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.NumberTheory.Padics.MahlerBasis | {
"line": 210,
"column": 4
} | {
"line": 210,
"column": 60
} | [
{
"pp": "case zero\np : ℕ\nhp : Fact (Nat.Prime p)\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : Module ℤ_[p] E\ninst✝¹ : IsBoundedSMul ℤ_[p] E\ninst✝ : IsUltrametricDist E\nf : C(ℤ_[p], E)\ns t : ℕ\nhst : ∀ (x y : ℤ_[p]), ‖x - y‖ ≤ ↑p ^ (-↑t) → ‖f x - f y‖ ≤ ‖f‖ / ↑p ^ s\nn : ℕ\nhk : 0 ≤ s\n⊢ ‖Δ_[1]^[... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Ostrowski | {
"line": 467,
"column": 2
} | {
"line": 469,
"column": 45
} | [
{
"pp": "f : AbsoluteValue ℚ ℝ\nhf_nontriv : f.IsNontrivial\n⊢ f ≈ real ∨ ∃! p, ∃ (x : Fact (Nat.Prime p)), f ≈ padic p",
"usedConstants": [
"Real.partialOrder",
"Real.instLE",
"Real",
"Nat.Prime",
"Rat",
"Rat.AbsoluteValue.equiv_real_of_unbounded",
"Rat.AbsoluteVal... | by_cases bdd : ∀ n : ℕ, f n ≤ 1
· exact .inr <| equiv_padic_of_bounded hf_nontriv bdd
· exact .inl <| equiv_real_of_unbounded bdd | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Ostrowski | {
"line": 467,
"column": 2
} | {
"line": 469,
"column": 45
} | [
{
"pp": "f : AbsoluteValue ℚ ℝ\nhf_nontriv : f.IsNontrivial\n⊢ f ≈ real ∨ ∃! p, ∃ (x : Fact (Nat.Prime p)), f ≈ padic p",
"usedConstants": [
"Real.partialOrder",
"Real.instLE",
"Real",
"Nat.Prime",
"Rat",
"Rat.AbsoluteValue.equiv_real_of_unbounded",
"Rat.AbsoluteVal... | by_cases bdd : ∀ n : ℕ, f n ≤ 1
· exact .inr <| equiv_padic_of_bounded hf_nontriv bdd
· exact .inl <| equiv_real_of_unbounded bdd | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Padics.MahlerBasis | {
"line": 239,
"column": 32
} | {
"line": 239,
"column": 67
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : Module ℤ_[p] E\ninst✝¹ : IsBoundedSMul ℤ_[p] E\ninst✝ : IsUltrametricDist E\nf : C(ℤ_[p], E)\nε : ℝ\nhε : ε > 0\nthis✝ : Tendsto (fun s ↦ ‖f‖ / ↑p ^ s) atTop (𝓝 0)\ns : ℕ\nhs : ‖f‖ / ↑p ^ s < ε\nhf : f ≠ 0\nthis : 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.MahlerBasis | {
"line": 241,
"column": 2
} | {
"line": 241,
"column": 42
} | [
{
"pp": "case h\np : ℕ\nhp : Fact (Nat.Prime p)\nE : Type u_1\ninst✝³ : NormedAddCommGroup E\ninst✝² : Module ℤ_[p] E\ninst✝¹ : IsBoundedSMul ℤ_[p] E\ninst✝ : IsUltrametricDist E\nf : C(ℤ_[p], E)\nε : ℝ\nhε : ε > 0\nthis : Tendsto (fun s ↦ ‖f‖ / ↑p ^ s) atTop (𝓝 0)\ns : ℕ\nhs : ‖f‖ / ↑p ^ s < ε\nt : ℕ\nht : ∀ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.MahlerBasis | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 59
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : Module ℤ_[p] E\ninst✝² : IsBoundedSMul ℤ_[p] E\ninst✝¹ : IsUltrametricDist E\ninst✝ : CompleteSpace E\na : ℕ → E\nha : Tendsto (fun x ↦ ‖a x‖) atTop (𝓝 0)\n⊢ Tendsto (fun x ↦ ‖mahlerTerm (a x) x‖) cofinite (𝓝 0)",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.MahlerBasis | {
"line": 305,
"column": 4
} | {
"line": 305,
"column": 39
