module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.InnerProductSpace.OfNorm | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 15
} | {
"line": 181,
"column": 16
} | [
{
"pp": "case pos\n𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : InnerProductSpaceable E\nhI : I = 0\n⊢ innerProp' E 0",
"ppTerm": "?pos✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case pos\n𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : InnerProductSpaceable E\nhI : I = 0\n⊢ innerProp' E 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 684,
"column": 41
} | {
"line": 684,
"column": 72
} | {
"line": 684,
"column": 73
} | [
{
"pp": "X : Type u_2\nY : Type u_3\ninst✝⁵ : EMetricSpace X\ninst✝⁴ : EMetricSpace Y\ninst✝³ : MeasurableSpace X\ninst✝² : BorelSpace X\ninst✝¹ : MeasurableSpace Y\ninst✝ : BorelSpace Y\nr : ℝ≥0\nf : X → Y\ns : Set X\nhr : 0 < r\nd : ℝ\nhd : 0 ≤ d\nh : HolderOnWith 0 r f s\nx : X\nhx : x ∈ s\n⊢ (f '' s).Subsin... | [
"X : Type u_2\nY : Type u_3\ninst✝⁵ : EMetricSpace X\ninst✝⁴ : EMetricSpace Y\ninst✝³ : MeasurableSpace X\ninst✝² : BorelSpace X\ninst✝¹ : MeasurableSpace Y\ninst✝ : BorelSpace Y\nr : ℝ≥0\nf : X → Y\ns : Set X\nhr : 0 < r\nd : ℝ\nhd : 0 ≤ d\nh : HolderOnWith 0 r f s\nx : X\nhx : x ∈ s\n⊢ (f '' s).Subsingleton"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.StandardSubspace | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 46
} | {
"line": 137,
"column": 47
} | [
{
"pp": "case mp\nH : Type u_1\ninst✝ : NormedAddCommGroup H\nipc : InnerProductSpace ℂ H\nS : ClosedSubmodule ℝ H\nx : H\nh : ∀ (a : ℝ), a • (scalarSMulCLE H UnitI).symm x ∈ S.mulI\n⊢ x ∈ S",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mp\nH : Type u_1\ninst✝ : NormedAddCommGroup H\nipc : InnerProductSpace ℂ H\nS : ClosedSubmodule ℝ H\nx : H\nh : ∀ (a : ℝ), a • (scalarSMulCLE H UnitI).symm x ∈ S.mulI\n⊢ x ∈ S"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.StandardSubspace | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 46
} | {
"line": 140,
"column": 47
} | [
{
"pp": "case mpr\nH : Type u_1\ninst✝ : NormedAddCommGroup H\nipc : InnerProductSpace ℂ H\nS : ClosedSubmodule ℝ H\nx : H\nh : ∀ (a : ℝ), a • x ∈ S\n⊢ x ∈ S.mulI.mulI",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
... | [
"case mpr\nH : Type u_1\ninst✝ : NormedAddCommGroup H\nipc : InnerProductSpace ℂ H\nS : ClosedSubmodule ℝ H\nx : H\nh : ∀ (a : ℝ), a • x ∈ S\n⊢ -x ∈ S"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 242,
"column": 4
} | {
"line": 242,
"column": 48
} | {
"line": 242,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\nthis : ∀ {h p1 p2 p3 : Prop}, (h → [p1, p2, p3].TFAE) → [h ∧ p1, h ∧ p2, h ∧ p3].TFAE\nhHerm : K.IsHermitian\nx✝ : Nontriv... | [
"𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\nthis : ∀ {h p1 p2 p3 : Prop}, (h → [p1, p2, p3].TFAE) → [h ∧ p1, h ∧ p2, h ∧ p3].TFAE\nhHerm : K.IsHermitian\nx✝ : Nontrivial V\nv : V... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.StandardSubspace | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 46
} | {
"line": 163,
"column": 0
} | [
{
"pp": "H : Type u_1\ninst✝ : NormedAddCommGroup H\nipc : InnerProductSpace ℂ H\nS T : ClosedSubmodule ℝ H\n⊢ (S.mulI ⊔ T.mulI)ᗮ = S.mulIᗮ ⊓ T.mulIᗮ",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"InnerProductSpace.toNormedSpace",
"Real",
"NormedSpace.toIsBoundedSMul",
... | [] | exact Eq.symm (inf_orthogonal S.mulI T.mulI) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 245,
"column": 4
} | {
"line": 245,
"column": 72
} | {
"line": 246,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\nthis : ∀ {h p1 p2 p3 : Prop}, (h → [p1, p2, p3].TFAE) → [h ∧ p1, h ∧ p2, h ∧ p3].TFAE\nhHerm : K.IsHermitian\nx✝ : Nontriv... | [
"𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\nthis : ∀ {h p1 p2 p3 : Prop}, (h → [p1, p2, p3].TFAE) → [h ∧ p1, h ∧ p2, h ∧ p3].TFAE\nhHerm : K.IsHermitian\nx✝ : Nontrivial V\nv✝ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.StandardSubspace | {
"line": 206,
"column": 21
} | {
"line": 206,
"column": 57
} | {
"line": 206,
"column": 58
} | [
{
"pp": "H : Type u_1\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℂ H\nS : StandardSubspace H\n⊢ S.toClosedSubmodule.mulI ⊓ S.toClosedSubmodule.mulI.mulI = ⊥",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",... | [
"H : Type u_1\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℂ H\nS : StandardSubspace H\n⊢ S.toClosedSubmodule ⊓ S.toClosedSubmodule.mulI = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.StandardSubspace | {
"line": 207,
"column": 17
} | {
"line": 207,
"column": 53
} | {
"line": 207,
"column": 54
} | [
{
"pp": "H : Type u_1\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℂ H\nS : StandardSubspace H\n⊢ S.toClosedSubmodule.mulI ⊔ S.toClosedSubmodule.mulI.mulI = ⊤",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",... | [
"H : Type u_1\ninst✝¹ : NormedAddCommGroup H\ninst✝ : InnerProductSpace ℂ H\nS : StandardSubspace H\n⊢ S.toClosedSubmodule ⊔ S.toClosedSubmodule.mulI = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.StarOrder | {
"line": 48,
"column": 6
} | {
"line": 49,
"column": 13
} | {
"line": 49,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nH : Type u_2\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup H\ninst✝³ : InnerProductSpace 𝕜 H\ninst✝² : CompleteSpace H\ninst✝¹ : Algebra ℝ (H →L[𝕜] H)\ninst✝ : IsScalarTower ℝ 𝕜 (H →L[𝕜] H)\nf : H →L[𝕜] H\nhf : f.IsPositive\nc✝ : ℝ\nc : ℝ := -c✝\nhc : 0 < c\nx : H\n⊢ re ⟪((algebr... | [
"𝕜 : Type u_1\nH : Type u_2\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup H\ninst✝³ : InnerProductSpace 𝕜 H\ninst✝² : CompleteSpace H\ninst✝¹ : Algebra ℝ (H →L[𝕜] H)\ninst✝ : IsScalarTower ℝ 𝕜 (H →L[𝕜] H)\nf : H →L[𝕜] H\nhf : f.IsPositive\nc✝ : ℝ\nc : ℝ := -c✝\nhc : 0 < c\nx : H\n⊢ 0 ≤ re ⟪f x, x⟫_𝕜"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 726,
