module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.MeasureTheory.Function.ConvergenceInMeasure | {
"line": 452,
"column": 2
} | {
"line": 452,
"column": 41
} | {
"line": 453,
"column": 2
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_5\ninst✝ : SeminormedAddCommGroup E\nf : ι → α → E\ng : α → E\nl : Filter ι\nδ : ℝ≥0∞\nhδ : 0 < δ\nhδ_top : δ ≠ ∞\nhfg : Tendsto (fun n ↦ essSup (fun x ↦ ‖(f n - g) x‖ₑ) μ) l (𝓝 0)\n⊢ Tendsto (fun i ↦ μ {x | δ ≤ edist (f i x)... | [
"α : Type u_1\nι : Type u_2\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_5\ninst✝ : SeminormedAddCommGroup E\nf : ι → α → E\ng : α → E\nl : Filter ι\nδ : ℝ≥0∞\nhδ : 0 < δ\nhδ_top : δ ≠ ∞\nhfg : ∀ ε > 0, ∀ᶠ (x : ι) in l, essSup (fun x_1 ↦ ‖(f x - g) x_1‖ₑ) μ ≤ ε\n⊢ ∀ ε > 0, ∀ᶠ (x : ι) in l, μ {x_1 | δ ≤ edist (... | rw [ENNReal.tendsto_nhds_zero] at hfg ⊢ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Algebra.Module.Multilinear.Bounded | {
"line": 54,
"column": 45
} | {
"line": 54,
"column": 56
} | {
"line": 54,
"column": 57
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\nF : Type u_3\nE : ι → Type u_4\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : (i : ι) → AddCommGroup (E i)\ninst✝⁵ : (i : ι) → Module 𝕜 (E i)\ninst✝⁴ : (i : ι) → TopologicalSpace (E i)\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : TopologicalSpace F\ninst✝ : Nonempty ι\ns :... | [
"ι : Type u_1\n𝕜 : Type u_2\nF : Type u_3\nE : ι → Type u_4\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : (i : ι) → AddCommGroup (E i)\ninst✝⁵ : (i : ι) → Module 𝕜 (E i)\ninst✝⁴ : (i : ι) → TopologicalSpace (E i)\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : TopologicalSpace F\ninst✝ : Nonempty ι\ns : Set ((i : ι... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Multilinear.Bounded | {
"line": 80,
"column": 14
} | {
"line": 80,
"column": 37
} | {
"line": 80,
"column": 37
} | [
{
"pp": "ι : Type u_1\n𝕜 : Type u_2\nF : Type u_3\nE : ι → Type u_4\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : (i : ι) → AddCommGroup (E i)\ninst✝⁵ : (i : ι) → Module 𝕜 (E i)\ninst✝⁴ : (i : ι) → TopologicalSpace (E i)\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : TopologicalSpace F\ninst✝ : Nonempty ι\ns :... | [
"ι : Type u_1\n𝕜 : Type u_2\nF : Type u_3\nE : ι → Type u_4\ninst✝⁷ : NormedField 𝕜\ninst✝⁶ : (i : ι) → AddCommGroup (E i)\ninst✝⁵ : (i : ι) → Module 𝕜 (E i)\ninst✝⁴ : (i : ι) → TopologicalSpace (E i)\ninst✝³ : AddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : TopologicalSpace F\ninst✝ : Nonempty ι\ns : Set ((i : ι... | rw [norm_mul, norm_div] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Normed.Ring.Units | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 13
} | {
"line": 174,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : HasSummableGeomSeries R\nx : Rˣ\n⊢ (fun t ↦ (↑x + t)⁻¹ʳ - ↑x⁻¹) =O[𝓝 0] fun t ↦ ‖t‖",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : HasSummableGeomSeries R\nx : Rˣ\n⊢ (fun t ↦ (↑x + t)⁻¹ʳ - ↑x⁻¹) =O[𝓝 0] fun t ↦ ‖t‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Ring.Units | {
"line": 191,
"column": 2
} | {
"line": 191,
"column": 33
} | {
"line": 191,
"column": 34
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : HasSummableGeomSeries R\nx : Rˣ\nh_is_o : (fun t ↦ (↑x + t)⁻¹ʳ - ↑x⁻¹) =o[𝓝 0] fun x ↦ 1\nh_lim : Tendsto (fun y ↦ y - ↑x) (𝓝 ↑x) (𝓝 0)\n⊢ Tendsto (fun e ↦ ‖e⁻¹ʳ - ↑x⁻¹‖) (𝓝 ↑x) (𝓝 0)",
"ppTerm": "?m.123",
"assigned": false,
"usedConstants":... | [
"R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : HasSummableGeomSeries R\nx : Rˣ\nh_is_o : (fun t ↦ (↑x + t)⁻¹ʳ - ↑x⁻¹) =o[𝓝 0] fun x ↦ 1\nh_lim : Tendsto (fun y ↦ y - ↑x) (𝓝 ↑x) (𝓝 0)\n⊢ Tendsto (fun e ↦ ‖e⁻¹ʳ - ↑x⁻¹‖) (𝓝 ↑x) (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Ring.Units | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 53
} | {
"line": 219,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : HasSummableGeomSeries R\nI : Ideal R\nx : R\nhxI : x ∈ I\nhx : ‖1 - x‖ < 1\nu : Rˣ := Units.oneSub (1 - x) hx\n⊢ 1 ∈ I",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : NormedRing R\ninst✝ : HasSummableGeomSeries R\nI : Ideal R\nx : R\nhxI : x ∈ I\nhx : ‖1 - x‖ < 1\nu : Rˣ := Units.oneSub (1 - x) hx\n⊢ 1 ∈ I"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Mul | {
"line": 42,
"column": 52
} | {
"line": 42,
"column": 63
} | {
"line": 42,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝³ : NonUnitalSeminormedRing R\ninst✝² : NormedSpace 𝕜 R\ninst✝¹ : IsScalarTower 𝕜 R R\ninst✝ : SMulCommClass 𝕜 R R\nx y : R\n⊢ ‖((LinearMap.mul 𝕜 R) x) ... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝³ : NonUnitalSeminormedRing R\ninst✝² : NormedSpace 𝕜 R\ninst✝¹ : IsScalarTower 𝕜 R R\ninst✝ : SMulCommClass 𝕜 R R\nx y : R\n⊢ ‖x * y‖ ≤ ‖x‖ * ‖y‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Mul | {
"line": 206,
"column": 15
} | {
"line": 206,
"column": 26
} | {
"line": 206,
"column": 27
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁴ : SeminormedRing R\ninst✝³ : NormedAlgebra 𝕜 R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : IsScalarTower 𝕜 R E\nx y : E\nh : (lsmul 𝕜 R).... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁴ : SeminormedRing R\ninst✝³ : NormedAlgebra 𝕜 R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : IsScalarTower 𝕜 R E\nx y : E\nh : (lsmul 𝕜 R).flip x = (ls... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Mul | {
"line": 222,
"column": 2
} | {
"line": 222,
"column": 13
} | {
"line": 222,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁴ : SeminormedRing R\ninst✝³ : NormedAlgebra 𝕜 R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : IsScalarTower 𝕜 R E\n⊢ ↑‖lsmul 𝕜 R‖₊ ≤ ↑1",
... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁴ : SeminormedRing R\ninst✝³ : NormedAlgebra 𝕜 R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : IsScalarTower 𝕜 R E\n⊢ ‖lsmul 𝕜 R‖ ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Mul | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 13
} | {
"line": 226,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁴ : SeminormedRing R\ninst✝³ : NormedAlgebra 𝕜 R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : IsScalarTower 𝕜 R E\n⊢ ↑‖lsmul 𝕜 R‖₊ ≤ 1",
... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : SeminormedAddCommGroup E\ninst✝⁵ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁴ : SeminormedRing R\ninst✝³ : NormedAlgebra 𝕜 R\ninst✝² : Module R E\ninst✝¹ : IsBoundedSMul R E\ninst✝ : IsScalarTower 𝕜 R E\n⊢ ‖lsmul 𝕜 R‖₊ ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Mul | {
"line": 271,
"column": 2
} | {
"line": 271,
"column": 13
} | {
"line": 271,
"column": 14
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁵ : NormedDivisionRing R\ninst✝⁴ : NormedAlgebra 𝕜 R\ninst✝³ : Module R E\ninst✝² : NormSMulClass R E\ninst✝¹ : IsScalarTower 𝕜 R E\ninst✝ : No... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁵ : NormedDivisionRing R\ninst✝⁴ : NormedAlgebra 𝕜 R\ninst✝³ : Module R E\ninst✝² : NormSMulClass R E\ninst✝¹ : IsScalarTower 𝕜 R E\ninst✝ : Nontrivial E\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Mul | {
"line": 295,
"column": 2
} | {
"line": 295,
"column": 25
} | {
"line": 295,
"column": 26
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁵ : NormedDivisionRing R\ninst✝⁴ : NormedAlgebra 𝕜 R\ninst✝³ : Module R E\ninst✝² : NormSMulClass R E\ninst✝¹ : IsScalarTower 𝕜 R E\ninst✝ : No... | [
"case refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : NontriviallyNormedField 𝕜\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace 𝕜 E\nR : Type u_3\ninst✝⁵ : NormedDivisionRing R\ninst✝⁴ : NormedAlgebra 𝕜 R\ninst✝³ : Module R E\ninst✝² : NormSMulClass R E\ninst✝¹ : IsScalarTower 𝕜 R E\ninst✝ : Nontrivial E\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.BoundedLinearMaps | {
"line": 135,
