module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 353,
"column": 2
} | {
"line": 353,
"column": 45
} | {
"line": 354,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nx : 𝕜\n𝕝 : Type u_4\ninst✝³ : DivisionSemiring 𝕝\ninst✝² : Module 𝕝 F\ninst✝¹ : SMulCommClass 𝕜 𝕝 F\ninst✝ : ContinuousConstSMul 𝕝 F\nn : ℕ\nc : 𝕝\nf : 𝕜 → F\n⊢ iteratedD... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nx : 𝕜\n𝕝 : Type u_4\ninst✝³ : DivisionSemiring 𝕝\ninst✝² : Module 𝕝 F\ninst✝¹ : SMulCommClass 𝕜 𝕝 F\ninst✝ : ContinuousConstSMul 𝕝 F\nn : ℕ\nc : 𝕝\nf : 𝕜 → F\n⊢ iteratedDeriv n (c • ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 361,
"column": 2
} | {
"line": 361,
"column": 45
} | {
"line": 362,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nx : 𝕜\n𝕝 : Type u_4\ninst✝³ : DivisionSemiring 𝕝\ninst✝² : Module 𝕝 F\ninst✝¹ : SMulCommClass 𝕜 𝕝 F\ninst✝ : ContinuousConstSMul 𝕝 F\nn : ℕ\nc : 𝕝\nf : 𝕜 → F\n⊢ iteratedD... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nx : 𝕜\n𝕝 : Type u_4\ninst✝³ : DivisionSemiring 𝕝\ninst✝² : Module 𝕝 F\ninst✝¹ : SMulCommClass 𝕜 𝕝 F\ninst✝ : ContinuousConstSMul 𝕝 F\nn : ℕ\nc : 𝕝\nf : 𝕜 → F\n⊢ iteratedDeriv n (fun ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 370,
"column": 2
} | {
"line": 370,
"column": 45
} | {
"line": 371,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝔸 : Type u_5\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nn : ℕ\nf : 𝕜 → 𝔸\nc : 𝔸\nhf : ContDiffAt 𝕜 (↑n) f x\n⊢ iteratedDeriv n (fun x ↦ c * f x) x = c * iteratedDeriv n f x",
"ppTerm": "?m.70",
"assigned": false,
"u... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝔸 : Type u_5\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nn : ℕ\nf : 𝕜 → 𝔸\nc : 𝔸\nhf : ContDiffAt 𝕜 (↑n) f x\n⊢ iteratedDeriv n (fun x ↦ c * f x) x = c * iteratedDeriv n f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 378,
"column": 2
} | {
"line": 378,
"column": 45
} | {
"line": 379,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_6\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nn : ℕ\nc : 𝕜'\nf : 𝕜 → 𝕜'\n⊢ iteratedDeriv n (fun x ↦ c * f x) x = c * iteratedDeriv n f x",
"ppTerm": "?m.63",
"assigned": false,
"usedConstants": [... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_6\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nn : ℕ\nc : 𝕜'\nf : 𝕜 → 𝕜'\n⊢ iteratedDeriv n (fun x ↦ c * f x) x = c * iteratedDeriv n f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 386,
"column": 2
} | {
"line": 386,
"column": 45
} | {
"line": 387,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_6\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nn : ℕ\nf : 𝕜 → 𝕜'\nc : 𝕜'\n⊢ iteratedDeriv n (fun x ↦ f x * c) x = iteratedDeriv n f x * c",
"ppTerm": "?m.63",
"assigned": false,
"usedConstants": [... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nx : 𝕜\n𝕜' : Type u_6\ninst✝¹ : NormedDivisionRing 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nn : ℕ\nf : 𝕜 → 𝕜'\nc : 𝕜'\n⊢ iteratedDeriv n (fun x ↦ f x * c) x = iteratedDeriv n f x * c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 397,
"column": 2
} | {
"line": 397,
"column": 45
} | {
"line": 398,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\nh : ContDiff 𝕜 (↑n) f\nc x : 𝕜\n⊢ iteratedDeriv n (fun x ↦ f (c * x)) x = c ^ n • iteratedDeriv n f (c * x)",
"ppTerm": "?m.85",
"assigned": false,
... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\nh : ContDiff 𝕜 (↑n) f\nc x : 𝕜\n⊢ iteratedDeriv n (fun x ↦ f (c * x)) x = c ^ n • iteratedDeriv n f (c * x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 403,
"column": 2
} | {
"line": 403,
"column": 32
} | {
"line": 403,
"column": 33
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nn : ℕ\nf : 𝕜 → 𝕜\nh : ContDiff 𝕜 (↑n) f\nc : 𝕜\n⊢ (iteratedDeriv n fun x ↦ f (c * x)) = fun x ↦ c ^ n * iteratedDeriv n f (c * x)",
"ppTerm": "?m.79",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
... | [
"𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nn : ℕ\nf : 𝕜 → 𝕜\nh : ContDiff 𝕜 (↑n) f\nc : 𝕜\n⊢ (iteratedDeriv n fun x ↦ f (c * x)) = fun x ↦ c ^ n * iteratedDeriv n f (c * x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 423,
"column": 2
} | {
"line": 423,
"column": 13
} | {
"line": 423,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nn : ℕ\nx : 𝕜\n𝔸 : Type u_5\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nf g : 𝕜 → 𝔸\nhf : ContDiffAt 𝕜 (↑n) f x\nhg : ContDiffAt 𝕜 (↑n) g x\n⊢ iteratedDeriv n (f * g) x =\n ∑ i ∈ Finset.range (n + 1), ↑(n.choose i) * iteratedDeriv i ... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nn : ℕ\nx : 𝕜\n𝔸 : Type u_5\ninst✝¹ : NormedRing 𝔸\ninst✝ : NormedAlgebra 𝕜 𝔸\nf g : 𝕜 → 𝔸\nhf : ContDiffAt 𝕜 (↑n) f x\nhg : ContDiffAt 𝕜 (↑n) g x\n⊢ iteratedDeriv n (f * g) x =\n ∑ i ∈ Finset.range (n + 1), ↑(n.choose i) * iteratedDeriv i f x * iterat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 429,
"column": 2
} | {
"line": 429,
"column": 13
} | {
"line": 429,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nm k : ℕ\n⊢ iteratedDeriv k (fun x ↦ x ^ m) x = ↑(m.descFactorial k) * x ^ (m - k)",
"ppTerm": "?m.68",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝ : NontriviallyNormedField 𝕜\nx : 𝕜\nm k : ℕ\n⊢ iteratedDeriv k (fun x ↦ x ^ m) x = ↑(m.descFactorial k) * x ^ (m - k)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 463,
"column": 4
} | {
"line": 463,
"column": 45
} | {
"line": 463,
"column": 46
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn✝ : ℕ\nf : 𝕜 → F\ns : 𝕜\nn : ℕ\nIH : (iteratedDeriv n fun z ↦ f (s + z)) = fun t ↦ iteratedDeriv n f (s + t)\n⊢ (iteratedDeriv (n + 1) fun z ↦ f (s + z)) = fun t ↦ it... | [
"case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn✝ : ℕ\nf : 𝕜 → F\ns : 𝕜\nn : ℕ\nIH : (iteratedDeriv n fun z ↦ f (s + z)) = fun t ↦ iteratedDeriv n f (s + t)\n⊢ (deriv fun t ↦ iteratedDeriv n f (s + t)) = fun t ↦ deriv (iterate... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 471,
"column": 4
} | {
"line": 471,
"column": 45
} | {
"line": 471,
"column": 46
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn✝ : ℕ\nf : 𝕜 → F\ns : 𝕜\nn : ℕ\nIH : (iteratedDeriv n fun z ↦ f (z + s)) = fun t ↦ iteratedDeriv n f (t + s)\n⊢ (iteratedDeriv (n + 1) fun z ↦ f (z + s)) = fun t ↦ it... | [
"case succ\n𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn✝ : ℕ\nf : 𝕜 → F\ns : 𝕜\nn : ℕ\nIH : (iteratedDeriv n fun z ↦ f (z + s)) = fun t ↦ iteratedDeriv n f (t + s)\n⊢ (deriv fun t ↦ iteratedDeriv n f (t + s)) = fun t ↦ deriv (iterate... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 479,
"column": 2
} | {
"line": 479,
"column": 72
} | {
"line": 480,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\ns : 𝕜\n⊢ (iteratedDeriv n fun z ↦ f (s - z)) = fun t ↦ (-1) ^ n • iteratedDeriv n f (s - t)",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": ... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nn : ℕ\nf : 𝕜 → F\ns : 𝕜\n⊢ ∀ (x : 𝕜), iteratedDeriv n (fun z ↦ f (s - z)) x = (-1) ^ n • iteratedDeriv n f (s - x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 507,
"column": 2
} | {
"line": 507,
"column": 22
} | {
"line": 507,
"column": 23
