module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid | {
"line": 575,
"column": 4
} | {
"line": 575,
"column": 15
} | {
"line": 575,
"column": 16
} | [
{
"pp": "case hr\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nn : ℕ\ninst✝¹ : NeZero n\ninst✝ : CharZero k\ns : Simplex k P n\nhmem1 : s.medial.points 0 ∈ affineSpan k (Set.range s.medial.points)\nhmem2 : s.medial.poi... | [
"case hr\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : DivisionRing k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : AffineSpace V P\nn : ℕ\ninst✝¹ : NeZero n\ninst✝ : CharZero k\ns : Simplex k P n\nhmem1 : s.medial.points 0 ∈ affineSpan k (Set.range s.medial.points)\nhmem2 : s.medial.points 0 ∈ affi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional | {
"line": 598,
"column": 4
} | {
"line": 598,
"column": 75
} | {
"line": 599,
"column": 4
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\nh : Collinear k s\np₁ p₂ p₃ : P\nhp₂ : p₂ ∈ s\nhp₃ : p₃ ∈ s\nhp₂p₃ : p₂ ≠ p₃\n⊢ vectorSpan k (insert p₁ s) = vectorSpan k {p₁, p₂, p₃}",
"ppTerm": "?m... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝³ : DivisionRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\ns : Set P\nh : Collinear k s\np₁ p₂ p₃ : P\nhp₂ : p₂ ∈ s\nhp₃ : p₃ ∈ s\nhp₂p₃ : p₂ ≠ p₃\n⊢ vectorSpan k (insert p₁ s) = (affineSpan k (insert p₁ ↑line[k, p₂, p₃])).direction"
] | conv_rhs => rw [← direction_affineSpan, ← affineSpan_insert_affineSpan] | Mathlib.Tactic.Conv._aux_Mathlib_Tactic_Conv___macroRules_Mathlib_Tactic_Conv_convRHS_1 | Mathlib.Tactic.Conv.convRHS |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 105,
"column": 49
} | {
"line": 105,
"column": 60
} | {
"line": 105,
"column": 61
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ENNReal.toReal 0\n⊢ Summable fun x ↦ 1",
"ppTerm": "?m.72",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ENNReal.toReal 0\n⊢ Summable fun x ↦ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 108,
"column": 49
} | {
"line": 108,
"column": 60
} | {
"line": 108,
"column": 61
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ∞.toReal\n⊢ Summable fun x ↦ 1",
"ppTerm": "?m.110",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ∞.toReal\n⊢ Summable fun x ↦ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 15
} | {
"line": 109,
"column": 16
} | [
{
"pp": "case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ∞.toReal\nH : Summable fun x ↦ 1\n⊢ BddAbove (Set.range fun i ↦ ‖f i‖)",
"ppTerm": "?inr.inl",
"assigned": false,
"usedConstants": [],
"usedFVars": ... | [
"case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Summable fun i ↦ ‖f i‖ ^ ∞.toReal\nH : Summable fun x ↦ 1\n⊢ BddAbove (Set.range fun i ↦ ‖f i‖)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 211,
"column": 6
} | {
"line": 212,
"column": 13
} | {
"line": 212,
"column": 14
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ∞\nhf : ∀ (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 27
} | {
"line": 129,
"column": 28
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhp : 0 < p.toReal\nhp₁ : 0 < p\nhp₂ : p < ∞\nhf : Summable fun i ↦ ‖f i‖ ^ p.toReal\n⊢ ∀ (s : Finset α), ∑ i ∈ s, ‖f i‖ ^ p.toReal ≤ ∑' (i : α), ‖f i‖ ^ p.toReal",
"ppTerm": "?m.62",
"assign... | [
"α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhp : 0 < p.toReal\nhp₁ : 0 < p\nhp₂ : p < ∞\nhf : Summable fun i ↦ ‖f i‖ ^ p.toReal\n⊢ ∀ (s : Finset α), ∑ i ∈ s, ‖f i‖ ^ p.toReal ≤ ∑' (i : α), ‖f i‖ ^ p.toReal"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 201,
"column": 17
} | {
"line": 201,
"column": 28
} | {
"line": 201,
"column": 29
} | [
{
"pp": "α : Type u_3\nE : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nx : α → E\nhx : Memℓp x 1\n⊢ Summable fun a ↦ ‖x a‖",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_3\nE : Type u_5\ninst✝¹ : NormedAddCommGroup E\ninst✝ : CompleteSpace E\nx : α → E\nhx : Memℓp x 1\n⊢ Summable fun a ↦ ‖x a‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 15
} | {
"line": 208,
"column": 16
} | [
{
"pp": "case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f ∞\n⊢ BddAbove (Set.range fun i ↦ ‖(-f) i‖)",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"S... | [
"case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f ∞\n⊢ BddAbove (Set.range fun i ↦ ‖f i‖)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 210,
"column": 4
} | {
"line": 210,
"column": 15
} | {
"line": 210,
"column": 16
} | [
{
"pp": "case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f p\nhp : 0 < p.toReal\n⊢ Summable fun i ↦ ‖(-f) i‖ ^ p.toReal",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedA... | [
"case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f p\nhp : 0 < p.toReal\n⊢ Summable fun i ↦ ‖f i‖ ^ p.toReal"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 230,
"column": 27
} | {
"line": 230,
"column": 38
} | {
"line": 230,
"column": 39
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\np : ℝ≥0∞\nf : (i : α) → E i\nhp : 0 < p.toReal\nhfq : Memℓp f 0\nhpq : 0 ≤ p\ni : α\nhi : i ∉ ⋯.toFinset\n⊢ f i = 0",
"ppTerm": "?m.305",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\np : ℝ≥0∞\nf : (i : α) → E i\nhp : 0 < p.toReal\nhfq : Memℓp f 0\nhpq : 0 ≤ p\ni : α\nhi : i ∉ ⋯.toFinset\n⊢ f i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 239,
"column": 4
} | {
"line": 239,
"column": 57
} | {
"line": 240,
"column": 6
} | [
{
"pp": "case h\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nq : ℝ≥0∞\nf : (i : α) → E i\nhfq : Memℓp f q\nhq : 0 < q.toReal\nhpq : q ≤ ∞\nA : ℝ\nhA : A ∈ upperBounds (Set.range fun i ↦ ‖f i‖ ^ q.toReal)\ni : α\nthis : 0 ≤ ‖f i‖ ^ q.toReal\n⊢ (fun i ↦ ‖f i‖) i ≤ A ^ q.toReal⁻¹",
... | [
"case h\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nq : ℝ≥0∞\nf : (i : α) → E i\nhfq : Memℓp f q\nhq : 0 < q.toReal\nhpq : q ≤ ∞\nA : ℝ\nhA : A ∈ upperBounds (Set.range fun i ↦ ‖f i‖ ^ q.toReal)\ni : α\nthis : 0 ≤ ‖f i‖ ^ q.toReal\n⊢ ‖f i‖ ≤ A ^ q.toReal⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 245,
"column": 8
} | {
"line": 245,
"column": 19
} | {
"line": 245,
"column": 20
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\np q : ℝ≥0∞\nf : (i : α) → E i\nhfq : Memℓp f q\nhpq : q ≤ p\nhq : 0 < q.toReal\nleft✝ : 0 < p.toReal\nhpq' : q.toReal ≤ p.toReal\nhf' : Summable fun i ↦ ‖f i‖ ^ q.toReal\n⊢ {x | 1 ≤ ‖f x‖ ^ q.toReal}.Finite",