"column": 30
} | {
"line": 135,
"column": 41
} | {
"line": 135,
"column": 42
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : Module 𝕜 F\nf : E → F\nhf : IsBoundedLinearMap 𝕜 f\n⊢ ∃ M, 0 < M ∧ ∀ (x : E), ‖-f x‖ ≤ M * ‖x‖",
"ppTerm": "?m.61",
"assigned": ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : Module 𝕜 F\nf : E → F\nhf : IsBoundedLinearMap 𝕜 f\n⊢ ∃ M, 0 < M ∧ ∀ (x : E), ‖f x‖ ≤ M * ‖x‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.BoundedLinearMaps | {
"line": 147,
"column": 50
} | {
"line": 147,
"column": 78
} | {
"line": 147,
"column": 79
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : Module 𝕜 F\nf g : E → F\nhf : IsBoundedLinearMap 𝕜 f\nhg : IsBoundedLinearMap 𝕜 g\n⊢ IsBoundedLinearMap 𝕜 fun e ↦ f e - g e",
"ppT... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : Semiring 𝕜\ninst✝³ : SeminormedAddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : SeminormedAddCommGroup F\ninst✝ : Module 𝕜 F\nf g : E → F\nhf : IsBoundedLinearMap 𝕜 f\nhg : IsBoundedLinearMap 𝕜 g\n⊢ IsBoundedLinearMap 𝕜 fun e ↦ f e + -g e"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.BoundedLinearMaps | {
"line": 237,
"column": 49
} | {
"line": 237,
"column": 72
} | {
"line": 237,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : SeminormedAddCommGroup G\ninst✝ : Module 𝕜 G\nf : E × F → G\nh : IsBoundedBilinearMap 𝕜 f\nC : ℝ\nl... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : SeminormedAddCommGroup G\ninst✝ : Module 𝕜 G\nf : E × F → G\nh : IsBoundedBilinearMap 𝕜 f\nC : ℝ\nleft✝ : C > 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.BoundedLinearMaps | {
"line": 254,
"column": 4
} | {
"line": 254,
"column": 84
} | {
"line": 254,
"column": 85
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : SeminormedAddCommGroup G\ninst✝ : Module 𝕜 G\nf : E × F → G\nh : IsBoundedBilinearMap 𝕜 f\nx : E × ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : Semiring 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : SeminormedAddCommGroup F\ninst✝² : Module 𝕜 F\ninst✝¹ : SeminormedAddCommGroup G\ninst✝ : Module 𝕜 G\nf : E × F → G\nh : IsBoundedBilinearMap 𝕜 f\nx : E × F\nthis : Te... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Idempotent | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 13
} | {
"line": 54,
"column": 14
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np q : M →L[R] M\nhp : IsIdempotentElem p\nhq : IsIdempotentElem q\n⊢ p = q ↔ (↑p).range = (↑q).range ∧ (↑p).ker = (↑q).ker",
"ppTerm": "?m.78",
"assigned": false,
"usedCons... | [
"R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np q : M →L[R] M\nhp : IsIdempotentElem p\nhq : IsIdempotentElem q\n⊢ p = q ↔ (↑p).range = (↑q).range ∧ (↑p).ker = (↑q).ker"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Idempotent | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 34
} | {
"line": 64,
"column": 4
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf T : M →L[R] M\nhf : IsIdempotentElem f\n⊢ (↑f).range ∈ Module.End.invtSubmodule ↑T ↔ f ∘SL T ∘SL f = T ∘SL f",
"ppTerm": "?m.136",
"assigned": false,
"usedConstants": [],... | [
"R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf T : M →L[R] M\nhf : IsIdempotentElem f\n⊢ (↑f).range ∈ Module.End.invtSubmodule ↑T ↔ f ∘SL T ∘SL f = T ∘SL f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Idempotent | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 34
} | {
"line": 75,
"column": 4
} | [
{
"pp": "R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf T : M →L[R] M\nhf : IsIdempotentElem f\n⊢ (↑f).ker ∈ Module.End.invtSubmodule ↑T ↔ f ∘SL T ∘SL f = f ∘SL T",
"ppTerm": "?m.135",
"assigned": false,
"usedConstants": [],
... | [
"R : Type u_1\nM : Type u_2\ninst✝³ : Ring R\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nf T : M →L[R] M\nhf : IsIdempotentElem f\n⊢ (↑f).ker ∈ Module.End.invtSubmodule ↑T ↔ f ∘SL T ∘SL f = f ∘SL T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Maps.Strict.Basic | {
"line": 144,
"column": 15
} | {
"line": 144,
"column": 39
} | {
"line": 144,
"column": 40
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nZ : Type u_3\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X → Y\ng : Y → Z\ng_emb : IsEmbedding g\nΦ : Quotient (ker (g ∘ f)) ≃ₜ Quotient (ker f) := Homeomorph.Quotient.congrRight ⋯\nkey : g ∘ kerLift f ∘ ⇑Φ = kerLift (g ∘ f)\nH ... | [
"X : Type u_1\nY : Type u_2\nZ : Type u_3\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X → Y\ng : Y → Z\ng_emb : IsEmbedding g\nΦ : Quotient (ker (g ∘ f)) ≃ₜ Quotient (ker f) := Homeomorph.Quotient.congrRight ⋯\nkey : g ∘ kerLift f ∘ ⇑Φ = kerLift (g ∘ f)\nH : IsEmbeddin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas | {
"line": 98,
"column": 36
} | {
"line": 98,
"column": 78
} | {
"line": 98,
"column": 79
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_4\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf : Measurable f\ng g' : α → E\ng'meas : StronglyMeasurable g'\nhg' : ∀ᵐ (x : α) ∂μ, ↑(f x) ≠ 0 → g x = g' x\nA : MeasurableSet {x | f x ≠ 0}\na : α\nha : ↑(f a) ≠ 0 →... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_4\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf : Measurable f\ng g' : α → E\ng'meas : StronglyMeasurable g'\nhg' : ∀ᵐ (x : α) ∂μ, ↑(f x) ≠ 0 → g x = g' x\nA : MeasurableSet {x | f x ≠ 0}\na : α\nha : ↑(f a) ≠ 0 → g a = g' a\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 45
} | {
"line": 109,
"column": 46
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_4\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf : Measurable f\ng g' : α → E\ng'meas : StronglyMeasurable g'\nhg' : (fun x ↦ ↑(f x) • g x) =ᵐ[μ] g'\nx : α\nhx : ↑(f x) • g x = g' x\nh'x : ¬f x = 0\n⊢ ↑(f x) ≠ 0",
... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_4\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf : Measurable f\ng g' : α → E\ng'meas : StronglyMeasurable g'\nhg' : (fun x ↦ ↑(f x) • g x) =ᵐ[μ] g'\nx : α\nhx : ↑(f x) • g x = g' x\nh'x : ¬f x = 0\n⊢ ¬f x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Complement | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 13
} | {
"line": 131,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nthis : IsIdempotentElem 0\n⊢ IsTopCompl ⊥ ⊤",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nthis : IsIdempotentElem 0\n⊢ IsTopCompl ⊥ ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Complement | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 13
} | {
"line": 136,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nthis : IsIdempotentElem (ContinuousLinearMap.id R M)\n⊢ IsTopCompl ⊤ ⊥",
"ppTerm": "?m.44",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []... | [
"R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nthis : IsIdempotentElem (ContinuousLinearMap.id R M)\n⊢ IsTopCompl ⊤ ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Complement | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 13
} | {
"line": 152,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : Submodule R M\nf : M →L[R] ↥p\nhf : ∀ (x : ↥p), f ↑x = x\n⊢ IsTopCompl p (↑f).ker",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝³ : Ring R\nM : Type u_2\ninst✝² : TopologicalSpace M\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\np : Submodule R M\nf : M →L[R] ↥p\nhf : ∀ (x : ↥p), f ↑x = x\n⊢ IsTopCompl p (↑f).ker"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Real | {
"line": 433,
"column": 2
} | {
"line": 433,
"column": 43
} | {
"line": 434,
"column": 2
} | [
{
"pp": "α : Type u_1\nι : Type u_3\nx✝ : MeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\ns : Finset ι\nt : ι → Set α\nh : ∀ i ∈ s, MeasurableSet (t i)\nH : (↑s).PairwiseDisjoint t\n⊢ ∑ x ∈ s, (μ (t x)).toReal ≤ (μ univ).toReal",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_1\nι : Type u_3\nx✝ : MeasurableSpace α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\ns : Finset ι\nt : ι → Set α\nh : ∀ i ∈ s, MeasurableSet (t i)\nH : (↑s).PairwiseDisjoint t\n⊢ (∑ a ∈ s, μ (t a)).toReal ≤ (μ univ).toReal"
