module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Analysis.Convex.Combination | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 71
} | {
"line": 132,
"column": 72
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝³ : Field R\ninst✝² : AddCommGroup E\ninst✝¹ : Module R E\nt : Finset ι\nw : ι → R\nz : ι → E\ninst✝ : (i : ι) → Decidable (w i ≠ 0)\ni : ι\nhit : i ∈ t\nhit' : i ∉ {i ∈ t | w i ≠ 0}\n⊢ w i = 0",
"ppTerm": "?m.46",
"assigned": false,
"usedConst... | [
"R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝³ : Field R\ninst✝² : AddCommGroup E\ninst✝¹ : Module R E\nt : Finset ι\nw : ι → R\nz : ι → E\ninst✝ : (i : ι) → Decidable (w i ≠ 0)\ni : ι\nhit : i ∈ t\nhit' : i ∉ {i ∈ t | w i ≠ 0}\n⊢ w i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 895,
"column": 73
} | {
"line": 895,
"column": 84
} | {
"line": 895,
"column": 85
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : DecidableEq ι\np : ι → P\nha : AffineIndependent k p\ni : ι\np₀ : P\nhp₀ : p₀ ∉ affineSpan k (p '' {x | x ≠ i})\nf : ι → P := update p i p₀\nh... | [
"k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : DivisionRing k\ninst✝³ : AddCommGroup V\ninst✝² : Module k V\ninst✝¹ : AffineSpace V P\nι : Type u_4\ninst✝ : DecidableEq ι\np : ι → P\nha : AffineIndependent k p\ni : ι\np₀ : P\nhp₀ : p₀ ∉ affineSpan k (p '' {x | x ≠ i})\nf : ι → P := update p i p₀\nhf : f = upda... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 216,
"column": 2
} | {
"line": 216,
"column": 54
} | {
"line": 217,
"column": 4
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ns : Set E\nt : Finset ι\nw : ι → R\nz : ι → E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nhs : Convex R s\nh₀ : ∀ i ∈ t, 0 ≤ w i\nh₁ : ∑ i ∈ t, w i = 1\nhz : ∀ i ∈ t, z i ∈ s\n⊢ ∑ i ∈ t... | [
"R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ns : Set E\nt : Finset ι\nw : ι → R\nz : ι → E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\nhs : Convex R s\nh₀ : ∀ i ∈ t, 0 ≤ w i\nh₁ : ∑ i ∈ t, w i = 1\nhz : ∀ i ∈ t, z i ∈ s\n⊢ ∑ i ∈ t, w i • z i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 942,
"column": 6
} | {
"line": 942,
"column": 43
} | {
"line": 943,
"column": 4
} | [
{
"pp": "case refine_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw : ι → k\ns : Finset ι\nhw : ∑ i ∈ s, w i = 1\ni₁... | [] | rw [Finset.sum_pi_single', if_pos h₁] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 942,
"column": 6
} | {
"line": 942,
"column": 43
} | {
"line": 943,
"column": 4
} | [
{
"pp": "case refine_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw : ι → k\ns : Finset ι\nhw : ∑ i ∈ s, w i = 1\ni₁... | [] | rw [Finset.sum_pi_single', if_pos h₁] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.AffineSpace.Independent | {
"line": 942,
"column": 6
} | {
"line": 942,
"column": 43
} | {
"line": 943,
"column": 4
} | [
{
"pp": "case refine_1\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁵ : Ring k\ninst✝⁴ : LinearOrder k\ninst✝³ : IsStrictOrderedRing k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nι : Type u_4\np : ι → P\nh : AffineIndependent k p\nw : ι → k\ns : Finset ι\nhw : ∑ i ∈ s, w i = 1\ni₁... | [] | rw [Finset.sum_pi_single', if_pos h₁] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.AlexandrovDiscrete | {
"line": 113,
"column": 4
} | {
"line": 113,
"column": 53
} | {
"line": 113,
"column": 54
} | [
{
"pp": "ι : Sort u_1\nα : Type u_3\ninst✝¹ : TopologicalSpace α\ninst✝ : AlexandrovDiscrete α\nf : ι → Set α\n⊢ (closure[inst✝¹] (⋃ i, f i))ᶜ = (⋃ i, closure[inst✝¹] (f i))ᶜ",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.iInter",
"Compl.... | [
"ι : Sort u_1\nα : Type u_3\ninst✝¹ : TopologicalSpace α\ninst✝ : AlexandrovDiscrete α\nf : ι → Set α\n⊢ interior (⋂ i, (f i)ᶜ) = ⋂ i, interior (f i)ᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.AlexandrovDiscrete | {
"line": 196,
"column": 27
} | {
"line": 196,
"column": 41
} | {
"line": 196,
"column": 42
} | [
{
"pp": "α : Type u_3\ninst✝ : TopologicalSpace α\nhα : ∀ (a : α), 𝓝 a = 𝓟 (nhdsKer {a})\nS : Set (Set α)\nhS : ∀ s ∈ S, ∀ (a : α), (nhdsKer {a} ∩ s).Nonempty → a ∈ s\na : α\nha : (nhdsKer {a} ∩ ⋃ i ∈ S, i).Nonempty\n⊢ a ∈ ⋃₀ S",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"congr... | [
"α : Type u_3\ninst✝ : TopologicalSpace α\nhα : ∀ (a : α), 𝓝 a = 𝓟 (nhdsKer {a})\nS : Set (Set α)\nhS : ∀ s ∈ S, ∀ (a : α), (nhdsKer {a} ∩ s).Nonempty → a ∈ s\na : α\nha : (⋃ i ∈ S, nhdsKer {a} ∩ i).Nonempty\n⊢ a ∈ ⋃₀ S"
] | inter_iUnion₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Connected.LocallyPathConnected | {
"line": 169,
"column": 33
} | {
"line": 169,
"column": 64
} | {
"line": 169,
"column": 64
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : LocallyPathConnectedSpace X\ne : Y → X\nhe : IsOpenEmbedding e\nthis : ∀ (y : Y), (𝓝 y).HasBasis (fun s ↦ s ∈ 𝓝 (e y) ∧ IsPathConnected s ∧ s ⊆ range e) fun x ↦ e ⁻¹' x\nx : Y\ns : Set X\nx✝ : s ∈ 𝓝 (e x) ∧... | [
"X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : LocallyPathConnectedSpace X\ne : Y → X\nhe : IsOpenEmbedding e\nthis : ∀ (y : Y), (𝓝 y).HasBasis (fun s ↦ s ∈ 𝓝 (e y) ∧ IsPathConnected s ∧ s ⊆ range e) fun x ↦ e ⁻¹' x\nx : Y\ns : Set X\nx✝ : s ∈ 𝓝 (e x) ∧ IsPathConne... | image_preimage_eq_of_subset hse | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Convex.Topology | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 68
} | {
"line": 171,
"column": 4
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : AddRightMono 𝕜\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nhx : x ∈ closure s\nh... | [
"𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : AddRightMono 𝕜\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nhx : x ∈ closure s\nhy : y ∈ inte... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 182,
"column": 2
} | {
"line": 182,
"column": 40
} | {
"line": 182,
"column": 41
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : AddRightMono 𝕜\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nhx : x ∈ closure s\nh... | [
"𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : AddRightMono 𝕜\ns : Set E\nhs : Convex 𝕜 s\nx y : E\nhx : x ∈ closure s\nhy : x + y ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 60
} | {
"line": 211,
"column": 61
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : ZeroLEOneClass 𝕜\ns : Set E\nhs : IsOpen s\n⊢ IsOpen ((convexHull 𝕜) s)",
... | [
"𝕜 : Type u_2\nE : Type u_3\ninst✝⁷ : Field 𝕜\ninst✝⁶ : PartialOrder 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : ZeroLEOneClass 𝕜\ns : Set E\nhs : IsOpen s\n⊢ (convexHull 𝕜) s ⊆ interior ((convexHull... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 321,
"column": 4
} | {
"line": 321,
"column": 15
} | {
"line": 321,
"column": 16
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\ns : Set E\n⊢ (closedConvexHull 𝕜) (closure s) ⊆ (closedConvexHull 𝕜) s",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"... | [
