module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 169,
"column": 29
} | {
"line": 169,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace 𝕜 F\nx✝² x✝¹ x✝ : E →ₗ[𝕜] E\nh₁ : (x✝¹ - x✝²).IsPositive\nh₂ : (x✝ - x✝¹).IsPositive\n⊢ (x✝ - x✝²).IsPositive",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : RCLike 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nf : E →ₗ[𝕜] E\n⊢ 0 ≤ f ↔ f.IsPositive",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 200,
"column": 32
} | {
"line": 200,
"column": 43
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace 𝕜 F\nT : E →ₗ[𝕜] E\nf : E ≃ₗᵢ[𝕜] F\nx✝ : T.IsSymmetric\nh : ∀ (x : F), 0 ≤ re ⟪T (f.symm x), f.symm x⟫\nx : E\n⊢ 0 ≤... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 238,
"column": 2
} | {
"line": 238,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : RCLike 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\np : E →ₗ[𝕜] E\nhp : p.IsSymmetricProjection\na : E\nha : a ∈ p.range\nhh : ∀ {T : E →ₗ[𝕜] E}, T.IsSymmetricProjection → re ⟪T a, a⟫ = ‖T a‖ ^ 2\nU : Submodule 𝕜 E\nw✝ : U.HasOrthogonalProj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 363,
"column": 2
} | {
"line": 363,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nS : E →L[𝕜] F\n⊢ (S ∘SL adjoint S).IsPositive",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 373,
"column": 2
} | {
"line": 373,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : CompleteSpace E\ninst✝ : CompleteSpace F\nS : E →L[𝕜] F\n⊢ (adjoint S ∘SL S).IsPositive",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 383,
"column": 2
} | {
"line": 383,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nT : E →ₗ[𝕜] E\nhT : T.IsPositive\nS : E →ₗ[𝕜]... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 388,
"column": 2
} | {
"line": 388,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nS : E →ₗ[𝕜] F\n⊢ (S ∘ₗ LinearMap.adjoint S).Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 398,
"column": 2
} | {
"line": 398,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁶ : RCLike 𝕜\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedAddCommGroup F\ninst✝³ : InnerProductSpace 𝕜 E\ninst✝² : InnerProductSpace 𝕜 F\ninst✝¹ : FiniteDimensional 𝕜 E\ninst✝ : FiniteDimensional 𝕜 F\nS : E →ₗ[𝕜] F\n⊢ (LinearMap.adjoint S ∘ₗ S).Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 439,
"column": 44
} | {
"line": 439,
"column": 91
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝³ : RCLike 𝕜\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : E →L[𝕜] E\nc : ℝ≥0\nhc : 0 < c\nh : ∀ (x : E), ‖x‖ ^ 2 * ↑c ≤ ‖⟪f x, x⟫‖\nh_anti : AntilipschitzWith c⁻¹ ⇑f\nx : E\nhx : x ∈ (↑f).rangeᗮ\n⊢ ‖x‖ ^ 2 * ↑c ≤ 0",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 461,
"column": 29
} | {
"line": 461,
"column": 40
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝⁴ : RCLike 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedAddCommGroup F\ninst✝¹ : InnerProductSpace 𝕜 E\ninst✝ : InnerProductSpace 𝕜 F\nx✝² x✝¹ x✝ : E →L[𝕜] E\nh₁ : (x✝¹ - x✝²).IsPositive\nh₂ : (x✝ - x✝¹).IsPositive\n⊢ (x✝ - x✝²).IsPositive",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 471,
"column": 2
} | {
"line": 471,
"column": 13
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : RCLike 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nf : E →L[𝕜] E\n⊢ 0 ≤ f ↔ f.IsPositive",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Positive | {
"line": 526,
"column": 13
} | {
"line": 526,
"column": 24
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : RCLike 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : InnerProductSpace 𝕜 E\nT : E ≃ₗ[𝕜] E\nhT : (↑T).IsPositive\nx : E\n⊢ ?m.87",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 52,
"column": 27
} | {
"line": 52,
"column": 38
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 93,
"column": 6
} | {
"line": 93,
"column": 17
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 78
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.ContinuousOfBounded | {