"column": 2
} | {
"line": 726,
"column": 44
} | {
"line": 726,
"column": 45
} | [
{
"pp": "X : Type u_2\nY : Type u_3\ninst✝⁵ : EMetricSpace X\ninst✝⁴ : EMetricSpace Y\ninst✝³ : MeasurableSpace X\ninst✝² : BorelSpace X\ninst✝¹ : MeasurableSpace Y\ninst✝ : BorelSpace Y\nK : ℝ≥0\nf : X → Y\ns : Set X\nh : LipschitzOnWith K f s\nd : ℝ\nhd : 0 ≤ d\n⊢ μH[d] (f '' s) ≤ ↑K ^ d * μH[d] s",
"ppTe... | [
"X : Type u_2\nY : Type u_3\ninst✝⁵ : EMetricSpace X\ninst✝⁴ : EMetricSpace Y\ninst✝³ : MeasurableSpace X\ninst✝² : BorelSpace X\ninst✝¹ : MeasurableSpace Y\ninst✝ : BorelSpace Y\nK : ℝ≥0\nf : X → Y\ns : Set X\nh : LipschitzOnWith K f s\nd : ℝ\nhd : 0 ≤ d\n⊢ μH[d] (f '' s) ≤ ↑K ^ d * μH[d] s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 749,
"column": 4
} | {
"line": 750,
"column": 11
} | {
"line": 750,
"column": 12
} | [
{
"pp": "𝕜 : Type u_4\nE : Type u_5\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedDivisionRing 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : NormSMulClass 𝕜 E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nd : ℝ\nhd : 0 ≤ d\nr✝ : 𝕜\nhr : r✝ ≠ 0\ns✝ : Set E\nr : 𝕜\ns : Set E\n⊢ μH[d] (r • s) ≤ ‖r‖₊ ^ d • μH[d] s",... | [
"𝕜 : Type u_4\nE : Type u_5\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedDivisionRing 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : NormSMulClass 𝕜 E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nd : ℝ\nhd : 0 ≤ d\nr✝ : 𝕜\nhr : r✝ ≠ 0\ns✝ : Set E\nr : 𝕜\ns : Set E\n⊢ μH[d] (r • s) ≤ ↑‖r‖₊ ^ d * μH[d] s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 329,
"column": 15
} | {
"line": 329,
"column": 65
} | {
"line": 329,
"column": 66
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace 𝕜 V\nH : Type u_4\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : RKHS 𝕜 H X V\ninst✝² : CompleteSpace H\ninst✝¹ : CompleteSpace V\nK : Matrix X X (V →L[�... | [
"𝕜 : Type u_1\ninst✝⁸ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace 𝕜 V\nH : Type u_4\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : RKHS 𝕜 H X V\ninst✝² : CompleteSpace H\ninst✝¹ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 903,
"column": 4
} | {
"line": 903,
"column": 46
} | {
"line": 903,
"column": 47
} | [
{
"pp": "ι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\ni : ι\n⊢ 0 ≤ ↑(b i) - ↑(a i)",
"ppTerm": "?m.140",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.instZero",
"Real.instSub... | [
"ι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\ni : ι\n⊢ a i ≤ b i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 927,
"column": 10
} | {
"line": 927,
"column": 49
} | {
"line": 927,
"column": 50
} | [
{
"pp": "case h'\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1) / ↑n... | [
"case h'\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1) / ↑n)\nA : Tends... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 946,
"column": 8
} | {
"line": 950,
"column": 39
} | {
"line": 951,
"column": 6
} | [
{
"pp": "case refine_1\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1... | [] | filter_upwards [B] with _ hn
apply Finset.sum_le_sum fun i _ => _
simp only [ENNReal.rpow_natCast]
intro i _
exact pow_le_pow_left' (hn i) _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 946,
"column": 8
} | {
"line": 950,
"column": 39
} | {
"line": 951,
"column": 6
} | [
{
"pp": "case refine_1\nι : Type u_4\ninst✝ : Fintype ι\na b : ι → ℚ\nH : ∀ (i : ι), a i < b i\nI : ∀ (i : ι), 0 ≤ ↑(b i) - ↑(a i)\nγ : ℕ → Type u_4 := fun n ↦ (i : ι) → Fin ⌈(↑(b i) - ↑(a i)) * ↑n⌉₊\nt : (n : ℕ) → γ n → Set (ι → ℝ) := fun n f ↦ univ.pi fun i ↦ Icc (↑(a i) + ↑↑(f i) / ↑n) (↑(a i) + (↑↑(f i) + 1... | [] | filter_upwards [B] with _ hn
apply Finset.sum_le_sum fun i _ => _
simp only [ENNReal.rpow_natCast]
intro i _
exact pow_le_pow_left' (hn i) _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 52,
"column": 27
} | {
"line": 52,
"column": 38
} | {
"line": 52,
"column": 39
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : NormedField 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 17
} | {
"line": 93,
"column": 18
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜... | [
"case refine_2\n𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 1037,
"column": 4
} | {
"line": 1038,
"column": 44
} | {
"line": 1038,
"column": 45
} | [
{
"pp": "E : Type u_5\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nv : E\ns : Set ℝ\nhv : v ≠ 0\nhn : ‖v‖ ≠ 0\nthis : μH[1] ((fun x ↦ ‖v‖ • x) '' ⇑(LinearMap.toSpanSingleton ℝ E (‖v‖⁻¹ • v)) '' s) = ‖v‖₊ • μH[1] s\n⊢ μH[1] ((fun r ↦ r • v) '' s) = ‖... | [
"E : Type u_5\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\ninst✝¹ : MeasurableSpace E\ninst✝ : BorelSpace E\nv : E\ns : Set ℝ\nhv : v ≠ 0\nhn : ‖v‖ ≠ 0\nthis : μH[1] ((fun x ↦ ‖v‖ • x) '' ⇑(LinearMap.toSpanSingleton ℝ E (‖v‖⁻¹ • v)) '' s) = ‖v‖₊ • μH[1] s\n⊢ μH[1] ((fun r ↦ r • v) '' s) = ‖v‖₊ • μH[1] ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 78
} | {
"line": 105,
"column": 79
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : NormedField 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 58
} | {
"line": 132,
"column": 59
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ |(o.areaForm x) y| ≤ ‖x‖ * ‖y‖",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AlternatingMap",
"Norm.norm",
"Eq.... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ |o.volumeForm ![x, y]| ≤ ‖x‖ * ‖y‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 115,
"column": 53
} | {
"line": 115,
"column": 64
} | {
