n z ∈ Box.Icc J → Box.Icc J ⊆ U → (∀ (i : ι), J.upper i - J.lower i = (I.upper i - I.lower i) / 2 ^ m) → p J\nhpI : ¬p I\ns : Box ι → Set ι\nhs : ∀ J ≤ I, ¬p ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.SubboxInduction | {
"line": 132,
"column": 56
} | {
"line": 132,
"column": 81
} | [
{
"pp": "ι : Type u_1\np : Box ι → Prop\nI : Box ι\nH_nhds :\n ∀ z ∈ Box.Icc I,\n ∃ U ∈ 𝓝[Box.Icc I] z,\n ∀ J ≤ I,\n ∀ (m : ℕ),\n z ∈ Box.Icc J → Box.Icc J ⊆ U → (∀ (i : ι), J.upper i - J.lower i = (I.upper i - I.lower i) / 2 ^ m) → p J\nhpI : ¬p I\ns : Box ι → Set ι\nhs : ∀ J ≤ I, ¬p ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.SubboxInduction | {
"line": 151,
"column": 72
} | {
"line": 151,
"column": 83
} | [
{
"pp": "ι : Type u_1\np : Box ι → Prop\nI : Box ι\nH_nhds :\n ∀ z ∈ Box.Icc I,\n ∃ U ∈ 𝓝[Box.Icc I] z,\n ∀ J ≤ I,\n ∀ (m : ℕ),\n z ∈ Box.Icc J → Box.Icc J ⊆ U → (∀ (i : ι), J.upper i - J.lower i = (I.upper i - I.lower i) / 2 ^ m) → p J\nJ : ℕ → Box ι\nhJmono : Antitone J\nhJle : ∀ (m ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Box.SubboxInduction | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 23
} | [
{
"pp": "ι : Type u_1\np : Box ι → Prop\nI : Box ι\nH_nhds :\n ∀ z ∈ Box.Icc I,\n ∃ U ∈ 𝓝[Box.Icc I] z,\n ∀ J ≤ I,\n ∀ (m : ℕ),\n z ∈ Box.Icc J → Box.Icc J ⊆ U → (∀ (i : ι), J.upper i - J.lower i = (I.upper i - I.lower i) / 2 ^ m) → p J\nJ : ℕ → Box ι\nhJmono : Antitone J\nhJle : ∀ (m ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 173,
"column": 37
} | {
"line": 173,
"column": 59
} | [
{
"pp": "ι : Type u_1\nI : Box ι\nπ : Prepartition I\nx : ι → ℝ\nJ₁ : Box ι\nh₁ : J₁ ∈ π\nhx₁ : x ∈ Box.Icc J₁\nJ₂ : Box ι\nh₂ : J₂ ∈ π\nhx₂ : x ∈ Box.Icc J₂\ni : ι\nH : ∀ (x_1 : ι), J₁.lower x_1 = x x_1 ↔ J₂.lower x_1 = x x_1\nhi₁ : J₁.lower i = x i\nhi₂ : J₂.lower i = x i\n⊢ x i < J₁.upper i",
"usedConsta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 174,
"column": 37
} | {
"line": 174,
"column": 59
} | [
{
"pp": "ι : Type u_1\nI : Box ι\nπ : Prepartition I\nx : ι → ℝ\nJ₁ : Box ι\nh₁ : J₁ ∈ π\nhx₁ : x ∈ Box.Icc J₁\nJ₂ : Box ι\nh₂ : J₂ ∈ π\nhx₂ : x ∈ Box.Icc J₂\ni : ι\nH : ∀ (x_1 : ι), J₁.lower x_1 = x x_1 ↔ J₂.lower x_1 = x x_1\nhi₁ : J₁.lower i = x i\nhi₂ : J₂.lower i = x i\nH₁ : x i < J₁.upper i\n⊢ x i < J₂.up... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 709,
"column": 14
} | {
"line": 709,
"column": 49
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Set E\nx : E\nh : Tendsto (fun r ↦ μ (s ∩ closedBall x r) / μ (closedBall x r)) (𝓝[>] 0) (𝓝 0)\nt : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 13
} | [
{
"pp": "ι : Type u_1\nI : Box ι\nπ : Prepartition I\ninst✝ : Fintype ι\nx : ι → ℝ\n⊢ InjOn (fun J ↦ {i | J.lower i = x i}) ↑({J ∈ π.boxes | x ∈ Box.Icc J})",
"usedConstants": [
"Eq.mpr",
"Real",
"Finset.coe_filter",
"BoxIntegral.Prepartition",
"congrArg",
"Finset",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Basic | {
"line": 480,
"column": 6
} | {
"line": 481,
"column": 73
} | [
{
"pp": "case refine_1.refine_2\nK : Type u_1\ninst✝⁹ : NormedField K\ninst✝⁸ : LinearOrder K\ninst✝⁷ : IsStrictOrderedRing K\ninst✝⁶ : HasSolidNorm K\ninst✝⁵ : FloorRing K\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace K E\ninst✝² : FiniteDimensional K E\ninst✝¹ : ProperSpace E\nL : Submodu... | refine Submodule.add_mem _ h_mem
(neg_mem (Set.mem_of_subset_of_mem ?_ (Subtype.mem (floor b x)))) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 45
} | [
{