] | rw [← ENNReal.toReal_sum (by finiteness)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Function.LpSpace.Indicator | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 84
} | {
"line": 57,
"column": 85
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup E\nhp : p ≠ ∞\nc : E\nε : ℝ≥0∞\nhε : ε ≠ 0\nh'p : p ≠ 0\nhp₀ : 0 < p\nhp₀' : 0 ≤ 1 / p.toReal\nhp₀'' : 0 < p.toReal\nthis : Tendsto (fun x ↦ ↑(‖c‖₊ * x ^ (1 / p.toReal))) (𝓝 0) (𝓝 ↑0)\nhε' : 0 < ε\n... | [
"α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup E\nhp : p ≠ ∞\nc : E\nε : ℝ≥0∞\nhε : ε ≠ 0\nh'p : p ≠ 0\nhp₀ : 0 < p\nhp₀' : 0 ≤ 1 / p.toReal\nhp₀'' : 0 < p.toReal\nthis : Tendsto (fun x ↦ ↑(‖c‖₊ * x ^ (1 / p.toReal))) (𝓝 0) (𝓝 ↑0)\nhε' : 0 < ε\nδ : ℝ≥0\nhδ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LpSpace.Indicator | {
"line": 158,
"column": 2
} | {
"line": 159,
"column": 9
} | {
"line": 159,
"column": 10
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup E\ns : Set α\nhs : MeasurableSet s\nhμs : μ s ≠ ∞\nc : E\n⊢ ‖indicatorConstLp p hs hμs c‖ₑ ≤ ‖c‖ₑ * μ s ^ (1 / p.toReal)",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq... | [
"α : Type u_1\nE : Type u_2\nm : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\ninst✝ : NormedAddCommGroup E\ns : Set α\nhs : MeasurableSet s\nhμs : μ s ≠ ∞\nc : E\n⊢ eLpNorm (↑↑(indicatorConstLp p hs hμs c)) p μ ≤ ‖c‖ₑ * μ s ^ p.toReal⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.IntegrableOn | {
"line": 242,
"column": 2
} | {
"line": 242,
"column": 13
} | {
"line": 242,
"column": 14
} | [
{
"pp": "case intro\nα : Type u_1\nβ : Type u_2\nε : Type u_3\nmα : MeasurableSpace α\nf : α → ε\nμ : Measure α\ninst✝³ : TopologicalSpace ε\ninst✝² : ContinuousENorm ε\ninst✝¹ : PseudoMetrizableSpace ε\ninst✝ : Finite β\nt : β → Set α\nval✝ : Fintype β\n⊢ IntegrableOn f (⋃ i, t i) μ ↔ ∀ (i : β), IntegrableOn f... | [
"case intro\nα : Type u_1\nβ : Type u_2\nε : Type u_3\nmα : MeasurableSpace α\nf : α → ε\nμ : Measure α\ninst✝³ : TopologicalSpace ε\ninst✝² : ContinuousENorm ε\ninst✝¹ : PseudoMetrizableSpace ε\ninst✝ : Finite β\nt : β → Set α\nval✝ : Fintype β\n⊢ IntegrableOn f (⋃ i, t i) μ ↔ ∀ (i : β), IntegrableOn f (t i) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.IntegrableOn | {
"line": 253,
"column": 2
} | {
"line": 253,
"column": 13
} | {
"line": 253,
"column": 14
} | [
{
"pp": "α : Type u_1\nE : Type u_5\nmα : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : MeasurableSingletonClass α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\ns : Set α\nhs : s.Finite\nf : α → E\n⊢ IntegrableOn f s μ",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedF... | [
"α : Type u_1\nE : Type u_5\nmα : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : MeasurableSingletonClass α\nμ : Measure α\ninst✝ : IsFiniteMeasure μ\ns : Set α\nhs : s.Finite\nf : α → E\n⊢ IntegrableOn f s μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 36
} | {
"line": 144,
"column": 37
} | [
{
"pp": "𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝² : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝¹ : SeminormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : MultilinearMap 𝕜 E G\nhf : Continuous[Pi.topologicalSpa... | [
"𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝² : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝¹ : SeminormedAddCommGroup G\ninst✝ : NormedSpace 𝕜 G\nf : MultilinearMap 𝕜 E G\nhf : Continuous[Pi.topologicalSpace, PseudoMe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 13
} | {
"line": 206,
"column": 14
} | [
{
"pp": "α : Type u_1\nε : Type u_5\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : TopologicalSpace ε\ninst✝ : ContinuousENorm ε\nf : α → ε\np : ℕ\nhf : MemLp f (↑p) μ\nhp : p ≠ 0\n⊢ Integrable (fun x ↦ ‖f x‖ₑ ^ p) μ",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"α : Type u_1\nε : Type u_5\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : TopologicalSpace ε\ninst✝ : ContinuousENorm ε\nf : α → ε\np : ℕ\nhf : MemLp f (↑p) μ\nhp : p ≠ 0\n⊢ Integrable (fun x ↦ ‖f x‖ₑ ^ p) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 13
} | {
"line": 210,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf : α → β\np : ℕ\nhf : MemLp f (↑p) μ\nhp : p ≠ 0\n⊢ Integrable (fun x ↦ ‖f x‖ ^ p) μ",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf : α → β\np : ℕ\nhf : MemLp f (↑p) μ\nhp : p ≠ 0\n⊢ Integrable (fun x ↦ ‖f x‖ ^ p) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 213,
"column": 48
} | {
"line": 213,
"column": 59
} | {
"line": 213,
"column": 60
} | [
{
"pp": "α : Type u_1\nε : Type u_5\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\ninst✝ : IsFiniteMeasure μ\nf : α → ε\np : ℕ\nhf : MemLp f (↑p) μ\n⊢ Integrable (fun x ↦ ‖f x‖ₑ ^ p) μ",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"... | [
"α : Type u_1\nε : Type u_5\nm : MeasurableSpace α\nμ : Measure α\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\ninst✝ : IsFiniteMeasure μ\nf : α → ε\np : ℕ\nhf : MemLp f (↑p) μ\n⊢ Integrable (fun x ↦ ‖f x‖ₑ ^ p) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 216,
"column": 48
} | {
"line": 216,
"column": 59
} | {
"line": 216,
"column": 60
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : IsFiniteMeasure μ\nf : α → β\np : ℕ\nhf : MemLp f (↑p) μ\n⊢ Integrable (fun x ↦ ‖f x‖ ^ p) μ",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGo... | [
"α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : IsFiniteMeasure μ\nf : α → β\np : ℕ\nhf : MemLp f (↑p) μ\n⊢ Integrable (fun x ↦ ‖f x‖ ^ p) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 80
} | {
"line": 168,
"column": 4
} | [
{
"pp": "case neg\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nf : MultilinearMap 𝕜 E G\nhf₀... | [
"case neg\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nf : MultilinearMap 𝕜 E G\nhf₀ : ∀ {m : (i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.IntegrableOn | {
"line": 414,
"column": 18
} | {
"line": 414,
"column": 29
} | {
"line": 414,
"column": 30
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\ns t : Set α\nμ : Measure α\nε' : Type u_7\ninst✝² : TopologicalSpace ε'\ninst✝¹ : ENormedAddMonoid ε'\ninst✝ : PseudoMetrizableSpace ε'\nf : α → ε'\nhf : IntegrableOn f s μ\nht : NullMeasurableSet t μ\nh't : ∀ᵐ (x : α) ∂μ, x ∈ t \\ s → f x = 0\nu : Set α := {x | x ... | [
"α : Type u_1\nmα : MeasurableSpace α\ns t : Set α\nμ : Measure α\nε' : Type u_7\ninst✝² : TopologicalSpace ε'\ninst✝¹ : ENormedAddMonoid ε'\ninst✝ : PseudoMetrizableSpace ε'\nf : α → ε'\nhf : IntegrableOn f s μ\nht : NullMeasurableSet t μ\nh't : ∀ᵐ (x : α) ∂μ, x ∈ t \\ s → f x = 0\nu : Set α := {x | x ∈ s ∧ f x ≠ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.IntegrableOn | {
"line": 457,
"column": 2
} | {
"line": 457,
"column": 13
} | {
"line": 457,
"column": 14
} | [
{
"pp": "α : Type u_1\nmα : MeasurableSpace α\ns : Set α\nμ : Measure α\nε' : Type u_7\ninst✝² : TopologicalSpace ε'\ninst✝¹ : ENormedAddMonoid ε'\ninst✝ : PseudoMetrizableSpace ε'\nf : α → ε'\nhs : MeasurableSet s\nhf : IntegrableOn f (s ∩ support f) μ\n⊢ IntegrableOn f s μ",
"ppTerm": "?m.24",
"assign... | [
"α : Type u_1\nmα : MeasurableSpace α\ns : Set α\nμ : Measure α\nε' : Type u_7\ninst✝² : TopologicalSpace ε'\ninst✝¹ : ENormedAddMonoid ε'\ninst✝ : PseudoMetrizableSpace ε'\nf : α → ε'\nhs : MeasurableSet s\nhf : IntegrableOn f (s ∩ support f) μ\n⊢ IntegrableOn f s μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 328,
"column": 4
} | {
"line": 328,
"column": 72
} | {
"line": 329,
"column": 6