"ppTerm": "?m.... | [
"α : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\np q : ℝ≥0∞\nf : (i : α) → E i\nhfq : Memℓp f q\nhpq : q ≤ p\nhq : 0 < q.toReal\nleft✝ : 0 < p.toReal\nhpq' : q.toReal ≤ p.toReal\nhf' : Summable fun i ↦ ‖f i‖ ^ q.toReal\n⊢ {x | 1 ≤ ‖f x‖ ^ q.toReal}.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 240,
"column": 6
} | {
"line": 240,
"column": 51
} | {
"line": 240,
"column": 52
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ∞\nhf : ∀ (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 278,
"column": 6
} | {
"line": 278,
"column": 49
} | {
"line": 278,
"column": 50
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ∞\nhf : ∀ (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 500,
"column": 2
} | {
"line": 500,
"column": 35
} | {
"line": 501,
"column": 2
} | [
{
"pp": "case inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ ‖0‖ = 0",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"CharP.cast_eq_zero",
"Norm.norm",
"False",
"Real.partialOrder",
"Real",
"FloorRing.toFloorSemiring",
... | [
"case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\n⊢ ‖0‖ = 0",
"case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < p.toReal\n⊢ ‖0‖ = 0"
] | · simp [lp.norm_eq_card_dsupport] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Calculus.SmoothSeries | {
"line": 283,
"column": 4
} | {
"line": 283,
"column": 69
} | {
"line": 284,
"column": 4
} | [
{
"pp": "α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ... | [
"α : Type u_1\n𝕜 : Type u_3\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : IsRCLikeNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : CompleteSpace F\ninst✝ : NormedSpace 𝕜 F\nf : α → E → F\nv : ℕ → α → ℝ\nN : ℕ∞\nhf : ∀ (i... | refine contDiff_tsum (fun i => (hf i).of_le (mod_cast hm)) h'u ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 504,
"column": 4
} | {
"line": 504,
"column": 39
} | {
"line": 504,
"column": 40
} | [
{
"pp": "case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < p.toReal\nhp' : 1 / p.toReal ≠ 0\n⊢ (∑' (i : α), ‖↑0 i‖ ^ p.toReal) ^ (1 / p.toReal) = 0",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr... | [
"case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nhp : 0 < p.toReal\nhp' : 1 / p.toReal ≠ 0\n⊢ 0 ^ p.toReal⁻¹ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 539,
"column": 4
} | {
"line": 539,
"column": 56
} | {
"line": 539,
"column": 57
} | [
{
"pp": "case inr.inl.inr\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nh✝ : Nonempty α\n⊢ IsLUB (Set.range fun i ↦ ‖↑(-f) i‖) ‖f‖",
"ppTerm": "?inr.inl.inr",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
... | [
"case inr.inl.inr\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nh✝ : Nonempty α\n⊢ IsLUB (Set.range fun i ↦ ‖↑f i‖) ‖f‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 543,
"column": 4
} | {
"line": 543,
"column": 63
} | {
"line": 543,
"column": 64
} | [
{
"pp": "case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E p)\nhp : 0 < p.toReal\n⊢ HasSum (fun i ↦ ‖↑(-f) i‖ ^ p.toReal) (‖f‖ ^ p.toReal)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Norm.norm",
"SeminormedAdd... | [
"case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E p)\nhp : 0 < p.toReal\n⊢ HasSum (fun i ↦ ‖↑f i‖ ^ p.toReal) (‖f‖ ^ p.toReal)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 167,
"column": 33
} | {
"line": 167,
"column": 73
} | {
"line": 167,
"column": 74
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\nf' : ι → E → E →L[𝕜] G\nx : E\n... | [
"ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\nf' : ι → E → E →L[𝕜] G\nx : E\nhf : ∀ᶠ (n :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Ball.Homeomorph | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 40
} | {
"line": 149,
"column": 41
} | [
{
"pp": "E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nP : Type u_2\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor E P\nc : P\nr : ℝ\nthis : 0 ∈ (univBall c r).source\n⊢ ↑(univBall c r).symm c = 0",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"... | [
"E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nP : Type u_2\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor E P\nc : P\nr : ℝ\nthis : 0 ∈ (univBall c r).source\n⊢ ↑(univBall c r).symm c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Ball.Homeomorph | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 33
} | {
"line": 153,
"column": 34
} | [
{
"pp": "E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nP : Type u_2\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor E P\nc : P\nr : ℝ\n⊢ Continuous ↑(univBall c r)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [... | [
"E : Type u_1\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : NormedSpace ℝ E\nP : Type u_2\ninst✝¹ : PseudoMetricSpace P\ninst✝ : NormedAddTorsor E P\nc : P\nr : ℝ\n⊢ Continuous ↑(univBall c r)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 631,
"column": 4
} | {
"line": 631,
"column": 28
} | {
"line": 631,
"column": 29
} | [
{
"pp": "case inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nC : ℝ\nhC : 0 ≤ C\nhCf : ∀ (i : α), ‖↑f i‖ ≤ C\nh✝ : IsEmpty α\n⊢ ‖f‖ ≤ C",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
... | [
"case inl\nα : Type u_3\nE : α → Type u_4\ninst✝ : (i : α) → NormedAddCommGroup (E i)\nf : ↥(lp E ∞)\nC : ℝ\nhC : 0 ≤ C\nhCf : ∀ (i : α), ‖↑f i‖ ≤ C\nh✝ : IsEmpty α\n⊢ 0 ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 683,
"column": 46
} | {
"line": 683,
"column": 57
} | {
"line": 683,
"column": 58
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np q : ℝ≥0∞\ninst✝⁶ : (i : α) → NormedAddCommGroup (E i)\ninst✝⁵ : NormedRing 𝕜\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : (i : α) → Module 𝕜 (E i)\ninst✝² : (i : α) → Module 𝕜' (E i)\ninst✝¹ : ∀ (i : α), IsBoundedSMul 𝕜 (E i)\ninst✝ : ∀ (i : α)... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np q : ℝ≥0∞\ninst✝⁶ : (i : α) → NormedAddCommGroup (E i)\ninst✝⁵ : NormedRing 𝕜\ninst✝⁴ : NormedRing 𝕜'\ninst✝³ : (i : α) → Module 𝕜 (E i)\ninst✝² : (i : α) → Module 𝕜' (E i)\ninst✝¹ : ∀ (i : α), IsBoundedSMul 𝕜 (E i)\ninst✝ : ∀ (i : α), IsBoundedS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 214,
"column": 29
} | {
"line": 214,