"𝕜 : Type u_2\nE : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : PartialOrder 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\ns : Set E\n⊢ (closedConvexHull 𝕜) (closure s) ⊆ (closedConvexHull 𝕜) s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Topology | {
"line": 415,
"column": 4
} | {
"line": 415,
"column": 71
} | {
"line": 416,
"column": 4
} | [
{
"pp": "case mp\n𝕜 : Type u_4\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\ns : Set 𝕜\nhs : Convex 𝕜 s\nx : 𝕜\nhx : x ∈ s\ny : 𝕜\nhy : y ∈ s\nh : x ≠ y\nhs' : (interior [x -[𝕜] y]).Nonempty → (interior s).Nonempty\n⊢ ... | [
"case mp\n𝕜 : Type u_4\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\ns : Set 𝕜\nhs : Convex 𝕜 s\nx : 𝕜\nhx : x ∈ s\ny : 𝕜\nhy : y ∈ s\nh : x ≠ y\nhs' : x ≠ y → (interior s).Nonempty\n⊢ (interior s).Nonempty"
] | rw [segment_eq_Icc', interior_Icc, nonempty_Ioo, inf_lt_sup] at hs' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Convex.Combination | {
"line": 371,
"column": 40
} | {
"line": 371,
"column": 51
} | {
"line": 371,
"column": 52
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁵ : Field R\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module R E\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ns : Set E\nx : E\ninst✝ : Fintype ι\nw : ι → R\nz : ι → E\nhw₀ : ∀ (i : ι), 0 ≤ w i\nhw₁ : ∑ i, w i = 1\nhz : ∀ (i : ι), z i ∈ s\nhx : ∑ i, w... | [
"R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁵ : Field R\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module R E\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ns : Set E\nx : E\ninst✝ : Fintype ι\nw : ι → R\nz : ι → E\nhw₀ : ∀ (i : ι), 0 ≤ w i\nhw₁ : ∑ i, w i = 1\nhz : ∀ (i : ι), z i ∈ s\nhx : ∑ i, w i • z i = x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 371,
"column": 77
} | {
"line": 371,
"column": 88
} | {
"line": 371,
"column": 89
} | [
{
"pp": "R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁵ : Field R\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module R E\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ns : Set E\nx : E\ninst✝ : Fintype ι\nw : ι → R\nz : ι → E\nhw₀ : ∀ (i : ι), 0 ≤ w i\nhw₁ : ∑ i, w i = 1\nhz : ∀ (i : ι), z i ∈ s\nhx : ∑ i, w... | [
"R : Type u_1\nE : Type u_3\nι : Type u_5\ninst✝⁵ : Field R\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module R E\ninst✝² : LinearOrder R\ninst✝¹ : IsStrictOrderedRing R\ns : Set E\nx : E\ninst✝ : Fintype ι\nw : ι → R\nz : ι → E\nhw₀ : ∀ (i : ι), 0 ≤ w i\nhw₁ : ∑ i, w i = 1\nhz : ∀ (i : ι), z i ∈ s\nhx : ∑ i, w i • z i = x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.LocallyConvex | {
"line": 163,
"column": 2
} | {
"line": 163,
"column": 17
} | {
"line": 163,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : Field 𝕜\ninst✝⁷ : PartialOrder 𝕜\ninst✝⁶ : ZeroLEOneClass 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : LocallyConvexSpace 𝕜 E\ns : Set E\nx : E\nhx : ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : Field 𝕜\ninst✝⁷ : PartialOrder 𝕜\ninst✝⁶ : ZeroLEOneClass 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousConstSMul 𝕜 E\ninst✝ : LocallyConvexSpace 𝕜 E\ns : Set E\nx : E\nhx : x ∉ s\nhscon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 385,
"column": 4
} | {
"line": 385,
"column": 66
} | {
"line": 385,
"column": 67
} | [
{
"pp": "case mp\nR : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns : Set E\nx : E\nι : Type\nt : Finset ι\nw : ι → R\nz : ι → E\nh : (∀ i ∈ t, 0 ≤ w i) ∧ ∑ i ∈ t, w i = 1 ∧ (∀ i ∈ t, z i ∈ s) ∧ t.centerMass w z =... | [
"case mp\nR : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns : Set E\nx : E\nι : Type\nt : Finset ι\nw : ι → R\nz : ι → E\nh : (∀ i ∈ t, 0 ≤ w i) ∧ ∑ i ∈ t, w i = 1 ∧ (∀ i ∈ t, z i ∈ s) ∧ t.centerMass w z = x\n⊢ (∀ a ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 64,
"column": 2
} | {
"line": 64,
"column": 35
} | {
"line": 64,
"column": 36
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na : E\nr : ℝ\n⊢ Convex ℝ (ball a r)",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Real.partialOrder",
"Real",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
... | [
"E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na : E\nr : ℝ\n⊢ Convex ℝ {y | dist y a < r}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 41
} | {
"line": 72,
"column": 42
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na : E\nr : ℝ\n⊢ Convex ℝ (closedBall a r)",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Real.partialOrder",
"Real",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid"... | [
"E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\na : E\nr : ℝ\n⊢ Convex ℝ {y | dist y a ≤ r}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 425,
"column": 2
} | {
"line": 425,
"column": 82
} | {
"line": 426,
"column": 4
} | [
{
"pp": "R : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns : Set E\nhs : s.Finite\n⊢ (convexHull R) s = {x | ∃ w, (∀ y ∈ s, 0 ≤ w y) ∧ ∑ y ∈ hs.toFinset, w y = 1 ∧ hs.toFinset.centerMass w id = x}",
"ppTerm": ... | [
"R : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns : Set E\nhs : s.Finite\n⊢ (convexHull R) s = {x | ∃ w, (∀ y ∈ s, 0 ≤ w y) ∧ ∑ y ∈ hs.toFinset, w y = 1 ∧ hs.toFinset.centerMass w id = x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 77
} | {
"line": 118,
"column": 2
} | [
{
"pp": "case neg\nF : Type u_2\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : Nontrivial F\nx✝ : F\nr : ℝ\nhr : 0 ≤ r\nx : F\nh : x ∈ closedBall 0 r\nU : Set F\nhU_sub : sphere 0 r ⊆ U\nhU : Convex ℝ U\nzero_mem : 0 ∈ U\nhr₀ : ¬r = 0\nx_zero : ¬x = 0\nz : F := (r * ‖x‖⁻¹) • x\nhz_def : z = (... | [
"case neg\nF : Type u_2\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace ℝ F\ninst✝ : Nontrivial F\nx✝ : F\nr : ℝ\nhr : 0 ≤ r\nx : F\nh : x ∈ closedBall 0 r\nU : Set F\nhU_sub : sphere 0 r ⊆ U\nhU : Convex ℝ U\nzero_mem : 0 ∈ U\nhr₀ : ¬r = 0\nx_zero : ¬x = 0\nz : F := (r * ‖x‖⁻¹) • x\nhz_def : z = (r * ‖x‖⁻¹) •... | have := StarConvex.smul_mem (hU.starConvex zero_mem) hz (by positivity) hr₁ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 173,
"column": 25
} | {
"line": 173,
"column": 41
} | {
"line": 173,
"column": 42
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nx : E\nhx : x = 0\n⊢ IsConnected {y | SameRay ℝ x y}",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real",
"IsConnected",
"congrArg",
... | [
"case pos\nE : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nx : E\nhx : x = 0\n⊢ IsConnected univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Convex | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 78
} | {
"line": 210,
"column": 79
} | [
{
"pp": "E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns : Set E\nα : Type u_2\nf : Filter α\nx : E\ny z : α → E\nr : α → E → Prop\nhy : Tendsto y f (𝓝 x)\nhz : Tendsto z f (𝓝 x)\nhr : ∀ᶠ (p : α × E) in f ×ˢ 𝓝[s] x, r p.1 p.2\nseg : ∀ᶠ (χ : α) in f, [y χ -[ℝ] z χ] ⊆ s\n⊢ ∀ᶠ (p : α... | [
"E : Type u_1\ninst✝¹ : SeminormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\ns : Set E\nα : Type u_2\nf : Filter α\nx : E\ny z : α → E\nr : α → E → Prop\nhy : Tendsto y f (𝓝 x)\nhz : Tendsto z f (𝓝 x)\nhr : ∀ᶠ (p : α × E) in f ×ˢ 𝓝[s] x, r p.1 p.2\nseg : ∀ᶠ (χ : α) in f, [y χ -[ℝ] z χ] ⊆ s\n⊢ ∀ᶠ (p : α × E) in Fil... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 541,