"pp": "case pos\nι : Type u_1\nI : Box ι\nπ : Prepartition I\nπi : (J : Box ι) → Prepartition J\nJ : Box ι\nhJ : J ∈ π.biUnion πi\n⊢ π.biUnionIndex πi J ≤ I",
"usedConstants": [
"BoxIntegral.Prepartition.le_of_mem",
"BoxIntegral.Prepartition.biUnionIndex",
"BoxIntegral.Prepartition.biUni... | exact π.le_of_mem (π.biUnionIndex_mem hJ) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 45
} | [
{
"pp": "case pos\nι : Type u_1\nI : Box ι\nπ : Prepartition I\nπi : (J : Box ι) → Prepartition J\nJ : Box ι\nhJ : J ∈ π.biUnion πi\n⊢ π.biUnionIndex πi J ≤ I",
"usedConstants": [
"BoxIntegral.Prepartition.le_of_mem",
"BoxIntegral.Prepartition.biUnionIndex",
"BoxIntegral.Prepartition.biUni... | exact π.le_of_mem (π.biUnionIndex_mem hJ) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 45
} | [
{
"pp": "case pos\nι : Type u_1\nI : Box ι\nπ : Prepartition I\nπi : (J : Box ι) → Prepartition J\nJ : Box ι\nhJ : J ∈ π.biUnion πi\n⊢ π.biUnionIndex πi J ≤ I",
"usedConstants": [
"BoxIntegral.Prepartition.le_of_mem",
"BoxIntegral.Prepartition.biUnionIndex",
"BoxIntegral.Prepartition.biUni... | exact π.le_of_mem (π.biUnionIndex_mem hJ) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 364,
"column": 4
} | {
"line": 364,
"column": 62
} | [
{
"pp": "ι : Type u_1\nI J✝ J₁ J₂ : Box ι\nπ π₁ π₂ : Prepartition I\nx : ι → ℝ\nπi πi₁ πi₂ : (J : Box ι) → Prepartition J\nboxes : Finset (WithBot (Box ι))\nle_of_mem : ∀ J ∈ boxes, J ≤ ↑I\npairwise_disjoint : (↑boxes).Pairwise Disjoint\nJ : Box ι\nhJ : some J ∈ boxes\n⊢ J ≤ I",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 390,
"column": 4
} | {
"line": 390,
"column": 41
} | [
{
"pp": "ι : Type u_1\nI : Box ι\nπ : Prepartition I\nboxes : Finset (WithBot (Box ι))\nle_of_mem : ∀ J ∈ boxes, J ≤ ↑I\npairwise_disjoint : (↑boxes).Pairwise Disjoint\nH : ∀ J ∈ boxes, J ≠ ⊥ → ∃ J' ∈ π, J ≤ ↑J'\nJ : Box ι\nhJ : ↑J ∈ boxes\n⊢ ∃ J' ∈ π, J ≤ J'",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 771,
"column": 8
} | {
"line": 771,
"column": 23
} | [
{
"pp": "case e_a\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Set E\nhs : MeasurableSet s\nx : E\nh : Tendsto (fun r ↦ μ (s ∩ closedBall x r) / μ (closedB... | inter_comm _ u, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar | {
"line": 771,
"column": 24
} | {
"line": 771,
"column": 39
} | [
{
"pp": "case e_a\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\ns : Set E\nhs : MeasurableSet s\nx : E\nh : Tendsto (fun r ↦ μ (s ∩ closedBall x r) / μ (closedB... | inter_comm _ u, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.BoxIntegral.Partition.Basic | {
"line": 541,
"column": 2
} | {
"line": 541,
"column": 13
} | [
{
"pp": "case h\nι : Type u_1\nI : Box ι\nπ : Prepartition I\np : Box ι → Prop\nhp : ∀ J ∈ π, p J\nJ : Box ι\n⊢ J ∈ π.filter p ↔ J ∈ π",
"usedConstants": [
"Eq.mpr",
"BoxIntegral.Prepartition.filter",
"BoxIntegral.Prepartition",
"congrArg",
"Membership.mem",
"id",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Tagged | {
"line": 143,
"column": 8
} | {
"line": 143,
"column": 34
} | [
{
"pp": "case refine_2\nι : Type u_1\nI : Box ι\np : (ι → ℝ) → Box ι → Prop\nπ : Prepartition I\nπi : (J : Box ι) → TaggedPrepartition J\nH : ∀ J ∈ π, ∀ J' ∈ πi J, p ((πi J).tag J') J'\nJ' : Box ι\nx✝ : ∃ J'_1 ∈ π, J' ∈ πi J'_1\nJ : Box ι\nhJ : J ∈ π\nhJ' : J' ∈ πi J\n⊢ p ((π.biUnionTagged πi).tag J') J'",
... | π.tag_biUnionTagged hJ hJ' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.BoxIntegral.Partition.Tagged | {
"line": 143,
"column": 2