"line": 115,
"column": 53
} | {
"line": 115,
"column": 64
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\nE : Type u_3\nF : Type u_4\ninst✝¹¹ : AddCommGroup E\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : IsTopologicalAddGroup E\ninst✝⁸ : AddCommGroup F\ninst✝⁷ : TopologicalSpace F\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : Module 𝕜 E\ninst✝⁴ : ContinuousSMul 𝕜 E\ninst✝³ : No... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 48
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\nthis : ∀ {h p1 p2 p3 : Prop}, (h → [p1, p2, p3].TFAE) → [h ∧ p1, h ∧ p2, h ∧ p3].TFAE\nhHerm : K.IsHermitian\nx✝ : Nontriv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 207,
"column": 4
} | {
"line": 207,
"column": 72
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝² : NormedAddCommGroup V\ninst✝¹ : InnerProductSpace 𝕜 V\ninst✝ : CompleteSpace V\nK : Matrix X X (V →L[𝕜] V)\nthis : ∀ {h p1 p2 p3 : Prop}, (h → [p1, p2, p3].TFAE) → [h ∧ p1, h ∧ p2, h ∧ p3].TFAE\nhHerm : K.IsHermitian\nx✝ : Nontriv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.PointwiseConvergence | {
"line": 42,
"column": 20
} | {
"line": 42,
"column": 36
} | [
{
"pp": "α : Type u_1\nR : Type u_2\n𝕜₁ : Type u_3\n𝕜₂ : Type u_4\n𝕜₃ : Type u_5\ninst✝⁷ : NormedField 𝕜₁\ninst✝⁶ : NormedField 𝕜₂\ninst✝⁵ : NormedField 𝕜₃\nσ : 𝕜₁ →+* 𝕜₂\nτ : 𝕜₃ →+* 𝕜₂\nD : Type u_6\nE : Type u_7\nF : Type u_8\nG : Type u_9\ninst✝⁴ : AddCommGroup E\ninst✝³ : TopologicalSpace E\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.Reproducing | {
"line": 291,
"column": 15
} | {
"line": 291,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁸ : RCLike 𝕜\nX : Type u_2\nV : Type u_3\ninst✝⁷ : NormedAddCommGroup V\ninst✝⁶ : InnerProductSpace 𝕜 V\nH : Type u_4\ninst✝⁵ : NormedAddCommGroup H\ninst✝⁴ : InnerProductSpace 𝕜 H\ninst✝³ : RKHS 𝕜 H X V\ninst✝² : CompleteSpace H\ninst✝¹ : CompleteSpace V\nK : Matrix X X (V →L[�... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 48,
"column": 36
} | {
"line": 48,
"column": 47
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhs : Convex ℝ s\nx ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 20
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\nhs : Convex ℝ s\nx ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 67
} | [
{
"pp": "case e_s\n𝕜 : Type u_1\nE : Type u_2\ninst✝⁸ : RCLike 𝕜\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : Module 𝕜 E\ninst✝⁵ : Module ℝ E\ninst✝⁴ : IsScalarTower ℝ 𝕜 E\ninst✝³ : TopologicalSpace E\ninst✝² : IsTopologicalAddGroup E\ninst✝¹ : ContinuousSMul 𝕜 E\ninst✝ : LocallyConvexSpace ℝ E\ns : Set E\n⊢ ⇑(toWea... | refine LinearMap.image_convexHull (toWeakSpace 𝕜 E).toLinearMap s | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 78,
"column": 4
} | {
"line": 79,
"column": 11
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\ninst✝⁶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 95,
"column": 2
} | {
"line": 96,
"column": 9
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : TopologicalSpace E\ninst✝⁶... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 22
} | [
{
"pp": "case refine_1\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : Topological... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakSpace | {
"line": 117,
"column": 4
} | {
"line": 117,
"column": 23
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹⁶ : RCLike 𝕜\ninst✝¹⁵ : AddCommGroup E\ninst✝¹⁴ : Module 𝕜 E\ninst✝¹³ : AddCommGroup F\ninst✝¹² : Module 𝕜 F\ninst✝¹¹ : Module ℝ E\ninst✝¹⁰ : IsScalarTower ℝ 𝕜 E\ninst✝⁹ : Module ℝ F\ninst✝⁸ : IsScalarTower ℝ 𝕜 F\ninst✝⁷ : Topological... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ |(o.areaForm x) y| ≤ ‖x‖ * ‖y‖",
"usedConstants": [
"AlternatingMap",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 58
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ (o.areaForm x) y ≤ ‖x‖ * ‖y‖",
"usedConstants": [
"AlternatingMap",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 143,