"column": 4
} | {
"line": 541,
"column": 29
} | {
"line": 541,
"column": 30
} | [
{
"pp": "R : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns t₁ t₂ : Finset E\nht₁ : t₁ ⊆ s\nht₂ : t₂ ⊆ s\nx✝ : E\nw₁ : E → R\nh₁w₁ : ∀ y ∈ t₁, 0 ≤ w₁ y\nh₂w₁ : ∑ y ∈ t₁, w₁ y = 1\nh₃w₁ : ∑ y ∈ t₁, w₁ y • y = x✝\nw₂... | [
"R : Type u_1\nE : Type u_3\ninst✝⁴ : Field R\ninst✝³ : AddCommGroup E\ninst✝² : Module R E\ninst✝¹ : LinearOrder R\ninst✝ : IsStrictOrderedRing R\ns t₁ t₂ : Finset E\nht₁ : t₁ ⊆ s\nht₂ : t₂ ⊆ s\nx✝ : E\nw₁ : E → R\nh₁w₁ : ∀ y ∈ t₁, 0 ≤ w₁ y\nh₂w₁ : ∑ y ∈ t₁, w₁ y = 1\nh₃w₁ : ∑ y ∈ t₁, w₁ y • y = x✝\nw₂ : E → R\nh₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.UniformConvergence | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 43
} | {
"line": 87,
"column": 44
} | [
{
"pp": "case hsmul_right\n𝕜 : Type u_1\nα : Type u_2\nE : Type u_3\nH : Type u_4\nhom : Type u_5\ninst✝¹⁰ : NormedField 𝕜\ninst✝⁹ : AddCommGroup H\ninst✝⁸ : Module 𝕜 H\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : UniformSpace E\ninst✝³ : IsUniformAddGroup E\ninst✝² :... | [
"case hsmul_right\n𝕜 : Type u_1\nα : Type u_2\nE : Type u_3\nH : Type u_4\nhom : Type u_5\ninst✝¹⁰ : NormedField 𝕜\ninst✝⁹ : AddCommGroup H\ninst✝⁸ : Module 𝕜 H\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : UniformSpace E\ninst✝³ : IsUniformAddGroup E\ninst✝² : ContinuousS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 131,
"column": 14
} | {
"line": 131,
"column": 56
} | {
"line": 131,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrd... | [
"𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\nι : Type u_5\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : PartialOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrderedModule �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 600,
"column": 55
} | {
"line": 600,
"column": 66
} | {
"line": 600,
"column": 67
} | [
{
"pp": "𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : Finite ι\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\ns : Set ι\nt✝ : (i : ι) → Set (E i)\nx : (i : ι) → E i\nval✝ : Fintype ι\nt : (i : ι) ... | [
"𝕜 : Type u_1\nι : Type u_2\nE : ι → Type u_3\ninst✝⁵ : Finite ι\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : (i : ι) → AddCommGroup (E i)\ninst✝ : (i : ι) → Module 𝕜 (E i)\ns : Set ι\nt✝ : (i : ι) → Set (E i)\nx : (i : ι) → E i\nval✝ : Fintype ι\nt : (i : ι) → Set (E i)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Combination | {
"line": 628,
"column": 6
} | {
"line": 628,
"column": 63
} | {
"line": 628,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsOrderedRing 𝕜\ninst✝¹ : AddCommGroup V\ninst✝ : Module 𝕜 V\nn : ℕ\ns : Simplex 𝕜 V n\nu : Finset (Fin (n + 1))\nw : Fin (n + 1) → 𝕜\nhw : ∀ i ∈ u, 0 ≤ w i\nhw1 : u.sum w = 1\nhw' : ∀ i ∈ u, w i ≤ 1\n⊢ ∑ i, (↑u).indi... | [
"𝕜 : Type u_1\nV : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsOrderedRing 𝕜\ninst✝¹ : AddCommGroup V\ninst✝ : Module 𝕜 V\nn : ℕ\ns : Simplex 𝕜 V n\nu : Finset (Fin (n + 1))\nw : Fin (n + 1) → 𝕜\nhw : ∀ i ∈ u, 0 ≤ w i\nhw1 : u.sum w = 1\nhw' : ∀ i ∈ u, w i ≤ 1\n⊢ ∑ i ∈ u, w i = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 215,
"column": 13
} | {
"line": 215,
"column": 24
} | {
"line": 215,
"column": 25
} | [
{
"pp": "case empty\n𝕜 : Type u_11\nE : Type u_12\nι : Type u_13\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\np : SeminormFamily 𝕜 E ι\nhp : ∀ (i : ι), Continuous[inst✝, _] ⇑(p i)\nr : ℝ\nhr : 0 < r\n⊢ Continuous[inst✝, _] ⇑(∅.sup p)",
"ppTerm": "?em... | [
"case empty\n𝕜 : Type u_11\nE : Type u_12\nι : Type u_13\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\np : SeminormFamily 𝕜 E ι\nhp : ∀ (i : ι), Continuous[inst✝, _] ⇑(p i)\nr : ℝ\nhr : 0 < r\n⊢ Continuous[inst✝, _] 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Convex.Jensen | {
"line": 394,
"column": 32
} | {
"line": 394,
"column": 43
} | {
"line": 394,
"column": 44
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : LinearOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrderedModule 𝕜 β... | [
"𝕜 : Type u_1\nE : Type u_2\nβ : Type u_4\ninst✝⁹ : Field 𝕜\ninst✝⁸ : LinearOrder 𝕜\ninst✝⁷ : IsStrictOrderedRing 𝕜\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : AddCommGroup β\ninst✝⁴ : LinearOrder β\ninst✝³ : IsOrderedAddMonoid β\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜 β\ninst✝ : IsStrictOrderedModule 𝕜 β\ns : Set E\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM | {
"line": 146,
"column": 24
} | {
"line": 146,
"column": 55
} | {
"line": 146,
"column": 55
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝⁸ : NormedField 𝕜₁\ninst✝⁷ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜₁ E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜₂ F\ninst✝¹ : UniformSpace F\ninst✝ : IsUniformAddGrou... | [
"𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝⁸ : NormedField 𝕜₁\ninst✝⁷ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁶ : AddCommGroup E\ninst✝⁵ : Module 𝕜₁ E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜₂ F\ninst✝¹ : UniformSpace F\ninst✝ : IsUniformAddGroup F\n𝔖 : Se... | UniformSpace.replaceTopology_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 403,
"column": 19
} | {
"line": 403,
"column": 58
} | {
"line": 403,
"column": 59
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\nF : Type u_7\nι : Type u_9\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\np : SeminormFamily 𝕜 E ι\nhp : WithSeminorms p\nu : F → E\nf : Filter F\ny₀ : E\nh : ∀ (s : Finset ι) (ε : ℝ), 0 < ε → ∀ᶠ (x : F) in f, (s.sup p)... | [
"𝕜 : Type u_2\nE : Type u_6\nF : Type u_7\nι : Type u_9\ninst✝³ : NormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : TopologicalSpace E\np : SeminormFamily 𝕜 E ι\nhp : WithSeminorms p\nu : F → E\nf : Filter F\ny₀ : E\nh : ∀ (s : Finset ι) (ε : ℝ), 0 < ε → ∀ᶠ (x : F) in f, (s.sup p) (u x - y₀) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 52
} | {
"line": 531,
"column": 2
} | [
{
"pp": "case mpr\n𝕜 : Type u_2\nE : Type u_6\nι : Type u_9\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\ninst✝ : TopologicalSpace E\ns : Set E\nhp : WithSeminorms p\nh : ∀ (I : Finset ι), ∃ r > 0, ∀ x ∈ s, (I.sup p) x < r\ns' : Set E\nhs' : s' ... | [
"case mpr\n𝕜 : Type u_2\nE : Type u_6\nι : Type u_9\ninst✝³ : NontriviallyNormedField 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\np : SeminormFamily 𝕜 E ι\ninst✝ : TopologicalSpace E\ns : Set E\nhp : WithSeminorms p\nh : ∀ (I : Finset ι), ∃ r > 0, ∀ x ∈ s, (I.sup p) x < r\ns' : Set E\nhs'✝ : s' ∈ p.basisSe... | rcases p.basisSets_iff.mp hs' with ⟨I, r, hr, hs'⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 603,
"column": 8
} | {
"line": 603,
"column": 59
} | {
"line": 603,
"column": 60
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | [
"𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs : s ∈ 𝓝 0\nc... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 609,