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nι : Type u_7\nn : ℕ\nx : 𝕜\nf : ι → 𝕜 → F\nI : Finset ι\ns : Set 𝕜\nhx : x ∈ s\nhs : UniqueDiffOn 𝕜 s\nhf : ∀ i ∈ I, ContDiffWithinAt 𝕜 (↑n) (f i) s x\n⊢ iteratedDerivWithin n... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nι : Type u_7\nn : ℕ\nx : 𝕜\nf : ι → 𝕜 → F\nI : Finset ι\ns : Set 𝕜\nhx : x ∈ s\nhs : UniqueDiffOn 𝕜 s\nhf : ∀ i ∈ I, ContDiffWithinAt 𝕜 (↑n) (f i) s x\n⊢ iteratedDerivWithin n (fun x ↦ ∑ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 511,
"column": 2
} | {
"line": 511,
"column": 13
} | {
"line": 511,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nι : Type u_7\nn : ℕ\nx : 𝕜\nf : ι → 𝕜 → F\nI : Finset ι\nhf : ∀ i ∈ I, ContDiffAt 𝕜 (↑n) (f i) x\n⊢ iteratedDeriv n (∑ i ∈ I, f i) x = ∑ i ∈ I, iteratedDeriv n (f i) x",
"pp... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nι : Type u_7\nn : ℕ\nx : 𝕜\nf : ι → 𝕜 → F\nI : Finset ι\nhf : ∀ i ∈ I, ContDiffAt 𝕜 (↑n) (f i) x\n⊢ iteratedDeriv n (∑ i ∈ I, f i) x = ∑ i ∈ I, iteratedDeriv n (f i) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.Lemmas | {
"line": 515,
"column": 2
} | {
"line": 515,
"column": 22
} | {
"line": 515,
"column": 23
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nι : Type u_7\nn : ℕ\nx : 𝕜\nf : ι → 𝕜 → F\nI : Finset ι\nhf : ∀ i ∈ I, ContDiffAt 𝕜 (↑n) (f i) x\n⊢ iteratedDeriv n (fun z ↦ ∑ i ∈ I, f i z) x = ∑ i ∈ I, iteratedDeriv n (f i) x... | [
"𝕜 : Type u_1\ninst✝² : NontriviallyNormedField 𝕜\nF : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nι : Type u_7\nn : ℕ\nx : 𝕜\nf : ι → 𝕜 → F\nI : Finset ι\nhf : ∀ i ∈ I, ContDiffAt 𝕜 (↑n) (f i) x\n⊢ iteratedDeriv n (fun z ↦ ∑ i ∈ I, f i z) x = ∑ i ∈ I, iteratedDeriv n (f i) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 249,
"column": 70
} | {
"line": 249,
"column": 81
} | {
"line": 249,
"column": 82
} | [
{
"pp": "f : ℝ → ℝ\na : ℝ\nf' : ℝ → ℝ := f ∘ Neg.neg\nb : ℝ\nhb₁ : b < a\nhb₂ : ∀ ⦃x : ℝ⦄, x ∈ Ioo b a → deriv f x ∈ Iic (-1)\nx : ℝ\nhx : x ∈ Ioo (-a) (-b)\nthis : deriv f' x = deriv f (-x) * deriv Neg.neg x\n⊢ deriv f' x = -deriv f (-x)",
"ppTerm": "?m.260",
"assigned": false,
"usedConstants": [],... | [
"f : ℝ → ℝ\na : ℝ\nf' : ℝ → ℝ := f ∘ Neg.neg\nb : ℝ\nhb₁ : b < a\nhb₂ : ∀ ⦃x : ℝ⦄, x ∈ Ioo b a → deriv f x ∈ Iic (-1)\nx : ℝ\nhx : x ∈ Ioo (-a) (-b)\nthis : deriv f' x = deriv f (-x) * deriv Neg.neg x\n⊢ deriv f' x = -deriv f (-x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 115,
"column": 6
} | {
"line": 120,
"column": 29
} | {
"line": 120,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nε : ℝ≥0∞\nε0 : ε ≠ 0\nf : α →ₛ ℝ≥0 := piecewise s hs (const α c) (const α 0)\nh : ¬∫⁻ (x : α), ↑(f x) ∂μ = ∞\nhc : ¬c = 0\n⊢ μ ... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nε : ℝ≥0∞\nε0 : ε ≠ 0\nf : α →ₛ ℝ≥0 := piecewise s hs (const α c) (const α 0)\nh : ¬∫⁻ (x : α), ↑(f x) ∂μ = ∞\nhc : ¬c = 0\n⊢ ¬μ s = ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 123,
"column": 6
} | {
"line": 123,
"column": 17
} | {
"line": 123,
"column": 18
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nε : ℝ≥0∞\nε0 : ε ≠ 0\nf : α →ₛ ℝ≥0 := piecewise s hs (const α c) (const α 0)\nh : ¬∫⁻ (x : α), ↑(f x) ∂μ = ∞\nhc : ¬c = 0\nne_t... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nε : ℝ≥0∞\nε0 : ε ≠ 0\nf : α →ₛ ℝ≥0 := piecewise s hs (const α c) (const α 0)\nh : ¬∫⁻ (x : α), ↑(f x) ∂μ = ∞\nhc : ¬c = 0\nne_top : μ s ≠ ∞... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 141,
"column": 10
} | {
"line": 141,
"column": 21
} | {
"line": 141,
"column": 22
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nε : ℝ≥0∞\nε0 : ε ≠ 0\nf : α →ₛ ℝ≥0 := piecewise s hs (const α c) (const α 0)\nh : ¬∫⁻ (x : α), ↑(f x) ∂μ = ∞\nhc : ¬c = 0\nne_t... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nε : ℝ≥0∞\nε0 : ε ≠ 0\nf : α →ₛ ℝ≥0 := piecewise s hs (const α c) (const α 0)\nh : ¬∫⁻ (x : α), ↑(f x) ∂μ = ∞\nhc : ¬c = 0\nne_top : μ s ≠ ∞... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 380,
"column": 2
} | {
"line": 380,
"column": 38
} | {
"line": 381,
"column": 4
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ x ∈ interior D, 0 < deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nthis : DifferentiableOn ℝ f (interior D)\n⊢ x < y → f x < f y",
"ppTerm": "?m.76",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ x ∈ interior D, 0 < deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nthis : DifferentiableOn ℝ f (interior D)\n⊢ x < y → f x < f y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 413,
"column": 2
} | {
"line": 413,
"column": 41
} | {
"line": 414,
"column": 4
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_nonneg : ∀ x ∈ interior D, 0 ≤ deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nhxy : x ≤ y\n⊢ f x ≤ f y",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [... | [
"D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_nonneg : ∀ x ∈ interior D, 0 ≤ deriv f x\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nhxy : x ≤ y\n⊢ f x ≤ f y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 446,
"column": 2
} | {
"line": 446,
"column": 42
} | {
"line": 447,
"column": 4
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ x ∈ interior D, deriv f x < 0\nx : ℝ\nhx : x ∈ D\ny : ℝ\n⊢ y ∈ D → x < y → f y < f x",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : ∀ x ∈ interior D, deriv f x < 0\nx : ℝ\nhx : x ∈ D\ny : ℝ\n⊢ y ∈ D → x < y → f y < f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 482,
"column": 2
} | {
"line": 482,
"column": 41
} | {
"line": 483,
"column": 4
} | [
{
"pp": "D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_nonpos : ∀ x ∈ interior D, deriv f x ≤ 0\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nhxy : x ≤ y\n⊢ f y ≤ f x",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedFVars": [... | [
"D : Set ℝ\nhD : Convex ℝ D\nf : ℝ → ℝ\nhf : ContinuousOn f D\nhf' : DifferentiableOn ℝ f (interior D)\nhf'_nonpos : ∀ x ∈ interior D, deriv f x ≤ 0\nx : ℝ\nhx : x ∈ D\ny : ℝ\nhy : y ∈ D\nhxy : x ≤ y\n⊢ f y ≤ f x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Deriv.MeanValue | {
"line": 534,
"column": 2
} | {
"line": 534,
"column": 17
} | {
"line": 534,
"column": 18
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\ns : Set E\nx y : E\nf' : E → StrongDual ℝ E\nhf : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s x\nhs : Convex ℝ s\nxs : x ∈ s\nys : y ∈ s\ng : ℝ → E := fun t ↦ (AffineMap.lineMap x y) t\nI : Set ℝ := Icc 0 1\nhsub : Ioo 0 1 ⊆ I\n... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : E → ℝ\ns : Set E\nx y : E\nf' : E → StrongDual ℝ E\nhf : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s x\nhs : Convex ℝ s\nxs : x ∈ s\nys : y ∈ s\ng : ℝ → E := fun t ↦ (AffineMap.lineMap x y) t\nI : Set ℝ := Icc 0 1\nhsub : Ioo 0 1 ⊆ I\nhmaps : Maps... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 209,
"column": 8
} | {
"line": 209,
"column": 57
} | {
"line": 209,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfmeas : Measurable f\nε : ℝ≥0∞\nε0 : ε ≠ 0\nthis : ε / 2 ≠ 0\nw : α → ℝ≥0\nwpos : ∀ (x : α), 0 < w x\nwmeas : Measurable w\nwint : ∫... | [
"α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfmeas : Measurable f\nε : ℝ≥0∞\nε0 : ε ≠ 0\nthis : ε / 2 ≠ 0\nw : α → ℝ≥0\nwpos : ∀ (x : α), 0 < w x\nwmeas : Measurable w\nwint : ∫⁻ (x : α), ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 216,