"column": 4
} | {
"line": 143,
"column": 15
} | [
{
"pp": "case «0».«1»\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nh : ⟪x, y⟫ = 0\nhij : (fun i ↦ i) ⟨0, ⋯⟩ ≠ (fun i ↦ i) ⟨1, ⋯⟩\n⊢ ⟪![x, y] ((fun i ↦ i) ⟨0, ⋯⟩), ![x, y] ((fun i ↦ i) ⟨1, ⋯⟩)⟫ = 0",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 33
} | [
{
"pp": "case «1».«0»\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nh : ⟪x, y⟫ = 0\nhij : (fun i ↦ i) ⟨1, ⋯⟩ ≠ (fun i ↦ i) ⟨0, ⋯⟩\n⊢ ⟪![x, y] ((fun i ↦ i) ⟨1, ⋯⟩), ![x, y] ((fun i ↦ i) ⟨0, ⋯⟩)⟫ = 0",
"usedC... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 362,
"column": 2
} | {
"line": 362,
"column": 46
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\na b : E\n⊢ ⟪a, b⟫ ^ 2 + (o.areaForm a) b ^ 2 = ‖a‖ ^ 2 * ‖b‖ ^ 2",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 463,
"column": 2
} | {
"line": 463,
"column": 54
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\n⊢ Complex.normSq ((o.kahler x) y) = ‖x‖ ^ 2 * ‖y‖ ^ 2",
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Complex.mul_im",
"Norm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 472,
"column": 29
} | {
"line": 472,
"column": 45
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\n⊢ ‖x‖ * ‖y‖ = 0",
"usedConstants": [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.nor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 475,
"column": 4
} | {
"line": 475,
"column": 15
} | [
{
"pp": "case inl.h\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\nthis : ‖x‖ * ‖y‖ = 0\nh : ‖x‖ = 0\n⊢ x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.InnerProductSpace.TwoDim | {
"line": 477,
"column": 4
} | {
"line": 477,
"column": 15
} | [
{
"pp": "case inr.h\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : InnerProductSpace ℝ E\ninst✝ : Fact (finrank ℝ E = 2)\no : Orientation ℝ E (Fin 2)\nx y : E\nhx : (o.kahler x) y = 0\nthis : ‖x‖ * ‖y‖ = 0\nh : ‖y‖ = 0\n⊢ y = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 48
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℂ E\nf : ℝ → E\ns : ℂ\nhf : MellinConvergent f s\n𝕜 : Type u_2\ninst✝³ : NormedAddCommGroup 𝕜\ninst✝² : SMulZeroClass 𝕜 E\ninst✝¹ : IsBoundedSMul 𝕜 E\ninst✝ : SMulCommClass ℂ 𝕜 E\nc : 𝕜\n⊢ MellinConvergent (fun t ↦ c • f t) s",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 67
} | [
{
"pp": "f : ℝ → ℂ\ns : ℂ\nhf : MellinConvergent f s\na : ℂ\n⊢ MellinConvergent (fun t ↦ f t / a) s",
"usedConstants": [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"Set.Ioi",
"instHSMul",
"MeasureTheory.Measure",
"instHDiv",
"HMul.hMul",
"Compl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 29
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf : ℝ → E\ns : ℂ\na : ℝ\nha : 0 < a\n⊢ mellin (fun t ↦ f (t * a)) s = ↑a ^ (-s) • mellin f s",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real",
"instHSMul",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 167,
"column": 6
} | {
"line": 167,
"column": 51
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf g : ℝ → E\ns : ℂ\nhf : MellinConvergent f s\nhg : MellinConvergent g s\n⊢ MellinConvergent (fun t ↦ f t + g t) s",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"instHSMul",
"MeasureTheory.Measur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 39
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf g : ℝ → E\ns : ℂ\nhf : MellinConvergent f s\nhg : MellinConvergent g s\n⊢ mellin (fun t ↦ f t + g t) s = mellin f s + mellin g s",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"instHSMul",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 172,
"column": 6
} | {
"line": 172,
"column": 51
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf g : ℝ → E\ns : ℂ\nhf : MellinConvergent f s\nhg : MellinConvergent g s\n⊢ MellinConvergent (fun t ↦ f t - g t) s",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"instHSMul",
"MeasureTheory.Measur... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 173,
"column": 4
} | {
"line": 173,
"column": 39