"column": 4
} | {
"line": 609,
"column": 15
} | {
"line": 609,
"column": 16
} | [
{
"pp": "case refine_3.refine_1\n𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ba... | [
"case refine_3.refine_1\n𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 625,
"column": 6
} | {
"line": 626,
"column": 35
} | {
"line": 626,
"column": 36
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | [
"𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs : s ∈ (Semino... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 629,
"column": 29
} | {
"line": 629,
"column": 40
} | {
"line": 629,
"column": 41
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | [
"𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs : s ∈ (Semino... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 632,
"column": 26
} | {
"line": 632,
"column": 37
} | {
"line": 632,
"column": 38
} | [
{
"pp": "𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs :... | [
"𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\ns : Set E\nhs : s ∈ (Semino... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 634,
"column": 4
} | {
"line": 634,
"column": 15
} | {
"line": 634,
"column": 16
} | [
{
"pp": "case refine_3.refine_2.inr\n𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (... | [
"case refine_3.refine_2.inr\n𝕜 : Type u_2\nE : Type u_6\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousConstSMul 𝕜 E\np : Seminorm 𝕜 E\nh : p.ball 0 1 ∈ 𝓝 0\nh' : IsVonNBounded 𝕜 (p.ball 0 1)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 312,
"column": 36
} | {
"line": 312,
"column": 59
} | {
"line": 312,
"column": 60
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric σ₁₂\ninst✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 340,
"column": 14
} | {
"line": 340,
"column": 25
} | {
"line": 340,
"column": 26
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ₁₂\nf : E →S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 369,
"column": 4
} | {
"line": 369,
"column": 71
} | {
"line": 370,
"column": 2
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : Rin... | [] | exact (hf x hx.le).trans ((div_le_iff₀' <| one_pos.trans hc).1 hcx) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 694,
"column": 25
} | {
"line": 694,
"column": 36
} | {
"line": 694,
"column": 37
} | [
{
"pp": "E : Type u_6\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\np : Seminorm ℝ E\nf : E →ₗ[ℝ] ℝ\nhfp : ∀ (x : E), f x ≤ p x\nx : E\n⊢ -f x ≤ p x",
"ppTerm": "?m.70",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"E : Type u_6\ninst✝¹ : AddCommGroup E\ninst✝ : Module ℝ E\np : Seminorm ℝ E\nf : E →ₗ[ℝ] ℝ\nhfp : ∀ (x : E), f x ≤ p x\nx : E\n⊢ -f x ≤ p x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 373,
"column": 4
} | {
"line": 373,
"column": 71
} | {
"line": 374,
"column": 4
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : Rin... | [
"case refine_2\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometri... | simp only [Seminorm.mem_ball_zero, mem_closedBall_zero_iff] at hf ⊢ | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 420,
"column": 24
} | {
"line": 420,
"column": 78
} | {
"line": 420,
"column": 79
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric σ₁₂\ninst✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Basic | {
"line": 422,
"column": 2
} | {
"line": 422,
"column": 49
} | {
"line": 422,
"column": 50
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : SeminormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric σ₁₂\ninst✝ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.NNNorm | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 40
} | {
"line": 83,
"column": 41
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type u_3\nE : Type u_4\nF : Type u_5\nG : Type u_6\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : NontriviallyNormedField 𝕜₂\ninst✝¹⁰ : NontriviallyNormedField 𝕜₃\ninst✝⁹ : SeminormedAddCommGroup E\ninst✝⁸ : SeminormedAddCommGroup F\ninst✝⁷ : SeminormedAddCommGr... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type u_3\nE : Type u_4\nF : Type u_5\nG : Type u_6\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : NontriviallyNormedField 𝕜₂\ninst✝¹⁰ : NontriviallyNormedField 𝕜₃\ninst✝⁹ : SeminormedAddCommGroup E\ninst✝⁸ : SeminormedAddCommGroup F\ninst✝⁷ : SeminormedAddCommGroup G\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.NNNorm | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 54
} | {
"line": 133,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NontriviallyNormedField 𝕜₂\ninst✝⁴ : SeminormedAddCommGroup E\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NontriviallyNormedField 𝕜₂\ninst✝⁴ : SeminormedAddCommGroup E\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ₁₂\nf : E →S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.NNNorm | {
"line": 177,
"column": 17
} | {
"line": 177,
"column": 28
} | {
"line": 177,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : DenselyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ₁₂\nf : E... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : SeminormedAddCommGroup F\ninst✝⁴ : DenselyNormedField 𝕜\ninst✝³ : NontriviallyNormedField 𝕜₂\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝ : RingHomIsometric σ₁₂\nf : E →SL[σ₁₂] F\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.NNNorm | {
"line": 216,
"column": 34
} | {
"line": 216,
"column": 84
} | {
"line": 216,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : DenselyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric σ₁₂\ninst... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_4\nF : Type u_5\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : SeminormedAddCommGroup F\ninst✝⁵ : DenselyNormedField 𝕜\ninst✝⁴ : NontriviallyNormedField 𝕜₂\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : NormedSpace 𝕜₂ F\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝¹ : RingHomIsometric σ₁₂\ninst✝ : NormedAl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 873,
"column": 2
} | {
"line": 884,
"column": 42
} | {
"line": 886,
"column": 0
} | [
{
"pp": "𝕜 : Type u_2\nF : Type u_7\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nq : Seminorm 𝕜 F\nhq : Continuous[PseudoMetricSpace.toUniformSpace.toTopologicalSpace, _] ⇑q\n⊢ ∃ C, 0 < C ∧ ∀ (x : F), q x ≤ C * ‖x‖",
"ppTerm": "?m.35",
"assigned": ... | [] | have hq' : Tendsto q (𝓝 0) (𝓝 0) := map_zero q ▸ hq.tendsto 0
rcases NormedAddGroup.nhds_zero_basis_norm_lt.mem_iff.mp (hq' <| Iio_mem_nhds one_pos)
with ⟨ε, ε_pos, hε⟩
rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
have : 0 < ‖c‖ / ε := by positivity
refine ⟨‖c‖ / ε, this, fun x ↦ ?_⟩
by_cases h... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.LocallyConvex.WithSeminorms | {
"line": 873,
"column": 2
} | {
"line": 884,
"column": 42
} | {
"line": 886,
"column": 0
} | [
{
"pp": "𝕜 : Type u_2\nF : Type u_7\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\nq : Seminorm 𝕜 F\nhq : Continuous[PseudoMetricSpace.toUniformSpace.toTopologicalSpace, _] ⇑q\n⊢ ∃ C, 0 < C ∧ ∀ (x : F), q x ≤ C * ‖x‖",