"column": 54
} | {
"line": 216,
"column": 72
} | {
"line": 216,
"column": 72
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfmeas : Measurable f\nε : ℝ≥0∞\nε0 : ε ≠ 0\nthis : ε / 2 ≠ 0\nw : α → ℝ≥0\nwpos : ∀ (x : α), 0 < w x\nwmeas : Measurable w\nwint : ∫... | [
"α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfmeas : Measurable f\nε : ℝ≥0∞\nε0 : ε ≠ 0\nthis : ε / 2 ≠ 0\nw : α → ℝ≥0\nwpos : ∀ (x : α), 0 < w x\nwmeas : Measurable w\nwint : ∫⁻ (x : α), ↑... | ENNReal.add_halves | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Log.Deriv | {
"line": 254,
"column": 2
} | {
"line": 254,
"column": 47
} | {
"line": 254,
"column": 48
} | [
{
"pp": "x : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ ∑ i ∈ Finset.range n, x ^ (i + 1) / (↑i + 1) + log (1 - x)\nF' : ℝ → ℝ := fun x ↦ -x ^ n / (1 - x)\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\nB : ∀ y ∈ Set.Icc (-|x|) |x|, |F' y| ≤ |x| ^ n / (1 - |x|)\nC : ‖F x - F 0‖ ≤ |x| ^ n / (1 - |x|) * ‖x - 0... | [
"x : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ ∑ i ∈ Finset.range n, x ^ (i + 1) / (↑i + 1) + log (1 - x)\nF' : ℝ → ℝ := fun x ↦ -x ^ n / (1 - x)\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\nB : ∀ y ∈ Set.Icc (-|x|) |x|, |F' y| ≤ |x| ^ n / (1 - |x|)\nC : ‖F x - F 0‖ ≤ |x| ^ n / (1 - |x|) * ‖x - 0‖\n⊢ |∑ x_1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Log.Deriv | {
"line": 304,
"column": 61
} | {
"line": 304,
"column": 81
} | {
"line": 304,
"column": 82
} | [
{
"pp": "x : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nhI : Set.Icc (-|x|) |x| ⊆ Set.Ioo (-1) 1\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\ny : ℝ\nhy : y ∈ Set.Icc (-|... | [
"x : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nhI : Set.Icc (-|x|) |x| ⊆ Set.Ioo (-1) 1\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\ny : ℝ\nhy : y ∈ Set.Icc (-|x|) |x|\nthi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Log.Deriv | {
"line": 305,
"column": 68
} | {
"line": 305,
"column": 88
} | {
"line": 305,
"column": 89
} | [
{
"pp": "case hd\nx : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := ⋯\nF' : ℝ → ℝ := ⋯\nhI : Set.Icc (-|x|) |x| ⊆ Set.Ioo (-1) 1\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\ny : ℝ\nhy : y ∈ Set.Icc (-|x|) |x|\nthis : y ^ 2 ≤ x ^ 2\n⊢ 0 < 1 - x ^ 2",
"ppTerm": "?hd",
"assigned": true,
"usedConstants": [
... | [
"case hd\nx : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nhI : Set.Icc (-|x|) |x| ⊆ Set.Ioo (-1) 1\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\ny : ℝ\nhy : y ∈ Set.Icc (-|x|)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Basic | {
"line": 325,
"column": 29
} | {
"line": 325,
"column": 40
} | {
"line": 325,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\nR : Type u_2\nG : Type u_3\nM : Type u_4\nN : Type u_5\nO : Type u_6\ninst✝³ : Semiring R\ninst✝² : PartialOrder R\ninst✝¹ : AddCommGroup G\ninst✝ : SMul R G\nC✝ C₁ C₂ C : ConvexCone R G\nh₁ : C.Pointed\nx y z : G\nxy : y - x ∈ C\nzy : z - y ∈ C\n⊢ z - x ∈ C",
"ppTerm": "?m.49",
... | [
"𝕜 : Type u_1\nR : Type u_2\nG : Type u_3\nM : Type u_4\nN : Type u_5\nO : Type u_6\ninst✝³ : Semiring R\ninst✝² : PartialOrder R\ninst✝¹ : AddCommGroup G\ninst✝ : SMul R G\nC✝ C₁ C₂ C : ConvexCone R G\nh₁ : C.Pointed\nx y z : G\nxy : y - x ∈ C\nzy : z - y ∈ C\n⊢ z - x ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Log.Deriv | {
"line": 313,
"column": 2
} | {
"line": 313,
"column": 47
} | {
"line": 313,
"column": 48
} | [
{
"pp": "x : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nhI : Set.Icc (-|x|) |x| ⊆ Set.Ioo (-1) 1\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\nB : ∀ y ∈ Set.Icc (-|x|) |x... | [
"x : ℝ\nh : |x| < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nhI : Set.Icc (-|x|) |x| ⊆ Set.Ioo (-1) 1\nA : ∀ y ∈ Set.Ioo (-1) 1, HasDerivAt F (F' y) y\nB : ∀ y ∈ Set.Icc (-|x|) |x|, ‖F' y‖ ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Basic | {
"line": 449,
"column": 2
} | {
"line": 449,
"column": 96
} | {
"line": 450,
"column": 4
} | [
{
"pp": "R : Type u_2\nM : Type u_4\ninst✝³ : Semiring R\ninst✝² : PartialOrder R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ ⊥.IsGenerating ↔ Subsingleton M",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Submodule.subsingleton_iff",
"c... | [
"R : Type u_2\nM : Type u_4\ninst✝³ : Semiring R\ninst✝² : PartialOrder R\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\n⊢ ⊥ = ⊤ ↔ Subsingleton (Submodule R M)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Log.Deriv | {
"line": 330,
"column": 37
} | {
"line": 330,
"column": 52
} | {
"line": 330,
"column": 53
} | [
{
"pp": "x : ℝ\nh₀ : 0 ≤ x\nh : x < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nA : ∀ y ∈ Set.Icc 0 x, HasDerivAt F (F' y) y\nthis : MonotoneOn F (Set.Icc 0 x)\n⊢ ∑ i ∈ Finset.range n, x ^... | [
"x : ℝ\nh₀ : 0 ≤ x\nh : x < 1\nn : ℕ\nF : ℝ → ℝ := fun x ↦ 1 / 2 * log ((1 + x) / (1 - x)) - ∑ i ∈ Finset.range n, x ^ (2 * i + 1) / (2 * ↑i + 1)\nF' : ℝ → ℝ := fun y ↦ (y ^ 2) ^ n / (1 - y ^ 2)\nA : ∀ y ∈ Set.Icc 0 x, HasDerivAt F (F' y) y\nthis : MonotoneOn F (Set.Icc 0 x)\n⊢ ∑ i ∈ Finset.range n, x ^ (2 * i + 1)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Basic | {
"line": 486,
"column": 16
} | {
"line": 488,
"column": 89
} | {
"line": 489,
"column": 4
} | [
{
"pp": "R : Type u_7\nM : Type u_8\ninst✝⁵ : Ring R\ninst✝⁴ : LinearOrder R\ninst✝³ : AddLeftStrictMono R\ninst✝² : AddCommGroup M\ninst✝¹ : Nontrivial M\ninst✝ : Module R M\nC : ConvexCone R M\nh : Submodule.span R ↑C = ⊤\nx : M\nhne : (↑C).Nonempty\n⊢ ∀ {a b : M}, a ∈ ↑C - ↑C → b ∈ ↑C - ↑C → a + b ∈ ↑C - ↑C"... | [] | by
rintro _ _ ⟨y₁, hy₁, z₁, hz₁, rfl⟩ ⟨y₂, hy₂, z₂, hz₂, rfl⟩
exact ⟨y₁ + y₂, C.add_mem hy₁ hy₂, z₁ + z₂, C.add_mem hz₁ hz₂, add_sub_add_comm ..⟩ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 292,
"column": 10
} | {
"line": 292,
"column": 21
} | {
"line": 292,
"column": 22
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfint : Integrable (fun x ↦ ↑(f x)) μ\nfmeas : AEMeasurable f μ\nε : ℝ≥0\nεpos : 0 < ↑ε\nδ : ℝ≥0\nδpos : 0 < δ\nhδε : δ < ε\nint_f_ne... | [
"α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ≥0\nfint : Integrable (fun x ↦ ↑(f x)) μ\nfmeas : AEMeasurable f μ\nε : ℝ≥0\nεpos : 0 < ↑ε\nδ : ℝ≥0\nδpos : 0 < δ\nhδε : δ < ε\nint_f_ne_top : ∫⁻ (a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Basic | {
"line": 634,
"column": 4
} | {
"line": 634,
"column": 15
} | {
"line": 634,
"column": 16
} | [
{
"pp": "R : Type u_2\ninst✝⁶ : Semiring R\ninst✝⁵ : PartialOrder R\nG : Type u_7\ninst✝⁴ : AddCommGroup G\ninst✝³ : PartialOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : Module R G\ninst✝ : PosSMulMono R G\nx : G\nhx_nonneg : x ∈ positive R G\nhx_ne_zero : x ≠ 0\nhx_nonpos : -x ∈ positive R G\n⊢ 0 < 0",
... | [
"R : Type u_2\ninst✝⁶ : Semiring R\ninst✝⁵ : PartialOrder R\nG : Type u_7\ninst✝⁴ : AddCommGroup G\ninst✝³ : PartialOrder G\ninst✝² : IsOrderedAddMonoid G\ninst✝¹ : Module R G\ninst✝ : PosSMulMono R G\nx : G\nhx_nonneg : x ∈ positive R G\nhx_ne_zero : x ≠ 0\nhx_nonpos : -x ∈ positive R G\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Log.Deriv | {