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf g : ℝ → E\ns : ℂ\nhf : MellinConvergent f s\nhg : MellinConvergent g s\n⊢ mellin (fun t ↦ f t - g t) s = mellin f s - mellin g s",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"instHSMul",
"Real... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 46,
"column": 43
} | {
"line": 46,
"column": 54
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nx : ℝ\ns : ℂ\nf : E\n⊢ (-↑x).im ≤ π",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"Real.pi",
"congrArg",
"Complex.im",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 26
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹⁰ : NormedField 𝕜₁\ninst✝⁹ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : Module 𝕜₁ E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : Module 𝕜₂ F\ninst✝² : IsTopologi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | {
"line": 344,
"column": 87
} | {
"line": 347,
"column": 30
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝¹⁰ : NormedField 𝕜₁\ninst✝⁹ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁸ : AddCommGroup E\ninst✝⁷ : TopologicalSpace E\ninst✝⁶ : Module 𝕜₁ E\ninst✝⁵ : AddCommGroup F\ninst✝⁴ : TopologicalSpace F\ninst✝³ : Module 𝕜₂ F\ninst✝² : IsTopologi... | by
refine Function.Injective.isEmbedding_induced fun A B hAB => ?_
rw [ContinuousLinearMapWOT.ext_dual_iff]
simpa [funext_iff] using hAB | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.MellinTransform | {
"line": 221,
"column": 6
} | {
"line": 222,
"column": 60
} | [
{
"pp": "f : ℝ → ℝ\nhfc : AEStronglyMeasurable f (volume.restrict (Ioi 0))\na s : ℝ\nhf : f =O[atTop] fun x ↦ x ^ (-a)\nhs : s < a\nd e : ℝ\nhe : ∀ b ≥ e, ‖f b‖ ≤ d * ‖b ^ (-a)‖\nhe' : 0 < max e 1\nt : ℝ\nht : t ∈ Ioi (max e 1)\nht' : 0 < t\n⊢ ‖t ^ (s - 1) * f t‖ ≤ t ^ (s - 1 + -a) * d",
"usedConstants": [
... | rw [norm_mul, rpow_add ht', ← norm_of_nonneg (rpow_nonneg ht'.le (-a)), mul_assoc,
mul_comm _ d, norm_of_nonneg (rpow_nonneg ht'.le _)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.MellinInversion | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhf : IntegrableOn (fun x ↦ |(-rexp (-x))| • ↑((rexp ∘ Neg.neg) x) ^ (↑σ - 1) • f ((rexp ∘ Neg.neg) x)) univ volume\nhFf : VerticalIntegrable (mellin f) σ volume\nhfx : Co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 111,
"column": 6
} | {
"line": 111,
"column": 66
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhFf : VerticalIntegrable (mellin f) σ volume\nhfx : ContinuousAt f x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nh2π : 2 * π ≠ 0\n⊢ Int... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | {
"line": 397,
"column": 20
} | {
"line": 397,
"column": 31
} | [
{
"pp": "𝕜₁ : Type u_1\n𝕜₂ : Type u_2\ninst✝⁹ : NormedField 𝕜₁\ninst✝⁸ : NormedField 𝕜₂\nσ : 𝕜₁ →+* 𝕜₂\nE : Type u_3\nF : Type u_4\ninst✝⁷ : AddCommGroup E\ninst✝⁶ : TopologicalSpace E\ninst✝⁵ : Module 𝕜₁ E\ninst✝⁴ : AddCommGroup F\ninst✝³ : TopologicalSpace F\ninst✝² : Module 𝕜₂ F\ninst✝¹ : IsTopologic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\nhfx : ContinuousAt f x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nhFf : Integrable (𝓕 g) volume\n⊢ ContinuousAt f (rexp (- -Real.log ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinInversion | {
"line": 127,
"column": 22
} | {
"line": 127,
"column": 43
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℂ E\ninst✝ : CompleteSpace E\nσ : ℝ\nf : ℝ → E\nx : ℝ\nhx : 0 < x\ng : ℝ → E := fun u ↦ rexp (-σ * u) • f (rexp (-u))\nhf : Integrable g volume\nhFf : Integrable (𝓕 g) volume\nhfx : ContinuousAt g (-Real.log x)\n⊢ ↑x ^ ↑(-σ) • rexp (Rea... | ← rpow_def_of_pos hx, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 52,
"column": 2
} | {
"line": 57,
"column": 9
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\nx : ℝ\n⊢ HasDerivAt (fun y ↦ -Complex.cos (2 * z * ↑y) / (2 * z)) (Complex.sin (2 * z * ↑x)) x",
"usedConstants": [
"HasDerivAt.fun_neg",
"instInnerProductSpaceRealComplex",