"line": 115,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : NormedField 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 58
} | {
"line": 135,
"column": 59
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ (o.areaForm x) y ≤ ‖x‖ * ‖y‖",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"AlternatingMap",
"Norm.norm",
"Eq.mp... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ o.volumeForm ![x, y] ≤ ‖x‖ * ‖y‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 143,
"column": 4
} | {
"line": 143,
"column": 15
} | {
"line": 143,
"column": 16
} | [
{
"pp": "case «0».«1»\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nh : ⟪x, y⟫ = 0\nhij : (fun i ↦ i) ⟨0, ⋯⟩ ≠ (fun i ↦ i) ⟨1, ⋯⟩\n⊢ ⟪![x, y] ((fun i ↦ i) ⟨0, ⋯⟩), ![x, y] ((fun i ↦ i) ⟨1, ⋯⟩)⟫ = 0",
"ppTer... | [
"case «0».«1»\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nh : ⟪x, y⟫ = 0\nhij : (fun i ↦ i) ⟨0, ⋯⟩ ≠ (fun i ↦ i) ⟨1, ⋯⟩\n⊢ ⟪x, y⟫ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 33
} | {
"line": 144,
"column": 34
} | [
{
"pp": "case «1».«0»\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nh : ⟪x, y⟫ = 0\nhij : (fun i ↦ i) ⟨1, ⋯⟩ ≠ (fun i ↦ i) ⟨0, ⋯⟩\n⊢ ⟪![x, y] ((fun i ↦ i) ⟨1, ⋯⟩), ![x, y] ((fun i ↦ i) ⟨0, ⋯⟩)⟫ = 0",
"ppTer... | [
"case «1».«0»\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nh : ⟪x, y⟫ = 0\nhij : (fun i ↦ i) ⟨1, ⋯⟩ ≠ (fun i ↦ i) ⟨0, ⋯⟩\n⊢ ⟪x, y⟫ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Hausdorff | {
"line": 1119,
"column": 2
} | {
"line": 1119,
"column": 13
} | {
"line": 1119,
"column": 14
} | [
{
"pp": "𝕜 : Type u_4\nE : Type u_5\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nK : Submodule 𝕜 E\ninst✝ : K.HasOrthogonalProjection\nd : ℝ\ns : Set E\nhs : 0 ≤ d\n⊢ μH[d] (⇑K.orthogonalProjectionOnto '' s) ≤ μH[d] s",... | [
"𝕜 : Type u_4\nE : Type u_5\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nK : Submodule 𝕜 E\ninst✝ : K.HasOrthogonalProjection\nd : ℝ\ns : Set E\nhs : 0 ≤ d\n⊢ μH[d] (⇑K.orthogonalProjectionOnto '' s) ≤ μH[d] s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 49,
"column": 36
} | {
"line": 49,
"column": 47
} | {
"line": 49,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhs : Convex ℝ s\nx ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhs : Convex ℝ s\nx : E\nhx : (t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 46
} | {
"line": 362,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\na b : E\n⊢ ⟪a, b⟫ ^ 2 + (o.areaForm a) b ^ 2 = ‖a‖ ^ 2 * ‖b‖ ^ 2",
"ppTerm": "?m.81",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.m... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\na b : E\n⊢ ⟪a, b⟫ * ⟪a, b⟫ + (o.areaForm a) b * (o.areaForm a) b = ‖a‖ * ‖a‖ * (‖b‖ * ‖b‖)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 20
} | {
"line": 58,
"column": 21
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhs : Convex ℝ s\nx ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhs : Convex ℝ s\nx : E\nhx : (t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 67
} | {
"line": 69,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\n⊢ ⇑(toWeakSpace 𝕜 ... | [] | refine LinearMap.image_convexHull (toWeakSpace 𝕜 E).toLinearMap s | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 26
} | {
"line": 347,
"column": 27
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹⁰ : NormedField 𝕜₁\ninst✝⁹ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : Module 𝕜₁ E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : Module 𝕜₂ F\ninst✝² : IsTopologi... | [
"𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹⁰ : NormedField 𝕜₁\ninst✝⁹ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : Module 𝕜₁ E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : Module 𝕜₂ F\ninst✝² : IsTopologicalAddGroup ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | {
"line": 344,
"column": 87
} | {
"line": 347,
"column": 30
} | {
"line": 349,
"column": 0
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹⁰ : NormedField 𝕜₁\ninst✝⁹ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : Module 𝕜₁ E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : Module 𝕜₂ F\ninst✝² : IsTopologi... | [] | by
refine Function.Injective.isEmbedding_induced fun A B hAB => ?_
rw [ContinuousLinearMapWOT.ext_dual_iff]
simpa [funext_iff] using hAB | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 78,
"column": 4
} | {
"line": 79,
"column": 11
} | {
"line": 79,
"column": 12
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\ninst✝⁶... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : IsTopolog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | {
"line": 397,
"column": 20
} | {
"line": 397,
"column": 31
} | {
"line": 397,
"column": 32
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝⁹ : NormedField 𝕜₁\ninst✝⁸ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜₁ E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜₂ F\ninst✝¹ : IsTopologic... | [
"𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝⁹ : NormedField 𝕜₁\ninst✝⁸ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜₁ E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜₂ F\ninst✝¹ : IsTopologicalAddGroup F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 95,
"column": 2
} | {
"line": 96,
"column": 9
} | {
"line": 96,
"column": 10
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\ninst✝⁶... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : IsTopolog... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 463,
"column": 2
} | {
"line": 463,
"column": 54
} | {
"line": 463,
"column": 55
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ Complex.normSq ((o.kahler x) y) = ‖x‖ ^ 2 * ‖y‖ ^ 2",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceReal... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ ⟪x, y⟫ * ⟪x, y⟫ + (o.areaForm x) y * (o.areaForm x) y = ‖x‖ * ‖x‖ * (‖y‖ * ‖y‖)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 472,