"line": 372,
"column": 6
} | {
"line": 372,
"column": 28
} | {
"line": 372,
"column": 29
} | [
{
"pp": "x : ℝ\nh : |x| < 1\ni : ℕ\n⊢ |x| ^ (i + 1) / (0 + 1) ≤ |x| ^ i",
"ppTerm": "?m.346",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"instHDiv",
"HMul.hMul",
"Real.lattice",
"DivisionCommMonoid.toDivisionMonoid",
"Real.in... | [
"x : ℝ\nh : |x| < 1\ni : ℕ\n⊢ |x| ^ i * |x| ≤ |x| ^ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Pointed | {
"line": 290,
"column": 25
} | {
"line": 290,
"column": 36
} | {
"line": 290,
"column": 37
} | [
{
"pp": "R : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁷ : Semiring R\ninst✝⁶ : PartialOrder R\ninst✝⁵ : IsOrderedRing R\ninst✝⁴ : AddCommMonoid E\ninst✝³ : PartialOrder E\ninst✝² : IsOrderedAddMonoid E\ninst✝¹ : Module R E\ninst✝ : PosSMulMono R E\nc : failed to pretty print expression (use 'set... | [
"R : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁷ : Semiring R\ninst✝⁶ : PartialOrder R\ninst✝⁵ : IsOrderedRing R\ninst✝⁴ : AddCommMonoid E\ninst✝³ : PartialOrder E\ninst✝² : IsOrderedAddMonoid E\ninst✝¹ : Module R E\ninst✝ : PosSMulMono R E\nc : failed to pretty print expression (use 'set_option pp.r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Pointed | {
"line": 338,
"column": 6
} | {
"line": 338,
"column": 17
} | {
"line": 338,
"column": 18
} | [
{
"pp": "case pos\nR : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup E\ninst✝ : Module R E\nC : PointedCone R E\nr : R\nx✝ : E\nhx : x✝ ∈ C.support.carrier\nhr : 0 ≤ r\n⊢ r • x✝ ∈ C.support.carrier",
"ppTerm": "?p... | [
"case pos\nR : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup E\ninst✝ : Module R E\nC : PointedCone R E\nr : R\nx✝ : E\nhx : x✝ ∈ C.support.carrier\nhr : 0 ≤ r\n⊢ r • x✝ ∈ C ∧ -(r • x✝) ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Convex.Cone.Pointed | {
"line": 340,
"column": 6
} | {
"line": 340,
"column": 17
} | {
"line": 340,
"column": 18
} | [
{
"pp": "case neg\nR : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup E\ninst✝ : Module R E\nC : PointedCone R E\nr : R\nx✝ : E\nhx : x✝ ∈ C.support.carrier\nhr✝ : ¬0 ≤ r\nhr : 0 ≤ -r\n⊢ r • x✝ ∈ C.support.carrier",
... | [
"case neg\nR : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁴ : Ring R\ninst✝³ : LinearOrder R\ninst✝² : IsOrderedRing R\ninst✝¹ : AddCommGroup E\ninst✝ : Module R E\nC : PointedCone R E\nr : R\nx✝ : E\nhx : x✝ ∈ C.support.carrier\nhr✝ : ¬0 ≤ r\nhr : 0 ≤ -r\n⊢ r • x✝ ∈ C ∧ -(r • x✝) ∈ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 318,
"column": 35
} | {
"line": 318,
"column": 94
} | {
"line": 318,
"column": 95
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nint_f : ∫⁻ (x : α), ↑((piecewise s hs (const α c) (const α 0)) x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nhc : ¬c = 0\n⊢ μ s < ∞",
"p... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nint_f : ∫⁻ (x : α), ↑((piecewise s hs (const α c) (const α 0)) x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nhc : ¬c = 0\n⊢ ¬μ s = ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Cone.Extension | {
"line": 72,
"column": 4
} | {
"line": 84,
"column": 39
} | {
"line": 85,
"column": 2
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : PointedCone ℝ E\nf : E →ₗ.[ℝ] ℝ\nnonneg : ∀ (x : ↥f.domain), ↑x ∈ s → 0 ≤ ↑f x\ndense : ∀ (y : E), ∃ x, ↑x + y ∈ s\nhdom : f.domain ≠ ⊤\ny : E\nhy : y ∉ f.domain\n⊢ ∃ c, (∀ (x : ↥f.domain), -↑x - y ∈ s → ↑f x ≤ c) ∧ ∀ (x : ↥f.domain), ↑x + ... | [] | set Sp := f '' { x : f.domain | (x : E) + y ∈ s }
set Sn := f '' { x : f.domain | -(x : E) - y ∈ s }
suffices (upperBounds Sn ∩ lowerBounds Sp).Nonempty by
simpa only [Sp, Sn, Set.Nonempty, upperBounds, lowerBounds, forall_mem_image] using! this
refine exists_between_of_forall_le (Nonempty.image f ?_)... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Convex.Cone.Extension | {
"line": 72,
"column": 4
} | {
"line": 84,
"column": 39
} | {
"line": 85,
"column": 2
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : PointedCone ℝ E\nf : E →ₗ.[ℝ] ℝ\nnonneg : ∀ (x : ↥f.domain), ↑x ∈ s → 0 ≤ ↑f x\ndense : ∀ (y : E), ∃ x, ↑x + y ∈ s\nhdom : f.domain ≠ ⊤\ny : E\nhy : y ∉ f.domain\n⊢ ∃ c, (∀ (x : ↥f.domain), -↑x - y ∈ s → ↑f x ≤ c) ∧ ∀ (x : ↥f.domain), ↑x + ... | [] | set Sp := f '' { x : f.domain | (x : E) + y ∈ s }
set Sn := f '' { x : f.domain | -(x : E) - y ∈ s }
suffices (upperBounds Sn ∩ lowerBounds Sp).Nonempty by
simpa only [Sp, Sn, Set.Nonempty, upperBounds, lowerBounds, forall_mem_image] using! this
refine exists_between_of_forall_le (Nonempty.image f ?_)... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 338,
"column": 10
} | {
"line": 338,
"column": 21
} | {
"line": 338,
"column": 22
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nint_f : ∫⁻ (x : α), ↑((piecewise s hs (const α c) (const α 0)) x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nhc : ¬c = 0\nμs_lt_top : μ s < ... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nc : ℝ≥0\ns : Set α\nhs : MeasurableSet s\nint_f : ∫⁻ (x : α), ↑((piecewise s hs (const α c) (const α 0)) x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nhc : ¬c = 0\nμs_lt_top : μ s < ∞\nthis : 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Gauge | {
"line": 122,
"column": 54
} | {
"line": 122,
"column": 65
} | {
"line": 122,
"column": 66
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : Set E\nsymmetric : ∀ x ∈ s, -x ∈ s\nx✝ x : E\nh : -x ∈ s\n⊢ x ∈ s",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : Set E\nsymmetric : ∀ x ∈ s, -x ∈ s\nx✝ x : E\nh : -x ∈ s\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 309,
"column": 48
} | {
"line": 309,
"column": 59
} | {
"line": 309,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nhK : IsComplete K\nP : ∀ {n : ℕ}, 0 < (1 / 2) ^ n\nc : 𝕜\nhc : 1 < ‖c‖\nx ... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nhK : IsComplete K\nP : ∀ {n : ℕ}, 0 < (1 / 2) ^ n\nc : 𝕜\nhc : 1 < ‖c‖\nx : E\nhx : x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 370,
"column": 28
} | {
"line": 370,
"column": 65
} | {
"line": 370,
"column": 66
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nint_f : ∫⁻ (x : α), ↑(f x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), ↑(fs x) ≤ ↑(f x)\nint_fs : ∫⁻ (x : α), ↑(f x) ∂μ < (SimpleFunc.... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nint_f : ∫⁻ (x : α), ↑(f x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), ↑(fs x) ≤ ↑(f x)\nint_fs : ∫⁻ (x : α), ↑(f x) ∂μ < (SimpleFunc.map ENNReal.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 376,
"column": 4
} | {
"line": 376,
"column": 41
} | {
"line": 376,
"column": 42
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nint_f : ∫⁻ (x : α), ↑(f x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), fs x ≤ f x\nint_fs : ∫⁻ (x : α), ↑(f x) ∂μ ≤ ∫⁻ (x : α), ↑(fs x... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nint_f : ∫⁻ (x : α), ↑(f x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), fs x ≤ f x\nint_fs : ∫⁻ (x : α), ↑(f x) ∂μ ≤ ∫⁻ (x : α), ↑(fs x) ∂μ + ε / 2... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 330,
"column": 8
} | {
"line": 330,
"column": 99