"IsModuleTopology.toContinuousSMul",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"... | have a : HasDerivAt (fun y : ℂ => y * (2 * z)) _ x := hasDerivAt_mul_const _
have b : HasDerivAt (Complex.cos ∘ fun y : ℂ => (y * (2 * z))) _ x :=
HasDerivAt.comp (x : ℂ) (Complex.hasDerivAt_cos (x * (2 * z))) a
have c := (b.comp_ofReal.div_const (2 * z)).fun_neg
simp at c ⊢; field_simp at c ⊢; simp only [mul... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 52,
"column": 2
} | {
"line": 57,
"column": 9
} | [
{
"pp": "z : ℂ\nhz : z ≠ 0\nx : ℝ\n⊢ HasDerivAt (fun y ↦ -Complex.cos (2 * z * ↑y) / (2 * z)) (Complex.sin (2 * z * ↑x)) x",
"usedConstants": [
"HasDerivAt.fun_neg",
"instInnerProductSpaceRealComplex",
"IsModuleTopology.toContinuousSMul",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"... | have a : HasDerivAt (fun y : ℂ => y * (2 * z)) _ x := hasDerivAt_mul_const _
have b : HasDerivAt (Complex.cos ∘ fun y : ℂ => (y * (2 * z))) _ x :=
HasDerivAt.comp (x : ℂ) (Complex.hasDerivAt_cos (x * (2 * z))) a
have c := (b.comp_ofReal.div_const (2 * z)).fun_neg
simp at c ⊢; field_simp at c ⊢; simp only [mul... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd | {
"line": 69,
"column": 6
} | {
"line": 69,
"column": 17
} | [
{
"pp": "z : ℂ\nn : ℕ\nhn : 2 ≤ n\nhz : z ≠ 0\nx : ℝ\na✝ : x ∈ uIcc 0 (π / 2)\n⊢ HasDerivAt (fun y ↦ ↑(cos y)) (-↑(sin x)) x",
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 30
} | [
{
"pp": "case h\nn : ℕ\nx✝ : ℂ\n⊢ logTaylor (n + 1) x✝ = (logTaylor n + fun z ↦ (-1) ^ (n + 1) * z ^ n / ↑n) x✝",
"usedConstants": [
"instHDiv",
"HMul.hMul",
"Complex.instDivInvMonoid",
"Complex.instMul",
"id",
"HDiv.hDiv",
"instOfNatNat",
"Complex.instNatCast... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 83,
"column": 17
} | {
"line": 83,
"column": 49
} | [
{
"pp": "case succ\nn : ℕ\nih : logTaylor n 0 = 0\n⊢ logTaylor (n + 1) 0 = 0",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"False",
"Nat.instMulZeroClass",
"instHDiv",
"HMul.hMul",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 95,
"column": 4
} | {
"line": 98,
"column": 18
} | [
{
"pp": "case succ\nz : ℂ\nn : ℕ\nih : HasDerivAt (logTaylor (n + 1)) (∑ j ∈ Finset.range n, (-1) ^ j * z ^ j) z\n⊢ HasDerivAt (fun z ↦ (-1) ^ (n + 1 + 1) * (z ^ (n + 1) / (↑n + 1))) ((-1) ^ n * z ^ n) z",
"usedConstants": [
"IsModuleTopology.toContinuousSMul",
"NormedCommRing.toNormedRing",
... | have : HasDerivAt (fun x : ℂ ↦ (x ^ (n + 1) / (n + 1))) (z ^ n) z := by
simp_rw [div_eq_mul_inv]
convert! HasDerivAt.mul_const (hasDerivAt_pow (n + 1) z) (((n : ℂ) + 1)⁻¹) using 1
simp [field] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Analysis.MellinTransform | {
"line": 364,
"column": 6
} | {
"line": 365,
"column": 97
} | [
{
"pp": "case hbc.inr\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b : ℝ\nf : ℝ → E\ns : ℂ\nhfc : LocallyIntegrableOn f (Ioi 0) volume\nhf_top : f =O[atTop] fun x ↦ x ^ (-a)\nhs_top : s.re < a\nhf_bot : f =O[𝓝[>] 0] fun x ↦ x ^ (-b)\nhs_bot : b < s.re\nF : ℂ → ℝ → E := fun z t ↦ ↑t ... | refine
le_add_of_nonneg_of_le (rpow_pos_of_pos ht _).le (rpow_le_rpow_of_exponent_ge ht h.le ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 34
} | [
{
"pp": "case convert_3\ns : ℂ\nhs : 0 < s.re\n⊢ (fun x ↦ rexp (-x)) =O[atTop] fun x ↦ x ^ (-(s.re + 1))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 73,
"column": 34
} | {
"line": 73,
"column": 45
} | [
{
"pp": "s✝ : ℂ\nhs✝ : ∀ (m : ℕ), s✝ ≠ -↑m\ns : ℂ\nhsre : -↑0 < s.re\nhs : ∀ (m : ℕ), s ≠ -↑m\n⊢ 0 < s.re",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 75,
"column": 40
} | {
"line": 75,
"column": 51
} | [
{
"pp": "s✝ : ℂ\nhs✝ : ∀ (m : ℕ), s✝ ≠ -↑m\ns : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nhsre : 0 < s.re\nthis : IsOpen {s | 0 < s.re}\n⊢ 0 < s.re",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 115,
"column": 62
} | {
"line": 115,
"column": 73
} | [
{
