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.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 148,
"column": 2
} | {
"line": 148,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Preorder R\nm : Matrix (Fin 2) (Fin 2) R\ng : GL (Fin 2) R\n⊢ ((↑g)⁻¹ * m * ↑g).IsHyperbolic ↔ m.IsHyperbolic",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Topology | {
"line": 223,
"column": 28
} | {
"line": 223,
"column": 39
} | [
{
"pp": "τ : ℍ\nU : Set ℝ\nhU : U ∈ map (fun τ ↦ ‖↑τ‖) (𝓝 τ)\ns : Set ℍ\nhs' : (fun τ ↦ ‖↑τ‖) '' s ⊆ U\nε : ℝ\nhεpos : ε > 0\nhεs : Metric.ball (↑τ) ε ⊆ UpperHalfPlane.coe '' s\nr : ℝ\nhr : r ∈ Metric.ball ‖↑τ‖ ε\nhr' : 0 ≤ r\nthis : ↑r / ↑‖↑τ‖ * ↑τ ∈ Metric.ball (↑τ) ε\nξ : ℍ\nhξs : ξ ∈ s\nhξτ : ↑ξ = ↑r / ↑‖↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : Preorder R\nm : Matrix (Fin 2) (Fin 2) R\ng : GL (Fin 2) R\n⊢ ((↑g)⁻¹ * m * ↑g).IsElliptic ↔ m.IsElliptic",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 49,
"column": 4
} | {
"line": 50,
"column": 55
} | [
{
"pp": "cd : Fin 2 → ℝ\nz : ℂ\nhz : z.im ≠ 0\nh : (↑(cd 0) * z + ↑(cd 1)).im = Complex.im 0\n⊢ cd 0 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty | {
"line": 87,
"column": 2
} | {
"line": 88,
"column": 39
} | [
{
"pp": "⊢ Tendsto UpperHalfPlane.coe atImInfty (comap Complex.im atTop)",
"usedConstants": [
"Eq.mpr",
"Real",
"UpperHalfPlane.coe",
"congrArg",
"Complex.im",
"UpperHalfPlane.atImInfty",
"Function.comp",
"id",
"Filter.atTop",
"funext",
"Uppe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty | {
"line": 96,
"column": 2
} | {
"line": 96,
"column": 38
} | [
{
"pp": "g : GL (Fin 2) ℝ\nhg : ↑g 1 0 = 0\n⊢ 0 < |↑g 0 0 / ↑g 1 1|",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Real",
"Preorder.toLT",
"instHDiv",
"Real.lattice",
"abs",
"congrArg"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 238,
"column": 30
} | {
"line": 238,
"column": 41
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\ng : GL (Fin 2) R\nhP : C (↑g 1 0) * X ^ 2 + C (↑g 1 1 - ↑g 0 0) * X - C (↑g 0 1) = 0\n⊢ ↑g 0 1 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 239,
"column": 30
} | {
"line": 239,
"column": 41
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\ng : GL (Fin 2) R\nhP : C (↑g 1 0) * X ^ 2 + C (↑g 1 1 - ↑g 0 0) * X - C (↑g 0 1) = 0\nhb : ↑g 0 1 = 0\n⊢ ↑g 1 0 = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 240,
"column": 34
} | {
"line": 240,
"column": 59
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\ng : GL (Fin 2) R\nhP : C (↑g 1 0) * X ^ 2 + C (↑g 1 1 - ↑g 0 0) * X - C (↑g 0 1) = 0\nhb : ↑g 0 1 = 0\nhc : ↑g 1 0 = 0\n⊢ ↑g 1 1 = ↑g 0 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 250,
"column": 47
} | {
"line": 250,
"column": 87
} | [
{
"pp": "K : Type u_2\ninst✝¹ : Field K\ng : GL (Fin 2) K\ninst✝ : NeZero 2\nhg : g.IsParabolic\n⊢ (↑g).trace ^ 2 = 4 * (↑g).det",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 251,
"column": 2
} | {
"line": 253,
"column": 27
} | [
{
"pp": "K : Type u_2\ninst✝¹ : Field K\ng : GL (Fin 2) K\ninst✝ : NeZero 2\nhg : g.IsParabolic\nthis : (↑g).trace ^ 2 = 4 * (↑g).det\n⊢ (↑g).parabolicEigenvalue ≠ 0",
"usedConstants": [
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"IsDomain.to_noZeroDivisors",
"ins... | rw [parabolicEigenvalue, div_ne_zero_iff, eq_true_intro (two_ne_zero' K), and_true,
Ne, ← sq_eq_zero_iff, this, show (4 : K) = 2 ^ 2 by norm_num, mul_eq_zero,
sq_eq_zero_iff, not_or] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 148,
"column": 2
} | {
"line": 149,
"column": 36
} | [
{
"pp": "case pos\ng : GL (Fin 2) ℝ\nz : ℂ\nh : 0 < ↑(GeneralLinearGroup.det g)\n⊢ ((ContinuousAlgEquiv.refl ℝ ℂ) (num g z / denom g z)).im =\n ↑(GeneralLinearGroup.det g) * z.im / Complex.normSq (denom g z)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 148,
"column": 2
} | {
"line": 149,
"column": 36
} | [
{
"pp": "case neg\ng : GL (Fin 2) ℝ\nz : ℂ\nh : ¬0 < ↑(GeneralLinearGroup.det g)\n⊢ (Complex.conjCAE (num g z / denom g z)).im = -↑(GeneralLinearGroup.det g) * z.im / Complex.normSq (denom g z)",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"NegZeroClass.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 172,
"column": 27
} | {
"line": 172,
"column": 64
} | [
{
"pp": "g h : GL (Fin 2) ℝ\nz : ℍ\nu : ℂ\nhu : (σ g) ((σ h) ↑z) = u\n⊢ u.im ≠ 0",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"RCLike.toNormedAlgebra",
"UpperHalfPlane.coe",
"Real.instZero",
"congrArg",
"Complex.im",
"Com... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 273,
"column": 22
} | {
"line": 273,
"column": 42
} | [
{
"pp": "K : Type u_2\ninst✝¹ : Field K\ng : GL (Fin 2) K\ninst✝ : CharZero K\nn : ℕ\nhn : n ≠ 0\na : K\nm : Matrix (Fin 2) (Fin 2) K\nhg : ↑g = (Matrix.scalar (Fin 2)) a + m\nhm0 : m ≠ 0\nhmsq : m ^ 2 = 0\nthis : a ≠ 0\n⊢ (↑n * a ^ (n - 1)) • m ≠ 0",