"column": 29
} | {
"line": 472,
"column": 45
} | {
"line": 472,
"column": 46
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\n⊢ ‖x‖ * ‖y‖ = 0",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"NormedCommRing.toNormedRing",
"A... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\n⊢ x = 0 ∨ y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 475,
"column": 4
} | {
"line": 475,
"column": 15
} | {
"line": 475,
"column": 16
} | [
{
"pp": "case inl\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\nthis : ‖x‖ * ‖y‖ = 0\nh : ‖x‖ = 0\n⊢ x = 0",
"ppTerm": "?inl",
"assigned": false,
"usedConstants": [],
"u... | [
"case inl\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\nthis : ‖x‖ * ‖y‖ = 0\nh : ‖x‖ = 0\n⊢ x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 477,
"column": 4
} | {
"line": 477,
"column": 15
} | {
"line": 477,
"column": 16
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\nthis : ‖x‖ * ‖y‖ = 0\nh : ‖y‖ = 0\n⊢ y = 0",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"u... | [
"case inr\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\nthis : ‖x‖ * ‖y‖ = 0\nh : ‖y‖ = 0\n⊢ y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 22
} | {
"line": 116,
"column": 23
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : Topological... | [
"case refine_1\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 23
} | {
"line": 117,
"column": 24
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : Topological... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 46,
"column": 43
} | {
"line": 46,
"column": 54
} | {
"line": 46,
"column": 55
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nx : ℝ\ns : ℂ\nf : E\n⊢ (-↑x).im ≤ π",
"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.pi",
"congrArg",
"Complex.im",
"id",
"Su... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nx : ℝ\ns : ℂ\nf : E\n⊢ 0 ≤ π"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 100,
"column": 6
} | {
"line": 100,
"column": 33
} | {
"line": 100,
"column": 34
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhf : IntegrableOn (fun x ↦ |(-rexp (-x))| • ↑((rexp ∘ Neg.neg) x) ^ (↑σ - 1) • f ((rexp ∘ Neg.neg) x)) univ volume\nhFf : VerticalIntegrable (mellin f) σ volume\nhfx : Co... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhf : IntegrableOn (fun x ↦ |(-rexp (-x))| • ↑((rexp ∘ Neg.neg) x) ^ (↑σ - 1) • f ((rexp ∘ Neg.neg) x)) univ volume\nhFf : VerticalIntegrable (mellin f) σ volume\nhfx : ContinuousAt f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 66
} | {
"line": 105,
"column": 67
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhFf : VerticalIntegrable (mellin f) σ volume\nhfx : ContinuousAt f x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nh2π : 2 * π ≠ 0\n⊢ Int... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhFf : VerticalIntegrable (mellin f) σ volume\nhfx : ContinuousAt f x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nh2π : 2 * π ≠ 0\n⊢ Integrable (𝓕 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 33
} | {
"line": 110,
"column": 34
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhfx : ContinuousAt f x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nhFf : Integrable (𝓕 g) volume\n⊢ ContinuousAt f (rexp (- -Real.log ... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhfx : ContinuousAt f x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nhFf : Integrable (𝓕 g) volume\n⊢ ContinuousAt f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 121,
"column": 22
} | {
"line": 121,
"column": 43
} | {
"line": 121,
"column": 44
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nhFf : Integrable (𝓕 g) volume\nhfx : ContinuousAt g (-Real.log x)\n⊢ ↑x ^ ↑(-σ) • rexp (Rea... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nhFf : Integrable (𝓕 g) volume\nhfx : ContinuousAt g (-Real.log x)\n⊢ ↑x ^ ↑(-σ) • x ^ σ • f (rexp (Real... | ← rpow_def_of_pos hx, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 76,
"column": 82
} | {
"line": 78,
"column": 56
} | {
"line": 80,
"column": 0
} | [
{
"pp": "n : ℕ\n⊢ logTaylor (n + 1) = logTaylor n + fun z ↦ (-1) ^ (n + 1) * z ^ n / ↑n",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"instHDiv",
"HMul.hMul",
"Complex.instDivInvMonoid",
"Complex.instMul",
"id",
"HDiv.hDiv",
"instOfNatNat",
... | [] | by
funext
simpa only [logTaylor] using! Finset.sum_range_succ .. | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 83,
"column": 17
} | {
"line": 83,
"column": 49
} | {
"line": 83,
"column": 50
} | [
{
"pp": "case succ\nn : ℕ\nih : logTaylor n 0 = 0\n⊢ logTaylor (n + 1) 0 = 0",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"False",
"Nat.instMulZeroClass",... | [
"case succ\nn : ℕ\nih : logTaylor n 0 = 0\n⊢ ¬n = 0 ∨ n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 29
} | {
"line": 152,
"column": 30
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → E\ns : ℂ\na : ℝ\nha : 0 < a\n⊢ mellin (fun t ↦ f (t * a)) s = ↑a ^ (-s) • mellin f s",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → E\ns : ℂ\na : ℝ\nha : 0 < a\n⊢ mellin (fun t ↦ f (a * t)) s = ↑a ^ (-s) • mellin f s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 95,
"column": 4
} | {
"line": 98,
"column": 18
} | {
"line": 99,
"column": 4
} | [
{
"pp": "case succ\nz : ℂ\nn : ℕ\nih : HasDerivAt (logTaylor (n + 1)) (∑ j ∈ Finset.range n, (-1) ^ j * z ^ j) z\n⊢ HasDerivAt (fun z ↦ (-1) ^ (n + 1 + 1) * (z ^ (n + 1) / (↑n + 1))) ((-1) ^ n * z ^ n) z",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"IsModuleTopology.toContinuousSM... | [