"pp": "n : ℕ\nih : ContinuousAt Gamma (-(↑n + 1))\nthis : ContinuousAt (fun s ↦ Gamma (s - 1 + 1)) (-↑n)\n⊢ ContinuousAt Gamma (-↑n)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Deriv | {
"line": 139,
"column": 4
} | {
"line": 139,
"column": 15
} | [
{
"pp": "case neg\ns : ℂ\nhs : s ≠ 0\nh : ∀ (m : ℕ), s ≠ -↑m\n⊢ HasDerivWithinAt (fun x ↦ x * Gamma x) (Gamma s + s * deriv Gamma s) {0}ᶜ s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Complex.LogBounds | {
"line": 319,
"column": 6
} | {
"line": 319,
"column": 17
} | [
{
"pp": "g : ℝ → ℂ\nt : ℂ\nhg : Tendsto (fun x ↦ ↑x * g x) atTop (𝓝 t)\n⊢ (fun x ↦ (↑x * g x) ^ 2 * ↑x⁻¹) =O[atTop] fun x ↦ ↑x⁻¹",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"Complex.instNormedAddCommGroup",
"DivInvOneMonoid.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 24
} | [
{
"pp": "case h.e'_4\ns t a b : ℝ\nhs : 0 < s\nht : 0 < t\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\nf : ℝ → ℝ → ℝ → ℝ := fun c u x ↦ rexp (-c * x) * x ^ (c * (u - 1))\ne : (1 / a).HolderConjugate (1 / b)\nhab' : b = 1 - a\nhst : 0 < a * s + b * t\nposf : ∀ (c u x : ℝ), x ∈ Ioi 0 → 0 ≤ f c u x\nposf' : ∀ (c u : ... | one_div_one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 91,
"column": 2
} | {
"line": 92,
"column": 9
} | [
{
"pp": "u v : ℂ\n⊢ v.betaIntegral u = u.betaIntegral v",
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real",
"MeasureTheory.Measure",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"Comple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 399,
"column": 2
} | {
"line": 399,
"column": 33
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na b : ℝ\nf : ℝ → E\ns : ℂ\nhfc : LocallyIntegrableOn f (Ioi 0) volume\nhf_top : f =O[atTop] fun x ↦ x ^ (-a)\nhs_top : s.re < a\nhf_bot : f =O[𝓝[>] 0] fun x ↦ x ^ (-b)\nhs_bot : b < s.re\nF : ℂ → ℝ → E := fun z t ↦ ↑t ^ (z - 1) • f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.MellinTransform | {
"line": 444,
"column": 4
} | {
"line": 444,
"column": 53
} | [
{
"pp": "s : ℂ\nhs : 0 < s.re\n⊢ -1 < (s - 1).re",
"usedConstants": [
"Eq.mpr",
"Real",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"Real.instLT",
"AddZeroClass.toAddZero",
"Complex.addGroupW... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 176,
"column": 2
} | {
"line": 176,
"column": 32
} | [
{
"pp": "f : ℝ → ℝ\nx : ℝ\nn : ℕ\nhf_conv : ConvexOn ℝ (Ioi 0) f\nhf_feq : ∀ {y : ℝ}, 0 < y → f (y + 1) = f y + log y\nhn : n ≠ 0\nhx : 0 < x\nhx' : x ≤ 1\nhn' : 0 < ↑n\nthis : f ↑n + x * log ↑n = (1 - x) * f ↑n + x * f (↑n + 1)\n⊢ f ((1 - x) * ↑n + x * (↑n + 1)) ≤ (1 - x) * f ↑n + x * f (↑n + 1)",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.AsymptoticCone | {
"line": 51,
"column": 21
} | {
"line": 51,
"column": 53
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝⁴ : NormedAddCommGroup V\ninst✝³ : NormedSpace ℝ V\ninst✝² : MetricSpace P\ninst✝¹ : NormedAddTorsor V P\ninst✝ : FiniteDimensional ℝ V\ns : Set P\np : P\nhs : ∀ i ∈ Metric.sphere 0 1, s ∈ asymptoticNhds ℝ P i\n⊢ s ∈ cobounded P",
"usedConstants": [
"Pure.pure... | asymptoticNhds_eq_smul_vadd _ p, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 368,
"column": 4
} | {
"line": 368,
"column": 44
} | [
{
"pp": "x : ℝ\nhx : x ∈ Icc 1 2\nhmin : IsMinOn Γ (Icc 1 2) x\n⊢ Γ (3 / 2) < Γ 1 ∧ Γ (3 / 2) < Γ 2 ∧ Γ x ≤ Γ (3 / 2)",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
"instHDiv",
"congrArg",
"Real.instDivInvMonoid",
"Real.Gamma_one",
"Nat.instAtLeastTwoHA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 353,
"column": 33
} | {
"line": 353,
"column": 44
} | [
{
"pp": "m : ℕ\nIH : ∀ (s : ℂ), ⌊1 - s.re⌋₊ = m → Tendsto s.GammaSeq atTop (𝓝 (Gamma s))\ns : ℂ\nhs : ↑(m + 1) ≤ 1 - s.re ∧ 1 - s.re < ↑(m + 1) + 1\nhsne : s ≠ 0\nthis : s.re ≤ -↑m\n⊢ 0 ≤ 1 - (s + 1).re",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 132,
"column": 2
} | {
"line": 134,
"column": 53
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | have ⟨p⟩ : Nonempty P := inferInstance
rw [← asymptoticNhds_vadd_pure 0 p, asymptoticNhds_zero', vadd_pure]