} | {
"line": 144,
"column": 23
} | [
{
"pp": "case refine_2\nι : Type u_1\nI : Box ι\np : (ι → ℝ) → Box ι → Prop\nπ : Prepartition I\nπi : (J : Box ι) → TaggedPrepartition J\nH : ∀ J ∈ π, ∀ J' ∈ πi J, p ((πi J).tag J') J'\nJ' : Box ι\nx✝ : ∃ J'_1 ∈ π, J' ∈ πi J'_1\nJ : Box ι\nhJ : J ∈ π\nhJ' : J' ∈ πi J\n⊢ p ((π.biUnionTagged πi).tag J') J'",
... | · rw [π.tag_biUnionTagged hJ hJ']
exact H J hJ J' hJ' | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.BoxIntegral.Partition.Tagged | {
"line": 352,
"column": 4
} | {
"line": 352,
"column": 15
} | [
{
"pp": "ι : Type u_1\nI✝ J✝ : Box ι\nπ π₁ π₂ : TaggedPrepartition I✝\nx : ι → ℝ\nr r₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nI J : Box ι\nh : I ≤ J\nt₁ : Box ι → ι → ℝ\nht₁ : ∀ (J : Box ι), t₁ J ∈ Box.Icc I\nb₁ : Finset (Box ι)\nh₁le : ∀ J ∈ b₁, J ≤ I\nh₁d : (↑b₁).Pairwise (Disjoint on Box.toSet)\nt₂ : Box ι → ι → ℝ\nht... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Split | {
"line": 159,
"column": 6
} | {
"line": 159,
"column": 51
} | [
{
"pp": "case inl\nι : Type u_1\nM : Type u_2\nn : ℕ\nI✝ J : Box ι\ni✝ : ι\nx✝ : ℝ\nI : Box ι\ni : ι\nx : ℝ\n⊢ I.splitLower i x ≤ ↑I",
"usedConstants": [
"BoxIntegral.Box.splitLower_le"
]
},
{
"pp": "case inr\nι : Type u_1\nM : Type u_2\nn : ℕ\nI✝ J : Box ι\ni✝ : ι\nx✝ : ℝ\nI : Box ι\ni : ... | exacts [Box.splitLower_le, Box.splitUpper_le] | Batteries.Tactic._aux_Batteries_Tactic_Init___elabRules_Batteries_Tactic_exacts_1 | Batteries.Tactic.exacts |
Mathlib.Analysis.BoxIntegral.Partition.Split | {
"line": 243,
"column": 4
} | {
"line": 243,
"column": 50
} | [
{
"pp": "ι : Type u_1\nI : Box ι\ns✝ : Finset (ι × ℝ)\na : ι × ℝ\ns : Finset (ι × ℝ)\nx✝ : a ∉ s\nhs : (splitMany I s).IsPartition\n⊢ (splitMany I (insert a s)).IsPartition",
"usedConstants": [
"Eq.mpr",
"Real",
"BoxIntegral.Prepartition",
"instDecidableEqProd",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 349,
"column": 4
} | {
"line": 349,
"column": 37
} | [
{
"pp": "case inr\nι : Type u_1\ninst✝ : Fintype ι\nI : Box ι\nc₁ c₂ : ℝ≥0\nl : IntegrationParams\nr₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ₁ π₂ : TaggedPrepartition I\nh₁ : l.MemBaseSet I c₁ r₁ π₁\nh₂ : l.MemBaseSet I c₂ r₂ π₂\nhU : π₁.iUnion = π₂.iUnion\nH :\n ∀ {ι : Type u_1} [inst : Fintype ι] {I : Box ι} {c₁ c₂ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 376,
"column": 4
} | {
"line": 376,
"column": 26
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nI : Box ι\nc : ℝ≥0\nl : IntegrationParams\nπ : TaggedPrepartition I\nr : (ι → ℝ) → ↑(Set.Ioi 0)\nhπ : l.MemBaseSet I c r π\np : Box ι → Prop\nhD : l.bDistortion = true\nπ₁ : Prepartition I\nhπ₁U : π₁.iUnion = ↑I \\ π.iUnion\nhc : π₁.distortion ≤ c\nπ₂ : TaggedPrepartiti... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 451,
"column": 2
} | {
"line": 451,
"column": 61
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nl : IntegrationParams\nI : Box ι\nπ₀ : Prepartition I\n⊢ (toFilteriUnion I π₀).HasBasis (fun r ↦ ∀ (c : ℝ≥0), l.RCond (r c)) fun r ↦\n {π | ∃ c, l.MemBaseSet I c (r c) π ∧ π.iUnion = π₀.iUnion}",
"usedConstants": [
"BoxIntegral.IntegrationParams.toFilterDis... | have := fun c => l.hasBasis_toFilterDistortioniUnion I c π₀ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 452,
"column": 2
} | {
"line": 452,
"column": 44