"usedConstants": [
"GroupWithZero.toMonoidWithZero... | simp [this, hm0, hn] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 273,
"column": 22
} | {
"line": 273,
"column": 42
} | [
{
"pp": "K : Type u_2\ninst✝¹ : Field K\ng : GL (Fin 2) K\ninst✝ : CharZero K\nn : ℕ\nhn : n ≠ 0\na : K\nm : Matrix (Fin 2) (Fin 2) K\nhg : ↑g = (Matrix.scalar (Fin 2)) a + m\nhm0 : m ≠ 0\nhmsq : m ^ 2 = 0\nthis : a ≠ 0\n⊢ (↑n * a ^ (n - 1)) • m ≠ 0",
"usedConstants": [
"GroupWithZero.toMonoidWithZero... | simp [this, hm0, hn] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 273,
"column": 22
} | {
"line": 273,
"column": 42
} | [
{
"pp": "K : Type u_2\ninst✝¹ : Field K\ng : GL (Fin 2) K\ninst✝ : CharZero K\nn : ℕ\nhn : n ≠ 0\na : K\nm : Matrix (Fin 2) (Fin 2) K\nhg : ↑g = (Matrix.scalar (Fin 2)) a + m\nhm0 : m ≠ 0\nhmsq : m ^ 2 = 0\nthis : a ≠ 0\n⊢ (↑n * a ^ (n - 1)) • m ≠ 0",
"usedConstants": [
"GroupWithZero.toMonoidWithZero... | simp [this, hm0, hn] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.MFDeriv.FDeriv | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 74
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nE' : Type u_3\ninst✝¹ : NormedAddCommGroup E'\ninst✝ : NormedSpace 𝕜 E'\nf : E → E'\ns : Set E\nx : E\nf' : TangentSpace 𝓘(𝕜, E) x →L[𝕜] TangentSpace 𝓘(𝕜, E') (f x)\n⊢ HasMF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 277,
"column": 4
} | {
"line": 277,
"column": 53
} | [
{
"pp": "case refine_2\nK : Type u_2\ninst✝¹ : Field K\ng : GL (Fin 2) K\ninst✝ : CharZero K\nn : ℕ\nhn : n ≠ 0\na : K\nm : Matrix (Fin 2) (Fin 2) K\nhg : ↑g = m\nhm0 : m ≠ 0\nhmsq : ↑g ^ 2 = 0\nha : a = 0\n⊢ (↑(g ^ 2)).det = 0",
"usedConstants": [
"Units.val",
"Eq.mpr",
"congrArg",
... | rw [Units.val_pow_eq_pow_val, hmsq, det_zero ⟨0⟩] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 303,
"column": 4
} | {
"line": 303,
"column": 15
} | [
{
"pp": "case mpr.inl\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nhx : x ≠ 0\nh_det : det (upperRightHom x) = 1 ∨ det (upperRightHom x) = -1\nhg10 : ↑(upperRightHom x) 1 0 = 0\n⊢ ↑(upperRightHom x) 0 0 = ↑(upperRightHom x) 1 1 ∧ ↑(upperRightHom x) 0 1 ≠ 0",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.FinTwo | {
"line": 303,
"column": 4
} | {
"line": 303,
"column": 15
} | [
{
"pp": "case mpr.inr\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\nx : K\nhx : x ≠ 0\nh_det : det (-upperRightHom x) = 1 ∨ det (-upperRightHom x) = -1\nhg10 : ↑(-upperRightHom x) 1 0 = 0\n⊢ ↑(-upperRightHom x) 0 0 = ↑(-upperRightHom x) 1 1 ∧ ↑(-upperRightHom x) 0 1 ≠ 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 320,
"column": 2
} | {
"line": 320,
"column": 43
} | [
{
"pp": "z : ℍ\n⊢ ModularGroup.T • z = 1 +ᵥ z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 336,
"column": 27
} | {
"line": 336,
"column": 38
} | [
{
"pp": "a b c d : ℝ\nh : a * d - b * c = 1\nhc : ↑⟨!![a, b; c, d], ⋯⟩ 1 0 ≠ 0\nh_denom : ∀ (z : ℍ), denom (toGL ⟨!![a, b; c, d], ⋯⟩) ↑z ≠ 0\n⊢ c ≠ 0",
"usedConstants": [
"Real",
"Real.instZero",
"id",
"Ne",
"Zero.toOfNat0",
"OfNat.ofNat"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 342,
"column": 41
} | {
"line": 342,
"column": 52
} | [
{
"pp": "a b c d : ℝ\nh : a * d - b * c = 1\nh_denom : ∀ (z : ℍ), denom (toGL ⟨!![a, b; c, d], ⋯⟩) ↑z ≠ 0\nz : ℂ\nhz : 0 < z.im\nhc : ↑c ≠ 0\n⊢ ↑c * z + ↑d ≠ 0",
"usedConstants": [
"HMul.hMul",
"Complex.instZero",
"Complex.instMul",
"id",
"Ne",
"Complex.ofReal",
"in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 362,
"column": 31
} | {
"line": 362,
"column": 63
} | [
{
"pp": "z : ℍ\n⊢ ↑√z.im ≠ 0",
"usedConstants": [
"Eq.mpr",
"Real",
"Real.instZero",
"congrArg",
"Complex.instZero",
"Real.instLT",
"id",
"_private.Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction.0.UpperHalfPlane.toSL2R_smul_I._simp_1_1",
"Ne",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 421,
"column": 2
} | {
"line": 421,
"column": 19
} | [
{
"pp": "a b : SL(2, ℤ)\ni j : Fin 2\nh : ∀ (i j : Fin 2), ↑↑(coe a) i j = ↑↑(coe b) i j\n⊢ ↑a i j = ↑b i j",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | {
"line": 482,
"column": 2
} | {
"line": 482,
"column": 13
} | [
{
"pp": "g : SL(2, ℤ)\nz : ℍ\n⊢ (g • z).im = z.im / Complex.normSq (denom (toGL ((SpecialLinearGroup.map (Int.castRingHom ℝ)) g)) ↑z)",
"usedConstants": [
"Real",
"instHSMul",
"Matrix.SpecialLinearGroup",
"MonoidHom.instFunLike",
"instHDiv",
"UpperHalfPlane.SLAction",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 46
} | [
{
"pp": "case left\nn : ℕ∞ω\nz : ℂ\nhz : 0 < z.im\n⊢ Tendsto id (𝓝 z) (𝓝 ↑(↑ofComplex z))",
"usedConstants": [