"column": 60
} | {
"line": 214,
"column": 61
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\nf' : ι → E → E →L[𝕜] G\nx : E\n... | [
"ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : IsRCLikeNormedField 𝕜\ninst✝² : NormedSpace 𝕜 E\nG : Type u_4\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : ι → E → G\nf' : ι → E → E →L[𝕜] G\nx : E\nr : ℝ\nhf : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 742,
"column": 68
} | {
"line": 742,
"column": 79
} | {
"line": 742,
"column": 80
} | [
{
"pp": "α : Type u_3\nE : Type u_5\ninst✝ : NormedAddCommGroup E\nf : ↥(lp (fun x ↦ E) 1)\n⊢ Summable fun a ↦ ‖‖↑f a‖‖",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"congrArg",
"Sum... | [
"α : Type u_3\nE : Type u_5\ninst✝ : NormedAddCommGroup E\nf : ↥(lp (fun x ↦ E) 1)\n⊢ Summable fun a ↦ ‖↑f a‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 755,
"column": 34
} | {
"line": 755,
"column": 45
} | {
"line": 755,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf g : ↥(lp (fun x ↦ E) 1)\n⊢ Summabl... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf g : ↥(lp (fun x ↦ E) 1)\n⊢ Summable fun a ↦ ‖↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 755,
"column": 74
} | {
"line": 755,
"column": 85
} | {
"line": 755,
"column": 86
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf g : ↥(lp (fun x ↦ E) 1)\n⊢ Summabl... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf g : ↥(lp (fun x ↦ E) 1)\n⊢ Summable fun a ↦ ‖↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 758,
"column": 55
} | {
"line": 758,
"column": 66
} | {
"line": 758,
"column": 67
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nc : 𝕜\nf : ↥(lp (fun x ↦ E) 1)\n⊢ S... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nc : 𝕜\nf : ↥(lp (fun x ↦ E) 1)\n⊢ Summable fun ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 759,
"column": 18
} | {
"line": 759,
"column": 29
} | {
"line": 759,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf : ↥(lp (fun x ↦ E) 1)\n⊢ ‖{ toFun ... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE✝ : α → Type u_4\np q : ℝ≥0∞\ninst✝⁵ : (i : α) → NormedAddCommGroup (E✝ i)\nE : Type u_5\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedRing 𝕜\ninst✝² : Module 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : CompleteSpace E\nf : ↥(lp (fun x ↦ E) 1)\n⊢ ‖∑' (i : α), ↑f i‖ ≤ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 794,
"column": 4
} | {
"line": 794,
"column": 15
} | {
"line": 794,
"column": 16
} | [
{
"pp": "case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : (i : α) → StarAddMonoid (E i)\ninst✝ : ∀ (i : α), NormedStarGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f ∞\n⊢ BddAbove (Set.range fun i ↦ ‖star f i‖)",
"ppTerm": "?inr.inl",
"assigned": true,
... | [
"case inr.inl\nα : Type u_3\nE : α → Type u_4\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : (i : α) → StarAddMonoid (E i)\ninst✝ : ∀ (i : α), NormedStarGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f ∞\n⊢ BddAbove (Set.range fun i ↦ ‖f i‖)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 796,
"column": 4
} | {
"line": 796,
"column": 15
} | {
"line": 796,
"column": 16
} | [
{
"pp": "case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : (i : α) → StarAddMonoid (E i)\ninst✝ : ∀ (i : α), NormedStarGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f p\nhp : 0 < p.toReal\n⊢ Summable fun i ↦ ‖star f i‖ ^ p.toReal",
"ppTerm": "?inr.inr... | [
"case inr.inr\nα : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : (i : α) → StarAddMonoid (E i)\ninst✝ : ∀ (i : α), NormedStarGroup (E i)\nf : (i : α) → E i\nhf : Memℓp f p\nhp : 0 < p.toReal\n⊢ Summable fun i ↦ ‖f i‖ ^ p.toReal"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 892,
"column": 24
} | {
"line": 896,
"column": 66
} | {
"line": 898,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np q : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\nI : Type u_5\nB : I → Type u_6\ninst✝³ : (i : I) → NonUnitalNormedRing (B i)\ninst✝² : (i : I) → StarRing (B i)\ninst✝¹ : ∀ (i : I), NormedStarGroup (B i)\ninst✝ : ∀ (i : I), CStarRin... | [] | by
rw [← sq, ← Real.le_sqrt (norm_nonneg _) (norm_nonneg _)]
refine lp.norm_le_of_forall_le ‖star f * f‖.sqrt_nonneg fun i => ?_
rw [Real.le_sqrt (norm_nonneg _) (norm_nonneg _), sq, ← CStarRing.norm_star_mul_self]
exact lp.norm_apply_le_norm ENNReal.top_ne_zero (star f * f) i | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1094,
"column": 2
} | {
"line": 1094,
"column": 39
} | {
"line": 1094,
"column": 40
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\nhp : 0 < p.toReal\nf : (i : α) → E i\ns : Finset α\nh : ∀ i ∉ s, ‖if i ∈ s then f i else 0‖ ^ p.toReal = 0\nh' : ∀ i ∈ s, ‖f i‖ ^ p.toReal = ‖if i ∈ s then f i else 0‖ ^ p.toReal\n⊢ HasSum (fun... | [
"α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\nhp : 0 < p.toReal\nf : (i : α) → E i\ns : Finset α\nh : ∀ i ∉ s, ‖if i ∈ s then f i else 0‖ ^ p.toReal = 0\nh' : ∀ i ∈ s, ‖f i‖ ^ p.toReal = ‖if i ∈ s then f i else 0‖ ^ p.toReal\n⊢ HasSum (fun i ↦ ‖if i ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1110,
"column": 39
} | {
"line": 1110,
"column": 50
} | {
"line": 1110,
"column": 51
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np✝ : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\ni : α\nx : E i\nthis : Nonempty α\np : ℝ≥0\nhp : 0 < ↑p\n⊢ 0 < (↑p).toReal",
"ppTerm": "?m.119",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"ENNReal.o... | [
"α : Type u_3\nE : α → Type u_4\np✝ : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\ni : α\nx : E i\nthis : Nonempty α\np : ℝ≥0\nhp : 0 < ↑p\n⊢ 0 < p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1152,
"column": 6
} | {
"line": 1153,
"column": 38
} | {
"line": 1153,
"column": 39
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\nhp : 0 < p.toReal\nf : ↥(lp E p)\ns : Finset α\nF : α → ℝ := fun i ↦ ‖↑f i‖ ^ p.toReal - ‖↑(f - ∑ i ∈ s, lp.single p i (↑f i)) i‖ ^ p.toReal\ni : α\nhi : i ∉ s\nthis : ‖↑f i‖ ^ p.toReal - ‖↑f i... | [
"α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\ninst✝ : DecidableEq α\nhp : 0 < p.toReal\nf : ↥(lp E p)\ns : Finset α\nF : α → ℝ := fun i ↦ ‖↑f i‖ ^ p.toReal - ‖↑(f - ∑ i ∈ s, lp.single p i (↑f i)) i‖ ^ p.toReal\ni : α\nhi : i ∉ s\nthis : ‖↑f i‖ ^ p.toReal - ‖↑f i - if i ∈ s ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1183,