} | {
"line": 331,
"column": 10
} | [
{
"pp": "case hz\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nhK : IsComplete K\nP : ∀ {n : ℕ}, 0 < (1 / 2) ^ n\nc : 𝕜\nhc : 1 ... | [
"case hz\n𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nhK : IsComplete K\nP : ∀ {n : ℕ}, 0 < (1 / 2) ^ n\nc : 𝕜\nhc : 1 < ‖c‖\nx : E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 385,
"column": 48
} | {
"line": 385,
"column": 66
} | {
"line": 385,
"column": 66
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nint_f : ∫⁻ (x : α), ↑(f x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), fs x ≤ f x\nint_fs : ∫⁻ (x : α), ↑(f x) ∂μ ≤ ∫⁻ (x : α), ↑(fs x... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nint_f : ∫⁻ (x : α), ↑(f x) ∂μ ≠ ∞\nε : ℝ≥0∞\nε0 : ε ≠ 0\nfs : α →ₛ ℝ≥0\nfs_le_f : ∀ (x : α), fs x ≤ f x\nint_fs : ∫⁻ (x : α), ↑(f x) ∂μ ≤ ∫⁻ (x : α), ↑(fs x) ∂μ + ε / 2... | ENNReal.add_halves | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 335,
"column": 10
} | {
"line": 335,
"column": 48
} | {
"line": 335,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nhK : IsComplete K\nP : ∀ {n : ℕ}, 0 < (1 / 2) ^ n\nc : 𝕜\nhc : 1 < ‖c‖\nx ... | [
"𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nf : E → F\nK : Set (E →L[𝕜] F)\nhK : IsComplete K\nP : ∀ {n : ℕ}, 0 < (1 / 2) ^ n\nc : 𝕜\nhc : 1 < ‖c‖\nx : E\nhx : x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 403,
"column": 4
} | {
"line": 403,
"column": 15
} | {
"line": 403,
"column": 16
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nfint : Integrable (fun x ↦ ↑(f x)) μ\nε : ℝ≥0\nεpos : 0 < ↑ε\nIf : ∫⁻ (x : α), ↑(f x) ∂μ < ∞\ng : α → ℝ≥0\ngf : ∀ (x : α), g x ≤ f x\ngcont : UpperSemiconti... | [
"α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nfint : Integrable (fun x ↦ ↑(f x)) μ\nε : ℝ≥0\nεpos : 0 < ↑ε\nIf : ∫⁻ (x : α), ↑(f x) ∂μ < ∞\ng : α → ℝ≥0\ngf : ∀ (x : α), g x ≤ f x\ngcont : UpperSemicontinuous g\ngin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Cone.Extension | {
"line": 148,
"column": 71
} | {
"line": 153,
"column": 35
} | {
"line": 155,
"column": 0
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\ns : PointedCone ℝ E\nf : E →ₗ.[ℝ] ℝ\nnonneg : ∀ (x : ↥f.domain), ↑x ∈ s → 0 ≤ ↑f x\ndense : ∀ (y : E), ∃ x, ↑x + y ∈ s\n⊢ ∃ g, (∀ (x : ↥f.domain), g ↑x = ↑f x) ∧ ∀ x ∈ s, 0 ≤ g x",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants... | [] | by
rcases RieszExtension.exists_top s f nonneg dense
with ⟨⟨g_dom, g⟩, ⟨-, hfg⟩, rfl : g_dom = ⊤, hgs⟩
refine ⟨g.comp (LinearMap.id.codRestrict ⊤ fun _ ↦ trivial), ?_, ?_⟩
· exact fun x => (hfg rfl).symm
· exact fun x hx => hgs ⟨x, _⟩ hx | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Convex.Cone.Extension | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 20
} | {
"line": 171,
"column": 21
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : ↥f.domain), ↑f x ≤ N ↑x\nN_0 : N 0 = 0\ns : PointedCone ℝ (E × ℝ) := { carrier := {p | N p.1 ≤ p.2}, a... | [
"E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : ↥f.domain), ↑f x ≤ N ↑x\nN_0 : N 0 = 0\ns : PointedCone ℝ (E × ℝ) := { carrier := {p | N p.1 ≤ p.2}, add_mem' := ⋯... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 413,
"column": 8
} | {
"line": 413,
"column": 19
} | {
"line": 413,
"column": 20
} | [
{
"pp": "case refine_2\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nfint : Integrable (fun x ↦ ↑(f x)) μ\nε : ℝ≥0\nεpos : 0 < ↑ε\nIf : ∫⁻ (x : α), ↑(f x) ∂μ < ∞\ng : α → ℝ≥0\ngf : ∀ (x : α), g x ≤ f x\ngcont :... | [
"case refine_2\nα : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : MeasurableSpace α\ninst✝¹ : BorelSpace α\nμ : Measure α\ninst✝ : μ.WeaklyRegular\nf : α → ℝ≥0\nfint : Integrable (fun x ↦ ↑(f x)) μ\nε : ℝ≥0\nεpos : 0 < ↑ε\nIf : ∫⁻ (x : α), ↑(f x) ∂μ < ∞\ng : α → ℝ≥0\ngf : ∀ (x : α), g x ≤ f x\ngcont : UpperSemico... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Cone.Extension | {
"line": 181,
"column": 33
} | {
"line": 181,
"column": 44
} | {
"line": 181,
"column": 45
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : ↥f.domain), ↑f x ≤ N ↑x\nN_0 : N 0 = 0\ns : PointedCone ℝ (E × ℝ) := { carrier := {p | N p.1 ≤ p.2}, a... | [
"E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : ↥f.domain), ↑f x ≤ N ↑x\nN_0 : N 0 = 0\ns : PointedCone ℝ (E × ℝ) := { carrier := {p | N p.1 ≤ p.2}, add_mem' := ⋯... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Cone.Extension | {
"line": 182,
"column": 20
} | {
"line": 182,
"column": 31
} | {
"line": 182,
"column": 32
} | [
{
"pp": "E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : ↥f.domain), ↑f x ≤ N ↑x\nN_0 : N 0 = 0\ns : PointedCone ℝ (E × ℝ) := { carrier := {p | N p.1 ≤ p.2}, a... | [
"E : Type u_2\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\nf : E →ₗ.[ℝ] ℝ\nN : E → ℝ\nN_hom : ∀ (c : ℝ), 0 < c → ∀ (x : E), N (c • x) = c * N x\nN_add : ∀ (x y : E), N (x + y) ≤ N x + N y\nhf : ∀ (x : ↥f.domain), ↑f x ≤ N ↑x\nN_0 : N 0 = 0\ns : PointedCone ℝ (E × ℝ) := { carrier := {p | N p.1 ≤ p.2}, add_mem' := ⋯... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 375,
"column": 2
} | {
"line": 375,
"column": 61
} | {
"line": 376,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nf : E → F\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\ninst✝ : CompleteSpace F\n⊢ Measurab... | [
"𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace 𝕜 F\nf : E → F\ninst✝² : MeasurableSpace E\ninst✝¹ : OpensMeasurableSpace E\ninst✝ : CompleteSpace F\nthis : IsComplete univ... | have : IsComplete (univ : Set (E →L[𝕜] F)) := complete_univ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Convex.Gauge | {
"line": 441,
"column": 6
} | {
"line": 441,
"column": 31
} | {
"line": 441,
"column": 32
} | [
{
"pp": "E : Type u_2\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns : Set E\nx : E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhc : Convex ℝ s\nhs₀ : s ∈ 𝓝 0\nha : Absorbent ℝ s\nε : ℝ\nhε₀ : 0 < ε\n⊢ ∀ᶠ (x_1 : E) in 𝓝 x, gauge s x_1 ∈ Icc (gauge s x - ε) (ga... | [
"E : Type u_2\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns : Set E\nx : E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhc : Convex ℝ s\nhs₀ : s ∈ 𝓝 0\nha : Absorbent ℝ s\nε : ℝ\nhε₀ : 0 < ε\n⊢ ∀ᶠ (x_1 : E) in map (fun x_1 ↦ x + x_1) (𝓝 0), gauge s x_1 ∈ Icc (gaug... | ← map_add_left_nhds_zero, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 68,
"column": 4
} | {
"line": 70,
"column": 48
} | {
"line": 71,
"column": 4
} | [
{
"pp": "case refine_2\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : Module ℝ E\ninst✝ : ContinuousSMul ℝ E\ns : Set E\nhs₀ : 0 ∈ s\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nx₀ : E\nhx₀ : x₀ ∉ s\nf : E →ₗ.[ℝ] ℝ := LinearPMap.mkSpanSingleton x₀ 1 ⋯\nφ : ... | [
"case refine_2\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : Module ℝ E\ninst✝ : ContinuousSMul ℝ E\ns : Set E\nhs₀ : 0 ∈ s\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nx₀ : E\nhx₀ : x₀ ∉ s\nf : E →ₗ.[ℝ] ℝ := LinearPMap.mkSpanSingleton x₀ 1 ⋯\nφ : E →ₗ[ℝ] ℝ\nh... | refine
φ.continuous_of_nonzero_on_open _ (hs₂.vadd (-x₀)) (Nonempty.vadd_set ⟨0, hs₀⟩)
(vadd_set_subset_iff.mpr fun x hx => ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 402,
"column": 2