"ppTerm": "?m.35",
"assigned": ... | [] | have hq' : Tendsto q (𝓝 0) (𝓝 0) := map_zero q ▸ hq.tendsto 0
rcases NormedAddGroup.nhds_zero_basis_norm_lt.mem_iff.mp (hq' <| Iio_mem_nhds one_pos)
with ⟨ε, ε_pos, hε⟩
rcases NormedField.exists_one_lt_norm 𝕜 with ⟨c, hc⟩
have : 0 < ‖c‖ / ε := by positivity
refine ⟨‖c‖ / ε, this, fun x ↦ ?_⟩
by_cases h... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Germ.Basic | {
"line": 759,
"column": 4
} | {
"line": 759,
"column": 78
} | {
"line": 760,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nl : Filter α\nf✝ g✝ h✝ : α → β\ninst✝² : Mul β\ninst✝¹ : LE β\ninst✝ : ExistsMulOfLE β\nx y : l.Germ β\nf g : α → β\nh : f ≤ᶠ[l] g\nc : (x : α) → f x ≤ g x → β\nhc : ∀ (x : α) (hx : f x ≤ g x), g x = f x * c x hx\n⊢ ∃ c, ↑g = ↑f * c",
"ppTerm"... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nl : Filter α\nf✝ g✝ h✝ : α → β\ninst✝² : Mul β\ninst✝¹ : LE β\ninst✝ : ExistsMulOfLE β\nx y : l.Germ β\nf g : α → β\nh : f ≤ᶠ[l] g\nc : (x : α) → f x ≤ g x → β\nhc : ∀ (x : α) (hx : f x ≤ g x), g x = f x * c x hx\n⊢ g =ᶠ[l] (fun f g x ↦ (fun x1 x2 ↦ x1 * x2) ... | refine ⟨ofFun fun x ↦ if hx : f x ≤ g x then c x hx else f x, coe_eq.2 ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Order.Filter.ENNReal | {
"line": 34,
"column": 2
} | {
"line": 34,
"column": 57
} | {
"line": 34,
"column": 58
} | [
{
"pp": "case e'_3\nf : Filter ℝ\nhf : ¬IsBounded (fun x1 x2 ↦ x1 ≤ x2) f\n⊢ {a | ∀ᶠ (n : ℝ) in f, n ≤ a} = ∅",
"ppTerm": "?e'_3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Preorder.toLT",
"congrArg",
"Filter.Eventually",
"PartialOrder.toPreorder",
... | [
"case e'_3\nf : Filter ℝ\nhf : ¬IsBounded (fun x1 x2 ↦ x1 ≤ x2) f\n⊢ ∀ (x : ℝ), ∃ᶠ (x_1 : ℝ) in f, x < x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 57
} | {
"line": 44,
"column": 58
} | [
{
"pp": "case e'_3\nf : Filter ℝ\nhf : ¬IsBounded (fun x1 x2 ↦ x1 ≥ x2) f\n⊢ {a | ∀ᶠ (n : ℝ) in f, a ≤ n} = ∅",
"ppTerm": "?e'_3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Preorder.toLT",
"congrArg",
"Filter.Eventually",
"PartialOrder.toPreorder",
... | [
"case e'_3\nf : Filter ℝ\nhf : ¬IsBounded (fun x1 x2 ↦ x1 ≥ x2) f\n⊢ ∀ (x : ℝ), ∃ᶠ (x_1 : ℝ) in f, x_1 < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 91,
"column": 45
} | {
"line": 91,
"column": 60
} | {
"line": 91,
"column": 61
} | [
{
"pp": "ι : Type u_1\nf : Filter ι\nu : ι → ℝ≥0\ninst✝ : f.NeBot\nb : ℝ\nhb : ∀ (a : ℝ), (∀ᶠ (a_1 : ι) in f, ↑(u a_1) ≤ a) → b ≤ a\nx : ℝ\nx✝ : 0 ≤ x\n⊢ (∀ᶠ (a : ι) in f, ↑(u a) ≤ ↑(NNReal.mk x x✝)) → ↑(NNReal.mk ↑b.toNNReal ⋯) ≤ ↑(NNReal.mk x x✝)",
"ppTerm": "?m.41",
"assigned": true,
"usedConstan... | [
"ι : Type u_1\nf : Filter ι\nu : ι → ℝ≥0\ninst✝ : f.NeBot\nb : ℝ\nhb : ∀ (a : ℝ), (∀ᶠ (a_1 : ι) in f, ↑(u a_1) ≤ a) → b ≤ a\nx : ℝ\nx✝ : 0 ≤ x\n⊢ (∀ᶠ (a : ι) in f, ↑(u a) ≤ x) → b ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Bilinear | {
"line": 172,
"column": 18
} | {
"line": 172,
"column": 46
} | {
"line": 172,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type u_3\nE : Type u_4\nF : Type u_6\nG : Type u_8\ninst✝¹⁰ : SeminormedAddCommGroup E\ninst✝⁹ : SeminormedAddCommGroup F\ninst✝⁸ : SeminormedAddCommGroup G\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NontriviallyNormedField 𝕜₂\ninst✝⁵ : NontriviallyNormedField ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\n𝕜₃ : Type u_3\nE : Type u_4\nF : Type u_6\nG : Type u_8\ninst✝¹⁰ : SeminormedAddCommGroup E\ninst✝⁹ : SeminormedAddCommGroup F\ninst✝⁸ : SeminormedAddCommGroup G\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NontriviallyNormedField 𝕜₂\ninst✝⁵ : NontriviallyNormedField 𝕜₃\ninst✝⁴ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 112,
"column": 2
} | {
"line": 112,
"column": 57
} | {
"line": 112,
"column": 58
} | [
{
"pp": "case e'_2\nf : Filter ℝ≥0\nhf : ¬IsBounded (fun x1 x2 ↦ x1 ≤ x2) f\n⊢ {a | ∀ᶠ (n : ℝ≥0) in f, n ≤ a} = ∅",
"ppTerm": "?e'_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"_private.Mathlib.Order.Filter.ENNReal.0.NNReal.limsSup_of_not_is... | [
"case e'_2\nf : Filter ℝ≥0\nhf : ¬IsBounded (fun x1 x2 ↦ x1 ≤ x2) f\n⊢ ∀ (x : ℝ≥0), ∃ᶠ (x_1 : ℝ≥0) in f, x < x_1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 13
} | {
"line": 135,
"column": 14
} | [
{
"pp": "case pos\nι : Type u_1\nf : Filter ι\nu : ι → ℝ≥0\nhf : IsCoboundedUnder (fun x1 x2 ↦ x1 ≥ x2) f u\nc r : ℝ\nhr : r < c\n⊢ (∀ᶠ (a : ι) in f, r < ↑(u a)) ↔ 0 ≤ r → ∀ᶠ (a : ι) in f, r < ↑(u a)",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.instLE",
... | [
"case pos\nι : Type u_1\nf : Filter ι\nu : ι → ℝ≥0\nhf : IsCoboundedUnder (fun x1 x2 ↦ x1 ≥ x2) f u\nc r : ℝ\nhr : r < c\n⊢ 0 ≤ r ∨ ∀ᶠ (a : ι) in f, r < ↑(u a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 149,
"column": 2
} | {
"line": 149,
"column": 13
} | {
"line": 149,
"column": 14
} | [
{
"pp": "case pos\nι : Type u_1\nf : Filter ι\nu : ι → ℝ≥0\nhf✝ : f.NeBot\nhf : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nthis : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nc r : ℝ\nhr : r < c\n⊢ (∃ᶠ (a : ι) in f, r < ↑(u a)) ↔ 0 ≤ r → ∃ᶠ (a : ι) in f, r < ↑(u a)",
"ppTerm": "?pos✝",
"assigned": true,
... | [
"case pos\nι : Type u_1\nf : Filter ι\nu : ι → ℝ≥0\nhf✝ : f.NeBot\nhf : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nthis : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nc r : ℝ\nhr : r < c\n⊢ 0 ≤ r ∨ ∃ᶠ (a : ι) in f, r < ↑(u a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 24
} | {
"line": 176,
"column": 25
} | [
{
"pp": "α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha_top : a ≠ ∞\n⊢ limsup (fun x ↦ u x * a) f = a * limsup u f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.... | [
"α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha_top : a ≠ ∞\n⊢ limsup (fun x ↦ a * u x) f = a * limsup u f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 188,
"column": 2
} | {
"line": 188,
"column": 24
} | {
"line": 188,
"column": 25
} | [
{
"pp": "α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha₀ : a ≠ 0\nha_top : a ≠ ∞\n⊢ liminf (fun x ↦ u x * a) f = a * liminf u f",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Filter.liminf",
"CommSemiring.toNonUnitalCommSemiring",
... | [
"α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha₀ : a ≠ 0\nha_top : a ≠ ∞\n⊢ liminf (fun x ↦ a * u x) f = a * liminf u f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 199,
"column": 2
} | {
"line": 199,
"column": 24
} | {
"line": 199,
"column": 25
} | [
{
"pp": "α : Type u_1\nf : Filter α\ninst✝ : f.NeBot\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha_top : a ≠ ∞\n⊢ liminf (fun x ↦ u x * a) f = a * liminf u f",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"Filter.liminf",
"CommSemiring.toNonUnitalCommSemiring"... | [
"α : Type u_1\nf : Filter α\ninst✝ : f.NeBot\nu : α → ℝ≥0∞\na : ℝ≥0∞\nha_top : a ≠ ∞\n⊢ liminf (fun x ↦ a * u x) f = a * liminf u f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 24
} | {
"line": 220,
"column": 25
} | [
{