"column": 4
} | {
"line": 1184,
"column": 38
} | {
"line": 1184,
"column": 39
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : DecidableEq α\ninst✝ : Fact (1 ≤ p)\nhp : p ≠ ∞\nf : ↥(lp E p)\nhp₀ : 0 < p\nhp' : 0 < p.toReal\nthis :\n ∀ ε > 0,\n ∀ᶠ (x : Finset α) in (SummationFilter.unconditional α).filter,\n dist (∑ b ∈ x, ‖... | [
"α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝² : (i : α) → NormedAddCommGroup (E i)\ninst✝¹ : DecidableEq α\ninst✝ : Fact (1 ≤ p)\nhp : p ≠ ∞\nf : ↥(lp E p)\nhp₀ : 0 < p\nhp' : 0 < p.toReal\nthis :\n ∀ ε > 0,\n ∀ᶠ (x : Finset α) in (SummationFilter.unconditional α).filter,\n dist (∑ b ∈ x, ‖↑f b‖ ^ p.to... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1268,
"column": 4
} | {
"line": 1268,
"column": 54
} | {
"line": 1268,
"column": 55
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np✝ q✝ : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\ninst✝³ : NormedRing 𝕜\ninst✝² : (i : α) → Module 𝕜 (E i)\ninst✝¹ : ∀ (i : α), IsBoundedSMul 𝕜 (E i)\np q r : ℝ≥0∞\ninst✝ : Fact (1 ≤ p)\ni : α\nx : ↥(lp E p)\nhp : p ≠ 0\n⊢ ‖(eva... | [
"𝕜 : Type u_1\n𝕜' : Type u_2\nα : Type u_3\nE : α → Type u_4\np✝ q✝ : ℝ≥0∞\ninst✝⁴ : (i : α) → NormedAddCommGroup (E i)\ninst✝³ : NormedRing 𝕜\ninst✝² : (i : α) → Module 𝕜 (E i)\ninst✝¹ : ∀ (i : α), IsBoundedSMul 𝕜 (E i)\np q r : ℝ≥0∞\ninst✝ : Fact (1 ≤ p)\ni : α\nx : ↥(lp E p)\nhp : p ≠ 0\n⊢ ‖↑x i‖ ≤ ‖x‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Lp.lpSpace | {
"line": 1303,
"column": 4
} | {
"line": 1303,
"column": 13
} | {
"line": 1304,
"column": 4
} | [
{
"pp": "α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_5\nl : Filter ι\ninst✝ : l.NeBot\n_i : Fact (1 ≤ p)\nhp : p ≠ ∞\nC : ℝ\nF : ι → ↥(lp E p)\nhCF : ∀ᶠ (k : ι) in l, ‖F k‖ ≤ C\nf : (a : α) → E a\nhf : Tendsto (id fun i ↦ ↑(F i)) l (𝓝 f)\ns : Finset α\nhp' ... | [
"α : Type u_3\nE : α → Type u_4\np : ℝ≥0∞\ninst✝¹ : (i : α) → NormedAddCommGroup (E i)\nι : Type u_5\nl : Filter ι\ninst✝ : l.NeBot\n_i : Fact (1 ≤ p)\nhp : p ≠ ∞\nC : ℝ\nF : ι → ↥(lp E p)\nhCF : ∀ᶠ (k : ι) in l, ‖F k‖ ≤ C\nf : (a : α) → E a\nhf : Tendsto (id fun i ↦ ↑(F i)) l (𝓝 f)\ns : Finset α\nhp' : p ≠ 0\nhp'... | intro a _ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Analysis.SpecialFunctions.PolynomialExp | {
"line": 32,
"column": 20
} | {
"line": 33,
"column": 9
} | {
"line": 33,
"column": 10
} | [
{
"pp": "case monomial\nn : ℕ\nc : ℝ\n⊢ Tendsto (fun x ↦ eval x ((monomial n) c) / rexp x) atTop (𝓝 0)",
"ppTerm": "?monomial",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"S... | [
"case monomial\nn : ℕ\nc : ℝ\n⊢ Tendsto (fun x ↦ c * (x ^ n * (rexp x)⁻¹)) atTop (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.PolynomialExp | {
"line": 34,
"column": 21
} | {
"line": 34,
"column": 42
} | {
"line": 34,
"column": 43
} | [
{
"pp": "case add\np q : ℝ[X]\nhp : Tendsto (fun x ↦ eval x p / rexp x) atTop (𝓝 0)\nhq : Tendsto (fun x ↦ eval x q / rexp x) atTop (𝓝 0)\n⊢ Tendsto (fun x ↦ eval x (p + q) / rexp x) atTop (𝓝 0)",
"ppTerm": "?add",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
... | [
"case add\np q : ℝ[X]\nhp : Tendsto (fun x ↦ eval x p / rexp x) atTop (𝓝 0)\nhq : Tendsto (fun x ↦ eval x q / rexp x) atTop (𝓝 0)\n⊢ Tendsto (fun x ↦ eval x p / rexp x + eval x q / rexp x) atTop (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.PolynomialExp | {
"line": 30,
"column": 93
} | {
"line": 34,
"column": 52
} | {
"line": 36,
"column": 0
} | [
{
"pp": "p : ℝ[X]\n⊢ Tendsto (fun x ↦ eval x p / rexp x) atTop (𝓝 0)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCo... | [] | by
induction p using Polynomial.induction_on' with
| monomial n c => simpa [exp_neg, div_eq_mul_inv, mul_assoc]
using tendsto_const_nhds.mul (tendsto_pow_mul_exp_neg_atTop_nhds_zero n)
| add p q hp hq => simpa [add_div] using hp.add hq | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.SmoothTransition | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 20
} | {
"line": 95,
"column": 2
} | [
{
"pp": "p : ℝ[X]\n⊢ Tendsto (fun x ↦ Polynomial.eval x⁻¹ p * rexp (-x⁻¹)) (𝓝 0 ⊓ 𝓟 {x | ¬x ≤ 0}) (𝓝 0)",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"Real.instLE",
"Real",
"Preorder.toLT",
"HMul.hMul",
"Real.instZ... | [
"p : ℝ[X]\n⊢ Tendsto (fun x ↦ Polynomial.eval x⁻¹ p * rexp (-x⁻¹)) (𝓝 0 ⊓ 𝓟 {x | 0 < x}) (𝓝 0)"
] | simp only [not_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 107,
"column": 2
} | {
"line": 107,
"column": 13
} | {
"line": 107,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nf' g' : E\ns : Set ℝ\nx : ℝ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\n⊢ HasDerivWithinAt (fun t ↦ ⟪f t, g t⟫) (⟪f x, g'⟫ + ⟪f', g... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nf' g' : E\ns : Set ℝ\nx : ℝ\nhf : HasDerivWithinAt f f' s x\nhg : HasDerivWithinAt g g' s x\n⊢ HasDerivWithinAt (fun t ↦ ⟪f t, g t⟫) (⟪f x, g'⟫ + ⟪f', g x⟫) s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 44
} | {
"line": 112,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nf' g' : E\nx : ℝ\n⊢ HasDerivAt f f' x → HasDerivAt g g' x → HasDerivAt (fun t ↦ ⟪f t, g t⟫) (⟪f x, g'⟫ + ⟪f', g x⟫) x",
"ppTerm": "?m.63",
"assi... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nf g : ℝ → E\nf' g' : E\nx : ℝ\n⊢ HasDerivWithinAt f f' Set.univ x →\n HasDerivWithinAt g g' Set.univ x → HasDerivWithinAt (fun t ↦ ⟪f t, g t⟫) (⟪f x, g'⟫ + ⟪f', g x⟫) Set.uni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 45
} | {
"line": 156,
"column": 46
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nn : WithTop ℕ∞\nx : E\nhx : x ≠ 0\nthis : ‖id x‖ ^ 2 ≠ 0\n⊢ ContDiffAt ℝ n Norm.norm x",
"ppTerm": "?m.76",
"assigned": false,
"usedConstants": [],
"... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : NormedSpace ℝ E\nn : WithTop ℕ∞\nx : E\nhx : x ≠ 0\nthis : ‖id x‖ ^ 2 ≠ 0\n⊢ ContDiffAt ℝ n Norm.norm x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 217,
"column": 2
} | {
"line": 217,
"column": 13
} | {
"line": 217,
"column": 14
} | [
{
"pp": "F : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nf : ℝ → F\nf' : F\nx : ℝ\nhf : HasDerivAt f f' x\n⊢ HasDerivAt (fun x ↦ ‖f x‖ ^ 2) (2 * ⟪f x, f'⟫) x",