"case succ\nz : ℂ\nn : ℕ\nih : HasDerivAt (logTaylor (n + 1)) (∑ j ∈ Finset.range n, (-1) ^ j * z ^ j) z\nthis : HasDerivAt (fun x ↦ x ^ (n + 1) / (↑n + 1)) (z ^ n) z\n⊢ HasDerivAt (fun z ↦ (-1) ^ (n + 1 + 1) * (z ^ (n + 1) / (↑n + 1))) ((-1) ^ n * z ^ n) z"
] | have : HasDerivAt (fun x : ℂ ↦ (x ^ (n + 1) / (n + 1))) (z ^ n) z := by
simp_rw [div_eq_mul_inv]
convert! HasDerivAt.mul_const (hasDerivAt_pow (n + 1) z) (((n : ℂ) + 1)⁻¹) using 1
simp [field] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 34
} | {
"line": 58,
"column": 35
} | [
{
"pp": "case convert_3\ns : ℂ\nhs : 0 < s.re\n⊢ (fun x ↦ rexp (-x)) =O[atTop] fun x ↦ x ^ (-(s.re + 1))",
"ppTerm": "?convert_3",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case convert_3\ns : ℂ\nhs : 0 < s.re\n⊢ (fun x ↦ rexp (-x)) =O[atTop] fun x ↦ x ^ (-(s.re + 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 73,
"column": 34
} | {
"line": 73,
"column": 45
} | {
"line": 73,
"column": 46
} | [
{
"pp": "s✝ : ℂ\nhs✝ : ∀ (m : ℕ), s✝ ≠ -↑m\ns : ℂ\nhsre : -↑0 < s.re\nhs : ∀ (m : ℕ), s ≠ -↑m\n⊢ 0 < s.re",
"ppTerm": "?m.75",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"s✝ : ℂ\nhs✝ : ∀ (m : ℕ), s✝ ≠ -↑m\ns : ℂ\nhsre : -↑0 < s.re\nhs : ∀ (m : ℕ), s ≠ -↑m\n⊢ 0 < s.re"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 75,
"column": 40
} | {
"line": 75,
"column": 51
} | {
"line": 75,
"column": 52
} | [
{
"pp": "s✝ : ℂ\nhs✝ : ∀ (m : ℕ), s✝ ≠ -↑m\ns : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nhsre : 0 < s.re\nthis : IsOpen {s | 0 < s.re}\n⊢ 0 < s.re",
"ppTerm": "?m.109",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"s✝ : ℂ\nhs✝ : ∀ (m : ℕ), s✝ ≠ -↑m\ns : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nhsre : 0 < s.re\nthis : IsOpen {s | 0 < s.re}\n⊢ 0 < s.re"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 219,
"column": 6
} | {
"line": 220,
"column": 60
} | {
"line": 221,
"column": 6
} | [
{
"pp": "f : ℝ → ℝ\nhfc : AEStronglyMeasurable f (volume.restrict (Ioi 0))\na s : ℝ\nhf : f =O[atTop] fun x ↦ x ^ (-a)\nhs : s < a\nd e : ℝ\nhe : ∀ (b : ℝ), e ≤ b → ‖f b‖ ≤ d * ‖b ^ (-a)‖\nhe' : 0 < max e 1\nt : ℝ\nht : t ∈ Ioi (max e 1)\nht' : 0 < t\n⊢ ‖t ^ (s - 1) * f t‖ ≤ t ^ (s - 1 + -a) * d",
"ppTerm":... | [
"f : ℝ → ℝ\nhfc : AEStronglyMeasurable f (volume.restrict (Ioi 0))\na s : ℝ\nhf : f =O[atTop] fun x ↦ x ^ (-a)\nhs : s < a\nd e : ℝ\nhe : ∀ (b : ℝ), e ≤ b → ‖f b‖ ≤ d * ‖b ^ (-a)‖\nhe' : 0 < max e 1\nt : ℝ\nht : t ∈ Ioi (max e 1)\nht' : 0 < t\n⊢ t ^ (s - 1) * ‖f t‖ ≤ t ^ (s - 1) * (d * ‖t ^ (-a)‖)"
] | rw [norm_mul, rpow_add ht', ← norm_of_nonneg (rpow_nonneg ht'.le (-a)), mul_assoc,
mul_comm _ d, norm_of_nonneg (rpow_nonneg ht'.le _)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 115,
"column": 62
} | {
"line": 115,
"column": 73
} | {
"line": 115,
"column": 74
} | [
{
"pp": "n : ℕ\nih : ContinuousAt Gamma (-(↑n + 1))\nthis : ContinuousAt (fun s ↦ Gamma (s - 1 + 1)) (-↑n)\n⊢ ContinuousAt Gamma (-↑n)",
"ppTerm": "?m.65",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nih : ContinuousAt Gamma (-(↑n + 1))\nthis : ContinuousAt (fun s ↦ Gamma (s - 1 + 1)) (-↑n)\n⊢ ContinuousAt Gamma (-↑n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 52,
"column": 2
} | {
"line": 57,
"column": 9
} | {
"line": 59,
"column": 0
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\nx : ℝ\n⊢ HasDerivAt (fun y ↦ -Complex.cos (2 * z * ↑y) / (2 * z)) (Complex.sin (2 * z * ↑x)) x",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"HasDerivAt.fun_neg",
"instInnerProductSpaceRealComplex",
"IsModuleTopology.toContinuousSMul",
... | [] | have a : HasDerivAt (fun y : ℂ => y * (2 * z)) _ x := hasDerivAt_mul_const _
have b : HasDerivAt (Complex.cos ∘ fun y : ℂ => (y * (2 * z))) _ x :=
HasDerivAt.comp (x : ℂ) (Complex.hasDerivAt_cos (x * (2 * z))) a
have c := (b.comp_ofReal.div_const (2 * z)).fun_neg
simp at c ⊢; field_simp at c ⊢; simp only [mul... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 52,
"column": 2
} | {
"line": 57,
"column": 9
} | {
"line": 59,
"column": 0
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\nx : ℝ\n⊢ HasDerivAt (fun y ↦ -Complex.cos (2 * z * ↑y) / (2 * z)) (Complex.sin (2 * z * ↑x)) x",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"HasDerivAt.fun_neg",
"instInnerProductSpaceRealComplex",
"IsModuleTopology.toContinuousSMul",
... | [] | have a : HasDerivAt (fun y : ℂ => y * (2 * z)) _ x := hasDerivAt_mul_const _
have b : HasDerivAt (Complex.cos ∘ fun y : ℂ => (y * (2 * z))) _ x :=
HasDerivAt.comp (x : ℂ) (Complex.hasDerivAt_cos (x * (2 * z))) a
have c := (b.comp_ofReal.div_const (2 * z)).fun_neg
simp at c ⊢; field_simp at c ⊢; simp only [mul... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 69,
"column": 6
} | {
"line": 69,
"column": 17
} | {
"line": 69,
"column": 18
} | [
{
"pp": "z : ℂ\nn : ℕ\nhn : 2 ≤ n\nhz : z ≠ 0\nx : ℝ\na✝ : x ∈ uIcc 0 (π / 2)\n⊢ HasDerivAt (fun y ↦ ↑(cos y)) (-↑(sin x)) x",
"ppTerm": "?m.158",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedComm... | [
"z : ℂ\nn : ℕ\nhn : 2 ≤ n\nhz : z ≠ 0\nx : ℝ\na✝ : x ∈ uIcc 0 (π / 2)\n⊢ HasDerivAt (fun y ↦ Complex.cos ↑y) (-Complex.sin ↑x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 293,
"column": 2
} | {
"line": 293,
"column": 13
} | {
"line": 293,
"column": 14
} | [
{
"pp": "z : ℂ\nhz : ‖z‖ < 1\n⊢ HasSum (fun n ↦ z ^ n / ↑n) (-log (1 - z) + ∑ i ∈ Finset.range 1, z ^ i / ↑i)",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"CharP.cast_eq_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
... | [
"z : ℂ\nhz : ‖z‖ < 1\n⊢ HasSum (fun n ↦ z ^ n / ↑n) (-log (1 - z))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 324,
"column": 6
} | {
"line": 324,
"column": 17