"UpperHalfPlane.ofComplex",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"UpperHalfPlane.coe",
"congrArg",
"Complex.instNormedField",
"PseudoMetricSp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 15
} | [
{
"pp": "case right\nn : ℕ∞ω\nz : ℂ\nhz : 0 < z.im\n⊢ ContDiffWithinAt ℂ n (↑(extChartAt 𝓘(ℂ, ℂ) (↑ofComplex z)) ∘ ↑ofComplex ∘ ↑(extChartAt 𝓘(ℂ, ℂ) z).symm)\n (Set.range ↑𝓘(ℂ, ℂ)) (↑(extChartAt 𝓘(ℂ, ℂ) z) z)",
"usedConstants": [
"UpperHalfPlane.ofComplex",
"Eq.mpr",
"InnerProductSp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 35
} | [
{
"pp": "n : ℕ∞ω\nf : ℍ → ℂ\nτ : ℍ\n⊢ ContMDiffAt 𝓘(ℂ, ℂ) 𝓘(ℂ, ℂ) n f τ ↔ ContMDiffAt 𝓘(ℂ, ℂ) 𝓘(ℂ, ℂ) n (f ∘ ↑ofComplex) ↑τ",
"usedConstants": [
"UpperHalfPlane.ofComplex",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"chartedSpaceSelf",
"Comple... | refine ⟨fun hf ↦ ?_, fun hf ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 57
} | [
{
"pp": "case refine_2\nn : ℕ∞ω\nf : ℍ → ℂ\nτ : ℍ\nhf : ContMDiffAt 𝓘(ℂ, ℂ) 𝓘(ℂ, ℂ) n (f ∘ ↑ofComplex) ↑τ\n⊢ ContMDiffAt 𝓘(ℂ, ℂ) 𝓘(ℂ, ℂ) n f τ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 35
} | [
{
"pp": "f : ℍ → ℂ\nτ : ℍ\n⊢ MDiffAt f τ ↔ MDiffAt (f ∘ ↑ofComplex) ↑τ",
"usedConstants": [
"UpperHalfPlane.ofComplex",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"chartedSpaceSelf",
"Complex.instNormedAddCommGroup",
"UpperHalfPlane.coe",
... | refine ⟨fun hf ↦ ?_, fun hf ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 77,
"column": 4
} | {
"line": 77,
"column": 57
} | [
{
"pp": "case refine_2\nf : ℍ → ℂ\nτ : ℍ\nhf : MDiffAt (f ∘ ↑ofComplex) ↑τ\n⊢ MDiffAt f τ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 13
} | [
{
"pp": "n : ℕ∞ω\ng : GL (Fin 2) ℝ\n⊢ ContMDiff 𝓘(ℂ, ℂ) 𝓘(ℂ, ℂ) n fun τ ↦ (denom g ↑τ)⁻¹",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 104,
"column": 2
} | {
"line": 104,
"column": 33
} | [
{
"pp": "n : ℕ∞ω\ng : GL (Fin 2) ℝ\nhg : 0 < ↑(Matrix.GeneralLinearGroup.det g)\nτ : ℍ\n⊢ ContMDiffAt 𝓘(ℂ, ℂ) 𝓘(ℂ, ℂ) n (↑(extChartAt 𝓘(ℂ, ℂ) (g • τ)) ∘ fun τ ↦ g • τ) τ",
"usedConstants": [
"UpperHalfPlane.glAction",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.to... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Euclidean.Inversion.Basic | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 43
} | [
{
"pp": "V : Type u_1\nP : Type u_2\ninst✝³ : NormedAddCommGroup V\ninst✝² : InnerProductSpace ℝ V\ninst✝¹ : MetricSpace P\ninst✝ : NormedAddTorsor V P\nc x y : P\nhx : x ≠ c\nhy : y ≠ c\nR : ℝ\n⊢ dist ((R / ‖x -ᵥ c‖) ^ 2 • (x -ᵥ c)) ((R / ‖y -ᵥ c‖) ^ 2 • (y -ᵥ c)) = R ^ 2 / (‖x -ᵥ c‖ * ‖y -ᵥ c‖) * dist x y",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 15
} | [
{
"pp": "case h\nf : ℍ → ℂ\nhf : DifferentiableOn ℂ (f ∘ ↑ofComplex) {z | 0 < z.im}\nτ : ℍ\nthis : AnalyticOnNhd ℂ (f ∘ ↑ofComplex) {z | 0 < z.im}\nw : ℍ\nhτ : ∀ᶠ (a : ℍ) in 𝓝 τ, ↑a ∈ {↑τ}ᶜ → (f ∘ ↑ofComplex) ↑a ≠ 0\na : ℍ\nha : ↑a ∈ {↑τ}ᶜ → (f ∘ ↑ofComplex) ↑a ≠ 0\n⊢ a ∈ {τ}ᶜ → f a ≠ 0",
"usedConstants": ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 137,
"column": 59
} | {
"line": 137,
"column": 70
} | [
{
"pp": "f g : ℍ → ℂ\nhf : MDiff f\nhg : MDiff g\nhfg : f * g = 0\n⊢ ∀ (x : ℍ), f x = 0 ∨ g x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 144,
"column": 64
} | {
"line": 144,
"column": 75
} | [
{
"pp": "ι : Type u_1\nf : ι → ℍ → ℂ\ns : Finset ι\nhf : ∀ i ∈ s, MDiff (f i)\nh0 : ∏ i ∈ s, f i = 0\n⊢ ∀ (x : ℍ), ∏ i ∈ s, f i x = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 162,
"column": 4
} | {
"line": 164,
"column": 52
} | [
{
"pp": "g : GL (Fin 2) ℝ\nhg : 0 < (↑g).det\nτ : ℍ\nthis : HasStrictDerivAt (num g / denom g) (↑(↑g).det / denom g ↑τ ^ 2) ↑τ\n⊢ HasStrictDerivAt (fun z ↦ ↑(g • ↑ofComplex z)) (↑(↑g).det / denom g ↑τ ^ 2) ↑τ",
"usedConstants": [
"UpperHalfPlane.glAction",
"Topology.IsOpenEmbedding.map_nhds_eq",... | refine this.congr_of_eventuallyEq ?_
rw [← isOpenEmbedding_coe.map_nhds_eq, eventuallyEq_map]
simp [Function.comp_def, coe_smul_of_det_pos hg] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 162,
"column": 4
} | {
"line": 164,
"column": 52
} | [
{
"pp": "g : GL (Fin 2) ℝ\nhg : 0 < (↑g).det\nτ : ℍ\nthis : HasStrictDerivAt (num g / denom g) (↑(↑g).det / denom g ↑τ ^ 2) ↑τ\n⊢ HasStrictDerivAt (fun z ↦ ↑(g • ↑ofComplex z)) (↑(↑g).det / denom g ↑τ ^ 2) ↑τ",
"usedConstants": [
"UpperHalfPlane.glAction",
"Topology.IsOpenEmbedding.map_nhds_eq",... | refine this.congr_of_eventuallyEq ?_
rw [← isOpenEmbedding_coe.map_nhds_eq, eventuallyEq_map]
simp [Function.comp_def, coe_smul_of_det_pos hg] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Complex.UpperHalfPlane.Manifold | {
"line": 186,
"column": 2
} | {
"line": 186,
"column": 37
} | [
{