"ppTerm": "?m.75",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nf : ℝ → F\nf' : F\nx : ℝ\nhf : HasDerivAt f f' x\n⊢ HasDerivAt (fun x ↦ ‖f x‖ ^ 2) (2 * ⟪f x, f'⟫) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Calculus | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 13
} | {
"line": 226,
"column": 14
} | [
{
"pp": "F : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nf : ℝ → F\nf' : F\ns : Set ℝ\nx : ℝ\nhf : HasDerivWithinAt f f' s x\n⊢ HasDerivWithinAt (fun x ↦ ‖f x‖ ^ 2) (2 * ⟪f x, f'⟫) s x",
"ppTerm": "?m.75",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"F : Type u_3\ninst✝¹ : NormedAddCommGroup F\ninst✝ : InnerProductSpace ℝ F\nf : ℝ → F\nf' : F\ns : Set ℝ\nx : ℝ\nhf : HasDerivWithinAt f f' s x\n⊢ HasDerivWithinAt (fun x ↦ ‖f x‖ ^ 2) (2 * ⟪f x, f'⟫) s x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.SmoothTransition | {
"line": 140,
"column": 2
} | {
"line": 140,
"column": 13
} | {
"line": 140,
"column": 14
} | [
{
"pp": "n : ℕ∞\n⊢ ContDiff ℝ (↑n) expNegInvGlue",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ∞\n⊢ ContDiff ℝ (↑n) expNegInvGlue"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.SmoothTransition | {
"line": 203,
"column": 4
} | {
"line": 203,
"column": 42
} | {
"line": 203,
"column": 43
} | [
{
"pp": "case inr\nx : ℝ\nhx : x < 1\n⊢ x.smoothTransition = 1 ↔ 1 ≤ x",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Real.instLE",
"Real",
"Preorder.toLT",
"eq_false",
"congrArg",
"PartialOrder.toPreorder",
"id",
... | [
"case inr\nx : ℝ\nhx : x < 1\n⊢ x < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 116,
"column": 8
} | {
"line": 116,
"column": 74
} | {
"line": 116,
"column": 75
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α → ℝ\ns : ... | [
"α : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α → ℝ\ns : Set H\nF' : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 112,
"column": 4
} | {
"line": 118,
"column": 34
} | {
"line": 119,
"column": 2
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α... | [] | rcases subsingleton_or_nontrivial H with hH | hH
· have : Subsingleton (H →L[𝕜] E) := inferInstance
convert! hasFDerivAt_of_subsingleton _ x₀
· have : ¬(CompleteSpace (H →L[𝕜] E)) := by
simpa [SeparatingDual.completeSpace_continuousLinearMap_iff] using hE
simp only [integral, hE, ↓reduceDI... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 112,
"column": 4
} | {
"line": 118,
"column": 34
} | {
"line": 119,
"column": 2
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α... | [] | rcases subsingleton_or_nontrivial H with hH | hH
· have : Subsingleton (H →L[𝕜] E) := inferInstance
convert! hasFDerivAt_of_subsingleton _ x₀
· have : ¬(CompleteSpace (H →L[𝕜] E)) := by
simpa [SeparatingDual.completeSpace_continuousLinearMap_iff] using hE
simp only [integral, hE, ↓reduceDI... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Convolution | {
"line": 215,
"column": 6
} | {
"line": 215,
"column": 35
} | {
"line": 216,
"column": 4
} | [
{
"pp": "case refine_1.hy\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedAddCommGroup E'\ninst✝⁸ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NormedSpace 𝕜 E\ninst✝⁵ : NormedSpace 𝕜 E'\ninst✝⁴... | [] | rwa [neg_sub, sub_add_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.Analysis.Convolution | {
"line": 302,
"column": 2
} | {
"line": 317,
"column": 74
} | {
"line": 319,
"column": 0
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup E'\ninst✝⁹ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedSpace 𝕜 E'\ninst✝⁵ : NormedSpace 𝕜... | [] | let u := (Homeomorph.neg G).trans (Homeomorph.addRight x₀)
let v := (Homeomorph.neg G).trans (Homeomorph.addLeft x₀)
apply ((u.isCompact_preimage.mpr h).bddAbove_image hg.norm.continuousOn).convolutionExistsAt' L
isClosed_closure.measurableSet subset_closure (hf.integrableOn_isCompact h)
have A : AEStronglyMe... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Convolution | {
"line": 302,
"column": 2
} | {
"line": 317,
"column": 74
} | {
"line": 319,
"column": 0
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedAddCommGroup E'\ninst✝⁹ : NormedAddCommGroup F\nf : G → E\ng : G → E'\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedSpace 𝕜 E'\ninst✝⁵ : NormedSpace 𝕜... | [] | let u := (Homeomorph.neg G).trans (Homeomorph.addRight x₀)
let v := (Homeomorph.neg G).trans (Homeomorph.addLeft x₀)
apply ((u.isCompact_preimage.mpr h).bddAbove_image hg.norm.continuousOn).convolutionExistsAt' L
isClosed_closure.measurableSet subset_closure (hf.integrableOn_isCompact h)
have A : AEStronglyMe... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 381,
"column": 51
} | {
"line": 381,
"column": 77
} | {
"line": 381,
"column": 78
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜... | [
"ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convolution | {
"line": 557,
"column": 6
} | {
"line": 557,
"column": 67
} | {
"line": 557,
"column": 68
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace 𝕜 F\nL : E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 406,
"column": 2
} | {
"line": 406,
"column": 42
} | {
"line": 406,
"column": 43
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜... | [
"ι : Type u_1\nl : Filter ι\nE : Type u_2\ninst✝⁶ : NormedAddCommGroup E\n𝕜 : Type u_3\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : IsRCLikeNormedField 𝕜\ninst✝³ : NormedSpace 𝕜 E\nG : Type u_4\ninst✝² : NormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\nf : ι → E → G\ng : E → G\nf' : ι → E → E →L[𝕜] G\ng' : E ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 13
} | {
"line": 456,
"column": 14
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nG : Type u_3\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf' : ι → 𝕜 → G\nl' : Filter 𝕜\nhf' : UniformCauchySeqOnFilter f' l l'\nu : Set ((𝕜 →L[𝕜] G) × (𝕜 →L[𝕜] G))\nhu : u ∈ uniformity (𝕜 →L[𝕜] G)\n⊢ ∀... | [
"ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\nG : Type u_3\ninst✝¹ : NormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf' : ι → 𝕜 → G\nl' : Filter 𝕜\nhf' : UniformCauchySeqOnFilter f' l l'\nu : Set ((𝕜 →L[𝕜] G) × (𝕜 →L[𝕜] G))\nhu : u ∈ uniformity (𝕜 →L[𝕜] G)\n⊢ ∀ᶠ (m : (ι × ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.UniformLimitsDeriv | {
"line": 497,
"column": 2
} | {
"line": 497,
"column": 42
} | {
"line": 497,
"column": 43
} | [
{