"pp": "α : Type u_1\nf : Filter α\ninst✝ : CountableInterFilter f\nu : α → ℝ≥0∞\na : ℝ≥0∞\n⊢ limsup (fun x ↦ u x * a) f = a * limsup u f",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
... | [
"α : Type u_1\nf : Filter α\ninst✝ : CountableInterFilter f\nu : α → ℝ≥0∞\na : ℝ≥0∞\n⊢ limsup (fun x ↦ a * u x) f = a * limsup u f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 227,
"column": 6
} | {
"line": 228,
"column": 90
} | {
"line": 229,
"column": 4
} | [
{
"pp": "α : Type u_1\nf : Filter α\ninst✝ : CountableInterFilter f\nu v : α → ℝ≥0∞\n⊢ limsup (u * v) f ≤ limsup (fun x ↦ limsup u f * v x) f",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"le_rfl",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring... | [] | refine limsup_le_limsup ?_
filter_upwards [@eventually_le_limsup _ f _ u] with x hx using mul_le_mul' hx le_rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Filter.ENNReal | {
"line": 227,
"column": 6
} | {
"line": 228,
"column": 90
} | {
"line": 229,
"column": 4
} | [
{
"pp": "α : Type u_1\nf : Filter α\ninst✝ : CountableInterFilter f\nu v : α → ℝ≥0∞\n⊢ limsup (u * v) f ≤ limsup (fun x ↦ limsup u f * v x) f",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"le_rfl",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring... | [] | refine limsup_le_limsup ?_
filter_upwards [@eventually_le_limsup _ f _ u] with x hx using mul_le_mul' hx le_rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Probability.ConditionalProbability | {
"line": 189,
"column": 2
} | {
"line": 191,
"column": 23
} | {
"line": 193,
"column": 0
} | [
{
"pp": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\n⊢ μ ≪ μ[|univ]",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"congrArg",
"CommSemirin... | [] | rw [cond, restrict_univ]
refine absolutelyContinuous_smul ?_
simp [measure_ne_top] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Probability.ConditionalProbability | {
"line": 189,
"column": 2
} | {
"line": 191,
"column": 23
} | {
"line": 193,
"column": 0
} | [
{
"pp": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\n⊢ μ ≪ μ[|univ]",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"congrArg",
"CommSemirin... | [] | rw [cond, restrict_univ]
refine absolutelyContinuous_smul ?_
simp [measure_ne_top] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Probability.ConditionalProbability | {
"line": 218,
"column": 61
} | {
"line": 218,
"column": 76
} | {
"line": 218,
"column": 77
} | [
{
"pp": "Ω : Type u_1\nm : MeasurableSpace Ω\ns : Set Ω\nhms : MeasurableSet s\nμ : Measure Ω\nt : Set Ω\n⊢ (μ s)⁻¹ • μ (t ∩ s) = (μ s)⁻¹ * μ (s ∩ t)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
... | [
"Ω : Type u_1\nm : MeasurableSpace Ω\ns : Set Ω\nhms : MeasurableSet s\nμ : Measure Ω\nt : Set Ω\n⊢ (μ s)⁻¹ • μ (s ∩ t) = (μ s)⁻¹ * μ (s ∩ t)"
] | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Probability.ConditionalProbability | {
"line": 221,
"column": 59
} | {
"line": 221,
"column": 74
} | {
"line": 221,
"column": 75
} | [
{
"pp": "Ω : Type u_1\nm : MeasurableSpace Ω\ns t : Set Ω\nht : MeasurableSet t\nμ : Measure Ω\n⊢ (μ s)⁻¹ • μ (t ∩ s) = (μ s)⁻¹ * μ (s ∩ t)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"HMul.h... | [
"Ω : Type u_1\nm : MeasurableSpace Ω\ns t : Set Ω\nht : MeasurableSet t\nμ : Measure Ω\n⊢ (μ s)⁻¹ • μ (s ∩ t) = (μ s)⁻¹ * μ (s ∩ t)"
] | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Probability.ConditionalProbability | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 20
} | {
"line": 224,
"column": 21
} | [
{
"pp": "Ω : Type u_1\nm : MeasurableSpace Ω\nμ : Measure Ω\ns : Set Ω\nhs₀ : μ s ≠ 0\nhs : μ s ≠ ∞\n⊢ μ[s | s] = 1",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"HMul.hMul",
"MeasureTheo... | [
"Ω : Type u_1\nm : MeasurableSpace Ω\nμ : Measure Ω\ns : Set Ω\nhs₀ : μ s ≠ 0\nhs : μ s ≠ ∞\n⊢ (μ s)⁻¹ * μ s = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 255,
"column": 28
} | {
"line": 255,
"column": 39
} | {
"line": 255,
"column": 40
} | [
{
"pp": "α : Type u_1\nf : Filter α\nu : α → ℝ\nh₁ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nr : ℝ≥0\nh : ∀ y > ↑r, ∀ᶠ (a : α) in f, u a < y\nx : ℝ≥0\nhx : some x > ↑r\n⊢ ↑x > ↑r",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"Eq.mp... | [
"α : Type u_1\nf : Filter α\nu : α → ℝ\nh₁ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nr : ℝ≥0\nh : ∀ y > ↑r, ∀ᶠ (a : α) in f, u a < y\nx : ℝ≥0\nhx : some x > ↑r\n⊢ r < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 257,
"column": 6
} | {
"line": 257,
"column": 39
} | {
"line": 257,
"column": 40
} | [
{
"pp": "case inl\nα : Type u_1\nf : Filter α\nu : α → ℝ\nh₁ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nr : ℝ≥0\nh : ∀ y > ↑r, ∀ᶠ (a : α) in f, u a < y\nx : ℝ≥0\nhx : some x > ↑r\na : α\nha : u a < ↑x\nha₀ : u a ≤ 0\n⊢ ENNReal.ofReal (u a) < some x",
"ppTerm... | [
"case inl\nα : Type u_1\nf : Filter α\nu : α → ℝ\nh₁ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nr : ℝ≥0\nh : ∀ y > ↑r, ∀ᶠ (a : α) in f, u a < y\nx : ℝ≥0\nhx : some x > ↑r\na : α\nha : u a < ↑x\nha₀ : u a ≤ 0\n⊢ 0 < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Probability.ConditionalProbability | {
"line": 277,
"column": 42
} | {
"line": 277,
"column": 57
} | {
"line": 277,
"column": 58
} | [
{
"pp": "Ω : Type u_1\nm : MeasurableSpace Ω\ns t : Set Ω\nhms : MeasurableSet s\nhmt : MeasurableSet t\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\n⊢ μ[t | s] = (μ s)⁻¹ * μ (t ∩ s)",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"MeasureTheory.... | [
"Ω : Type u_1\nm : MeasurableSpace Ω\ns t : Set Ω\nhms : MeasurableSet s\nhmt : MeasurableSet t\nμ : Measure Ω\ninst✝ : IsFiniteMeasure μ\n⊢ μ[t | s] = (μ s)⁻¹ * μ (s ∩ t)"
] | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Filter.ENNReal | {
"line": 261,
"column": 38
} | {
"line": 261,
"column": 56
} | {
"line": 261,
"column": 57
} | [
{
"pp": "α : Type u_1\nf : Filter α\nu : α → ℝ\nh₁ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nr : ℝ≥0\nh : ∀ y > ↑r, ∀ᶠ (a : α) in f, ENNReal.ofReal (u a) < y\nx : ℝ\nhx : x > ↑r\nthis : 0 < x\n⊢ ENNReal.ofReal x > ↑r",
"ppTerm": "?m.167",
"assigned": tr... | [
"α : Type u_1\nf : Filter α\nu : α → ℝ\nh₁ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f u\nr : ℝ≥0\nh : ∀ y > ↑r, ∀ᶠ (a : α) in f, ENNReal.ofReal (u a) < y\nx : ℝ\nhx : x > ↑r\nthis : 0 < x\n⊢ ↑r < x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 290,
"column": 38
} | {
"line": 290,
"column": 56
} | {
"line": 290,
"column": 57
} | [
{
"pp": "α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\nh₁ : ∀ᶠ (a : α) in f, u a ≠ ∞\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nhf : f.NeBot\nthis✝ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nr : ℝ\nhr : 0 ≤ r\nh : ∀ y > ENNReal.ofReal r, ∀ᶠ (a : α) in f, u a < y\nx : ℝ\... | [
"α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\nh₁ : ∀ᶠ (a : α) in f, u a ≠ ∞\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nhf : f.NeBot\nthis✝ : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nr : ℝ\nhr : 0 ≤ r\nh : ∀ y > ENNReal.ofReal r, ∀ᶠ (a : α) in f, u a < y\nx : ℝ\nhx : x > r\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.ENNReal | {