} | {
"line": 402,
"column": 46
} | {
"line": 402,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\ninst✝⁴ : CompleteSpace F\ninst✝³ : MeasurableSpace 𝕜\ninst✝² : OpensMeasurableSpace 𝕜\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\nf : 𝕜 → F\n⊢ Measurable (deriv f)",
... | [
"𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nF : Type u_3\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\ninst✝⁴ : CompleteSpace F\ninst✝³ : MeasurableSpace 𝕜\ninst✝² : OpensMeasurableSpace 𝕜\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\nf : 𝕜 → F\n⊢ Measurable (deriv f)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 51
} | {
"line": 101,
"column": 2
} | [
{
"pp": "case inr.inl\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\na₀ : E\nha₀ : a₀ ∈ s\nht : Convex ℝ ∅\ndisj : Disjoint s ∅\n⊢ ∃ f u, (∀ a ∈ s, f a < u) ∧ ∀ b... | [] | exact ⟨0, 1, fun a _ha => zero_lt_one, by simp⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 51
} | {
"line": 101,
"column": 2
} | [
{
"pp": "case inr.inl\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\na₀ : E\nha₀ : a₀ ∈ s\nht : Convex ℝ ∅\ndisj : Disjoint s ∅\n⊢ ∃ f u, (∀ a ∈ s, f a < u) ∧ ∀ b... | [] | exact ⟨0, 1, fun a _ha => zero_lt_one, by simp⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 100,
"column": 4
} | {
"line": 100,
"column": 51
} | {
"line": 101,
"column": 2
} | [
{
"pp": "case inr.inl\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\na₀ : E\nha₀ : a₀ ∈ s\nht : Convex ℝ ∅\ndisj : Disjoint s ∅\n⊢ ∃ f u, (∀ a ∈ s, f a < u) ∧ ∀ b... | [] | exact ⟨0, 1, fun a _ha => zero_lt_one, by simp⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 464,
"column": 4
} | {
"line": 464,
"column": 64
} | {
"line": 464,
"column": 65
} | [
{
"pp": "F : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\nr s ε x : ℝ\nhx : x ∈ B f K r s ε\n⊢ ∃ L ∈ K, x ∈ A f L r ε ∧ x ∈ A f L s ε",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u_1\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nf : ℝ → F\nK : Set F\nr s ε x : ℝ\nhx : x ∈ B f K r s ε\n⊢ ∃ L ∈ K, x ∈ A f L r ε ∧ x ∈ A f L s ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.SeparatingDual | {
"line": 76,
"column": 15
} | {
"line": 76,
"column": 40
} | {
"line": 76,
"column": 41
} | [
{
"pp": "R : Type u_1\nV : Type u_2\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : TopologicalSpace V\ninst✝² : TopologicalSpace R\ninst✝¹ : Module R V\ninst✝ : SeparatingDual R V\nx y : V\nh : x ≠ y\nf : StrongDual R V\nhf : f (x - y) ≠ 0\n⊢ f x ≠ f y",
"ppTerm": "?m.43",
"assigned": true,
"us... | [
"R : Type u_1\nV : Type u_2\ninst✝⁵ : Ring R\ninst✝⁴ : AddCommGroup V\ninst✝³ : TopologicalSpace V\ninst✝² : TopologicalSpace R\ninst✝¹ : Module R V\ninst✝ : SeparatingDual R V\nx y : V\nh : x ≠ y\nf : StrongDual R V\nhf : f (x - y) ≠ 0\n⊢ ¬f x = f y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 164,
"column": 33
} | {
"line": 164,
"column": 52
} | {
"line": 164,
"column": 53
} | [
{
"pp": "E : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) t\nf : StrongDual ℝ E\nu : ℝ\nhfA : ∀ a ∈ interior s, f a < u\nhfB : ∀ b ∈ t,... | [
"E : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) t\nf : StrongDual ℝ E\nu : ℝ\nhfA : ∀ a ∈ interior s, f a < u\nhfB : ∀ b ∈ t, u ≤ f b\na ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 165,
"column": 33
} | {
"line": 165,
"column": 52
} | {
"line": 165,
"column": 53
} | [
{
"pp": "E : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) t\nf : StrongDual ℝ E\nu : ℝ\nhfA : ∀ a ∈ interior s, f a < u\nhfB : ∀ b ∈ t,... | [
"E : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) t\nf : StrongDual ℝ E\nu : ℝ\nhfA : ∀ a ∈ interior s, f a < u\nhfB : ∀ b ∈ t, u ≤ f b\na ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 75
} | {
"line": 168,
"column": 76
} | [
{
"pp": "case refine_2\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) t\nhsint : (interior s).Nonempty\nhtne : t.Nonempty\nf : Stron... | [
"case refine_2\nE : Type u_2\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup E\ninst✝² : Module ℝ E\ns t : Set E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul ℝ E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) t\nhsint : (interior s).Nonempty\nhtne : t.Nonempty\nf : StrongDual ℝ E\nu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.SeparatingDual | {
"line": 176,
"column": 23
} | {
"line": 176,
"column": 39
} | {
"line": 176,
"column": 40
} | [
{
"pp": "R : Type u_1\nV : Type u_2\ninst✝¹⁵ : Field R\ninst✝¹⁴ : AddCommGroup V\ninst✝¹³ : TopologicalSpace R\ninst✝¹² : TopologicalSpace V\ninst✝¹¹ : IsTopologicalRing R\ninst✝¹⁰ : Module R V\ninst✝⁹ : SeparatingDual R V\ninst✝⁸ : IsTopologicalAddGroup V\ninst✝⁷ : ContinuousSMul R V\nS : Type u_3\ninst✝⁶ : Co... | [
"R : Type u_1\nV : Type u_2\ninst✝¹⁵ : Field R\ninst✝¹⁴ : AddCommGroup V\ninst✝¹³ : TopologicalSpace R\ninst✝¹² : TopologicalSpace V\ninst✝¹¹ : IsTopologicalRing R\ninst✝¹⁰ : Module R V\ninst✝⁹ : SeparatingDual R V\ninst✝⁸ : IsTopologicalAddGroup V\ninst✝⁷ : ContinuousSMul R V\nS : Type u_3\ninst✝⁶ : CommSemiring S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.SeparatingDual | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 63
} | {
"line": 190,
"column": 64
} | [
{
"pp": "R : Type u_4\nV : Type u_5\nW : Type u_6\ninst✝¹³ : NormedField R\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : AddCommGroup W\ninst✝¹⁰ : TopologicalSpace R\ninst✝⁹ : TopologicalSpace V\ninst✝⁸ : TopologicalSpace W\ninst✝⁷ : IsTopologicalRing R\ninst✝⁶ : Module R V\ninst✝⁵ : Module R W\ninst✝⁴ : SeparatingDual ... | [
"R : Type u_4\nV : Type u_5\nW : Type u_6\ninst✝¹³ : NormedField R\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : AddCommGroup W\ninst✝¹⁰ : TopologicalSpace R\ninst✝⁹ : TopologicalSpace V\ninst✝⁸ : TopologicalSpace W\ninst✝⁷ : IsTopologicalRing R\ninst✝⁶ : Module R V\ninst✝⁵ : Module R W\ninst✝⁴ : SeparatingDual R V\ninst✝³ ... | ← ContinuousLinearMap.comp_assoc _ f.toContinuousLinearMap, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 221,
"column": 18
} | {
"line": 221,
"column": 29
} | {
"line": 221,
"column": 30
} | [
{
"pp": "E : Type u_2\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns✝ t✝ : Set E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝\nht₁ : Convex ℝ t✝\nht₂ : IsCompact t✝\ndisj : Disjoint s✝ t✝\nf : ... | [
"E : Type u_2\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns✝ t✝ : Set E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝\nht₁ : Convex ℝ t✝\nht₂ : IsCompact t✝\ndisj : Disjoint s✝ t✝\nf : StrongDual ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 221,
"column": 37
} | {
"line": 221,
"column": 48
} | {
"line": 221,
"column": 49
} | [
{
"pp": "E : Type u_2\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns✝ t✝ : Set E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝\nht₁ : Convex ℝ t✝\nht₂ : IsCompact t✝\ndisj : Disjoint s✝ t✝\nf : ... | [
"E : Type u_2\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns✝ t✝ : Set E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝\nht₁ : Convex ℝ t✝\nht₂ : IsCompact t✝\ndisj : Disjoint s✝ t✝\nf : StrongDual ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 221,
"column": 56