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nl : IntegrationParams\nI : Box ι\nπ₀ : Prepartition I\nthis :\n ∀ (c : ℝ≥0),\n (l.toFilterDistortioniUnion I c π₀).HasBasis l.RCond fun r ↦ {π | l.MemBaseSet I c r π ∧ π.iUnion = π₀.iUnion}\n⊢ (toFilteriUnion I π₀).HasBasis (fun r ↦ ∀ (c : ℝ≥0), l.RCond (r c)) fun r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 457,
"column": 2
} | {
"line": 457,
"column": 90
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nl : IntegrationParams\nI : Box ι\n⊢ (toFilteriUnion I ⊤).HasBasis (fun r ↦ ∀ (c : ℝ≥0), l.RCond (r c)) fun r ↦\n {π | ∃ c, l.MemBaseSet I c (r c) π ∧ π.IsPartition}",
"usedConstants": [
"Eq.mpr",
"BoxIntegral.IntegrationParams.toFilteriUnion",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 463,
"column": 2
} | {
"line": 463,
"column": 33
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nl : IntegrationParams\nI : Box ι\n⊢ (l.toFilter I).HasBasis (fun r ↦ ∀ (c : ℝ≥0), l.RCond (r c)) fun r ↦ {π | ∃ c, l.MemBaseSet I c (r c) π}",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"Real.instZero",
"congrArg",
"BoxIntegr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.ZLattice.Basic | {
"line": 745,
"column": 20
} | {
"line": 745,
"column": 51
} | [
{
"pp": "K : Type u_1\ninst✝⁴ : NormedField K\nE : Type u_2\nF : Type u_3\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace K E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace K F\nL : Submodule ℤ E\ne : F ≃ₗ[K] E\nx✝ : E\nh : x✝ ∈ L\n⊢ (↑ℤ ↑e.symm) x✝ ∈ ZLattice.comap K L ↑e",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 492,
"column": 2
} | {
"line": 492,
"column": 41
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nc : ℝ≥0\nl : IntegrationParams\nI : Box ι\nhc : ⊤.distortion ≤ c\nr : (ι → ℝ) → ↑(Set.Ioi 0)\nhc' : ⊤.compl.distortion ≤ c\n⊢ ∃ π, l.MemBaseSet I c r π ∧ π.IsPartition",
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"BoxIntegral.Box.toSet"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Filter | {
"line": 506,
"column": 2
} | {
"line": 506,
"column": 13
} | [
{
"pp": "ι : Type u_1\ninst✝ : Fintype ι\nI✝ J : Box ι\nc c₁ c₂ : ℝ≥0\nl✝ l₁ l₂ : IntegrationParams\nr₁ r₂ : (ι → ℝ) → ↑(Set.Ioi 0)\nπ π₁ π₂ : TaggedPrepartition I✝\nr : (ι → ℝ) → ↑(Set.Ioi 0)\nl : IntegrationParams\nI : Box ι\n⊢ (l.toFilterDistortion I I.distortion).NeBot",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 50
} | [
{
"pp": "𝕜 : Type u_7\ninst✝¹ : RCLike 𝕜\nn : Type u_8\ninst✝ : Fintype n\nx : EuclideanSpace 𝕜 n\n⊢ ‖x‖ = √(∑ i, ‖x.ofLp i‖ ^ 2)",
"usedConstants": [
"PiLp.instNorm",
"Norm.norm",
"Eq.mpr",
"Real",
"Finset.univ",
"congrArg",
"Finset",
"Membership.mem",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Partition.Additive | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 16
} | [
{
"pp": "ι : Type u_1\nM : Type u_2\nn : ℕ\nN : Type u_3\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMonoid N\nI₀✝ : WithTop (Box ι)\nI : Box ι\ni : ι\ninst✝ : Finite ι\nf : Box ι → M\nI₀ : WithTop (Box ι)\nhf :\n ∀ (I : Box ι),\n ↑I ≤ I₀ →\n ∀ {i : ι} {x : ℝ},\n x ∈ Set.Ioo (I.lower i) (I.upper ... | refine ⟨f, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.BoxIntegral.Partition.Additive | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 94
} | [
{
"pp": "ι : Type u_1\nM : Type u_2\nn : ℕ\nN : Type u_3\ninst✝² : AddCommMonoid M\ninst✝¹ : AddCommMonoid N\nI₀✝ : WithTop (Box ι)\nI✝ : Box ι\ni : ι\ninst✝ : Finite ι\nf : Box ι → M\nI₀ : WithTop (Box ι)\nhf : ∀ (I : Box ι), ↑I ≤ I₀ → ∀ (s : Finset (ι × ℝ)), ∑ J ∈ (splitMany I s).boxes, f J = f I\nI : Box ι\n... | have Hle : ∀ J ∈ π, ↑J ≤ I₀ := fun J hJ => (WithTop.coe_le_coe.2 <| π.le_of_mem hJ).trans hI | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.BoxIntegral.Partition.Additive | {