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε : Type u_8\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ∞\nh : Integrable f (c • μ)\n⊢ Integrable f μ",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε : Type u_8\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ∞\nh : Integrable f (c • μ)\n⊢ Integrable f μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 334,
"column": 30
} | {
"line": 334,
"column": 41
} | {
"line": 334,
"column": 42
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε : Type u_8\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ∞\n⊢ c⁻¹ ≠ 0",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ENNReal.in... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε : Type u_8\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ∞\n⊢ ¬c = ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 334,
"column": 50
} | {
"line": 334,
"column": 61
} | {
"line": 334,
"column": 62
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε : Type u_8\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ∞\n⊢ c⁻¹ ≠ ∞",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ENNReal.in... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε : Type u_8\ninst✝¹ : TopologicalSpace ε\ninst✝ : ESeminormedAddMonoid ε\nf : α → ε\nc : ℝ≥0∞\nh₁ : c ≠ 0\nh₂ : c ≠ ∞\n⊢ ¬c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 449,
"column": 2
} | {
"line": 449,
"column": 39
} | {
"line": 449,
"column": 40
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_8\ninst✝² : TopologicalSpace ε'\ninst✝¹ : ESeminormedAddCommMonoid ε'\ninst✝ : ContinuousAdd ε'\nι : Type u_9\ns : Finset ι\nf : ι → α → ε'\nhf : ∀ i ∈ s, Integrable (f i) μ\n⊢ Integrable (fun a ↦ ∑ i ∈ s, f i a) μ",
"ppTerm": "?m.30",... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nε' : Type u_8\ninst✝² : TopologicalSpace ε'\ninst✝¹ : ESeminormedAddCommMonoid ε'\ninst✝ : ContinuousAdd ε'\nι : Type u_9\ns : Finset ι\nf : ι → α → ε'\nhf : ∀ i ∈ s, Integrable (f i) μ\n⊢ Integrable (fun a ↦ (∑ c ∈ s, f c) a) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 541,
"column": 31
} | {
"line": 541,
"column": 64
} | {
"line": 541,
"column": 65
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf g : α → β\nhf : Integrable f μ\nhg : Integrable g μ\n⊢ Integrable (f - g) μ",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MeasureTheory.Measure",
"congr... | [
"α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nμ : Measure α\ninst✝ : NormedAddCommGroup β\nf g : α → β\nhf : Integrable f μ\nhg : Integrable g μ\n⊢ Integrable (f + -g) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.IntegrableOn | {
"line": 602,
"column": 4
} | {
"line": 602,
"column": 20
} | {
"line": 602,
"column": 21
} | [
{
"pp": "case neg\nα : Type u_1\nE : Type u_5\nmα : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nμ : Measure α\nl : Filter α\n𝕜 : Type u_7\ninst✝¹ : NormedField 𝕜\ninst✝ : NormedSpace 𝕜 E\nf : α → E\nc : 𝕜\nhc : ¬c = 0\n⊢ IntegrableAtFilter (c • f) l μ ↔ c = 0 ∨ IntegrableAtFilter f l μ",
"ppTerm":... | [
"case neg\nα : Type u_1\nE : Type u_5\nmα : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\nμ : Measure α\nl : Filter α\n𝕜 : Type u_7\ninst✝¹ : NormedField 𝕜\ninst✝ : NormedSpace 𝕜 E\nf : α → E\nc : 𝕜\nhc : ¬c = 0\n⊢ IntegrableAtFilter (c • f) l μ ↔ IntegrableAtFilter f l μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 670,
"column": 4
} | {
"line": 671,
"column": 11
} | {
"line": 671,
"column": 12
} | [
{
"pp": "case a\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousENorm E\nf : α → E\nhf : Integrable f μ\nε : ℝ≥0∞\nhε : 0 < ε\nhε' : ε ≠ ∞\n⊢ ε⁻¹ ^ ENNReal.toReal 1 < ∞",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq... | [
"case a\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousENorm E\nf : α → E\nhf : Integrable f μ\nε : ℝ≥0∞\nhε : 0 < ε\nhε' : ε ≠ ∞\n⊢ 0 < ε"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 672,
"column": 4
} | {
"line": 672,
"column": 59
} | {
"line": 673,
"column": 6
} | [
{
"pp": "case a\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousENorm E\nf : α → E\nhf : Integrable f μ\nε : ℝ≥0∞\nhε : 0 < ε\nhε' : ε ≠ ∞\n⊢ eLpNorm f 1 μ ^ ENNReal.toReal 1 < ∞",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [... | [
"case a\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousENorm E\nf : α → E\nhf : Integrable f μ\nε : ℝ≥0∞\nhε : 0 < ε\nhε' : ε ≠ ∞\n⊢ eLpNorm f 1 μ < ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 772,
"column": 4
} | {
"line": 773,
"column": 11
} | {
"line": 773,
"column": 12
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : MeasurableSingletonClass α\nf : α → β\nhs : Summable fun x ↦ ‖f x‖\n⊢ (Function.support f).Countable",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"id",
"SubtractionMonoid.toSub... | [
"α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : MeasurableSingletonClass α\nf : α → β\nhs : Summable fun x ↦ ‖f x‖\n⊢ {x | ¬f x = 0}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 778,
"column": 4
} | {
"line": 778,
"column": 67
} | {
"line": 778,
"column": 68
} | [
{
"pp": "case refine_1\nα : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : MeasurableSingletonClass α\nf : α → β\nhs : Summable fun x ↦ ‖f x‖\nhs' : (Function.support f).Countable\nthis✝ : MeasurableSpace β := borel β\nthis : BorelSpace β\n⊢ {x | 0 x ≠ f x}.Countable",
... | [
"case refine_1\nα : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup β\ninst✝ : MeasurableSingletonClass α\nf : α → β\nhs : Summable fun x ↦ ‖f x‖\nhs' : (Function.support f).Countable\nthis✝ : MeasurableSpace β := borel β\nthis : BorelSpace β\n⊢ {x | ¬f x = 0}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.FiniteDimension | {
"line": 163,
"column": 6
} | {
"line": 163,
"column": 58
} | {
"line": 164,
"column": 6
} | [
{
"pp": "𝕜 : Type u\nhnorm : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nl : E →ₗ[𝕜] 𝕜\nhl : IsClosed[inst✝²] ↑l.ker\nH : ¬finrank 𝕜 ↥l.range = 0\nthis : finrank 𝕜 ↥l.range... | [
"𝕜 : Type u\nhnorm : NontriviallyNormedField 𝕜\nE : Type v\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : IsTopologicalAddGroup E\ninst✝ : ContinuousSMul 𝕜 E\nl : E →ₗ[𝕜] 𝕜\nhl : IsClosed[inst✝²] ↑l.ker\nH : ¬finrank 𝕜 ↥l.range = 0\nthis : finrank 𝕜 ↥l.range = 1\nhi : F... | rw [← LinearMap.range_eq_top, Submodule.range_liftQ] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Integral.IntegrableOn | {
"line": 798,
"column": 2
} | {
"line": 798,
"column": 13
} | {
"line": 798,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nmα : MeasurableSpace α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : CompactSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : PseudoMetrizableSpace β\nμ : Measure α\nf : α → β\nhf : Continuous[inst✝⁴, inst✝¹] f\n⊢ AEStronglyMeasurable f μ",
"ppTerm"... | [
"α : Type u_1\nβ : Type u_2\nmα : MeasurableSpace α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OpensMeasurableSpace α\ninst✝² : CompactSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : PseudoMetrizableSpace β\nμ : Measure α\nf : α → β\nhf : Continuous[inst✝⁴, inst✝¹] f\n⊢ AEStronglyMeasurable f μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 798,
"column": 6
} | {
"line": 798,
"column": 71
} | {
"line": 798,
"column": 72
} | [
{
"pp": "case pos\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf : Measurable f\ng : α → E\nH : AEStronglyMeasurable (fun x ↦ ↑(f x) • g x) μ\n⊢ AEMeasurable (fun a ↦ ‖g a‖ₑ) (μ.withDensity fun x ↦ ↑(f x))",
"ppTerm"... | [
"case pos\nα : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf : α → ℝ≥0\nhf : Measurable f\ng : α → E\nH : AEStronglyMeasurable (fun x ↦ ↑(f x) • g x) μ\n⊢ AEMeasurable (fun x ↦ ↑(f x) * ‖g x‖ₑ) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 400,
"column": 2
} | {
"line": 400,
"column": 37
} | {
"line": 400,
"column": 38
} | [
{