"pp": "case h\ng : GL (Fin 2) ℝ\nhg : 0 < (↑g).det\nτ : ℍ\nz : ℂ\nhz : z ∈ upperHalfPlaneSet\n⊢ DifferentiableAt ℂ (fun z ↦ ↑(g • ↑ofComplex z)) z",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Norm.Transitivity | {
"line": 217,
"column": 4
} | {
"line": 217,
"column": 52
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝⁶ : CommRing R\nL : Type u_6\nK : Type u_7\ninst✝⁵ : Field K\ninst✝⁴ : Field L\ninst✝³ : Algebra K L\ninst✝² : Algebra R L\ninst✝¹ : Algebra R K\ninst✝ : IsScalarTower R K L\nx : L\nhx : IsIntegral R x\nh : ¬FiniteDimensional K L\n⊢ IsIntegral R ((norm K) x)",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Norm.Transitivity | {
"line": 245,
"column": 2
} | {
"line": 245,
"column": 26
} | [
{
"pp": "case pos\nL : Type u_6\nK : Type u_7\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nx : L\nh : FiniteDimensional K L\nF : IntermediateField K L := K⟮x⟯\n⊢ (norm K) x = (norm K) (gen K x) ^ finrank (↥K⟮x⟯) L",
"usedConstants": [
"Eq.mpr",
"MonoidHom.instFunLike",
"NonUni... | nth_rw 1 [← coe_gen K x] | Mathlib.Tactic._aux_Mathlib_Tactic_NthRewrite___macroRules_Mathlib_Tactic_tacticNth_rw______1 | Mathlib.Tactic.tacticNth_rw_____ |
Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | {
"line": 49,
"column": 49
} | {
"line": 49,
"column": 60
} | [
{
"pp": "⊢ sinh ~[𝓝 0] id",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | {
"line": 311,
"column": 49
} | {
"line": 311,
"column": 60
} | [
{
"pp": "⊢ sinh ~[𝓝 0] id",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | {
"line": 408,
"column": 48
} | {
"line": 408,
"column": 76
} | [
{
"pp": "x : ℝ\n⊢ 0 < sinh x ↔ 0 < x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | {
"line": 411,
"column": 51
} | {
"line": 411,
"column": 79
} | [
{
"pp": "x : ℝ\n⊢ sinh x ≤ 0 ↔ x ≤ 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | {
"line": 414,
"column": 48
} | {
"line": 414,
"column": 76
} | [
{
"pp": "x : ℝ\n⊢ sinh x < 0 ↔ x < 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | {
"line": 417,
"column": 51
} | {
"line": 417,
"column": 79
} | [
{
"pp": "x : ℝ\n⊢ 0 ≤ sinh x ↔ 0 ≤ x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Matrix | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 29
} | [
{
"pp": "case h\nn : Type u_1\ninst✝² : Fintype n\ninst✝¹ : DecidableEq n\nA : Type u_4\ninst✝ : CommRing A\nx : GL n A\n⊢ x ∈ Set.range ⇑toGL ↔ x ∈ ⇑GeneralLinearGroup.det ⁻¹' {1}",
"usedConstants": [
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"Matrix.SpecialLinearGroup",
"MonoidH... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Matrix | {
"line": 158,
"column": 24
} | {
"line": 158,
"column": 48
} | [
{
"pp": "n : Type u_1\nR : Type u_2\ninst✝⁵ : Fintype n\ninst✝⁴ : DecidableEq n\ninst✝³ : CommRing R\ninst✝² : TopologicalSpace R\ninst✝¹ : IsTopologicalRing R\ninst✝ : T0Space R\n⊢ IsClosed[Units.instTopologicalSpaceUnits] (Set.range ⇑toGL)",
"usedConstants": [
"Eq.mpr",
"Matrix.SpecialLinearGr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Metric | {
"line": 119,
"column": 4
} | {
"line": 119,
"column": 94
} | [
{
"pp": "z✝ w✝ : ℍ\nr : ℝ\nz w : ℍ\nh : dist z w = 0\n⊢ z = w",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.Metric | {
"line": 223,
"column": 6
} | {
"line": 223,
"column": 50
} | [
{
"pp": "case hbc._a.hab\nz w : ℍ\n⊢ dist { re := 0, im := z.im } { re := 0, im := w.im } ≤ dist ↑z ↑w",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"False",
"Real.partialOrder",
"Real",
"Real.lattice",
"Complex.instNormedAddCommGroup",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ProperAction.Basic | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 59
} | [
{
"pp": "G : Type u_1\nX : Type u_2\ninst✝⁴ : Group G\ninst✝³ : MulAction G X\ninst✝² : TopologicalSpace G\ninst✝¹ : TopologicalSpace X\nh_proper : ProperSMul G X\ninst✝ : T1Space G\nf : X → G × X := fun x ↦ (1, x)\nproper_f : IsProperMap f\ng : G × X → X × X := fun gx ↦ (gx.1 • gx.2, gx.2)\nproper_g : IsProper... | have : g ∘ f = fun x ↦ (x, x) := by ext x <;> simp [f, g] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Algebra.ProperAction.Basic | {
"line": 292,
"column": 2
} | {
"line": 293,
"column": 9
} | [
{
"pp": "case isProperMap_smul_pair\nG : Type u_1\nX : Type u_2\ninst✝⁶ : Group G\ninst✝⁵ : MulAction G X\ninst✝⁴ : TopologicalSpace G\ninst✝³ : TopologicalSpace X\ninst✝² : ContinuousSMul G X\ninst✝¹ : IsTopologicalGroup G\ninst✝ : IsPretransitive G X\nx : X\nhx : IsProperMap fun g ↦ g • x\nf : G × G → G × X :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 32
} | [
{
"pp": "X : Type u_1\nx : OnePoint X\n⊢ x ≠ ∞ ↔ ∃ y, ↑y = x",
"usedConstants": [
"OnePoint.infty",
"OnePoint.some",
"Exists",
"Ne",
"OnePoint.rec",
"Iff",
"Eq",
"OnePoint"
]
}
] | induction x using OnePoint.rec | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 157,