} | {
"line": 324,
"column": 18
} | [
{
"pp": "g : ℝ → ℂ\nt : ℂ\nhg : Tendsto (fun x ↦ ↑x * g x) atTop (𝓝 t)\n⊢ (fun x ↦ (↑x * g x) ^ 2 * ↑x⁻¹) =O[atTop] fun x ↦ ↑x⁻¹",
"ppTerm": "?m.146",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"Complex.in... | [
"g : ℝ → ℂ\nt : ℂ\nhg : Tendsto (fun x ↦ ↑x * g x) atTop (𝓝 t)\n⊢ (fun x ↦ (↑x * g x) ^ 2 * (↑x)⁻¹) =O[atTop] fun x ↦ (↑x)⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 108,
"column": 8
} | {
"line": 108,
"column": 24
} | {
"line": 108,
"column": 25
} | [
{
"pp": "case e'_4\ns t a b : ℝ\nhs : 0 < s\nht : 0 < t\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\nf : ℝ → ℝ → ℝ → ℝ := fun c u x ↦ rexp (-c * x) * x ^ (c * (u - 1))\ne : (1 / a).HolderConjugate (1 / b)\nhab' : b = 1 - a\nhst : 0 < a * s + b * t\nposf : ∀ (c u x : ℝ), x ∈ Ioi 0 → 0 ≤ f c u x\nposf' : ∀ (c u : ℝ)... | [
"case e'_4\ns t a b : ℝ\nhs : 0 < s\nht : 0 < t\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\nf : ℝ → ℝ → ℝ → ℝ := fun c u x ↦ rexp (-c * x) * x ^ (c * (u - 1))\ne : (1 / a).HolderConjugate (1 / b)\nhab' : b = 1 - a\nhst : 0 < a * s + b * t\nposf : ∀ (c u x : ℝ), x ∈ Ioi 0 → 0 ≤ f c u x\nposf' : ∀ (c u : ℝ), ∀ᵐ (x : ℝ)... | one_div_one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.MellinTransform | {
"line": 361,
"column": 6
} | {
"line": 362,
"column": 97
} | {
"line": 363,
"column": 6
} | [
{
"pp": "case hbc.inr\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b : ℝ\nf : ℝ → E\ns : ℂ\nhfc : LocallyIntegrableOn f (Ioi 0) volume\nhf_top : f =O[atTop] fun x ↦ x ^ (-a)\nhs_top : s.re < a\nhf_bot : f =O[𝓝[>] 0] fun x ↦ x ^ (-b)\nhs_bot : b < s.re\nF : ℂ → ℝ → E := fun z t ↦ ↑t ... | [
"case hbc.inr\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b : ℝ\nf : ℝ → E\ns : ℂ\nhfc : LocallyIntegrableOn f (Ioi 0) volume\nhf_top : f =O[atTop] fun x ↦ x ^ (-a)\nhs_top : s.re < a\nhf_bot : f =O[𝓝[>] 0] fun x ↦ x ^ (-b)\nhs_bot : b < s.re\nF : ℂ → ℝ → E := fun z t ↦ ↑t ^ (z - 1) • ... | refine
le_add_of_nonneg_of_le (rpow_pos_of_pos ht _).le (rpow_le_rpow_of_exponent_ge ht h.le ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 91,
"column": 2
} | {
"line": 92,
"column": 9
} | {
"line": 92,
"column": 10
} | [
{
"pp": "u v : ℂ\n⊢ v.betaIntegral u = u.betaIntegral v",
"ppTerm": "?m.2",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"MeasureTheory.Measure",
"HMul.hMul",
"Complex.instNorme... | [
"u v : ℂ\n⊢ ∫ (x : ℝ) in 0..1, ↑x ^ (v + -1) * (-↑x + 1) ^ (u + -1) = ∫ (x : ℝ) in 0..1, ↑x ^ (u + -1) * (-↑x + 1) ^ (v + -1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 32
} | {
"line": 175,
"column": 4
} | [
{
"pp": "f : ℝ → ℝ\nx : ℝ\nn : ℕ\nhf_conv : ConvexOn ℝ (Ioi 0) f\nhf_feq : ∀ {y : ℝ}, 0 < y → f (y + 1) = f y + log y\nhn : n ≠ 0\nhx : 0 < x\nhx' : x ≤ 1\nhn' : 0 < ↑n\nthis : f ↑n + x * log ↑n = (1 - x) * f ↑n + x * f (↑n + 1)\n⊢ f ((1 - x) * ↑n + x * (↑n + 1)) ≤ (1 - x) * f ↑n + x * f (↑n + 1)",
"ppTerm"... | [
"f : ℝ → ℝ\nx : ℝ\nn : ℕ\nhf_conv : ConvexOn ℝ (Ioi 0) f\nhf_feq : ∀ {y : ℝ}, 0 < y → f (y + 1) = f y + log y\nhn : n ≠ 0\nhx : 0 < x\nhx' : x ≤ 1\nhn' : 0 < ↑n\nthis : f ↑n + x * log ↑n = (1 - x) * f ↑n + x * f (↑n + 1)\n⊢ f ((1 - x) * ↑n + x * (↑n + 1)) ≤ (1 - x) * f ↑n + x * f (↑n + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 366,
"column": 4
} | {
"line": 366,
"column": 44
} | {
"line": 366,
"column": 45
} | [
{
"pp": "x : ℝ\nhx : x ∈ Icc 1 2\nhmin : IsMinOn Γ (Icc 1 2) x\n⊢ Γ (3 / 2) < Γ 1 ∧ Γ (3 / 2) < Γ 2 ∧ Γ x ≤ Γ (3 / 2)",
"ppTerm": "?m.134",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"instHDiv",
"congrArg",
"Real.instDivInvMonoid",
... | [
"x : ℝ\nhx : x ∈ Icc 1 2\nhmin : IsMinOn Γ (Icc 1 2) x\n⊢ Γ x ≤ Γ (3 / 2)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.AsymptoticCone | {
"line": 51,
"column": 21
} | {
"line": 51,
"column": 53
} | {
"line": 51,
"column": 54
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : FiniteDimensional ℝ V\ns : Set P\np : P\nhs : ∀ i ∈ Metric.sphere 0 1, s ∈ asymptoticNhds ℝ P i\n⊢ s ∈ cobounded P",
"ppTerm": "?m.90",
"assigned": ... | [
"V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : FiniteDimensional ℝ V\ns : Set P\np : P\nhs : ∀ i ∈ Metric.sphere 0 1, s ∈ atTop • 𝓝 i +ᵥ pure p\n⊢ s ∈ cobounded P"
] | asymptoticNhds_eq_smul_vadd _ p, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 132,
"column": 2
} | {
"line": 134,
"column": 53
} | {
"line": 136,
"column": 0
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | [] | have ⟨p⟩ : Nonempty P := inferInstance
rw [← asymptoticNhds_vadd_pure 0 p, asymptoticNhds_zero', vadd_pure]
exact (Equiv.vaddConst p).surjective.filter_map_top | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 132,
"column": 2
} | {
"line": 134,
"column": 53
} | {
"line": 136,
"column": 0
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | [] | have ⟨p⟩ : Nonempty P := inferInstance
rw [← asymptoticNhds_vadd_pure 0 p, asymptoticNhds_zero', vadd_pure]
exact (Equiv.vaddConst p).surjective.filter_map_top | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 150,
"column": 11
} | {
"line": 150,
"column": 43
} | {
"line": 151,
"column": 4
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V\ninst✝ : Co... | asymptoticNhds_eq_smul_vadd _ p, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 162,
"column": 13
} | {
"line": 162,
"column": 45
} | {
"line": 162,
"column": 46
} | [
{
"pp": "case a\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAd... | [
"case a\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V\nin... | asymptoticNhds_eq_smul_vadd _ p, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 174,
"column": 6
} | {
"line": 174,
"column": 38
} | {
"line": 174,
"column": 39