} | {
"line": 221,
"column": 67
} | {
"line": 221,
"column": 68
} | [
{
"pp": "E : Type u_2\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns✝ t✝ : Set E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝\nht₁ : Convex ℝ t✝\nht₂ : IsCompact t✝\ndisj : Disjoint s✝ t✝\nf : ... | [
"E : Type u_2\ninst✝⁵ : TopologicalSpace E\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ns✝ t✝ : Set E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul ℝ E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : IsClosed s✝\nht₁ : Convex ℝ t✝\nht₂ : IsCompact t✝\ndisj : Disjoint s✝ t✝\nf : StrongDual ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.SeparatingDual | {
"line": 194,
"column": 58
} | {
"line": 194,
"column": 74
} | {
"line": 194,
"column": 75
} | [
{
"pp": "R : Type u_4\nV : Type u_5\nW : Type u_6\ninst✝¹³ : NormedField R\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : AddCommGroup W\ninst✝¹⁰ : TopologicalSpace R\ninst✝⁹ : TopologicalSpace V\ninst✝⁸ : TopologicalSpace W\ninst✝⁷ : IsTopologicalRing R\ninst✝⁶ : Module R V\ninst✝⁵ : Module R W\ninst✝⁴ : SeparatingDual ... | [
"R : Type u_4\nV : Type u_5\nW : Type u_6\ninst✝¹³ : NormedField R\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : AddCommGroup W\ninst✝¹⁰ : TopologicalSpace R\ninst✝⁹ : TopologicalSpace V\ninst✝⁸ : TopologicalSpace W\ninst✝⁷ : IsTopologicalRing R\ninst✝⁶ : Module R V\ninst✝⁵ : Module R W\ninst✝⁴ : SeparatingDual R V\ninst✝³ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.SeparatingDual | {
"line": 195,
"column": 52
} | {
"line": 195,
"column": 79
} | {
"line": 195,
"column": 80
} | [
{
"pp": "R : Type u_4\nV : Type u_5\nW : Type u_6\ninst✝¹³ : NormedField R\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : AddCommGroup W\ninst✝¹⁰ : TopologicalSpace R\ninst✝⁹ : TopologicalSpace V\ninst✝⁸ : TopologicalSpace W\ninst✝⁷ : IsTopologicalRing R\ninst✝⁶ : Module R V\ninst✝⁵ : Module R W\ninst✝⁴ : SeparatingDual ... | [
"R : Type u_4\nV : Type u_5\nW : Type u_6\ninst✝¹³ : NormedField R\ninst✝¹² : AddCommGroup V\ninst✝¹¹ : AddCommGroup W\ninst✝¹⁰ : TopologicalSpace R\ninst✝⁹ : TopologicalSpace V\ninst✝⁸ : TopologicalSpace W\ninst✝⁷ : IsTopologicalRing R\ninst✝⁶ : Module R V\ninst✝⁵ : Module R W\ninst✝⁴ : SeparatingDual R V\ninst✝³ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 275,
"column": 2
} | {
"line": 275,
"column": 37
} | {
"line": 275,
"column": 38
} | [
{
"pp": "case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nht : Con... | [
"case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nht : Convex ℝ t\ndis... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 37
} | {
"line": 295,
"column": 38
} | [
{
"pp": "case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nht₁ : Co... | [
"case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs₁ : Convex ℝ s\nhs₂ : IsOpen s\nht₁ : Convex ℝ t\nht... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 305,
"column": 68
} | {
"line": 305,
"column": 79
} | {
"line": 305,
"column": 80
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoint (interior s) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 306,
"column": 4
} | {
"line": 306,
"column": 39
} | {
"line": 306,
"column": 40
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs : Convex ℝ s\nht : Convex ℝ t\nh... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.CompleteCodomain | {
"line": 64,
"column": 2
} | {
"line": 64,
"column": 83
} | {
"line": 65,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nF : Type u_3\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nι : Type u_4\ninst✝⁴ : Finite ι\nM : ι → Type u_5\ninst✝³ : (i : ι) → NormedAddCommGroup (M i)\ninst✝² : (i : ι) → NormedSpace 𝕜 (M i)\ninst✝¹ : ∀ (i : ι), SeparatingDual 𝕜 (M i... | [
"𝕜 : Type u_1\nF : Type u_3\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace 𝕜 F\nι : Type u_4\ninst✝⁴ : Finite ι\nM : ι → Type u_5\ninst✝³ : (i : ι) → NormedAddCommGroup (M i)\ninst✝² : (i : ι) → NormedSpace 𝕜 (M i)\ninst✝¹ : ∀ (i : ι), SeparatingDual 𝕜 (M i)\ninst✝ : C... | have : ∀ i, ∃ φ : StrongDual 𝕜 (M i), φ (m i) = 1 := fun i ↦ exists_eq_one (hm i) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 39
} | {
"line": 307,
"column": 40
} | [
{
"pp": "case refine_3\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs : Convex ℝ s\nht : Convex ℝ t\nh... | [
"case refine_3\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\ns t : Set E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nhs : Convex ℝ s\nht : Convex ℝ t\nhst : Disjoin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 333,
"column": 68
} | {
"line": 333,
"column": 79
} | {
"line": 333,
"column": 80
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\nx : E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nA : Set E\nhA : Convex ℝ A\nhxA : x ∉ interior A\nhAint ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\nx : E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nA : Set E\nhA : Convex ℝ A\nhxA : x ∉ interior A\nhAint : (interior ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 334,
"column": 4
} | {
"line": 334,
"column": 39
} | {
"line": 334,
"column": 40
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\nx : E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nA : Set E\nhA : Convex ℝ A\nhxA : x ∉ int... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module ℝ E\nx : E\ninst✝⁴ : RCLike 𝕜\ninst✝³ : Module 𝕜 E\ninst✝² : IsScalarTower ℝ 𝕜 E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nA : Set E\nhA : Convex ℝ A\nhxA : x ∉ interior A\nhAi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 344,
"column": 2
} | {
"line": 344,
"column": 54
} | {
"line": 344,
"column": 55
} | [
{
"pp": "case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns t : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Con... | [
"case h\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns t : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s\nhs₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 350,
"column": 18
} | {
"line": 350,
"column": 29
} | {
"line": 350,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns✝ t✝ : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns✝ t✝ : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 350,
"column": 37
} | {
"line": 350,
"column": 48
} | {
"line": 350,
"column": 49
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns✝ t✝ : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns✝ t✝ : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 512,
"column": 43
} | {
"line": 512,
"column": 75
} | {
"line": 512,
"column": 76
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f μ\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\ngcont : LowerSemicontinuous g\ng_integrabl... | [
"α : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f μ\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\ngcont : LowerSemicontinuous g\ng_integrable : Integrab... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 350,
"column": 56
} | {
"line": 350,
"column": 67
} | {
"line": 350,
"column": 68