"column": 74
} | {
"line": 158,
"column": 58
} | [
{
"pp": "X : Type u_1\nx : OnePoint X\n⊢ x ∉ range some ↔ x = ∞",
"usedConstants": [
"Eq.mpr",
"OnePoint.infty",
"congrArg",
"Compl.compl",
"Iff.rfl",
"OnePoint.compl_range_coe",
"OnePoint.some",
"Membership.mem",
"Set.instSingletonSet",
"id",
... | by
rw [← mem_compl_iff, compl_range_coe, mem_singleton_iff] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 208,
"column": 4
} | {
"line": 208,
"column": 29
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝ : TopologicalSpace X\ns t : Set (OnePoint X)\nhms : ∞ ∈ s → IsCompact (some ⁻¹' s)ᶜ\nhs : IsOpen[inst✝] (some ⁻¹' s)\nhmt : ∞ ∈ t → IsCompact (some ⁻¹' t)ᶜ\nht : IsOpen[inst✝] (some ⁻¹' t)\nhms' : ∞ ∈ s\nhmt' : ∞ ∈ t\n⊢ IsCompact (some ⁻¹' (s ∩ t))ᶜ",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 245,
"column": 6
} | {
"line": 245,
"column": 50
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\ns : Set X\n⊢ IsOpen[instTopologicalSpace] (some '' s) ↔ IsOpen[inst✝] s",
"usedConstants": [
"Eq.mpr",
"congrArg",
"OnePoint.infty_notMem_image_coe",
"OnePoint.some",
"id",
"OnePoint.isOpen_iff_of_notMem",
"Iff",
... | isOpen_iff_of_notMem infty_notMem_image_coe, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 52
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝ : TopologicalSpace X\ns : Set (OnePoint X)\nx : X\nh : (𝓝[≠] x).NeBot\n⊢ (𝓝[≠] ↑x).NeBot",
"usedConstants": [
"Eq.mpr",
"OnePoint.nhdsWithin_coe",
"OnePoint.some_eq_iff._simp_1",
"congrArg",
"Filter.map",
"Compl.compl",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 472,
"column": 2
} | {
"line": 472,
"column": 32
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nx y : OnePoint X\n⊢ Inseparable x y ↔ x = ∞ ∧ y = ∞ ∨ ∃ x', x = ↑x' ∧ ∃ y', y = ↑y' ∧ Inseparable x' y'",
"usedConstants": [
"OnePoint.infty",
"OnePoint.some",
"Exists",
"OnePoint.rec",
"And",
"Iff",
"Or",
"Eq... | induction x using OnePoint.rec | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 531,
"column": 2
} | {
"line": 531,
"column": 32
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ns : Set (OnePoint X)\ninst✝¹ : WeaklyLocallyCompactSpace X\ninst✝ : R1Space X\nkey : ∀ (z : X), Disjoint (𝓝 ↑z) (𝓝 ∞)\nx y : OnePoint X\n⊢ x ⤳ y ∨ Disjoint (𝓝 x) (𝓝 y)",
"usedConstants": [
"Specializes",
"Filter.instCompleteLa... | induction x using OnePoint.rec | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 554,
"column": 2
} | {
"line": 555,
"column": 9
} | [
{
"pp": "case h\nX : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : Infinite X\ninst✝ : DiscreteTopology X\ninhabited_h : Inhabited X\n⊢ ¬Tendsto (⇑CofiniteTopology.of.symm) (𝓝 (CofiniteTopology.of ↑default))\n (𝓝 (CofiniteTopology.of.symm (CofiniteTopology.of ↑default)))",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.CompactlyGeneratedSpace | {
"line": 300,
"column": 2
} | {
"line": 302,
"column": 45
} | [
{
"pp": "X : Type u\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactlyGeneratedSpace X\ns : Set X\nhs : ∀ ⦃K : Set X⦄, IsCompact K → IsOpen[inst✝¹] (s ∩ K)\n⊢ IsOpen[inst✝¹] s",
"usedConstants": [
"Eq.mpr",
"Continuous",
"congrArg",
"Set.preimage_inter_range",
"id",
"Set.ins... | refine isOpen' fun K _ _ _ f hf ↦ ?_
rw [← Set.preimage_inter_range]
exact (hs (isCompact_range hf)).preimage hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Compactness.CompactlyGeneratedSpace | {
"line": 300,
"column": 2
} | {
"line": 302,
"column": 45
} | [
{
"pp": "X : Type u\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactlyGeneratedSpace X\ns : Set X\nhs : ∀ ⦃K : Set X⦄, IsCompact K → IsOpen[inst✝¹] (s ∩ K)\n⊢ IsOpen[inst✝¹] s",
"usedConstants": [
"Eq.mpr",
"Continuous",
"congrArg",
"Set.preimage_inter_range",
"id",
"Set.ins... | refine isOpen' fun K _ _ _ f hf ↦ ?_
rw [← Set.preimage_inter_range]
exact (hs (isCompact_range hf)).preimage hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 570,
"column": 6
} | {
"line": 570,
"column": 64
} | [
{
"pp": "case coe\nX✝ : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X✝\ns : Set (OnePoint X✝)\nX : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : DiscreteTopology X\ny : OnePoint X\nx✝¹ : y ∈ univ\nval : X\nx✝ : ↑val ∈ univ\nhxy : ↑val ≠ y\n⊢ IsOpen[inst✝¹] (some ⁻¹' {↑val})",
"usedConstants": [
... | exacts [isOpen_discrete _, (Option.some_ne_none val).symm] | Batteries.Tactic._aux_Batteries_Tactic_Init___elabRules_Batteries_Tactic_exacts_1 | Batteries.Tactic.exacts |
Mathlib.Topology.Compactness.CompactlyGeneratedSpace | {
"line": 335,
"column": 6
} | {
"line": 335,
"column": 21
} | [
{