"line": 294,
"column": 32
} | {
"line": 294,
"column": 66
} | {
"line": 294,
"column": 67
} | [
{
"pp": "α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\nh₁ : ∀ᶠ (a : α) in f, u a ≠ ∞\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nhf : f.NeBot\nthis : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nr : ℝ\nhr : 0 ≤ r\nh : ∀ y > r, ∀ᶠ (a : α) in f, (u a).toReal < y\nx : ℝ≥0\nhx :... | [
"α : Type u_1\nf : Filter α\nu : α → ℝ≥0∞\nh₁ : ∀ᶠ (a : α) in f, u a ≠ ∞\nh₂ : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nhf : f.NeBot\nthis : IsCoboundedUnder (fun x1 x2 ↦ x1 ≤ x2) f fun a ↦ (u a).toReal\nr : ℝ\nhr : 0 ≤ r\nh : ∀ y > r, ∀ᶠ (a : α) in f, (u a).toReal < y\nx : ℝ≥0\nhx : some x > EN... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.MeasurableSpace.Pi | {
"line": 94,
"column": 4
} | {
"line": 94,
"column": 64
} | {
"line": 95,
"column": 4
} | [
{
"pp": "case a\nι : Type u_1\nα : ι → Type u_2\ninst✝ : Finite ι\nC : (i : ι) → Set (Set (α i))\nhC : ∀ (i : ι), IsCountablySpanning (C i)\nval✝ : Encodable ι\ns : (i : ι) → Set (α i)\nhs : s ∈ univ.pi C\ni : ι\n⊢ MeasurableSet (eval i ⁻¹' s i)",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": ... | [
"case a\nι : Type u_1\nα : ι → Type u_2\ninst✝ : Finite ι\nC : (i : ι) → Set (Set (α i))\nhC : ∀ (i : ι), IsCountablySpanning (C i)\nval✝ : Encodable ι\ns : (i : ι) → Set (α i)\nhs : s ∈ univ.pi C\ni : ι\n⊢ MeasurableSet (s i)"
] | apply @measurable_pi_apply _ _ (fun i => generateFrom (C i)) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Probability.UniformOn | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 90
} | {
"line": 157,
"column": 0
} | [
{
"pp": "Ω : Type u_1\ninst✝¹ : MeasurableSpace Ω\ninst✝ : MeasurableSingletonClass Ω\ns t : Set Ω\nhsf : s.Finite\nh : #⋯.toFinset = #hsf.toFinset\n⊢ ⋯.toFinset = hsf.toFinset",
"ppTerm": "?m.118",
"assigned": true,
"usedConstants": [
"Eq.ge",
"Set.Finite.inter_of_left",
"Set.inte... | [] | exact Finset.eq_of_subset_of_card_le (Set.Finite.toFinset_mono s.inter_subset_left) h.ge | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Function.EssSup | {
"line": 374,
"column": 6
} | {
"line": 374,
"column": 81
} | {
"line": 376,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0\nhf : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) (ae μ) f\nr : ℝ≥0∞\n⊢ r ≤ ⨅ a ∈ fun x ↦ (map f (ae μ)).sets {x_1 | (fun x_2 ↦ (fun x1 x2 ↦ x1 ≤ x2) x_2 x) x_1}, ↑a ↔\n r ≤ essSup (fun x ↦ ↑(f x)) μ",
"ppTerm": "?m.35",
"assigned": tr... | [] | simp [essSup, limsup, limsSup, eventually_map, ENNReal.forall_ennreal]; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.EssSup | {
"line": 374,
"column": 6
} | {
"line": 374,
"column": 81
} | {
"line": 376,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nf : α → ℝ≥0\nhf : IsBoundedUnder (fun x1 x2 ↦ x1 ≤ x2) (ae μ) f\nr : ℝ≥0∞\n⊢ r ≤ ⨅ a ∈ fun x ↦ (map f (ae μ)).sets {x_1 | (fun x_2 ↦ (fun x1 x2 ↦ x1 ≤ x2) x_2 x) x_1}, ↑a ↔\n r ≤ essSup (fun x ↦ ↑(f x)) μ",
"ppTerm": "?m.35",
"assigned": tr... | [] | simp [essSup, limsup, limsSup, eventually_map, ENNReal.forall_ennreal]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.SpecialFunctions.Basic | {
"line": 58,
"column": 2
} | {
"line": 59,
"column": 9
} | {
"line": 59,
"column": 10
} | [
{
"pp": "α : Type u_1\nx✝ : MeasurableSpace α\nf : α → ℝ\nμ : Measure α\nt : ℝ\nht : t ≠ 0\nhf : AEMeasurable (fun x ↦ rexp (t * f x)) μ\n⊢ AEMeasurable f μ",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nx✝ : MeasurableSpace α\nf : α → ℝ\nμ : Measure α\nt : ℝ\nht : t ≠ 0\nhf : AEMeasurable (fun x ↦ rexp (t * f x)) μ\n⊢ AEMeasurable f μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Pi | {
"line": 300,
"column": 2
} | {
"line": 300,
"column": 45
} | {
"line": 300,
"column": 46
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_3\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝ : ∀ (i : ι), SigmaFinite (μ i)\nf : (i : ι) → α i\n⊢ (Measure.pi μ) {f} = ∏ i, (μ i) {f i}",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedF... | [
"ι : Type u_1\nα : ι → Type u_3\ninst✝² : Fintype ι\ninst✝¹ : (i : ι) → MeasurableSpace (α i)\nμ : (i : ι) → Measure (α i)\ninst✝ : ∀ (i : ι), SigmaFinite (μ i)\nf : (i : ι) → α i\n⊢ (Measure.pi μ) {f} = ∏ i, (μ i) {f i}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 58
} | {
"line": 51,
"column": 59
} | [
{
"pp": "case hfq\nα : Type u_1\nε : Type u_2\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : ENorm ε\nf : α → ε\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ∞\nhfp : eLpNorm f p μ < ∞\n⊢ eLpNorm' f p.toReal μ < ∞",
"ppTerm": "?hfq",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"case hfq\nα : Type u_1\nε : Type u_2\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : ENorm ε\nf : α → ε\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ∞\nhfp : eLpNorm f p μ < ∞\n⊢ eLpNorm' f p.toReal μ < ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 59,
"column": 4
} | {
"line": 59,
"column": 77
} | {
"line": 60,
"column": 6
} | [
{
"pp": "α : Type u_1\nε : Type u_2\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : ENorm ε\nf : α → ε\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ∞\nh : ∫⁻ (a : α), ‖f a‖ₑ ^ p.toReal ∂μ < ∞\nhp' : 0 < p.toReal\nthis : 0 < 1 / p.toReal\n⊢ eLpNorm f p μ < ∞",
"ppTerm": "?m.68",
"assigned": true,
"... | [
"α : Type u_1\nε : Type u_2\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : ENorm ε\nf : α → ε\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ∞\nh : ∫⁻ (a : α), ‖f a‖ₑ ^ p.toReal ∂μ < ∞\nhp' : 0 < p.toReal\nthis : 0 < 1 / p.toReal\n⊢ (∫⁻ (x : α), ‖f x‖ₑ ^ p.toReal ∂μ) ^ p.toReal⁻¹ < ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Pi | {
"line": 562,
"column": 2
} | {
"line": 563,
"column": 9
} | {
"line": 563,
"column": 10
} | [
{
"pp": "ι✝ : Type u_1\nι' : Type u_2\nα : ι✝ → Type u_3\ninst✝⁷ : Fintype ι✝\nm : (i : ι✝) → OuterMeasure (α i)\ninst✝⁶ : (i : ι✝) → MeasurableSpace (α i)\nμ✝ : (i : ι✝) → Measure (α i)\ninst✝⁵ : ∀ (i : ι✝), SigmaFinite (μ✝ i)\nι : Type u_4\ninst✝⁴ : Fintype ι\nX : ι → Type u_5\ninst✝³ : (i : ι) → PseudoMetric... | [
"ι✝ : Type u_1\nι' : Type u_2\nα : ι✝ → Type u_3\ninst✝⁷ : Fintype ι✝\nm : (i : ι✝) → OuterMeasure (α i)\ninst✝⁶ : (i : ι✝) → MeasurableSpace (α i)\nμ✝ : (i : ι✝) → Measure (α i)\ninst✝⁵ : ∀ (i : ι✝), SigmaFinite (μ✝ i)\nι : Type u_4\ninst✝⁴ : Fintype ι\nX : ι → Type u_5\ninst✝³ : (i : ι) → PseudoMetricSpace (X i)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | {
"line": 74,
"column": 37
} | {
"line": 74,
"column": 58
} | {
"line": 74,
"column": 59
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ c *... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ c * ‖g x‖ₑ\nhp ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | {
"line": 76,
"column": 6
} | {
"line": 76,
"column": 58
} | {
"line": 76,
"column": 59
} | [
{
"pp": "case pos\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ, ‖f... | [
"case pos\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ c * ‖... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 232,