"pp": "ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nf : ι → 𝕜 → G\ng : 𝕜 → G\nf' : ι → 𝕜 → G\ng' : 𝕜 → G\nx : 𝕜\ninst✝¹ : IsRCLikeNormedField 𝕜\ninst✝ : l.NeBot\ns : Set 𝕜\nhs : IsOpen[PseudoMetri... | [
"ι : Type u_1\nl : Filter ι\n𝕜 : Type u_2\ninst✝⁴ : NontriviallyNormedField 𝕜\nG : Type u_3\ninst✝³ : NormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nf : ι → 𝕜 → G\ng : 𝕜 → G\nf' : ι → 𝕜 → G\ng' : 𝕜 → G\nx : 𝕜\ninst✝¹ : IsRCLikeNormedField 𝕜\ninst✝ : l.NeBot\ns : Set 𝕜\nhs : IsOpen[PseudoMetricSpace.toUni... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ParametricIntegral | {
"line": 225,
"column": 4
} | {
"line": 226,
"column": 77
} | {
"line": 227,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α → ℝ\ns : ... | [
"α : Type u_1\ninst✝⁶ : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_2\ninst✝⁵ : RCLike 𝕜\nE : Type u_3\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\ninst✝² : NormedSpace 𝕜 E\nH : Type u_4\ninst✝¹ : NormedAddCommGroup H\ninst✝ : NormedSpace 𝕜 H\nF : H → α → E\nx₀ : H\nbound : α → ℝ\ns : Set H\nF' : ... | refine (convex_ball _ _).lipschitzOnWith_of_nnnorm_hasFDerivWithin_le
(fun x x_in ↦ (ha_deriv x (hε x_in)).hasFDerivWithinAt) fun x x_in ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Convolution | {
"line": 582,
"column": 21
} | {
"line": 582,
"column": 32
} | {
"line": 582,
"column": 33
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace 𝕜 F\nL : E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 162,
"column": 2
} | {
"line": 162,
"column": 29
} | {
"line": 162,
"column": 30
} | [
{
"pp": "F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ng : ℝ → F\na : ℝ\n⊢ ∫ (x : ℝ), g (x * a) = |a⁻¹| • ∫ (y : ℝ), g y",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
... | [
"F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ng : ℝ → F\na : ℝ\n⊢ ∫ (x : ℝ), g (a * x) = |a⁻¹| • ∫ (y : ℝ), g y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 166,
"column": 2
} | {
"line": 166,
"column": 29
} | {
"line": 166,
"column": 30
} | [
{
"pp": "F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ng : ℝ → F\na : ℝ\n⊢ ∫ (x : ℝ), g (x * a⁻¹) = |a| • ∫ (y : ℝ), g y",
"ppTerm": "?m.43",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u_2\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\ng : ℝ → F\na : ℝ\n⊢ ∫ (x : ℝ), g (x * a⁻¹) = |a| • ∫ (y : ℝ), g y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 181,
"column": 4
} | {
"line": 183,
"column": 49
} | {
"line": 185,
"column": 2
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\nthis : ∀ {g : E → F}, Integrabl... | [] | refine ⟨fun hf => ?_, fun hf => this hf hR⟩
convert! this hf (inv_ne_zero hR)
rw [← mul_smul, mul_inv_cancel₀ hR, one_smul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 181,
"column": 4
} | {
"line": 183,
"column": 49
} | {
"line": 185,
"column": 2
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\nthis : ∀ {g : E → F}, Integrabl... | [] | refine ⟨fun hf => ?_, fun hf => this hf hR⟩
convert! this hf (inv_ne_zero hR)
rw [← mul_smul, mul_inv_cancel₀ hR, one_smul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 64
} | {
"line": 189,
"column": 65
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\ng : E → F\nhg : Integrable g μ\... | [
"F : Type u_1\ninst✝⁶ : NormedAddCommGroup F\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nf : E → F\nR : ℝ\nhR : R ≠ 0\ng : E → F\nhg : Integrable g μ\nS : ℝ\nhS :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 32
} | {
"line": 198,
"column": 33
} | [
{
"pp": "F : Type u_1\ninst✝ : NormedAddCommGroup F\ng : ℝ → F\nR : ℝ\nhR : R ≠ 0\n⊢ Integrable (fun x ↦ g (R * x)) volume ↔ Integrable g volume",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"F : Type u_1\ninst✝ : NormedAddCommGroup F\ng : ℝ → F\nR : ℝ\nhR : R ≠ 0\n⊢ Integrable (fun x ↦ g (R * x)) volume ↔ Integrable g volume"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.NormedSpace | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 29
} | {
"line": 206,
"column": 30
} | [
{
"pp": "F : Type u_1\ninst✝ : NormedAddCommGroup F\ng : ℝ → F\nR : ℝ\nhR : R ≠ 0\n⊢ Integrable (fun x ↦ g (x * R)) volume ↔ Integrable g volume",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
... | [
"F : Type u_1\ninst✝ : NormedAddCommGroup F\ng : ℝ → F\nR : ℝ\nhR : R ≠ 0\n⊢ Integrable (fun x ↦ g (R * x)) volume ↔ Integrable g volume"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Metrizable.Urysohn | {
"line": 42,
"column": 2
} | {
"line": 42,
"column": 54
} | {
"line": 43,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : RegularSpace X\ninst✝ : SecondCountableTopology X\n⊢ ∃ f, IsInducing f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Real",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceNat",
"Membership.mem... | [
"X : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : RegularSpace X\ninst✝ : SecondCountableTopology X\nB : Set (Set X)\nhBc : B.Countable\nhB : IsTopologicalBasis B\n⊢ ∃ f, IsInducing f"
] | rcases exists_countable_basis X with ⟨B, hBc, -, hB⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 113,
"column": 6
} | {
"line": 113,
"column": 51
} | {
"line": 113,
"column": 52
} | [
{
"pp": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns k : Set α\nhk : IsCompact k\nh'k : k ⊆ s \\ μ.everywherePosSubset s\nx : α\nhx : x ∈ k\n⊢ ∃ u ∈ 𝓝[s] x, μ u = 0",
"ppTerm": "?m.72",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"used... | [
"α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns k : Set α\nhk : IsCompact k\nh'k : k ⊆ s \\ μ.everywherePosSubset s\nx : α\nhx : x ∈ k\n⊢ ∃ u ∈ 𝓝[s] x, μ u = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 175,
"column": 21
} | {
"line": 175,
"column": 58
} | {
"line": 175,
"column": 59
} | [
{
"pp": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : μ.IsEverywherePos s\nc : ℝ≥0∞\nhc : c ≠ 0\nx : α\nhx : x ∈ s\nn : Set α\nhn : n ∈ 𝓝[s] x\n⊢ 0 < (c • μ) n",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"ENNReal.instCanoni... | [
"α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : μ.IsEverywherePos s\nc : ℝ≥0∞\nhc : c ≠ 0\nx : α\nhx : x ∈ s\nn : Set α\nhn : n ∈ 𝓝[s] x\n⊢ 0 < c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 179,
"column": 22
} | {
"line": 179,
"column": 33
} | {
"line": 179,
"column": 34
} | [
{