"line": 150,
"column": 2
} | {
"line": 164,
"column": 55
} | [
{
"pp": "ι : Type u_1\nM : Type u_2\ninst✝¹ : AddCommMonoid M\nI₀ : WithTop (Box ι)\nI : Box ι\ninst✝ : Finite ι\nf : ι →ᵇᵃ[I₀] M\nhI : ↑I ≤ I₀\nπ₁ π₂ : Prepartition I\nh : π₁.iUnion = π₂.iUnion\n⊢ ∑ J ∈ π₁.boxes, f J = ∑ J ∈ π₂.boxes, f J",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Real",
... | rcases exists_splitMany_inf_eq_filter_of_finite {π₁, π₂} ((finite_singleton _).insert _) with
⟨s, hs⟩
simp only [inf_splitMany] at hs
rcases hs _ (Or.inl rfl), hs _ (Or.inr rfl) with ⟨h₁, h₂⟩; clear hs
rw [h] at h₁
calc
∑ J ∈ π₁.boxes, f J = ∑ J ∈ π₁.boxes, ∑ J' ∈ (splitMany J s).boxes, f J' :=
Fi... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.BoxIntegral.Partition.Additive | {
"line": 150,
"column": 2
} | {
"line": 164,
"column": 55
} | [
{
"pp": "ι : Type u_1\nM : Type u_2\ninst✝¹ : AddCommMonoid M\nI₀ : WithTop (Box ι)\nI : Box ι\ninst✝ : Finite ι\nf : ι →ᵇᵃ[I₀] M\nhI : ↑I ≤ I₀\nπ₁ π₂ : Prepartition I\nh : π₁.iUnion = π₂.iUnion\n⊢ ∑ J ∈ π₁.boxes, f J = ∑ J ∈ π₂.boxes, f J",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Real",
... | rcases exists_splitMany_inf_eq_filter_of_finite {π₁, π₂} ((finite_singleton _).insert _) with
⟨s, hs⟩
simp only [inf_splitMany] at hs
rcases hs _ (Or.inl rfl), hs _ (Or.inr rfl) with ⟨h₁, h₂⟩; clear hs
rw [h] at h₁
calc
∑ J ∈ π₁.boxes, f J = ∑ J ∈ π₁.boxes, ∑ J' ∈ (splitMany J s).boxes, f J' :=
Fi... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 502,
"column": 41
} | {
"line": 502,
"column": 52
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nE : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : Fintype ι\nb : OrthonormalBasis ι 𝕜 E\nv : EuclideanSpace 𝕜 ι\n⊢ ∑ i, v.ofLp i • b i = b.repr.symm v",
"usedConstants": [
"LinearIsometryEquiv.instEquivLike... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 556,
"column": 2
} | {
"line": 556,
"column": 82
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_3\ninst✝⁴ : RCLike 𝕜\nE : Type u_4\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace 𝕜 E\ninst✝¹ : Fintype ι\nU : Submodule 𝕜 E\ninst✝ : U.HasOrthogonalProjection\nb : OrthonormalBasis ι 𝕜 ↥U\nx : E\n⊢ U.orthogonalProjection x = ∑ i, ⟪↑(b i), x⟫ • b i",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Integrability | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 55
} | [
{
"pp": "ι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nl : IntegrationParams\nhl : l.bRiemann = false\ns : Set (ι → ℝ)\nhs : MeasurableSet s\nI : Box ι\ny : E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nε : ℝ≥0\nε0 : 0 < ε\nA : μ (s ∩ Box.Icc I)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Integrability | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 58
} | [
{
"pp": "case hbc.refine_2\nι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nl : IntegrationParams\nhl : l.bRiemann = false\ns : Set (ι → ℝ)\nhs : MeasurableSet s\nI : Box ι\ny : E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nε : ℝ≥0\nε0 : 0 < ε\nA ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 982,
"column": 2
} | {
"line": 982,
"column": 27
} | [
{
"pp": "ι : Type u_1\nF : Type u_5\ninst✝³ : NormedAddCommGroup F\ninst✝² : InnerProductSpace ℝ F\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\na b : OrthonormalBasis ι ℝ F\n⊢ a.toBasis.det ⇑b ^ 2 = 1",
"usedConstants": [