"column": 2
} | {
"line": 232,
"column": 63
} | {
"line": 232,
"column": 64
} | [
{
"pp": "case neg.inr\nα : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nε'' : Type u_8\ninst✝¹ : TopologicalSpace ε''\ninst✝ : ESeminormedAddMonoid ε''\nc : ε''\nhc' : ‖c‖ₑ ≠ ∞\np : ℝ≥0∞\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ∞\nhp : 0 < p.toReal\nhμ : ¬μ = 0\nhc : ¬‖c‖ₑ = 0\nhμ_ne_top : μ Set.univ ≠ ∞\n⊢ ‖c‖... | [
"case neg.inr\nα : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nε'' : Type u_8\ninst✝¹ : TopologicalSpace ε''\ninst✝ : ESeminormedAddMonoid ε''\nc : ε''\nhc' : ‖c‖ₑ ≠ ∞\np : ℝ≥0∞\nhp_ne_zero : p ≠ 0\nhp_ne_top : p ≠ ∞\nhp : 0 < p.toReal\nhμ : ¬μ = 0\nhc : ¬‖c‖ₑ = 0\nhμ_ne_top : μ Set.univ ≠ ∞\n⊢ μ Set.univ ^ p.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 285,
"column": 32
} | {
"line": 285,
"column": 71
} | {
"line": 285,
"column": 72
} | [
{
"pp": "α : Type u_1\nF : Type u_5\nG : Type u_6\nm0 : MeasurableSpace α\nq : ℝ\nμ : Measure α\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\ng : α → G\nhq : 0 ≤ q\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖\n⊢ ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ ‖g x‖ₑ",
"ppTerm": "?m.39",
"assigned": true,
"u... | [
"α : Type u_1\nF : Type u_5\nG : Type u_6\nm0 : MeasurableSpace α\nq : ℝ\nμ : Measure α\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\ng : α → G\nhq : 0 ≤ q\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖\n⊢ ∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 330,
"column": 28
} | {
"line": 330,
"column": 67
} | {
"line": 330,
"column": 68
} | [
{
"pp": "α : Type u_1\nF : Type u_5\nG : Type u_6\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\ng : α → G\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖\n⊢ ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ ‖g x‖ₑ",
"ppTerm": "?m.35",
"assigned": true,
"usedConsta... | [
"α : Type u_1\nF : Type u_5\nG : Type u_6\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedAddCommGroup G\nf : α → F\ng : α → G\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖\n⊢ ∀ᵐ (x : α) ∂μ, ‖f x‖ ≤ ‖g x‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.SMul | {
"line": 102,
"column": 2
} | {
"line": 103,
"column": 9
} | {
"line": 103,
"column": 10
} | [
{
"pp": "case inr\nα : Type u_1\nF : Type u_2\nm : MeasurableSpace α\nq : ℝ\nμ : Measure α\ninst✝³ : NormedAddCommGroup F\n𝕜 : Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : Module 𝕜 F\ninst✝ : NormSMulClass 𝕜 F\nf : α → F\nc : 𝕜\nhq_pos : 0 < q\nhc : c ≠ 0\n⊢ eLpNorm' f q μ ≤ eLpNorm' (c • f) q μ / ‖c‖... | [
"case inr\nα : Type u_1\nF : Type u_2\nm : MeasurableSpace α\nq : ℝ\nμ : Measure α\ninst✝³ : NormedAddCommGroup F\n𝕜 : Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : Module 𝕜 F\ninst✝ : NormSMulClass 𝕜 F\nf : α → F\nc : 𝕜\nhq_pos : 0 < q\nhc : c ≠ 0\n⊢ eLpNorm' f q μ ≤ ‖c‖ₑ⁻¹ * eLpNorm' (c • f) q μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.SMul | {
"line": 115,
"column": 2
} | {
"line": 116,
"column": 9
} | {
"line": 116,
"column": 10
} | [
{
"pp": "case inr\nα : Type u_1\nF : Type u_2\nm : MeasurableSpace α\ninst✝³ : NormedAddCommGroup F\n𝕜 : Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : Module 𝕜 F\ninst✝ : NormSMulClass 𝕜 F\nc : 𝕜\nf : α → F\np : ℝ≥0∞\nμ : Measure α\nhc : c ≠ 0\n⊢ eLpNorm f p μ ≤ eLpNorm (c • f) p μ / ‖c‖ₑ",
"ppTerm... | [
"case inr\nα : Type u_1\nF : Type u_2\nm : MeasurableSpace α\ninst✝³ : NormedAddCommGroup F\n𝕜 : Type u_3\ninst✝² : NormedDivisionRing 𝕜\ninst✝¹ : Module 𝕜 F\ninst✝ : NormSMulClass 𝕜 F\nc : 𝕜\nf : α → F\np : ℝ≥0∞\nμ : Measure α\nhc : c ≠ 0\n⊢ eLpNorm f p μ ≤ ‖c‖ₑ⁻¹ * eLpNorm (c • f) p μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.SMul | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 38
} | {
"line": 120,
"column": 39
} | [
{
"pp": "α : Type u_1\nF : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nn : ℕ\nf : α → F\n⊢ eLpNorm (n • f) p μ = ↑n * eLpNorm f p μ",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"α : Type u_1\nF : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace ℝ F\nn : ℕ\nf : α → F\n⊢ eLpNorm (n • f) p μ = ↑n * eLpNorm f p μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 21
} | {
"line": 174,
"column": 22
} | [
{
"pp": "case pos\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ≥0∞\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ,... | [
"case pos\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ≥0∞\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | {
"line": 175,
"column": 4
} | {
"line": 175,
"column": 21
} | {
"line": 175,
"column": 22
} | [
{
"pp": "case neg\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ≥0∞\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ,... | [
"case neg\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_6\ninst✝³ : TopologicalSpace ε'\ninst✝² : ContinuousENorm ε'\nε : Type u_7\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\ng : α → ε'\np : ℝ≥0∞\nhg : AEStronglyMeasurable g μ\nh : ∀ᵐ (x : α) ∂μ, ‖f x‖ₑ ≤ c ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 392,
"column": 2
} | {
"line": 392,
"column": 57
} | {
"line": 393,
"column": 4
} | [
{
"pp": "α : Type u_1\nF : Type u_5\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup F\nf : α → F\nC : ℝ≥0\nhfC : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ ≤ C\n⊢ eLpNorm f p μ ≤ C • μ Set.univ ^ p.toReal⁻¹",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Real",
"instHS... | [
"α : Type u_1\nF : Type u_5\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup F\nf : α → F\nC : ℝ≥0\nhfC : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ ≤ C\n⊢ eLpNorm f p μ ≤ ↑C * μ Set.univ ^ p.toReal⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Basic | {
"line": 394,
"column": 31
} | {
"line": 394,
"column": 42
} | {
"line": 394,
"column": 43
} | [
{
"pp": "α : Type u_1\nF : Type u_5\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup F\nf : α → F\nC : ℝ≥0\nhfC : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ ≤ C\nx✝ : α\nhx : ‖f x✝‖₊ ≤ C\n⊢ ‖f x✝‖ₑ ≤ ↑C",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ENNReal.o... | [
"α : Type u_1\nF : Type u_5\nm0 : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup F\nf : α → F\nC : ℝ≥0\nhfC : ∀ᵐ (x : α) ∂μ, ‖f x‖₊ ≤ C\nx✝ : α\nhx : ‖f x✝‖₊ ≤ C\n⊢ ‖f x✝‖₊ ≤ C"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSeminorm.Monotonicity | {
"line": 231,
"column": 17
} | {
"line": 231,
"column": 28
} | {
"line": 231,
"column": 29
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nR : Type u_5\ninst✝² : NormedAddCommGroup R\ninst✝¹ : StarAddMonoid R\ninst✝ : NormedStarGroup R\np : ℝ≥0∞\nf : α → R\nhf : MemLp f p μ\n⊢ eLpNorm (star f) p μ < ∞",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nR : Type u_5\ninst✝² : NormedAddCommGroup R\ninst✝¹ : StarAddMonoid R\ninst✝ : NormedStarGroup R\np : ℝ≥0∞\nf : α → R\nhf : MemLp f p μ\n⊢ eLpNorm f p μ < ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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