"pp": "α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : μ.IsEverywherePos s\nc : ℝ≥0\nhc : c ≠ 0\n⊢ ↑c ≠ 0",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ENNReal.ofNNReal",
"congrArg",
"id",
"NN... | [
"α : Type u_1\ninst✝¹ : TopologicalSpace α\ninst✝ : MeasurableSpace α\nμ : Measure α\ns : Set α\nhs : μ.IsEverywherePos s\nc : ℝ≥0\nhc : c ≠ 0\n⊢ ¬c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 65
} | {
"line": 150,
"column": 66
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : No... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpace 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 51
} | {
"line": 153,
"column": 52
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : No... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpace 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 257,
"column": 4
} | {
"line": 258,
"column": 74
} | {
"line": 259,
"column": 4
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | [
"G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set G\nh : μ.IsE... | obtain ⟨i, hi, ni⟩ : ∃ i, y i ∈ W n * {z} ∧ n < i :=
((hz.frequently this).and_eventually (eventually_gt_atTop n)).exists | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 259,
"column": 44
} | {
"line": 259,
"column": 55
} | {
"line": 259,
"column": 56
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | [
"G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set G\nh : μ.IsE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 261,
"column": 37
} | {
"line": 261,
"column": 58
} | {
"line": 261,
"column": 59
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | [
"G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set G\nh : μ.IsE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 273,
"column": 30
} | {
"line": 273,
"column": 41
} | {
"line": 273,
"column": 42
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | [
"G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set G\nh : μ.IsE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 276,
"column": 4
} | {
"line": 276,
"column": 47
} | {
"line": 276,
"column": 48
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set ... | [
"G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nk : Set G\nh : μ.IsE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convolution | {
"line": 810,
"column": 9
} | {
"line": 810,
"column": 29
} | {
"line": 810,
"column": 30
} | [
{
"pp": "G : Type uG\nE' : Type uE'\ninst✝⁸ : NormedAddCommGroup E'\ninst✝⁷ : MeasurableSpace G\nμ : Measure G\ninst✝⁶ : SeminormedAddCommGroup G\ninst✝⁵ : BorelSpace G\ninst✝⁴ : SecondCountableTopology G\ninst✝³ : μ.IsAddLeftInvariant\ninst✝² : SFinite μ\ninst✝¹ : NormedSpace ℝ E'\ninst✝ : CompleteSpace E'\nι ... | [
"G : Type uG\nE' : Type uE'\ninst✝⁸ : NormedAddCommGroup E'\ninst✝⁷ : MeasurableSpace G\nμ : Measure G\ninst✝⁶ : SeminormedAddCommGroup G\ninst✝⁵ : BorelSpace G\ninst✝⁴ : SecondCountableTopology G\ninst✝³ : μ.IsAddLeftInvariant\ninst✝² : SFinite μ\ninst✝¹ : NormedSpace ℝ E'\ninst✝ : CompleteSpace E'\nι : Type u_1\n... | dist_triangle_right, | Mathlib.Tactic.GRewrite.evalGRewriteSeq | null |
Mathlib.MeasureTheory.Measure.EverywherePos | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 52
} | {
"line": 299,
"column": 2
} | [
{
"pp": "G : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nK : Set ... | [
"case refine_1\nG : Type u_2\ninst✝⁸ : Group G\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : LocallyCompactSpace G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : IsFiniteMeasureOnCompacts μ\ninst✝ : μ.InnerRegularCompactLTTop\nK : S... | refine ⟨L, everywherePosSubset_subset μ K, ?_, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 192,
"column": 10
} | {
"line": 192,
"column": 80
} | {
"line": 192,
"column": 81
} | [
{
"pp": "case refine_2\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ... | [
"case refine_2\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 99,
"column": 6
} | {
"line": 99,
"column": 58
} | {
"line": 99,
"column": 59
} | [
{
"pp": "case hfs\nG : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : LocallyCompactSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : IsFiniteMeasureOnCompacts μ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ... | [
"case hfs\nG : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : LocallyCompactSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\ninst✝⁴ : MeasurableSpace G\ninst✝³ : BorelSpace G\nμ : Measure G\ninst✝² : IsFiniteMeasureOnCompacts μ\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ng : G →... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 197,
"column": 6
} | {
"line": 197,
"column": 34
} | {
"line": 197,
"column": 35
} | [
{
"pp": "case neg\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ni... | [
"case neg\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : Norm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 145,
"column": 26
} | {
"line": 145,
"column": 37
} | {
"line": 145,
"column": 38
} | [
{
"pp": "G : Type u_1\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : Group G\ninst✝⁷ : IsTopologicalGroup G\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : BorelSpace G\nμ ν : Measure G\ninst✝⁴ : IsFiniteMeasureOnCompacts μ\ninst✝³ : IsFiniteMeasureOnCompacts ν\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : ν.IsMulRightInvariant\ninst... | [
"G : Type u_1\ninst✝⁹ : TopologicalSpace G\ninst✝⁸ : Group G\ninst✝⁷ : IsTopologicalGroup G\ninst✝⁶ : MeasurableSpace G\ninst✝⁵ : BorelSpace G\nμ ν : Measure G\ninst✝⁴ : IsFiniteMeasureOnCompacts μ\ninst✝³ : IsFiniteMeasureOnCompacts ν\ninst✝² : μ.IsMulLeftInvariant\ninst✝¹ : ν.IsMulRightInvariant\ninst✝ : ν.IsOpen... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 220,
"column": 4
} | {
"line": 220,
"column": 65
} | {
"line": 220,
"column": 66
} | [
{
"pp": "𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : No... | [
"𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ninst✝⁶ : NormedSpace 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 161,
"column": 30
} | {
"line": 161,
"column": 68
} | {
"line": 162,
"column": 6
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn✝ : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ∞ f ∧ range f ⊆... | [] | gcongr; exact (hR i x).trans (IR i hi) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 161,