exact (Equiv.vaddConst p).surjective.filter_map_top | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 132,
"column": 2
} | {
"line": 134,
"column": 53
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | have ⟨p⟩ : Nonempty P := inferInstance
rw [← asymptoticNhds_vadd_pure 0 p, asymptoticNhds_zero', vadd_pure]
exact (Equiv.vaddConst p).surjective.filter_map_top | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 150,
"column": 11
} | {
"line": 150,
"column": 43
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | asymptoticNhds_eq_smul_vadd _ p, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 420,
"column": 6
} | {
"line": 420,
"column": 33
} | [
{
"pp": "case h.e'_11\n⊢ Ioi 0 = ⇑(DistribSMul.toLinearMap ℝ ℝ (1 / 2)).toAffineMap ⁻¹' Ioi 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 162,
"column": 13
} | {
"line": 162,
"column": 45
} | [
{
"pp": "case a\nk : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAd... | asymptoticNhds_eq_smul_vadd _ p, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup | {
"line": 435,
"column": 4
} | {
"line": 435,
"column": 41
} | [
{
"pp": "case refine_3\n⊢ ConvexOn ℝ (Ioi 0) fun s ↦ s * log 2",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Set.Ioi",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 174,
"column": 6
} | {
"line": 174,
"column": 38
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹² : Field k\ninst✝¹¹ : LinearOrder k\ninst✝¹⁰ : AddCommGroup V\ninst✝⁹ : Module k V\ninst✝⁸ : AddTorsor V P\ninst✝⁷ : TopologicalSpace V\ninst✝⁶ : TopologicalSpace k\ninst✝⁵ : OrderTopology k\ninst✝⁴ : IsStrictOrderedRing k\ninst✝³ : IsTopologicalAddGroup... | asymptoticNhds_eq_smul_vadd _ p, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Normed.Affine.Ceva | {
"line": 50,
"column": 57
} | {
"line": 50,
"column": 68
} | [
{
"pp": "𝕜 : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : SeminormedAddCommGroup V\ninst✝³ : NormedField 𝕜\ninst✝² : NormedSpace 𝕜 V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nt : Triangle 𝕜 P\np : Fin 3 → P\np' : P\nhp0 : ∀ (i : Fin 3), p i ≠ t.points (i + 2)\nhp : ∀ (i : Fin 3), p i ∈ affineS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 32
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝¹⁰ : Field k\ninst✝⁹ : LinearOrder k\ninst✝⁸ : AddCommGroup V\ninst✝⁷ : Module k V\ninst✝⁶ : AddTorsor V P\ninst✝⁵ : TopologicalSpace V\ninst✝⁴ : TopologicalSpace k\ninst✝³ : OrderTopology k\ninst✝² : IsStrictOrderedRing k\ninst✝¹ : IsTopologicalAddGroup V... | refine Filter.ext' fun p => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 432,
"column": 10
} | {
"line": 432,
"column": 15
} | [
{
"pp": "s : ℂ\nhs : ∀ (m : ℕ), s ≠ -↑m\nh_im : s.im = 0\n⊢ ↑s.re + ↑s.im * I = ↑s.re",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Complex.im",
"Complex.instMul",
"id",
"Complex.ofReal",
"Complex.re",
"ins... | h_im, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 457,
"column": 2
} | {
"line": 457,
"column": 72
} | [
{
"pp": "s : ℂ\nm : ℕ\nhs : s = -↑m\n⊢ s.re ≤ 0",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real",
"Real.instZero",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"Real.instAddGroup",
"SubtractionMonoid.toSubNegZe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.AsymptoticCone | {
"line": 328,
"column": 22
} | {
"line": 340,
"column": 85
} | [
{
"pp": "k : Type u_1\nV : Type u_2\ninst✝⁹ : Field k\ninst✝⁸ : LinearOrder k\ninst✝⁷ : IsStrictOrderedRing k\ninst✝⁶ : TopologicalSpace k\ninst✝⁵ : OrderTopology k\ninst✝⁴ : AddCommGroup V\ninst✝³ : Module k V\ninst✝² : TopologicalSpace V\ninst✝¹ : IsTopologicalAddGroup V\ninst✝ : ContinuousSMul k V\ns : Set V... | by
refine isClosed_iff_frequently.mp hs₂ _ <|
tendsto_snd (f := atTop (α := k)) |>.const_smul _ |>.vadd_const _ |>.frequently ?_
rw [mem_asymptoticCone_iff, asymptoticNhds_eq_smul_vadd v p, vadd_pure, frequently_map,
← map₂_smul, ← map_prod_eq_map₂, frequently_map] at hv
apply hv.mp
filter_upwards [tend... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 561,