"AlternatingMap",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1004,
"column": 4
} | {
"line": 1004,
"column": 15
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝⁹ : RCLike 𝕜\nE : Type u_4\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : InnerProductSpace 𝕜 E\nF : Type u_5\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝⁴ : NormedAddCommGroup F'\ninst✝³ : InnerProductSpace ℝ F'\ninst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1025,
"column": 46
} | {
"line": 1025,
"column": 57
} | [
{
"pp": "𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nE : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\nv : Set E\ninst✝ : FiniteDimensional 𝕜 E\nhv : Orthonormal 𝕜 Subtype.val\nu₀ : Set E\nhu₀s : u₀ ⊇ v\nhu₀ : Orthonormal 𝕜 Subtype.val\nhu₀_max : (span 𝕜 u₀)ᗮ = ⊥\nhu₀_finite : u₀.Finite\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1027,
"column": 4
} | {
"line": 1027,
"column": 19
} | [
{
"pp": "case refine_1\n𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nE : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\nv : Set E\ninst✝ : FiniteDimensional 𝕜 E\nhv : Orthonormal 𝕜 Subtype.val\nu₀ : Set E\nhu₀s : u₀ ⊇ v\nhu₀ : Orthonormal 𝕜 Subtype.val\nhu₀_max : (span 𝕜 u₀)ᗮ = ⊥\nhu₀_finit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1028,
"column": 4
} | {
"line": 1028,
"column": 19
} | [
{
"pp": "case refine_2\n𝕜 : Type u_3\ninst✝³ : RCLike 𝕜\nE : Type u_4\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\nv : Set E\ninst✝ : FiniteDimensional 𝕜 E\nhv : Orthonormal 𝕜 Subtype.val\nu₀ : Set E\nhu₀s : u₀ ⊇ v\nhu₀ : Orthonormal 𝕜 Subtype.val\nhu₀_max : (span 𝕜 u₀)ᗮ = ⊥\nhu₀_finit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1110,
"column": 2
} | {
"line": 1111,
"column": 64
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_3\ninst✝⁵ : RCLike 𝕜\nE : Type u_4\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : Fintype ι\ninst✝¹ : FiniteDimensional 𝕜 E\nn : ℕ\nhn : finrank 𝕜 E = n\ninst✝ : DecidableEq ι\nV : ι → Submodule 𝕜 E\nhV : IsInternal V\na : Fin n\nhV' : Orthogonal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Integrability | {
"line": 134,
"column": 2
} | {
"line": 139,
"column": 30
} | [
{
"pp": "case h\nι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nl : IntegrationParams\nI : Box ι\nf : (ι → ℝ) → E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nhl : l.bRiemann = false\nε : ℝ≥0\nε0 : 0 < ε\nδ : ℕ → ℝ≥0\nδ0 : ∀ (i : ℕ), 0 < δ i\nc✝ :... | have : ∀ J ∈ π.filter fun J => N (π.tag J) = n,
‖μ.real ↑J • f (π.tag J)‖ ≤ μ.real J * n := fun J hJ ↦ by
rw [TaggedPrepartition.mem_filter] at hJ
rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg measureReal_nonneg]
gcongr
exact hJ.2 ▸ Nat.le_ceil _ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1135,
"column": 2
} | {
"line": 1135,
"column": 13
} | [
{
"pp": "case i\nι : Type u_1\n𝕜 : Type u_3\ninst✝⁵ : RCLike 𝕜\nE : Type u_4\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : Fintype ι\ninst✝¹ : FiniteDimensional 𝕜 E\nn : ℕ\nhn : finrank 𝕜 E = n\ninst✝ : DecidableEq ι\nV : ι → Submodule 𝕜 E\nhV : IsInternal V\nhV' : OrthogonalFam... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.PiL2 | {
"line": 1202,
"column": 4
} | {
"line": 1202,
"column": 91
} | [
{