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : LinearOrder k\ninst✝¹⁰ : AddCommGroup V\ninst✝⁹ : Module k V\ninst✝⁸ : AddTorsor V P\ninst✝⁷ : TopologicalSpace V\ninst✝⁶ : TopologicalSpace k\ninst✝⁵ : OrderTopology k\ninst✝⁴ : IsStrictOrderedRing k\ninst✝³ : IsTopologicalAddGroup... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : LinearOrder k\ninst✝¹⁰ : AddCommGroup V\ninst✝⁹ : Module k V\ninst✝⁸ : AddTorsor V P\ninst✝⁷ : TopologicalSpace V\ninst✝⁶ : TopologicalSpace k\ninst✝⁵ : OrderTopology k\ninst✝⁴ : IsStrictOrderedRing k\ninst✝³ : IsTopologicalAddGroup V\ninst✝² :... | asymptoticNhds_eq_smul_vadd _ p, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Normed.Affine.Ceva | {
"line": 50,
"column": 57
} | {
"line": 50,
"column": 68
} | {
"line": 50,
"column": 69
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : NormedField 𝕜\ninst✝² : NormedSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle 𝕜 P\np : Fin 3 → P\np' : P\nhp0 : ∀ (i : Fin 3), p i ≠ t.points (i + 2)\nhp : ∀ (i : Fin 3), p i ∈ line[𝕜... | [
"𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : NormedField 𝕜\ninst✝² : NormedSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle 𝕜 P\np : Fin 3 → P\np' : P\nhp0 : ∀ (i : Fin 3), p i ≠ t.points (i + 2)\nhp : ∀ (i : Fin 3), p i ∈ line[𝕜, t.points (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 32
} | {
"line": 193,
"column": 2
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V\ninst✝ : Co... | refine Filter.ext' fun p => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 328,
"column": 22
} | {
"line": 340,
"column": 85
} | {
"line": 342,
"column": 0
} | [
{
"pp": "k : Type u_1\nV : Type u_2\ninst✝⁹ : Field k\ninst✝⁸ : LinearOrder k\ninst✝⁷ : IsStrictOrderedRing k\ninst✝⁶ : TopologicalSpace k\ninst✝⁵ : OrderTopology k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : TopologicalSpace V\ninst✝¹ : IsTopologicalAddGroup V\ninst✝ : ContinuousSMul k V\ns : Set V... | [] | by
refine isClosed_iff_frequently.mp hs₂ _ <|
tendsto_snd (f := atTop (α := k)) |>.const_smul _ |>.vadd_const _ |>.frequently ?_
rw [mem_asymptoticCone_iff, asymptoticNhds_eq_smul_vadd v p, vadd_pure, frequently_map,
← map₂_smul, ← map_prod_eq_map₂, frequently_map] at hv
apply hv.mp
filter_upwards [tend... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 352,
"column": 33
} | {
"line": 352,
"column": 44
} | {
"line": 352,
"column": 45
} | [
{
"pp": "m : ℕ\nIH : ∀ (s : ℂ), ⌊1 - s.re⌋₊ = m → Tendsto s.GammaSeq atTop (𝓝 (Gamma s))\ns : ℂ\nhs : ↑(m + 1) ≤ 1 - s.re ∧ 1 - s.re < ↑(m + 1) + 1\nhsne : s ≠ 0\nthis : s.re ≤ -↑m\n⊢ 0 ≤ 1 - (s + 1).re",
"ppTerm": "?m.213",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",... | [
"m : ℕ\nIH : ∀ (s : ℂ), ⌊1 - s.re⌋₊ = m → Tendsto s.GammaSeq atTop (𝓝 (Gamma s))\ns : ℂ\nhs : ↑(m + 1) ≤ 1 - s.re ∧ 1 - s.re < ↑(m + 1) + 1\nhsne : s ≠ 0\nthis : s.re ≤ -↑m\n⊢ s.re ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 87,
"column": 37
} | {
"line": 87,
"column": 53
} | {
"line": 87,
"column": 54
} | [
{
"pp": "case pos\nk : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\nhp : AffineIndependent k p\ns : Set ι\nhs : s.Nonempty\nfs : ↑s → Finset ι\nw : ↑s → ι → k\nhw : ∀ (i : ↑s), ∑ j ∈ fs i, w i j = 1\np' : P... | [
"case pos\nk : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\nhp : AffineIndependent k p\ns : Set ι\nhs : s.Nonempty\nfs : ↑s → Finset ι\nw : ↑s → ι → k\nhw : ∀ (i : ↑s), ∑ j ∈ fs i, w i j = 1\np' : P\nhp' : ∀ (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 87,
"column": 37
} | {
"line": 87,
"column": 53
} | {
"line": 87,
"column": 54
} | [
{
"pp": "case neg\nk : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\nhp : AffineIndependent k p\ns : Set ι\nhs : s.Nonempty\nfs : ↑s → Finset ι\nw : ↑s → ι → k\nhw : ∀ (i : ↑s), ∑ j ∈ fs i, w i j = 1\np' : P... | [
"case neg\nk : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\nhp : AffineIndependent k p\ns : Set ι\nhs : s.Nonempty\nfs : ↑s → Finset ι\nw : ↑s → ι → k\nhw : ∀ (i : ↑s), ∑ j ∈ fs i, w i j = 1\np' : P\nhp' : ∀ (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 431,
"column": 10
} | {
"line": 431,
"column": 15
} | {
"line": 431,
"column": 16
} | [
{
"pp": "s : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nh_im : s.im = 0\n⊢ ↑s.re + ↑s.im * I = ↑s.re",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Complex.im",
"Complex.instMul",
"id",
"Co... | [
"s : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nh_im : s.im = 0\n⊢ ↑s.re + ↑0 * I = ↑s.re"
] | h_im, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 19
} | {
"line": 148,
"column": 20
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\np' : P\nhp' : ∀ (i : Fin 3), p' ∈ line[k, t.points i, (AffineMap.lineMap (t.points (i + 1)) (t.points (i + 2)... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\np' : P\nhp' : ∀ (i : Fin 3), p' ∈ line[k, t.points i, (AffineMap.lineMap (t.points (i + 1)) (t.points (i + 2))) (r i)]\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 457,
"column": 2
} | {
"line": 457,
"column": 72
} | {
"line": 457,
"column": 73
} | [
{
"pp": "s : ℂ\nm : ℕ\nhs : s = -↑m\n⊢ s.re ≤ 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real",
"Real.instZero",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"Real.instA... | [
"s : ℂ\nm : ℕ\nhs : s = -↑m\n⊢ 0 ≤ ↑m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 20
} | {
"line": 155,
"column": 21
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 15
} | {
"line": 108,
"column": 16
} | [
{
"pp": "case refine_1\nR : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex R P m\ne : Fin (m + 1) ≃ Fin (n + 1)\nh : (s.reindex e).Regular\nσ : Equiv.Perm (Fin (m + 1))... | [