"pp": "𝕜 : Type u\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nn : ℕ\nEi : Fin n → Type u_1\ninst✝¹ : (i : Fin n) → SeminormedAddCommGroup (Ei i)\ninst✝ : (i : Fin n) → NormedSpace 𝕜 (Ei i)\nf : ContinuousMultilinearMap 𝕜 Ei G\nm : (i : Fi... | [
"𝕜 : Type u\nG : Type wG\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\nn : ℕ\nEi : Fin n → Type u_1\ninst✝¹ : (i : Fin n) → SeminormedAddCommGroup (Ei i)\ninst✝ : (i : Fin n) → NormedSpace 𝕜 (Ei i)\nf : ContinuousMultilinearMap 𝕜 Ei G\nm : (i : Fin n) → Ei i\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 879,
"column": 6
} | {
"line": 879,
"column": 48
} | {
"line": 879,
"column": 49
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nε : Type u_5\nε' : Type u_6\nε'' : Type u_7\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁹ : MeasurableSpace δ\ninst✝⁸ : NormedAddCommGroup β\ninst✝⁷ : NormedAddCommGroup γ\ninst✝⁶ : TopologicalSpace ε\ninst✝⁵ : ContinuousENorm ε\ninst✝⁴ : Topolo... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nε : Type u_5\nε' : Type u_6\nε'' : Type u_7\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁹ : MeasurableSpace δ\ninst✝⁸ : NormedAddCommGroup β\ninst✝⁷ : NormedAddCommGroup γ\ninst✝⁶ : TopologicalSpace ε\ninst✝⁵ : ContinuousENorm ε\ninst✝⁴ : TopologicalSpace ε... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 473,
"column": 42
} | {
"line": 473,
"column": 77
} | {
"line": 473,
"column": 78
} | [
{
"pp": "case h1\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nA : ∀ (f : ContinuousMultilinea... | [
"case h1\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nA : ∀ (f : ContinuousMultilinearMap 𝕜 E G ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 478,
"column": 4
} | {
"line": 478,
"column": 71
} | {
"line": 479,
"column": 4
} | [
{
"pp": "case refine_2\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nA : ∀ (f : ContinuousMult... | [
"case refine_2\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nA : ∀ (f : ContinuousMultilinearMap �... | simp only [Seminorm.mem_ball_zero, mem_closedBall_zero_iff] at hf ⊢ | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 892,
"column": 6
} | {
"line": 892,
"column": 48
} | {
"line": 892,
"column": 49
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nε : Type u_5\nε' : Type u_6\nε'' : Type u_7\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁹ : MeasurableSpace δ\ninst✝⁸ : NormedAddCommGroup β\ninst✝⁷ : NormedAddCommGroup γ\ninst✝⁶ : TopologicalSpace ε\ninst✝⁵ : ContinuousENorm ε\ninst✝⁴ : Topolo... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nε : Type u_5\nε' : Type u_6\nε'' : Type u_7\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝⁹ : MeasurableSpace δ\ninst✝⁸ : NormedAddCommGroup β\ninst✝⁷ : NormedAddCommGroup γ\ninst✝⁶ : TopologicalSpace ε\ninst✝⁵ : ContinuousENorm ε\ninst✝⁴ : TopologicalSpace ε... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 549,
"column": 33
} | {
"line": 549,
"column": 80
} | {
"line": 549,
"column": 81
} | [
{
"pp": "𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE' : ι' → Type wE'\ninst✝⁶ : Fintype ι'\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : Fintype ι\ninst✝¹ : (i' : ι') → SeminormedAddCommGroup (E' i')\ninst✝ ... | [
"𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE' : ι' → Type wE'\ninst✝⁶ : Fintype ι'\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝² : Fintype ι\ninst✝¹ : (i' : ι') → SeminormedAddCommGroup (E' i')\ninst✝ : (i' : ι') ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 598,
"column": 4
} | {
"line": 598,
"column": 15
} | {
"line": 598,
"column": 16
} | [
{
"pp": "case a\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁴ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : Fintype ι\ninst✝ : IsEmpty ι\nx : G\n⊢ ‖x‖... | [
"case a\n𝕜 : Type u\nι : Type v\nE : ι → Type wE\nG : Type wG\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁴ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 G\ninst✝¹ : Fintype ι\ninst✝ : IsEmpty ι\nx : G\n⊢ ‖x‖ ≤ ‖constOfI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 1124,
"column": 89
} | {
"line": 1126,
"column": 13
} | {
"line": 1128,
"column": 0
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\n𝕜 : Type u_8\ninst✝ : RCLike 𝕜\nf : α → 𝕜\nhf : Integrable f μ\n⊢ Integrable (fun x ↦ RCLike.im (f x)) μ",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real"... | [] | by
rw [← memLp_one_iff_integrable] at hf ⊢
exact hf.im | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 1145,
"column": 2
} | {
"line": 1145,
"column": 72
} | {
"line": 1145,
"column": 73
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nH : Type u_8\ninst✝ : NormedAddCommGroup H\nm0 : MeasurableSpace α\nμ' : Measure α\nf : α → H\nhm : m ≤ m0\nhf_meas_ae : AEStronglyMeasurable f (μ'.trim hm)\nhf : HasFiniteIntegral f (μ'.trim hm)\n⊢ HasFiniteIntegral f μ'",
"ppTerm": "?m.39",
"assigned": tru... | [
"α : Type u_1\nm : MeasurableSpace α\nH : Type u_8\ninst✝ : NormedAddCommGroup H\nm0 : MeasurableSpace α\nμ' : Measure α\nf : α → H\nhm : m ≤ m0\nhf_meas_ae : AEStronglyMeasurable f (μ'.trim hm)\nhf : HasFiniteIntegral f (μ'.trim hm)\n⊢ ∫⁻ (a : α), ‖f a‖ₑ ∂μ' < ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 743,
"column": 12
} | {
"line": 743,
"column": 32
} | {
"line": 743,
"column": 33
} | [
{
"pp": "case refine_1\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nn : ℕ\nA : Type u_1\ninst✝¹ : SeminormedRing A\ninst✝ : NormedAlgebra 𝕜 A\nm : Fin n.succ → A\n⊢ ¬List.map m (List.finRange n.succ) = []",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"con... | [
"case refine_1\n𝕜 : Type u\ninst✝² : NontriviallyNormedField 𝕜\nn : ℕ\nA : Type u_1\ninst✝¹ : SeminormedRing A\ninst✝ : NormedAlgebra 𝕜 A\nm : Fin n.succ → A\n⊢ ¬List.finRange n.succ = []"
] | List.map_eq_nil_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Function.L1Space.Integrable | {
"line": 1201,
"column": 14
} | {
"line": 1201,
"column": 25
} | {
"line": 1201,
"column": 26
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\nH : Type u_9\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedAddCommGroup H\n𝕜 : Type u_10\n𝕜' : Type u_11\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NontriviallyNormedField 𝕜'\ninst✝⁵ : NormedSpace 𝕜' E\ninst✝⁴ : NormedSpace 𝕜 H... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nE : Type u_8\nH : Type u_9\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedAddCommGroup H\n𝕜 : Type u_10\n𝕜' : Type u_11\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : NontriviallyNormedField 𝕜'\ninst✝⁵ : NormedSpace 𝕜' E\ninst✝⁴ : NormedSpace 𝕜 H\nσ : 𝕜 →+*... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Constructions.Polish.StronglyMeasurable | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 42
} | {
"line": 57,
"column": 43
} | [
{
"pp": "case inl\nι : Type u_1\nX : Type u_2\nE : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace E\ninst✝² : Countable ι\nf : ι → X → E\nhE : Nonempty E\ninst✝¹ : IsCompletelyMetrizableSpace E\nhf : ∀ (i : ι), StronglyMeasurable (f i)\ninst✝ : ⊥.IsCountablyGenerated\n⊢ StronglyMeasurable fun x... | [
"case inl\nι : Type u_1\nX : Type u_2\nE : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace E\ninst✝² : Countable ι\nf : ι → X → E\nhE : Nonempty E\ninst✝¹ : IsCompletelyMetrizableSpace E\nhf : ∀ (i : ι), StronglyMeasurable (f i)\ninst✝ : ⊥.IsCountablyGenerated\n⊢ StronglyMeasurable fun x ↦ ⊥.lim"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 168,
"column": 51
} | {
"line": 168,
"column": 93
} | {
"line": 168,
"column": 94
} | [
{
"pp": "X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrableOn f s μ\nT : Set (Set X)\nT_count : T.Countable\nT_open : ∀ u ∈ T,... | [
"X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrableOn f s μ\nT : Set (Set X)\nT_count : T.Countable\nT_open : ∀ u ∈ T, IsOpen[inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 170,
"column": 41
} | {
"line": 170,