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns✝ t✝ : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : TopologicalSpace E\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module ℝ E\ns✝ t✝ : Set E\ninst✝⁵ : RCLike 𝕜\ninst✝⁴ : Module 𝕜 E\ninst✝³ : IsScalarTower ℝ 𝕜 E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\nhs₁ : Convex ℝ s✝\nhs₂ : Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.Separation | {
"line": 399,
"column": 4
} | {
"line": 399,
"column": 60
} | {
"line": 399,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁹ : TopologicalSpace E\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module ℝ E\ns : Set E\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : ContinuousSMul 𝕜 E\ninst✝¹ : LocallyConvexSpace ℝ E\ninst✝ : Hereditari... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁹ : TopologicalSpace E\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : Module ℝ E\ns : Set E\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : ContinuousSMul 𝕜 E\ninst✝¹ : LocallyConvexSpace ℝ E\ninst✝ : HereditarilyLindelofSp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 518,
"column": 4
} | {
"line": 518,
"column": 54
} | {
"line": 518,
"column": 55
} | [
{
"pp": "case refine_4\nα : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f μ\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\ngcont : LowerSemicontinuous... | [
"case refine_4\nα : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f μ\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\ngcont : LowerSemicontinuous g\ng_integr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.VitaliCaratheodory | {
"line": 521,
"column": 4
} | {
"line": 521,
"column": 30
} | {
"line": 521,
"column": 31
} | [
{
"pp": "case refine_5\nα : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f μ\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\ngcont : LowerSemicontinuous... | [
"case refine_5\nα : Type u_1\ninst✝⁴ : TopologicalSpace α\ninst✝³ : MeasurableSpace α\ninst✝² : BorelSpace α\nμ : Measure α\ninst✝¹ : μ.WeaklyRegular\ninst✝ : SigmaFinite μ\nf : α → ℝ\nhf : Integrable f μ\nε : ℝ\nεpos : 0 < ε\ng : α → EReal\ng_lt_f : ∀ (x : α), ↑(-f x) < g x\ngcont : LowerSemicontinuous g\ng_integr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Order | {
"line": 41,
"column": 86
} | {
"line": 41,
"column": 96
} | {
"line": 41,
"column": 96
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nβ : Type u_3\ninst✝⁶ : UniformSpace β\ninst✝⁵ : AddGroup β\ninst✝⁴ : IsUniformAddGroup β\ninst✝³ : PartialOrder β\ninst✝² : OrderTopology β\ninst✝¹ : AddLeftMono β\ninst✝ : AddRightMono β\nf : ι → α → β\ng : α → β\nK : Set α\np : Filter ι\nu v : β\nhuv : u < v\nhg : ∀ x ∈ K,... | [] | simp [huv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.Algebra.IsUniformGroup.Order | {
"line": 41,
"column": 86
} | {
"line": 41,
"column": 96
} | {
"line": 41,
"column": 96
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nβ : Type u_3\ninst✝⁶ : UniformSpace β\ninst✝⁵ : AddGroup β\ninst✝⁴ : IsUniformAddGroup β\ninst✝³ : PartialOrder β\ninst✝² : OrderTopology β\ninst✝¹ : AddLeftMono β\ninst✝ : AddRightMono β\nf : ι → α → β\ng : α → β\nK : Set α\np : Filter ι\nu v : β\nhuv : u < v\nhg : ∀ x ∈ K,... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.IsUniformGroup.Order | {
"line": 41,
"column": 86
} | {
"line": 41,
"column": 96
} | {
"line": 41,
"column": 96
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nβ : Type u_3\ninst✝⁶ : UniformSpace β\ninst✝⁵ : AddGroup β\ninst✝⁴ : IsUniformAddGroup β\ninst✝³ : PartialOrder β\ninst✝² : OrderTopology β\ninst✝¹ : AddLeftMono β\ninst✝ : AddRightMono β\nf : ι → α → β\ng : α → β\nK : Set α\np : Filter ι\nu v : β\nhuv : u < v\nhg : ∀ x ∈ K,... | [] | simp [huv] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.IsUniformGroup.Order | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 13
} | {
"line": 44,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nβ : Type u_3\ninst✝⁶ : UniformSpace β\ninst✝⁵ : AddGroup β\ninst✝⁴ : IsUniformAddGroup β\ninst✝³ : PartialOrder β\ninst✝² : OrderTopology β\ninst✝¹ : AddLeftMono β\ninst✝ : AddRightMono β\nf : ι → α → β\ng : α → β\nK : Set α\np : Filter ι\nu v : β\nhuv : u < v\nhg : ∀ x ∈ K,... | [
"α : Type u_1\nι : Type u_2\nβ : Type u_3\ninst✝⁶ : UniformSpace β\ninst✝⁵ : AddGroup β\ninst✝⁴ : IsUniformAddGroup β\ninst✝³ : PartialOrder β\ninst✝² : OrderTopology β\ninst✝¹ : AddLeftMono β\ninst✝ : AddRightMono β\nf : ι → α → β\ng : α → β\nK : Set α\np : Filter ι\nu v : β\nhuv : u < v\nhg : ∀ x ∈ K, g x ≤ u\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 736,
"column": 6
} | {
"line": 736,
"column": 30
} | {
"line": 736,
"column": 31
} | [
{
"pp": "F : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nf : ℝ → F\ninst✝ : CompleteSpace F\nthis✝¹ : MeasurableSpace F := ⋯\nthis✝ : BorelSpace F\nt : Set ℝ\nt_count : t.Countable\nht : Dense t\nx : ℝ\n⊢ Ioi x ∩ closure t ⊆ closure (Ioi x ∩ t)",
"ppTerm": "?m.221",
"assigned": tr... | [
"F : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nf : ℝ → F\ninst✝ : CompleteSpace F\nthis✝¹ : MeasurableSpace F := borel F\nthis✝ : BorelSpace F\nt : Set ℝ\nt_count : t.Countable\nht : Dense t\nx : ℝ\n⊢ closure t ∩ Ioi x ⊆ closure (t ∩ Ioi x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap | {
"line": 267,
"column": 6
} | {
"line": 267,
"column": 75
} | {
"line": 267,
"column": 76
} | [
{
"pp": "case pos.refine_1.hfi\nX : Type u_1\nE : Type u_3\ninst✝² : MeasurableSpace X\nμ : Measure X\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : X → ℝ≥0\nf_meas : Measurable f\ng : X → E\nhE : CompleteSpace E\nhg : Integrable g (μ.withDensity fun x ↦ ↑(f x))\nc : E\ns : Set X\ns_meas : Measura... | [
"case pos.refine_1.hfi\nX : Type u_1\nE : Type u_3\ninst✝² : MeasurableSpace X\nμ : Measure X\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : X → ℝ≥0\nf_meas : Measurable f\ng : X → E\nhE : CompleteSpace E\nhg : Integrable g (μ.withDensity fun x ↦ ↑(f x))\nc : E\ns : Set X\ns_meas : MeasurableSet s\nhs... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 753,
"column": 2
} | {
"line": 753,
"column": 50
} | {
"line": 753,
"column": 51
} | [
{
"pp": "F : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nf : ℝ → F\ninst✝ : CompleteSpace F\n⊢ MeasurableSet {x | DifferentiableWithinAt ℝ f (Ioi x) x}",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
... | [
"F : Type u_1\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\nf : ℝ → F\ninst✝ : CompleteSpace F\n⊢ Measurable fun x ↦ DifferentiableWithinAt ℝ f (Ici x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.FDeriv.Measurable | {
"line": 758,
"column": 2
} | {
"line": 758,
"column": 38
} | {
"line": 758,
"column": 39
} | [
{
"pp": "F : Type u_1\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\nf : ℝ → F\ninst✝² : CompleteSpace F\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\n⊢ Measurable fun x ↦ derivWithin f (Ioi x) x",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
... | [
"F : Type u_1\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : NormedSpace ℝ F\nf : ℝ → F\ninst✝² : CompleteSpace F\ninst✝¹ : MeasurableSpace F\ninst✝ : BorelSpace F\n⊢ Measurable fun x ↦ derivWithin f (Ici x) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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