"case refine_1\nR : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex R P m\ne : Fin (m + 1) ≃ Fin (n + 1)\nh : (s.reindex e).Regular\nσ : Equiv.Perm (Fin (m + 1))\nx : P ≃ᵢ P... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 15
} | {
"line": 112,
"column": 16
} | [
{
"pp": "case refine_2\nR : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex R P m\ne : Fin (m + 1) ≃ Fin (n + 1)\nh : s.Regular\nσ : Equiv.Perm (Fin (n + 1))\nx : P ≃ᵢ P... | [
"case refine_2\nR : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex R P m\ne : Fin (m + 1) ≃ Fin (n + 1)\nh : s.Regular\nσ : Equiv.Perm (Fin (n + 1))\nx : P ≃ᵢ P\nhx : s.poi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 573,
"column": 4
} | {
"line": 573,
"column": 76
} | {
"line": 574,
"column": 4
} | [
{
"pp": "s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\n⊢ DifferentiableOn ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ",
"ppTerm": "?m.420",
"assigned": true,
"usedConstants": [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpac... | [
"s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\n⊢ Differentiable ℂ fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1)"
] | refine (Differentiable.mul ?_ (differentiable_const _)).differentiableOn | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 114,
"column": 82
} | {
"line": 132,
"column": 10
} | {
"line": 134,
"column": 0
} | [
{
"pp": "R : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nn : ℕ\ns : Simplex R P n\nhr : s.Regular\n⊢ s.Equilateral",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
... | [] | by
refine ⟨dist (s.points 0) (s.points 1), fun i j hij ↦ ?_⟩
have hn : n ≠ 0 := by lia
by_cases hi : i = 1
· rw [hi, dist_comm]
rcases hr (Equiv.swap 0 j) with ⟨x, hx⟩
nth_rw 2 [← x.dist_eq]
simp_rw [← Function.comp_apply (f := x), ← hx]
simp only [comp_apply, Equiv.swap_apply_left]
convert!... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 171,
"column": 6
} | {
"line": 171,
"column": 17
} | {
"line": 171,
"column": 18
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Polynomial.Factorization | {
"line": 49,
"column": 83
} | {
"line": 56,
"column": 82
} | {
"line": 58,
"column": 0
} | [
{
"pp": "f : ℝ[X]\nn : ℕ\nhf : f.IsMonicOfDegree (n + 1)\n⊢ ∃ f₁ f₂, (f₁.IsMonicOfDegree 1 ∨ f₁.IsMonicOfDegree 2) ∧ f = f₁ * f₂",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"Irreducible.natDegree_le_two",
"Semigroup.toMu... | [] | by
obtain ⟨f₁, hm, hirr, f₂, hf₂⟩ :=
exists_monic_irreducible_factor f <| not_isUnit_of_natDegree_pos f <|
by grind [IsMonicOfDegree.natDegree_eq]
refine ⟨f₁, f₂, ?_, hf₂⟩
have help {P : ℕ → Prop} {m : ℕ} (hm₀ : 0 < m) (hm₂ : m ≤ 2) (h : P m) : P 1 ∨ P 2 := by
interval_cases m <;> tauto
exact help... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 177,
"column": 38
} | {
"line": 177,
"column": 54
} | {
"line": 177,
"column": 55
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 178,
"column": 38
} | {
"line": 178,
"column": 54
} | {
"line": 178,
"column": 55
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 182,
"column": 47
} | {
"line": 182,
"column": 77
} | {
"line": 182,
"column": 78
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 184,
"column": 5
} | {
"line": 184,
"column": 35
} | {
"line": 184,
"column": 36
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 186,
"column": 68
} | {
"line": 186,
"column": 79
} | {
"line": 186,
"column": 80
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 31
} | {
"line": 113,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\nR : Type u_3\nM : Type u_4\ninst✝¹⁶ : Field 𝕜\ninst✝¹⁵ : CharZero 𝕜\ninst✝¹⁴ : Ring R\ninst✝¹³ : AddCommGroup M\ninst✝¹² : Algebra 𝕜 R\ninst✝¹¹ : Module 𝕜 M\ninst✝¹⁰ : Module R M\ninst✝⁹ : Module Rᵐᵒᵖ M\ninst✝⁸ : SMulCommClass R Rᵐᵒᵖ M\ninst✝⁷ : IsScalarTower 𝕜 R M\ninst✝⁶ : IsScala... | [
"𝕜 : Type u_1\nR : Type u_3\nM : Type u_4\ninst✝¹⁶ : Field 𝕜\ninst✝¹⁵ : CharZero 𝕜\ninst✝¹⁴ : Ring R\ninst✝¹³ : AddCommGroup M\ninst✝¹² : Algebra 𝕜 R\ninst✝¹¹ : Module 𝕜 M\ninst✝¹⁰ : Module R M\ninst✝⁹ : Module Rᵐᵒᵖ M\ninst✝⁸ : SMulCommClass R Rᵐᵒᵖ M\ninst✝⁷ : IsScalarTower 𝕜 R M\ninst✝⁶ : IsScalarTower 𝕜 Rᵐ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 43
} | {
"line": 115,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nR : Type u_3\nM : Type u_4\ninst✝¹⁶ : Field 𝕜\ninst✝¹⁵ : CharZero 𝕜\ninst✝¹⁴ : Ring R\ninst✝¹³ : AddCommGroup M\ninst✝¹² : Algebra 𝕜 R\ninst✝¹¹ : Module 𝕜 M\ninst✝¹⁰ : Module R M\ninst✝⁹ : Module Rᵐᵒᵖ M\ninst✝⁸ : SMulCommClass R Rᵐᵒᵖ M\ninst✝⁷ : IsScalarTower 𝕜 R M\ninst✝⁶ : IsScala... | [
"𝕜 : Type u_1\nR : Type u_3\nM : Type u_4\ninst✝¹⁶ : Field 𝕜\ninst✝¹⁵ : CharZero 𝕜\ninst✝¹⁴ : Ring R\ninst✝¹³ : AddCommGroup M\ninst✝¹² : Algebra 𝕜 R\ninst✝¹¹ : Module 𝕜 M\ninst✝¹⁰ : Module R M\ninst✝⁹ : Module Rᵐᵒᵖ M\ninst✝⁸ : SMulCommClass R Rᵐᵒᵖ M\ninst✝⁷ : IsScalarTower 𝕜 R M\ninst✝⁶ : IsScalarTower 𝕜 Rᵐ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 188,
"column": 36
} | {
"line": 188,
"column": 54
} | {
"line": 188,
"column": 55
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 189,
"column": 53
} | {
"line": 189,
"column": 83
} | {
"line": 189,
"column": 84
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 190,
"column": 48
} | {
"line": 190,
"column": 78
} | {
"line": 190,
"column": 79
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 192,
"column": 68
} | {
"line": 192,
"column": 79
} | {
"line": 192,
"column": 80
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 194,
"column": 36
} | {
"line": 194,
"column": 54
} | {
"line": 194,
"column": 55
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i + 2) (r ↑i)\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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