"pp": "X : Type u\ninst✝¹ : TopologicalSpace X\ninst✝ : T2Space X\nh : ∀ (s : Set X), (∀ (K : Set X), IsCompact K → IsClosed[inst✝¹] (s ∩ K)) → IsClosed[inst✝¹] s\ns : Set X\nhs :\n ∀ (K : Type u) [inst : TopologicalSpace K] [CompactSpace K] [T2Space K] (f : K → X),\n Continuous[_, inst✝¹] f → IsClosed (f... | Set.inter_comm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 587,
"column": 28
} | {
"line": 587,
"column": 39
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\ns : Set (OnePoint X)\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\ninst✝ : CompactSpace Y\ny : Y\nf : X → Y\nhf : IsEmbedding f\nhy : range f = {y}ᶜ\n_i : T2Space X\nN : Set Y\nhN : N ∈ 𝓝 y\nU : Set Y\nhU₁ : U ⊆ N\nhU₂ : IsOpen[inst✝²] U\nhU... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 597,
"column": 34
} | {
"line": 597,
"column": 50
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\ns : Set (OnePoint X)\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\ninst✝ : CompactSpace Y\ny : Y\nf : X → Y\nhf : IsEmbedding f\nhy : range f = {y}ᶜ\n_i : T2Space X\nthis : Tendsto f (coclosedCompact X) (𝓝 y)\np : X\n⊢ f p ≠ y",
"usedCon... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 598,
"column": 10
} | {
"line": 598,
"column": 26
} | [
{
"pp": "case coe\nX : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\ns : Set (OnePoint X)\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\ninst✝ : CompactSpace Y\ny : Y\nf : X → Y\nhf : IsEmbedding f\nhy : range f = {y}ᶜ\n_i : T2Space X\nthis : Tendsto f (coclosedCompact X) (𝓝 y)\np : X\nhp : f p ≠ y\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 603,
"column": 10
} | {
"line": 603,
"column": 26
} | [
{
"pp": "case inr\nX : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\ns : Set (OnePoint X)\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\ninst✝ : CompactSpace Y\ny : Y\nf : X → Y\nhf : IsEmbedding f\nhy : range f = {y}ᶜ\n_i : T2Space X\nthis : Tendsto f (coclosedCompact X) (𝓝 y)\nq : Y\nhq : q ≠ y\nhq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactification.OnePoint.Basic | {
"line": 599,
"column": 27
} | {
"line": 603,
"column": 42
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝³ : TopologicalSpace X\ns : Set (OnePoint X)\ninst✝² : TopologicalSpace Y\ninst✝¹ : T2Space Y\ninst✝ : CompactSpace Y\ny : Y\nf : X → Y\nhf : IsEmbedding f\nhy : range f = {y}ᶜ\n_i : T2Space X\nthis : Tendsto f (coclosedCompact X) (𝓝 y)\nq : Y\n⊢ (fun p ↦ p.elim y f) (... | by
rcases eq_or_ne q y with rfl | hq
· simp
· have hq' : q ∈ range f := by simpa [hy]
simpa [hq] using hq'.choose_spec | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Complex.ValueDistribution.Cartan | {
"line": 92,
"column": 4
} | {
"line": 92,
"column": 30
} | [
{
"pp": "case neg.inr.inl\nf : ℂ → ℂ\nh : ¬¬MeromorphicAt f 0\nhzero : meromorphicOrderAt f 0 = 0\n⊢ CircleIntegrable (fun x ↦ log ‖meromorphicTrailingCoeffAt f 0 - x‖) 0 1",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.ProperAction | {
"line": 84,
"column": 2
} | {
"line": 84,
"column": 51
} | [
{
"pp": "case inr\nK : Set ℍ\nhK : IsCompact K\nhKne : K.Nonempty\nδ : ℝ\nhδ : δ > 0\ng : SL(2, ℝ)\nhg : g • I ∈ K\nhδK : Complex.normSq (denom ((Matrix.SpecialLinearGroup.mapGL ℝ) g) ↑I) ≤ 1 / δ\n⊢ ↑g 1 0 ^ 2 + ↑g 1 1 ^ 2 ≤ 1 / δ",
"usedConstants": [
"Eq.mpr",
"Real.instLE",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.UpperHalfPlane.ProperAction | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 30
} | [
{
"pp": "K : Set ℍ\nhK : IsCompact K\n⊢ IsCompact ((fun g ↦ g • I) ⁻¹' K)",
"usedConstants": [
"_private.Mathlib.Analysis.Complex.UpperHalfPlane.ProperAction.0.UpperHalfPlane.absq_le"
]
}
] | obtain ⟨A, hA⟩ := absq_le hK | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 30
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℂ → E\na : WithTop E\nh : a = ⊤\nr : ℝ\n⊢ 0 r ≤ proximity f a r",
"usedConstants": [
"dite_cond_eq_true",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"WithTop.unt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 30
} | [
{
"pp": "case neg\nE : Type u_1\ninst✝ : NormedAddCommGroup E\nf : ℂ → E\na : WithTop E\nh : ¬a = ⊤\nr : ℝ\n⊢ 0 r ≤ proximity f a r",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"WithTop.untop₀",
"Real.posLog",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic | {
"line": 194,
"column": 2
} | {
"line": 194,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf₁ f₂ : ℂ → E\nh₁f₁ : Meromorphic f₁\nh₁f₂ : Meromorphic f₂\n⊢ proximity (f₁ + f₂) ⊤ ≤ proximity f₁ ⊤ + proximity f₂ ⊤ + fun x ↦ log 2",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem | {
"line": 112,
"column": 16
} | {
"line": 112,
"column": 27
} | [
{
"pp": "f : ℂ → ℂ\nh : Meromorphic f\nR : ℝ\n⊢ ‖(characteristic f ⊤ - characteristic f⁻¹ ⊤) R‖ ≤ max |log ‖f 0‖| |log ‖meromorphicTrailingCoeffAt f 0‖| * ‖1 R‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"HMul.hMu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem | {
"line": 146,
"column": 6
} | {
"line": 147,
"column": 13
} | [
{
"pp": "case pos\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na₀ : E\nf : ℂ → E\nr : ℝ\nh✝ : Meromorphic f\nh₁f : CircleIntegrable (fun x ↦ log⁺ ‖f x‖) 0 r\nh₂f : CircleIntegrable (fun x ↦ log⁺ ‖f x - a₀‖) 0 r\nθ : ℂ\nhθ : θ ∈ sphere 0 |r|\nh : 0 ≤ log⁺ ‖f θ‖ - log⁺ ‖f θ - a₀‖\n⊢ |log... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.FirstMainTheorem | {
"line": 163,
"column": 16
} | {
"line": 163,
"column": 27
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\na₀ : E\nf : ℂ → E\nh : Meromorphic f\nR : ℝ\n⊢ ‖(characteristic f ⊤ - characteristic (fun x ↦ f x - a₀) ⊤) R‖ ≤ (log⁺ ‖a₀‖ + log 2) * ‖1 R‖",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction | {
"line": 138,
"column": 4
} | {
"line": 138,
"column": 15
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf₁ f₂ : ℂ → E\nr : ℝ\nh₁f₁ : Meromorphic f₁\nh₁f₂ : Meromorphic f₂\nhr : 1 ≤ r\n⊢ ∀ a ∈ Finset.univ, Meromorphic (![f₁, f₂] a)",
"usedConstants": [
"Eq.mpr",
"Meromorphic",
"Finset.univ",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.CharacteristicFunction | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 13
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℂ E\nf₁ f₂ : ℂ → E\nr : ℝ\nh₁f₁ : Meromorphic f₁\nh₁f₂ : Meromorphic f₂\nhr : 1 ≤ r\nh_meromorphic : ∀ a ∈ Finset.univ, Meromorphic (![f₁, f₂] a)\n⊢ characteristic (f₁ + f₂) ⊤ r ≤ characteristic f₁ ⊤ r + characteristic f₂ ⊤ r + log 2",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.ConstantSpeed | {
"line": 67,
"column": 2
} | {
"line": 69,
"column": 53
} | [
{
"pp": "E : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : ℝ → E\ns : Set ℝ\nhs : s.Subsingleton\nl : ℝ≥0\n⊢ HasConstantSpeedOnWith f s l",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"sub_self",
"ENNReal.ofReal",
"congrArg",
"HEq.refl",
"Real.instSub",
... | rintro x hx y hy; cases hs hx hy
rw [eVariationOn.subsingleton f (fun y hy z hz => hs hy.1 hz.1 : (s ∩ Icc x x).Subsingleton)]
simp only [sub_self, mul_zero, ENNReal.ofReal_zero] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.ConstantSpeed | {
"line": 67,
"column": 2
} | {
"line": 69,
"column": 53
} | [
{
"pp": "E : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : ℝ → E\ns : Set ℝ\nhs : s.Subsingleton\nl : ℝ≥0\n⊢ HasConstantSpeedOnWith f s l",
"usedConstants": [
"Eq.mpr",
"Real",
"HMul.hMul",
"sub_self",
"ENNReal.ofReal",
"congrArg",
"HEq.refl",
"Real.instSub",
... | rintro x hx y hy; cases hs hx hy
rw [eVariationOn.subsingleton f (fun y hy z hz => hs hy.1 hz.1 : (s ∩ Icc x x).Subsingleton)]
simp only [sub_self, mul_zero, ENNReal.ofReal_zero] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.ConstantSpeed | {
"line": 112,
"column": 4
} | {
"line": 117,
"column": 89
} | [
{
"pp": "case inl.inr\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : ℝ → E\ns : Set ℝ\nl : ℝ≥0\nt : Set ℝ\nhfs : ∀ ⦃x : ℝ⦄, x ∈ s → ∀ ⦃y : ℝ⦄, y ∈ s → x ≤ y → eVariationOn f (s ∩ Icc x y) = ENNReal.ofReal (↑l * (y - x))\nhft : ∀ ⦃x : ℝ⦄, x ∈ t → ∀ ⦃y : ℝ⦄, y ∈ t → x ≤ y → eVariationOn f (t ∩ Icc x y) = ENNRea... | have : (s ∪ t) ∩ Icc z y = s ∩ Icc z x ∪ t ∩ Icc x y := by
ext w; constructor
· rintro ⟨ws | wt, zw, wy⟩
exacts [Or.inl ⟨ws, zw, hs.2 ws⟩, Or.inr ⟨wt, ht.2 wt, wy⟩]
· rintro (⟨ws, zw, wx⟩ | ⟨wt, xw, wy⟩)
exacts [⟨Or.inl ws, zw, wx.trans (ht.2 yt)⟩, ⟨Or.inr wt, (hs.2 zs).trans xw, wy⟩] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Semicontinuity.Lindelof | {
"line": 83,
"column": 4
} | {
"line": 83,
"column": 70
} | [
{
"pp": "X : Type u_1\nE : Type u_2\ninst✝⁶ : TopologicalSpace X\ninst✝⁵ : HereditarilyLindelofSpace X\ninst✝⁴ : LinearOrder E\ninst✝³ : TopologicalSpace E\ninst✝² : OrderClosedTopology E\ninst✝¹ : DenselyOrdered E\ninst✝ : SeparableSpace E\ns : X → E\n𝓕 : Set (X → E)\nh𝓕_cont : ∀ f ∈ 𝓕, UpperSemicontinuous ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.ConstantSpeed | {
"line": 166,
"column": 4
} | {
"line": 166,
"column": 19
} | [
{
"pp": "case mpr\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : ℝ → E\ns : Set ℝ\nh : eVariationOn f s = 0\nx : ℝ\nx✝¹ : x ∈ s\ny : ℝ\nx✝ : y ∈ s\n⊢ eVariationOn f (s ∩ Icc x y) = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Asymptotic | {
"line": 81,
"column": 49
} | {
"line": 81,
"column": 66
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nD : locallyFinsuppWithin univ ℤ\nh : 0 ≤ D\nh₁ : ¬D = 0\ne : E\nhe : single e 1 ≤ D\na : ℝ\nha : a > 0\nb c : ℝ\nhc : ∀ b ≥ c, ‖1 b‖ ≤ a * ‖logCounting (single e 1) b‖\nℓ : ℝ := 1 + max ‖e‖ (max |b| |c|)\nh₁ℓ : c ≤ ℓ\nh₂ℓ : 1 ≤ ℓ\n⊢ 1 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 101,