"column": 69
} | {
"line": 170,
"column": 70
} | [
{
"pp": "X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrableOn f s μ\nT : Set (Set X)\nT_count : T.Countable\nT_open : ∀ u ∈ T,... | [
"X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrableOn f s μ\nT : Set (Set X)\nT_count : T.Countable\nT_open : ∀ u ∈ T, IsOpen[inst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 865,
"column": 6
} | {
"line": 865,
"column": 17
} | {
"line": 865,
"column": 18
} | [
{
"pp": "𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹⁰ : Fintype ι'\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁷ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁶ : (i : ι) → SeminormedAd... | [
"𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹⁰ : Fintype ι'\ninst✝⁹ : NontriviallyNormedField 𝕜\ninst✝⁸ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁷ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁶ : (i : ι) → SeminormedAddCommGroup (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 94,
"column": 4
} | {
"line": 94,
"column": 53
} | {
"line": 94,
"column": 54
} | [
{
"pp": "case pos\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns : Set E\ny₀ : E\nh₀ : y₀ ∈ s\ninst✝ : SeparableSpace ↑s\nhp_ne_top : p ≠ ∞\nμ : Measure β\nhμ : ∀ᵐ (x :... | [
"case pos\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns : Set E\ny₀ : E\nh₀ : y₀ ∈ s\ninst✝ : SeparableSpace ↑s\nhp_ne_top : p ≠ ∞\nμ : Measure β\nhμ : ∀ᵐ (x : β) ∂μ, f x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 103,
"column": 4
} | {
"line": 103,
"column": 43
} | {
"line": 104,
"column": 6
} | [
{
"pp": "β : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns : Set E\ny₀ : E\nh₀ : y₀ ∈ s\ninst✝ : SeparableSpace ↑s\nhp_ne_top : p ≠ ∞\nμ : Measure β\nhμ : ∀ᵐ (x : β) ∂μ, f ... | [
"β : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns : Set E\ny₀ : E\nh₀ : y₀ ∈ s\ninst✝ : SeparableSpace ↑s\nhp_ne_top : p ≠ ∞\nμ : Measure β\nhμ : ∀ᵐ (x : β) ∂μ, f x ∈ closure[... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 291,
"column": 2
} | {
"line": 291,
"column": 91
} | {
"line": 292,
"column": 4
} | [
{
"pp": "X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : OpensMeasurableSpace X\nhf : LocallyIntegrable f (μ.restrict s)\nx : X\na✝ : x ∈ s\nt : Set X\nht_mem : t ∈ 𝓝 x\nht... | [
"X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : OpensMeasurableSpace X\nhf : LocallyIntegrable f (μ.restrict s)\nx : X\na✝ : x ∈ s\nt : Set X\nht_mem : t ∈ 𝓝 x\nht_int : Integ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 301,
"column": 4
} | {
"line": 305,
"column": 32
} | {
"line": 306,
"column": 2
} | [
{
"pp": "case pos\nX : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : OpensMeasurableSpace X\nhs : IsClosed[inst✝³] s\nhf : LocallyIntegrableOn f s μ\nx : X\nh : x ∈ s\n⊢ Integ... | [] | obtain ⟨t, ht_nhds, ht_int⟩ := hf x h
obtain ⟨u, hu_o, hu_x, hu_sub⟩ := mem_nhdsWithin.mp ht_nhds
refine ⟨u, hu_o.mem_nhds hu_x, ?_⟩
rw [IntegrableOn, restrict_restrict hu_o.measurableSet]
exact ht_int.mono_set hu_sub | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 301,
"column": 4
} | {
"line": 305,
"column": 32
} | {
"line": 306,
"column": 2
} | [
{
"pp": "case pos\nX : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ns : Set X\ninst✝ : OpensMeasurableSpace X\nhs : IsClosed[inst✝³] s\nhf : LocallyIntegrableOn f s μ\nx : X\nh : x ∈ s\n⊢ Integ... | [] | obtain ⟨t, ht_nhds, ht_int⟩ := hf x h
obtain ⟨u, hu_o, hu_x, hu_sub⟩ := mem_nhdsWithin.mp ht_nhds
refine ⟨u, hu_o.mem_nhds hu_x, ?_⟩
rw [IntegrableOn, restrict_restrict hu_o.measurableSet]
exact ht_int.mono_set hu_sub | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 124,
"column": 2
} | {
"line": 124,
"column": 13
} | {
"line": 124,
"column": 14
} | [
{
"pp": "case neg\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns : Set E\ny₀ : E\nh₀ : y₀ ∈ s\ninst✝ : SeparableSpace ↑s\nhp_ne_top : p ≠ ∞\nμ : Measure β\nhμ : ∀ᵐ (x :... | [
"case neg\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nhf : Measurable f\ns : Set E\ny₀ : E\nh₀ : y₀ ∈ s\ninst✝ : SeparableSpace ↑s\nhp_ne_top : p ≠ ∞\nμ : Measure β\nhμ : ∀ᵐ (x : β) ∂μ, f x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 15
} | {
"line": 162,
"column": 16
} | [
{
"pp": "case refine_2\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : BorelSpace E\nf : β → E\nhp_ne_top : p ≠ ∞\nμ : Measure β\nfmeas : Measurable f\ninst✝ : SeparableSpace ↑(Set.range f ∪ {0})\nhf : eLpNorm f p μ < ∞\n⊢ eL... | [
"case refine_2\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : BorelSpace E\nf : β → E\nhp_ne_top : p ≠ ∞\nμ : Measure β\nfmeas : Measurable f\ninst✝ : SeparableSpace ↑(Set.range f ∪ {0})\nhf : eLpNorm f p μ < ∞\n⊢ eLpNorm (fun x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 340,
"column": 2
} | {
"line": 340,
"column": 34
} | {
"line": 340,
"column": 35
} | [
{
"pp": "X : Type u_1\nε : Type u_3\ninst✝⁵ : MeasurableSpace X\ninst✝⁴ : TopologicalSpace X\ninst✝³ : TopologicalSpace ε\ninst✝² : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ninst✝¹ : PseudoMetrizableSpace ε\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrable f μ\n⊢ AEStronglyMeasurable f μ",
"ppTe... | [
"X : Type u_1\nε : Type u_3\ninst✝⁵ : MeasurableSpace X\ninst✝⁴ : TopologicalSpace X\ninst✝³ : TopologicalSpace ε\ninst✝² : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ninst✝¹ : PseudoMetrizableSpace ε\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrable f μ\n⊢ AEStronglyMeasurable f μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 56
} | {
"line": 177,
"column": 4
} | [
{
"pp": "β : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : BorelSpace E\nf : β → E\nhp : Fact (1 ≤ p)\nhp_ne_top : p ≠ ∞\nμ : Measure β\nfmeas : Measurable f\ninst✝ : SeparableSpace ↑(Set.range f ∪ {0})\nhf : MemLp f p μ\n⊢ Tend... | [
"β : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\np : ℝ≥0∞\ninst✝¹ : BorelSpace E\nf : β → E\nhp : Fact (1 ≤ p)\nhp_ne_top : p ≠ ∞\nμ : Measure β\nfmeas : Measurable f\ninst✝ : SeparableSpace ↑(Set.range f ∪ {0})\nhf : MemLp f p μ\n⊢ Tendsto (fun n ↦... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 31
} | {
"line": 349,
"column": 32
} | [
{
"pp": "X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrable f μ\nu : ℕ → Set X\nu_open : ∀ (n : ℕ), IsOpen[inst✝³] (u n)\nu_union : univ ... | [
"X : Type u_1\nε : Type u_3\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace ε\ninst✝¹ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ninst✝ : SecondCountableTopology X\nhf : LocallyIntegrable f μ\nu : ℕ → Set X\nu_open : ∀ (n : ℕ), IsOpen[inst✝³] (u n)\nu_union : univ ⊆ ⋃ n, u n\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 49
} | {
"line": 190,
"column": 50
} | [
{
"pp": "β : Type u_2\ninst✝¹ : MeasurableSpace β\np : ℝ≥0∞\nE : Type u_7\ninst✝ : NormedAddCommGroup E\nf : β → E\nμ : Measure β\nhf : MemLp f p μ\nhp_ne_top : p ≠ ∞\nε : ℝ≥0∞\nhε : ε ≠ 0\nthis✝¹ : MeasurableSpace E := borel E\nthis✝ : BorelSpace E\nf' : β → E := AEStronglyMeasurable.mk f ⋯\ng : β →ₛ E\nhg : e... | [
"β : Type u_2\ninst✝¹ : MeasurableSpace β\np : ℝ≥0∞\nE : Type u_7\ninst✝ : NormedAddCommGroup E\nf : β → E\nμ : Measure β\nhf : MemLp f p μ\nhp_ne_top : p ≠ ∞\nε : ℝ≥0∞\nhε : ε ≠ 0\nthis✝¹ : MeasurableSpace E := borel E\nthis✝ : BorelSpace E\nf' : β → E := AEStronglyMeasurable.mk f ⋯\ng : β →ₛ E\nhg : eLpNorm (f' -... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 441,
"column": 2
} | {
"line": 441,
"column": 39
} | {
"line": 441,
"column": 40
} | [
{
"pp": "X : Type u_1\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\nμ : Measure X\nε''' : Type u_9\ninst✝² : TopologicalSpace ε'''\ninst✝¹ : ESeminormedAddCommMonoid ε'''\ninst✝ : ContinuousAdd ε'''\nι : Type u_10\ns : Finset ι\nf : ι → X → ε'''\nhf : ∀ i ∈ s, LocallyIntegrable (f i) μ\n⊢ LocallyInt... | [