"pp": "ι : Type u_1\nι' : Type u_2\n𝕜 : Type u_3\ninst✝¹⁰ : RCLike 𝕜\nE✝ : Type u_4\ninst✝⁹ : NormedAddCommGroup E✝\ninst✝⁸ : InnerProductSpace 𝕜 E✝\nF : Type u_5\ninst✝⁷ : NormedAddCommGroup F\ninst✝⁶ : InnerProductSpace ℝ F\nF' : Type u_6\ninst✝⁵ : NormedAddCommGroup F'\ninst✝⁴ : InnerProductSpace ℝ F'\n... | rw [norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero (L (p1 x)) (L3 (p2 x)) Mx_orth] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.BoxIntegral.Integrability | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 13
} | [
{
"pp": "ι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nl : IntegrationParams\nI : Box ι\ny : E\nf g : (ι → ℝ) → E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nhf : HasIntegral I l f μ.toBoxAdditive.toSMul y\nhfg : f =ᶠ[ae (μ.restrict ↑I)] g\nhl :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Integrability | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 20
} | [
{
"pp": "case const\nι : Type u\nE : Type v\ninst✝³ : Fintype ι\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nI : Box ι\nl : IntegrationParams\nhl : l.bRiemann = false\ny : E\ns : Set (ι → ℝ)\nhs : MeasurableSet s\n⊢ HasIntegral I l (⇑(piecewise... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.UnitPartition | {
"line": 287,
"column": 43
} | {
"line": 292,
"column": 28
} | [
{
"pp": "n : ℕ\ninst✝ : NeZero n\nx : ℝ\na : ℤ\n⊢ ↑a < x ↔ ↑a ≤ (↑⌈↑n * x⌉ - 1) / ↑n",
"usedConstants": [
"Iff.mpr",
"Int.lt_ceil",
"Real.instIsOrderedRing",
"Int.cast",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"In... | by
have h : 0 < (n : ℝ) := Nat.cast_pos.mpr <| n.pos_of_neZero
rw [le_div_iff₀' h, le_sub_iff_add_le,
show (n : ℝ) * a + 1 = (n * a + 1 : ℤ) by norm_cast,
Int.cast_le, Int.add_one_le_iff, Int.lt_ceil, Int.cast_mul, Int.cast_natCast,
mul_lt_mul_iff_right₀ h] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho | {
"line": 124,
"column": 25
} | {
"line": 124,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : WellFoundedLT ι\nv : ι → E\ni j : ι\nhij : i < j\nb : ι → E := gramSchmidt 𝕜 v\nk : ι\nhki' : k ∈ Iio i\n⊢ k ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho | {
"line": 205,
"column": 4
} | {
"line": 205,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : WellFoundedLT ι\nf : ι → E\nn : ι\nh₀ : LinearIndependent 𝕜 (f ∘ Subtype.val)\nh : gramSchmidt 𝕜 f n = 0\nh₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho | {
"line": 257,
"column": 2
} | {
"line": 257,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : WellFoundedLT ι\nf : ι → E\nn : ι\nhn : (↑‖gramSchmidt 𝕜 f n‖)⁻¹ • gramSchmidt 𝕜 f n ≠ 0\n⊢ gramSchmidt 𝕜 f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 36
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝² : LinearOrder ι\ninst✝¹ : LocallyFiniteOrderBot ι\ninst✝ : WellFoundedLT ι\nf : ι → E\n⊢ span 𝕜 (Set.range (gramSchmidtNormed 𝕜 f)) = span 𝕜 (Set.range (gramSchmidt �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 17
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝⁴ : LinearOrder ι\ninst✝³ : LocallyFiniteOrderBot ι\ninst✝² : WellFoundedLT ι\ninst✝¹ : Fintype ι\ninst✝ : FiniteDimensional 𝕜 E\nh : finrank 𝕜 E = Fintype.card ι\nf : ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : RCLike 𝕜\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : InnerProductSpace 𝕜 E\nι : Type u_3\ninst✝⁴ : LinearOrder ι\ninst✝³ : LocallyFiniteOrderBot ι\ninst✝² : WellFoundedLT ι\ninst✝¹ : Fintype ι\ninst✝ : FiniteDimensional 𝕜 E\nh : finrank 𝕜 E = Fintype.card ι\nf : ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Orientation | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 13
} | [
{