"column": 4
} | {
"line": 117,
"column": 10
} | [
{
"pp": "E✝ : Type u_1\ninst✝² : NormedAddCommGroup E✝\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nD₁ D₂ : locallyFinsupp E ℤ\n⊢ (fun r ↦ ∑ᶠ (z : E), ↑(((toClosedBall r) (D₁ + D₂)) z) * log (r * ‖z‖⁻¹) + ↑((D₁ + D₂) 0) * log r) =\n (fun r ↦ ∑ᶠ (z : E), ↑(((toClosedBall r) D₁) z) * lo... | simp only [map_add, coe_add, Pi.add_apply, Int.cast_add]
ext r
have {A B C D : ℝ} : A + B + (C + D) = A + C + (B + D) := by ring
rw [Pi.add_apply, this]
congr 1
· have h₁s : ((D₁.toClosedBall r).support ∪ (D₂.toClosedBall r).support).Finite := by
apply Set.finite_union.2
constructor
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 101,
"column": 4
} | {
"line": 117,
"column": 10
} | [
{
"pp": "E✝ : Type u_1\ninst✝² : NormedAddCommGroup E✝\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nD₁ D₂ : locallyFinsupp E ℤ\n⊢ (fun r ↦ ∑ᶠ (z : E), ↑(((toClosedBall r) (D₁ + D₂)) z) * log (r * ‖z‖⁻¹) + ↑((D₁ + D₂) 0) * log r) =\n (fun r ↦ ∑ᶠ (z : E), ↑(((toClosedBall r) D₁) z) * lo... | simp only [map_add, coe_add, Pi.add_apply, Int.cast_add]
ext r
have {A B C D : ℝ} : A + B + (C + D) = A + C + (B + D) := by ring
rw [Pi.add_apply, this]
congr 1
· have h₁s : ((D₁.toClosedBall r).support ∪ (D₂.toClosedBall r).support).Finite := by
apply Set.finite_union.2
constructor
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Triplewise | {
"line": 85,
"column": 6
} | {
"line": 85,
"column": 17
} | [
{
"pp": "case cons.refine_2\nα : Type u_1\nl : List α\np : α → α → α → Prop\nhead : α\ntail : List α\nih : Triplewise p tail ↔ ∀ (i j k : Nat) (hij : i < j) (hjk : j < k) (hk : k < tail.length), p tail[i] tail[j] tail[k]\nh :\n ∀ (i j k : Nat) (hij : i < j) (hjk : j < k) (hk : k < tail.length + 1),\n p (hea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Triplewise | {
"line": 86,
"column": 6
} | {
"line": 86,
"column": 17
} | [
{
"pp": "case cons.refine_3\nα : Type u_1\nl : List α\np : α → α → α → Prop\nhead : α\ntail : List α\nih : Triplewise p tail ↔ ∀ (i j k : Nat) (hij : i < j) (hjk : j < k) (hk : k < tail.length), p tail[i] tail[j] tail[k]\nh :\n ∀ (i j k : Nat) (hij : i < j) (hjk : j < k) (hk : k < tail.length + 1),\n p (hea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 212,
"column": 6
} | {
"line": 212,
"column": 27
} | [
{
"pp": "E : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : DecidableEq E\ninst✝ : ProperSpace E\nD : locallyFinsupp E ℤ\ne : E\nhD : single e 1 ≤ D\na : ℝ\nha : a ∈ Ioi ‖e‖\nb : ℝ\nhb : b ∈ Ioi ‖e‖\nhab : a ≤ b\n⊢ a ∈ Ioi 0",
"usedConstants": [
"Eq.mpr",
"Real",
"Set.Ioi",
"Preor... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 209,
"column": 2
} | {
"line": 212,
"column": 55
} | [
{
"pp": "case hg\nE : Type u_1\ninst✝² : NormedAddCommGroup E\ninst✝¹ : DecidableEq E\ninst✝ : ProperSpace E\nD : locallyFinsupp E ℤ\ne : E\nhD : single e 1 ≤ D\n⊢ MonotoneOn (logCounting (D - single e 1)) (Ioi ‖e‖)",
"usedConstants": [
"Int.instAddCommGroup",
"AddGroup.toSubtractionMonoid",
... | · intro a ha b hb hab
apply logCounting_mono _ _ ((norm_nonneg e).trans_lt hb) hab
· simp [hD]
· simpa [mem_Ioi] using (norm_nonneg e).trans_lt ha | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 222,
"column": 54
} | {
"line": 222,
"column": 65
} | [
{
"pp": "E : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nf : locallyFinsupp E ℤ\nr : ℝ\nh : 0 ≤ f\nhr : 1 ≤ r\nh₃r : 0 < r\nthis : ∀ (z : E), 0 ≤ ↑(((toClosedBall r) f) z) * log (r * ‖z‖⁻¹)\n⊢ 0 ≤ ↑(f 0)",
"usedConstants": [
"Int.cast_nonneg_iff._simp_1",
"Int.cast",
"E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 228,
"column": 6
} | {
"line": 228,
"column": 23
} | [
{
"pp": "case pos.refine_1\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nf : locallyFinsupp E ℤ\nr : ℝ\nh : 0 ≤ f\nhr : 1 ≤ r\nh₃r : 0 < r\na : E\nh₁a : ¬a = 0\nh₂a : a ∈ closedBall 0 |r|\n⊢ 0 ≤ ↑(((toClosedBall r) f) a)",
"usedConstants": [
"Int.cast_nonneg_iff._simp_1",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 229,
"column": 6
} | {
"line": 229,
"column": 86
} | [
{
"pp": "case pos.refine_2\nE : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nf : locallyFinsupp E ℤ\nr : ℝ\nh : 0 ≤ f\nhr : 1 ≤ r\nh₃r : 0 < r\na : E\nh₁a : ¬a = 0\nh₂a : a ∈ closedBall 0 |r|\n⊢ 1 ≤ r * ‖a‖⁻¹",
"usedConstants": [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 13
} | [
{
"pp": "E : Type u_2\ninst✝¹ : NormedAddCommGroup E\ninst✝ : ProperSpace E\nf₁ f₂ : locallyFinsupp E ℤ\nr : ℝ\nh : 0 ≤ f₂ - f₁\nhr : 1 ≤ r\n⊢ 0 ≤ logCounting f₂ r - logCounting f₁ r",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Real.instLE",
"Real",
"Real.ins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.