"column": 4
} | {
"line": 561,
"column": 76
} | [
{
"pp": "s : ℂ\nh1 : AnalyticOnNhd ℂ (fun z ↦ (Gamma z)⁻¹ * (Gamma (z + 1 / 2))⁻¹) univ\n⊢ DifferentiableOn ℂ (fun z ↦ (Gamma (2 * z))⁻¹ * 2 ^ (2 * z - 1) / ↑√π) univ",
"usedConstants": [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Real.pi",
"NormedRing.toRing"... | refine (Differentiable.mul ?_ (differentiable_const _)).differentiableOn | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.Gamma.Beta | {
"line": 588,
"column": 2
} | {
"line": 589,
"column": 21
} | [
{
"pp": "s : ℝ\n⊢ ↑(Gamma s * Gamma (s + 1 / 2)) = ↑(Gamma (2 * s) * 2 ^ (1 - 2 * s) * √π)",
"usedConstants": [
"Eq.mpr",
"Real.instPow",
"Real",
"instHDiv",
"Real.pi",
"HMul.hMul",
"Real.instZeroLEOneClass",
"congrArg",
"Real.instDivInvMonoid",
"R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.MazurUlam | {
"line": 125,
"column": 8
} | {
"line": 125,
"column": 41
} | [
{
"pp": "E : Type u_1\nPE : Type u_2\nF : Type u_3\nPF : Type u_4\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\ninst✝⁵ : MetricSpace PE\ninst✝⁴ : NormedAddTorsor E PE\ninst✝³ : NormedAddCommGroup F\ninst✝² : NormedSpace ℝ F\ninst✝¹ : MetricSpace PF\ninst✝ : NormedAddTorsor F PF\nf : E ≃ᵢ F\n⊢ (f.tra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 86,
"column": 37
} | {
"line": 86,
"column": 53
} | [
{
"pp": "case pos\nk : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\nhp : AffineIndependent k p\ns : Set ι\nhs : s.Nonempty\nfs : ↑s → Finset ι\nw : ↑s → ι → k\nhw : ∀ (i : ↑s), ∑ j ∈ fs i, w i j = 1\np' : P... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 86,
"column": 37
} | {
"line": 86,
"column": 53
} | [
{
"pp": "case neg\nk : Type u_1\nV : Type u_2\nP : Type u_3\nι : Type u_4\ninst✝³ : Ring k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\np : ι → P\nhp : AffineIndependent k p\ns : Set ι\nhs : s.Nonempty\nfs : ↑s → Finset ι\nw : ↑s → ι → k\nhw : ∀ (i : ↑s), ∑ j ∈ fs i, w i j = 1\np' : P... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 19
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\np' : P\nhp' : ∀ (i : Fin 3), p' ∈ affineSpan k {t.points i, (AffineMap.lineMap (t.points (i + 1)) (t.points (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 153,
"column": 4
} | {
"line": 153,
"column": 20
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 169,
"column": 6
} | {
"line": 169,
"column": 17
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 175,
"column": 38
} | {
"line": 175,
"column": 54
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 176,
"column": 38
} | {
"line": 176,
"column": 54
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 180,
"column": 47
} | {
"line": 180,
"column": 77
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 15
} | [
{
"pp": "case refine_1.h\nR : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex R P m\ne : Fin (m + 1) ≃ Fin (n + 1)\nh : (s.reindex e).Regular\nσ : Equiv.Perm (Fin (m + 1... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.AffineSpace.Ceva | {
"line": 182,
"column": 5
} | {
"line": 182,
"column": 35
} | [
{
"pp": "k : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : CommRing k\ninst✝³ : NoZeroDivisors k\ninst✝² : AddCommGroup V\ninst✝¹ : Module k V\ninst✝ : AffineSpace V P\nt : Triangle k P\nr : Fin 3 → k\nh✝ : Nontrivial k\nw : ↑Set.univ → Fin 3 → k := fun i ↦ Finset.affineCombinationLineMapWeights (↑i + 1) (↑i +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Affine.Simplex | {
"line": 112,
"column": 4
} | {
"line": 112,
"column": 15
} | [
{
"pp": "case refine_2.h\nR : Type u_1\nV : Type u_2\nP : Type u_3\ninst✝⁴ : Ring R\ninst✝³ : SeminormedAddCommGroup V\ninst✝² : PseudoMetricSpace P\ninst✝¹ : Module R V\ninst✝ : NormedAddTorsor V P\nm n : ℕ\ns : Simplex R P m\ne : Fin (m + 1) ≃ Fin (n + 1)\nh : s.Regular\nσ : Equiv.Perm (Fin (n + 1))\nx : P ≃ᵢ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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