"pp": "case h\nR : Type u_1\ninst✝⁵ : CommRing R\ninst✝⁴ : LinearOrder R\ninst✝³ : IsStrictOrderedRing R\nM : Type u_2\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\nι : Type u_3\ninst✝ : IsEmpty ι\nx : M [⋀^ι]→ₗ[R] R\nhx : x ≠ 0\nh : LinearIndependent R ![x, AlternatingMap.constOfIsEmpty R M ι 1]\nf : M [⋀^ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 89,
"column": 6
} | {
"line": 89,
"column": 32
} | [
{
"pp": "ι : Type u\nE : Type v\nF : Type w\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nI : Box ι\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\nπ : Prepartition I\nπi : (J : Box ι) → TaggedPrepartition J\nJ : Box ι\nhJ : J ∈ π.boxes\nJ' : Box ι... | π.tag_biUnionTagged hJ hJ' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.InnerProductSpace.Orientation | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 15
} | [
{
"pp": "E : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : InnerProductSpace ℝ E\nι : Type u_2\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\ne f : OrthonormalBasis ι ℝ E\nh : 0 < e.toBasis.det ⇑f.toBasis\n⊢ 0 < e.toBasis.det ⇑f",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Orientation | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace ℝ E\nι : Type u_2\ninst✝² : Fintype ι\ninst✝¹ : DecidableEq ι\ne : OrthonormalBasis ι ℝ E\nx : Orientation ℝ E ι\ninst✝ : Nonempty ι\n⊢ ∀ (i : ι), (e.toBasis.adjustToOrientation x) i = e i ∨ (e.toBasis.adjustToOrientation x) i = -e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Orientation | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace ℝ E\nι : Type u_2\ninst✝² : Fintype ι\ninst✝¹ : DecidableEq ι\ne : OrthonormalBasis ι ℝ E\nx : Orientation ℝ E ι\ninst✝ : Nonempty ι\ni : ι\n⊢ (e.adjustToOrientation x) i = e i ∨ (e.adjustToOrientation x) i = -e i",
"usedConsta... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Orientation | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace ℝ E\nι : Type u_2\ninst✝² : Fintype ι\ninst✝¹ : DecidableEq ι\ne : OrthonormalBasis ι ℝ E\nx : Orientation ℝ E ι\ninst✝ : Nonempty ι\n⊢ (e.adjustToOrientation x).toBasis.det = e.toBasis.det ∨ (e.adjustToOrientation x).toBasis.det =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 244,
"column": 2
} | {
"line": 244,
"column": 51
} | [
{
"pp": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\ninst✝ : Fintype ι\nl : IntegrationParams\nf g : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny y' : F\nh : HasIntegral I l f vol y\nh' : HasIntegral... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Basic | {
"line": 255,
"column": 2
} | {
"line": 255,
"column": 51
} | [
{
"pp": "ι : Type u\nE : Type v\nF : Type w\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nI : Box ι\ninst✝ : Fintype ι\nl : IntegrationParams\nf : (ι → ℝ) → E\nvol : ι →ᵇᵃ[⊤] E →L[ℝ] F\ny : F\nhf : HasIntegral I l f vol y\n⊢ HasIntegral I l (-... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.BoxIntegral.Integrability | {
"line": 295,
"column": 6
} | {
"line": 295,
"column": 98
} | [
{
"pp": "case refine_3\nι : Type u\nE : Type v\ninst✝⁴ : Fintype ι\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : CompleteSpace E\nμ : Measure (ι → ℝ)\ninst✝ : IsLocallyFiniteMeasure μ\nI : Box ι\nl : IntegrationParams\nhl : l.bRiemann = false\nthis✝¹ : MeasurableSpace E := borel E\nthis✝ : ... | integral_biUnion_finset π.boxes (fun J _ => J.measurableSet_coe) π.pairwiseDisjoint (hfgi _) | Lean.Elab.Tactic.evalRewriteSeq | null |
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