"X : Type u_1\ninst✝⁴ : MeasurableSpace X\ninst✝³ : TopologicalSpace X\nμ : Measure X\nε''' : Type u_9\ninst✝² : TopologicalSpace ε'''\ninst✝¹ : ESeminormedAddCommMonoid ε'''\ninst✝ : ContinuousAdd ε'''\nι : Type u_10\ns : Finset ι\nf : ι → X → ε'''\nhf : ∀ i ∈ s, LocallyIntegrable (f i) μ\n⊢ LocallyIntegrable (fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.FiniteDimension | {
"line": 562,
"column": 6
} | {
"line": 562,
"column": 41
} | {
"line": 562,
"column": 42
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁴ : NontriviallyNormedField 𝕜\ninst✝¹³ : CompleteSpace 𝕜\ninst✝¹² : AddCommGroup E\ninst✝¹¹ : TopologicalSpace E\ninst✝¹⁰ : IsTopologicalAddGroup E\ninst✝⁹ : Module 𝕜 E\ninst✝⁸ : ContinuousSMul 𝕜 E\ninst✝⁷ : AddCommGroup F\ninst✝⁶ : TopologicalSpace ... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁴ : NontriviallyNormedField 𝕜\ninst✝¹³ : CompleteSpace 𝕜\ninst✝¹² : AddCommGroup E\ninst✝¹¹ : TopologicalSpace E\ninst✝¹⁰ : IsTopologicalAddGroup E\ninst✝⁹ : Module 𝕜 E\ninst✝⁸ : ContinuousSMul 𝕜 E\ninst✝⁷ : AddCommGroup F\ninst✝⁶ : TopologicalSpace F\ninst✝⁵ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 230,
"column": 4
} | {
"line": 230,
"column": 15
} | {
"line": 230,
"column": 16
} | [
{
"pp": "case hi\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nμ : Measure β\ninst✝ : SeparableSpace ↑(Set.range f ∪ {0})\nfmeas : Measurable f\nhf : Integrable f μ\n⊢ HasFiniteIntegral (fun x ↦ f x... | [
"case hi\nβ : Type u_2\nE : Type u_4\ninst✝⁴ : MeasurableSpace β\ninst✝³ : MeasurableSpace E\ninst✝² : NormedAddCommGroup E\ninst✝¹ : OpensMeasurableSpace E\nf : β → E\nμ : Measure β\ninst✝ : SeparableSpace ↑(Set.range f ∪ {0})\nfmeas : Measurable f\nhf : Integrable f μ\n⊢ HasFiniteIntegral (fun x ↦ f x) μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 1174,
"column": 6
} | {
"line": 1174,
"column": 58
} | {
"line": 1174,
"column": 59
} | [
{
"pp": "case h1\n𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹² : Fintype ι'\ninst✝¹¹ : NontriviallyNormedField 𝕜\ninst✝¹⁰ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁸ : (i : ι) → S... | [
"case h1\n𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹² : Fintype ι'\ninst✝¹¹ : NontriviallyNormedField 𝕜\ninst✝¹⁰ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁸ : (i : ι) → SeminormedAdd... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 1160,
"column": 4
} | {
"line": 1174,
"column": 92
} | {
"line": 1176,
"column": 0
} | [
{
"pp": "𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹² : Fintype ι'\ninst✝¹¹ : NontriviallyNormedField 𝕜\ninst✝¹⁰ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁸ : (i : ι) → Seminormed... | [] | intro x m
simp only [MultilinearMap.iteratedFDerivComponent, MultilinearMap.domDomRestrictₗ,
MultilinearMap.coe_mk, MultilinearMap.domDomRestrict_apply, coe_coe]
apply (f.le_opNorm _).trans _
classical
rw [← prod_compl_mul_prod s.toFinset, mul_assoc]
gcongr
· apply le_of_eq
have : ∀ ... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 1160,
"column": 4
} | {
"line": 1174,
"column": 92
} | {
"line": 1176,
"column": 0
} | [
{
"pp": "𝕜 : Type u\nι : Type v\nι' : Type v'\nE : ι → Type wE\nE₁ : ι → Type wE₁\nE' : ι' → Type wE'\nG : Type wG\nG' : Type wG'\ninst✝¹² : Fintype ι'\ninst✝¹¹ : NontriviallyNormedField 𝕜\ninst✝¹⁰ : (i : ι) → SeminormedAddCommGroup (E i)\ninst✝⁹ : (i : ι) → NormedSpace 𝕜 (E i)\ninst✝⁸ : (i : ι) → Seminormed... | [] | intro x m
simp only [MultilinearMap.iteratedFDerivComponent, MultilinearMap.domDomRestrictₗ,
MultilinearMap.coe_mk, MultilinearMap.domDomRestrict_apply, coe_coe]
apply (f.le_opNorm _).trans _
classical
rw [← prod_compl_mul_prod s.toFinset, mul_assoc]
gcongr
· apply le_of_eq
have : ∀ ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Normed.Module.Multilinear.Basic | {
"line": 1224,
"column": 4
} | {
"line": 1224,
"column": 15
} | {
"line": 1224,
"column": 16
} | [
{
"pp": "case h\n𝕜 : Type u\nι : Type v\nE₁ : ι → Type wE₁\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E₁ i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E₁ i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nf : ContinuousMultilinearMap... | [
"case h\n𝕜 : Type u\nι : Type v\nE₁ : ι → Type wE₁\nG : Type wG\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : (i : ι) → SeminormedAddCommGroup (E₁ i)\ninst✝³ : (i : ι) → NormedSpace 𝕜 (E₁ i)\ninst✝² : SeminormedAddCommGroup G\ninst✝¹ : NormedSpace 𝕜 G\ninst✝ : Fintype ι\nf : ContinuousMultilinearMap 𝕜 E₁ G\nk ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.FiniteDimension | {
"line": 720,
"column": 2
} | {
"line": 720,
"column": 17
} | {
"line": 720,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : CompleteSpace 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : ContinuousSMul 𝕜 E\np q : Submodule 𝕜 E\nh : IsCompl p q\nhp : IsClosed[inst✝⁴] ↑p\ninst✝... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : CompleteSpace 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : TopologicalSpace E\ninst✝³ : IsTopologicalAddGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : ContinuousSMul 𝕜 E\np q : Submodule 𝕜 E\nh : IsCompl p q\nhp : IsClosed[inst✝⁴] ↑p\ninst✝ : FiniteDim... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 320,
"column": 2
} | {
"line": 320,
"column": 47
} | {
"line": 320,
"column": 48
} | [
{
"pp": "α : Type u_1\nE : Type u_4\nF : Type u_5\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nμ : Measure α\nf : α →ₛ E\ng : α →ₛ F\n⊢ Integrable (⇑f) μ → Integrable (⇑g) μ → Integrable (⇑(f.pair g)) μ",
"ppTerm": "?m.26",
"assigned": true,
"usedConstant... | [
"α : Type u_1\nE : Type u_4\nF : Type u_5\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedAddCommGroup F\nμ : Measure α\nf : α →ₛ E\ng : α →ₛ F\n⊢ f.FinMeasSupp μ → g.FinMeasSupp μ → (f.pair g).FinMeasSupp μ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 347,
"column": 2
} | {
"line": 348,
"column": 50
} | {
"line": 348,
"column": 51
} | [
{
"pp": "α : Type u_1\nE : Type u_4\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\nhp_pos : p ≠ 0\nhp_ne_top : p ≠ ∞\nc : E\nhc : c ≠ 0\ns : Set α\nhs : MeasurableSet s\nhcs : MemLp (⇑(piecewise s hs (const α c) (const α 0))) p μ\nthis : support ⇑(const α c) = Set.univ\n⊢ μ ... | [
"α : Type u_1\nE : Type u_4\ninst✝¹ : MeasurableSpace α\ninst✝ : NormedAddCommGroup E\nμ : Measure α\np : ℝ≥0∞\nhp_pos : p ≠ 0\nhp_ne_top : p ≠ ∞\nc : E\nhc : c ≠ 0\ns : Set α\nhs : MeasurableSet s\nhcs : MemLp (⇑(piecewise s hs (const α c) (const α 0))) p μ\nthis : support ⇑(const α c) = Set.univ\n⊢ μ s < ∞"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 411,
"column": 6
} | {
"line": 411,
"column": 32
} | {
"line": 412,
"column": 6
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nι : Type u_3\nE : Type u_4\nF : Type u_5\n𝕜 : Type u_6\ninst✝⁵ : MeasurableSpace α\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\ninst✝² : NormedRing 𝕜\ninst✝¹ : Module 𝕜 E\ninst✝ : IsBoundedSMul 𝕜 E\nk : 𝕜\nf : ↥(simpleFunc E p ... | [
"α : Type u_1\nβ : Type u_2\nι : Type u_3\nE : Type u_4\nF : Type u_5\n𝕜 : Type u_6\ninst✝⁵ : MeasurableSpace α\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedAddCommGroup F\np : ℝ≥0∞\nμ : Measure α\ninst✝² : NormedRing 𝕜\ninst✝¹ : Module 𝕜 E\ninst✝ : IsBoundedSMul 𝕜 E\nk : 𝕜\nf : ↥(Lp E p μ)\ns : failed to pr... | rcases f with ⟨f, ⟨s, hs⟩⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 541,
"column": 4
} | {
"line": 542,
"column": 59
} | {
"line": 544,
"column": 0
} | [
{
"pp": "case mpr\nX : Type u_1\nε : Type u_3\ninst✝⁸ : MeasurableSpace X\ninst✝⁷ : TopologicalSpace X\ninst✝⁶ : TopologicalSpace ε\ninst✝⁵ : ContinuousENorm ε\nf : X → ε\nμ : Measure X\ninst✝⁴ : PseudoMetrizableSpace ε\na : X\ninst✝³ : LinearOrder X\ninst✝² : CompactIccSpace X\ninst✝¹ : NoMinOrder X\ninst✝ : O... | [] | exact integrableOn_Iic_iff_integrableAtFilter_atBot.mpr