"column": 30
} | {
"line": 161,
"column": 68
} | {
"line": 162,
"column": 6
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn✝ : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff ℝ ∞ f ∧ range f ⊆... | [] | gcongr; exact (hR i x).trans (IR i hi) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 169,
"column": 4
} | {
"line": 169,
"column": 25
} | {
"line": 170,
"column": 4
} | [
{
"pp": "case inr.refine_1\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := { f // support f ⊆ s ∧ HasCompactSupport f ∧ ContDiff... | [
"case inr.refine_1.h₁\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nn : ℕ∞\ns : Set E\nhs : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] s\nh's : s.Nonempty\nι : Type (max 0 u_1) := ⋯\nT : Set ι\nT_count : T.Countable\nhT : ⋃ f ∈ T, support ↑f ... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Calculus.BumpFunction.Normed | {
"line": 120,
"column": 4
} | {
"line": 120,
"column": 15
} | {
"line": 120,
"column": 16
} | [
{
"pp": "E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : HasContDiffBump E\ninst✝³ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : IsLocallyFiniteMeasure μ\nx : E\nhx : x ∉ closedBall c f.rOut\n⊢ f.rOut... | [
"E : Type u_1\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\ninst✝⁴ : HasContDiffBump E\ninst✝³ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝² : BorelSpace E\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : IsLocallyFiniteMeasure μ\nx : E\nhx : x ∉ closedBall c f.rOut\n⊢ f.rOut < dist x c"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Normed | {
"line": 129,
"column": 4
} | {
"line": 129,
"column": 50
} | {
"line": 129,
"column": 51
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : HasContDiffBump E\ninst✝⁴ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : μ.IsAddHaarMeasure\nK : ℝ\nh : f.rOu... | [
"E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : HasContDiffBump E\ninst✝⁴ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : μ.IsAddHaarMeasure\nK : ℝ\nh : f.rOut ≤ K * f.rI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.Normed | {
"line": 141,
"column": 4
} | {
"line": 141,
"column": 50
} | {
"line": 141,
"column": 51
} | [
{
"pp": "E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : HasContDiffBump E\ninst✝⁴ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : μ.IsAddHaarMeasure\nK : ℝ\nh : f.rOu... | [
"E : Type u_1\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : HasContDiffBump E\ninst✝⁴ : MeasurableSpace E\nc : E\nf : ContDiffBump c\nμ : Measure E\ninst✝³ : BorelSpace E\ninst✝² : FiniteDimensional ℝ E\ninst✝¹ : IsLocallyFiniteMeasure μ\ninst✝ : μ.IsAddHaarMeasure\nK : ℝ\nh : f.rOut ≤ K * f.rI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | {
"line": 242,
"column": 8
} | {
"line": 242,
"column": 19
} | {
"line": 242,
"column": 20
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nA : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (ball 0 1)\nf : E → ℝ\nf_support : support f = ball 0 1\nf_smooth : ContDiff ℝ ∞ f\nf_range : range f ⊆ Icc 0 1\nB : ∀ (x : E), f x ∈ Icc... | [
"E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : FiniteDimensional ℝ E\nA : IsOpen[PseudoMetricSpace.toUniformSpace.toTopologicalSpace] (ball 0 1)\nf : E → ℝ\nf_support : support f = ball 0 1\nf_smooth : ContDiff ℝ ∞ f\nf_range : range f ⊆ Icc 0 1\nB : ∀ (x : E), f x ∈ Icc 0 1\nx : E\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 302,
"column": 40
} | {
"line": 302,
"column": 57
} | {
"line": 302,
"column": 58
} | [
{
"pp": "α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nx y : Ordinal.{u}\nhxy : p.index x = p.index y\nx_le_y : x ≤ y\nH : x < y\nh : ∃ x, p.c x ∉ p.iUnionUpTo y ∧ p.R y ≤ p.τ * p.r x\nA : p.c (p.index y) ∉ ball (p.c (p.index x)) (p.r (p.index x))\n⊢ p.r (p.index y) ≤... | [
"α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nx y : Ordinal.{u}\nhxy : p.index x = p.index y\nx_le_y : x ≤ y\nH : x < y\nh : ∃ x, p.c x ∉ p.iUnionUpTo y ∧ p.R y ≤ p.τ * p.r x\nA : p.c (p.index y) ∉ ball (p.c (p.index x)) (p.r (p.index x))\n⊢ p.r (p.index y) ≤ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Covering.Besicovitch | {
"line": 364,
"column": 6
} | {
"line": 364,
"column": 77
} | {
"line": 365,
"column": 8
} | [
{
"pp": "α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nN : ℕ\nhN : IsEmpty (SatelliteConfig α N p.τ)\ni : Ordinal.{u}\nIH : ∀ y < i, y < p.lastStep → p.color y < N\nhi : i < p.lastStep\nA : Set ℕ :=\n ⋃ j,\n ⋃ (_ :\n (closedBall (p.c (p.index ↑j)) (p.r (p.ind... | [
"α : Type u_1\ninst✝¹ : MetricSpace α\nβ : Type u\ninst✝ : Nonempty β\np : TauPackage β α\nN : ℕ\nhN : IsEmpty (SatelliteConfig α N p.τ)\ni : Ordinal.{u}\nIH : ∀ y < i, y < p.lastStep → p.color y < N\nhi : i < p.lastStep\nA : Set ℕ :=\n ⋃ j,\n ⋃ (_ :\n (closedBall (p.c (p.index ↑j)) (p.r (p.index ↑j)) ∩ cl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Unique | {
"line": 398,
"column": 2
} | {
"line": 398,
"column": 93
} | {
"line": 398,
"column": 94
} | [
{
"pp": "case pos\nG : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : BorelSpace G\nμ' μ ν : Measure G\ninst✝³ : μ.IsHaarMeasure\ninst✝² : ν.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nhG : Loc... | [
"case pos\nG : Type u_1\ninst✝⁸ : TopologicalSpace G\ninst✝⁷ : Group G\ninst✝⁶ : IsTopologicalGroup G\ninst✝⁵ : MeasurableSpace G\ninst✝⁴ : BorelSpace G\nμ' μ ν : Measure G\ninst✝³ : μ.IsHaarMeasure\ninst✝² : ν.IsHaarMeasure\ninst✝¹ : IsFiniteMeasureOnCompacts μ'\ninst✝ : μ'.IsMulLeftInvariant\nhG : LocallyCompactS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.ContDiff.Convolution | {
"line": 270,
"column": 18
} | {
"line": 270,
"column": 91
} | {
"line": 271,
"column": 6
} | [
{
"pp": "case fst\n𝕜 : Type u𝕜\nG : Type uG\nE : Type uE\nE' : Type uE'\nF : Type uF\nP : Type uP\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedAddCommGroup E'\ninst✝¹¹ : NormedAddCommGroup F\nf : G → E\ninst✝¹⁰ : RCLike 𝕜\ninst✝⁹ : NormedSpace 𝕜 E\ninst✝⁸ : NormedSpace 𝕜 E'\ninst✝⁷ : NormedSpace ℝ F\ni... | [] | simp only [Pi.sub_apply, _root_.id, Prod.fst_sub, sub_zero, Prod.snd_sub] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
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