⟨hbot, hlocal.mono_set (Iic_subset_Iio.mpr hs'_mono)⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Function.LocallyIntegrable | {
"line": 655,
"column": 18
} | {
"line": 655,
"column": 29
} | {
"line": 655,
"column": 30
} | [
{
"pp": "X : Type u_1\nE : Type u_6\ninst✝⁸ : MeasurableSpace X\ninst✝⁷ : TopologicalSpace X\ninst✝⁶ : NormedAddCommGroup E\nμ : Measure X\ns : Set X\ninst✝⁵ : BorelSpace X\ninst✝⁴ : ConditionallyCompleteLinearOrder X\ninst✝³ : ConditionallyCompleteLinearOrder E\ninst✝² : OrderTopology X\ninst✝¹ : OrderTopology... | [
"X : Type u_1\nE : Type u_6\ninst✝⁸ : MeasurableSpace X\ninst✝⁷ : TopologicalSpace X\ninst✝⁶ : NormedAddCommGroup E\nμ : Measure X\ns : Set X\ninst✝⁵ : BorelSpace X\ninst✝⁴ : ConditionallyCompleteLinearOrder X\ninst✝³ : ConditionallyCompleteLinearOrder E\ninst✝² : OrderTopology X\ninst✝¹ : OrderTopology E\ninst✝ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.FinMeasAdditive | {
"line": 212,
"column": 32
} | {
"line": 212,
"column": 43
} | {
"line": 212,
"column": 44
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nβ : Type u_7\ninst✝ : SeminormedAddCommGroup β\nT : Set α → β\nC : ℝ\nhT : DominatedFinMeasAdditive μ T C\ns : Set α\nhs : MeasurableSet s\nhμs : μ s < ∞\n⊢ ‖(-T) s‖ ≤ C * μ.real s",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\nβ : Type u_7\ninst✝ : SeminormedAddCommGroup β\nT : Set α → β\nC : ℝ\nhT : DominatedFinMeasAdditive μ T C\ns : Set α\nhs : MeasurableSet s\nhμs : μ s < ∞\n⊢ ‖T s‖ ≤ C * μ.real s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 575,
"column": 2
} | {
"line": 575,
"column": 33
} | {
"line": 575,
"column": 34
} | [
{
"pp": "α : Type u_1\nE : Type u_4\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\np : ℝ≥0∞\nμ : Measure α\ninst✝ : Fact (1 ≤ p)\nf : ↥(simpleFunc E p μ)\n⊢ ‖f‖ = (eLpNorm (⇑(toSimpleFunc f)) p μ).toReal",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Norm.norm",
... | [
"α : Type u_1\nE : Type u_4\ninst✝² : MeasurableSpace α\ninst✝¹ : NormedAddCommGroup E\np : ℝ≥0∞\nμ : Measure α\ninst✝ : Fact (1 ≤ p)\nf : ↥(simpleFunc E p μ)\n⊢ ‖↑f‖ = (eLpNorm (⇑(toSimpleFunc f)) p μ).toReal"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Integral.FinMeasAdditive | {
"line": 267,
"column": 4
} | {
"line": 267,
"column": 45
} | {
"line": 267,
"column": 46
} | [
{
"pp": "case cons\nα : Type u_1\nm : MeasurableSpace α\nβ : Type u_7\ninst✝ : SeminormedAddCommGroup β\nι : Type u_8\ns✝ : Finset ι\nμ : ι → Measure α\nT : ι → Set α → β\nC : ι → ℝ\nhT : ∀ (i : ι), DominatedFinMeasAdditive (μ i) (T i) (C i)\ni : ι\ns : Finset ι\nhis : i ∉ s\nhs' : s.Nonempty\nih : DominatedFin... | [
"case cons\nα : Type u_1\nm : MeasurableSpace α\nβ : Type u_7\ninst✝ : SeminormedAddCommGroup β\nι : Type u_8\ns✝ : Finset ι\nμ : ι → Measure α\nT : ι → Set α → β\nC : ι → ℝ\nhT : ∀ (i : ι), DominatedFinMeasAdditive (μ i) (T i) (C i)\ni : ι\ns : Finset ι\nhis : i ∉ s\nhs' : s.Nonempty\nih : DominatedFinMeasAdditive... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Extend | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 15
} | {
"line": 162,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝⁷ : DivisionRing 𝕜\ninst✝⁶ : DivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup Eₗ\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜₂ F\ninst✝ ... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝⁷ : DivisionRing 𝕜\ninst✝⁶ : DivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup Eₗ\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜₂ F\ninst✝ : Module 𝕜 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Extend | {
"line": 157,
"column": 31
} | {
"line": 162,
"column": 17
} | {
"line": 162,
"column": 17
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝⁷ : DivisionRing 𝕜\ninst✝⁶ : DivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup Eₗ\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜₂ F\ninst✝ ... | [] | by
obtain ⟨C, h⟩ := h
intro x hx
specialize h x
rw [hx] at h
simpa using h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Normed.Operator.Extend | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 23
} | {
"line": 168,
"column": 24
} | [
{
"pp": "case h\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝⁷ : DivisionRing 𝕜\ninst✝⁶ : DivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup Eₗ\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜₂ F... | [
"case h\n𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝⁷ : DivisionRing 𝕜\ninst✝⁶ : DivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup Eₗ\ninst✝² : Module 𝕜 E\ninst✝¹ : Module 𝕜₂ F\ninst✝ : Mo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Extend | {
"line": 206,
"column": 4
} | {
"line": 206,
"column": 67
} | {
"line": 206,
"column": 68
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\ninst✝¹⁰ : NormedDivisionRing 𝕜\ninst✝⁹ : NormedDivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : SeminormedAddCommGroup Eₗ\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : Module 𝕜₂ F\ninst✝³ :... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\ninst✝¹⁰ : NormedDivisionRing 𝕜\ninst✝⁹ : NormedDivisionRing 𝕜₂\nσ₁₂ : 𝕜 →+* 𝕜₂\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : SeminormedAddCommGroup Eₗ\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : Module 𝕜₂ F\ninst✝³ : IsBoundedSM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Extend | {
"line": 324,
"column": 61
} | {
"line": 324,
"column": 72
} | {
"line": 324,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝¹³ : NormedField 𝕜\ninst✝¹² : NormedField 𝕜₂\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : Module 𝕜 E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜₂ F\ninst✝⁷ : NormedAddCommGroup Eₗ\ninst✝⁶ : NormedSpace 𝕜 Eₗ\ninst... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝¹³ : NormedField 𝕜\ninst✝¹² : NormedField 𝕜₂\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : Module 𝕜 E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜₂ F\ninst✝⁷ : NormedAddCommGroup Eₗ\ninst✝⁶ : NormedSpace 𝕜 Eₗ\ninst✝⁵ : Complet... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Extend | {
"line": 354,
"column": 15
} | {
"line": 354,
"column": 26
} | {
"line": 354,
"column": 27
} | [
{
"pp": "𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝¹³ : NormedField 𝕜\ninst✝¹² : NormedField 𝕜₂\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : Module 𝕜 E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜₂ F\ninst✝⁷ : NormedAddCommGroup Eₗ\ninst✝⁶ : NormedSpace 𝕜 Eₗ\ninst... | [
"𝕜 : Type u_1\n𝕜₂ : Type u_2\nE : Type u_3\nEₗ : Type u_4\nF : Type u_5\nFₗ : Type u_6\ninst✝¹³ : NormedField 𝕜\ninst✝¹² : NormedField 𝕜₂\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : Module 𝕜 E\ninst✝⁹ : AddCommGroup F\ninst✝⁸ : Module 𝕜₂ F\ninst✝⁷ : NormedAddCommGroup Eₗ\ninst✝⁶ : NormedSpace 𝕜 Eₗ\ninst✝⁵ : Complet... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.SimpleFuncDenseLp | {
"line": 760,
"column": 6
} | {
"line": 760,
"column": 17
} | {
"line": 760,
"column": 18
} | [
{
"pp": "case hμ\nα : Type u_1\ninst✝² : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\nG : Type u_7\ninst✝¹ : NormedAddCommGroup G\ninst✝ : PartialOrder G\nhp : Fact (1 ≤ p)\nhp_ne_top : p ≠ ∞\ng : { g // 0 ≤ g }\nthis✝¹ : MeasurableSpace G := borel G\nthis✝ : BorelSpace G\nhg_memLp : MemLp (↑↑↑g) p μ\nzero_mem :... | [
"case hμ\nα : Type u_1\ninst✝² : MeasurableSpace α\np : ℝ≥0∞\nμ : Measure α\nG : Type u_7\ninst✝¹ : NormedAddCommGroup G\ninst✝ : PartialOrder G\nhp : Fact (1 ≤ p)\nhp_ne_top : p ≠ ∞\ng : { g // 0 ≤ g }\nthis✝¹ : MeasurableSpace G := borel G\nthis✝ : BorelSpace G\nhg_memLp : MemLp (↑↑↑g) p μ\nzero_mem : 0 ∈ (Set.ra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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