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : Module ℤ_[p] E\ninst✝² : IsBoundedSMul ℤ_[p] E\ninst✝¹ : IsUltrametricDist E\ninst✝ : CompleteSpace E\na : ℕ → E\nha : Tendsto a atTop (𝓝 0)\nm n : ℕ\nhmn : m ≤ n\nh_van : ∀ (i : ℕ), m.choose (i + (n + 1)) = 0\n⊢ Sum... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.MahlerBasis | {
"line": 348,
"column": 2
} | {
"line": 349,
"column": 9
} | [
{
"pp": "case h.e'_6\np : ℕ\nhp : Fact (Nat.Prime p)\nE : Type u_1\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : Module ℤ_[p] E\ninst✝² : IsBoundedSMul ℤ_[p] E\ninst✝¹ : IsUltrametricDist E\ninst✝ : CompleteSpace E\nf : C(ℤ_[p], E)\nthis : HasSum (fun n ↦ mahlerTerm (Δ_[1]^[n] (⇑f) 0) n) (mahlerSeries fun x ↦ Δ_[1]^... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.WithVal | {
"line": 70,
"column": 8
} | {
"line": 70,
"column": 58
} | [
{
"pp": "case neg\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nhp0' : 0 < ↑p\nhp0 : 0 < (↑p)⁻¹\nhp1' : 1 < ↑p\nhp1 : (↑p)⁻¹ < 1\nn : ℕ\nhn : Valued.v (↑p ^ n) = exp (-↑n)\nx y : WithVal (Rat.padicValuation p)\nx' : ℚ := (WithVal.equiv (Rat.padicValuation p)) x\nhx : x' = (WithVal.equiv (Rat.padicValuation p)) x\ny' : ℚ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.WithVal | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 30
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx✝ : ℚ_[p]\n⊢ x✝ ∈ closure (Set.range ⇑((Rat.castHom ℚ_[p]).comp (WithVal.equiv (Rat.padicValuation p)).toRingHom))",
"usedConstants": [
"Int.instAddCommGroup",
"NormedCommRing.toNormedRing",
"Eq.mpr",
"Int.instAddCommMonoid",
"Normed... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.WithVal | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 55
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : WithVal (Rat.padicValuation p)\n⊢ withValUniformEquiv ↑x = ↑((WithVal.equiv (Rat.padicValuation p)) x)",
"usedConstants": [
"Int.instAddCommGroup",
"NormedCommRing.toNormedRing",
"Int.instAddCommMonoid",
"NormedCommRing.toSeminormedComm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.WithVal | {
"line": 172,
"column": 2
} | {
"line": 172,
"column": 54
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx : ℚ\nh : ‖↑x‖ ≤ 1\n⊢ ¬p ∣ x.den",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.WithVal | {
"line": 179,
"column": 8
} | {
"line": 179,
"column": 32
} | [
{
"pp": "case hp\np : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ IsClosed {a | ‖withValUniformEquiv a‖ ≤ 1 ↔ Valued.v a ≤ 1}",
"usedConstants": [
"Int.instAddCommGroup",
"NormedCommRing.toNormedRing",
"Set.ext",
"Norm.norm",
"Eq.mpr",
"Int.instAddCommMonoid",
"LinearOrderedCo... | Set.ext fun _ ↦ Iff.comm | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.WithVal | {
"line": 183,
"column": 4
} | {
"line": 183,
"column": 35
} | [
{
"pp": "case hp\np : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ IsClopen {y | ‖y‖ ≤ 1}",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Pell | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 71
} | [
{
"pp": "x y : ℤ\nhy : y ≠ 0\na : ℤ\nh₀ : 0 < a * a\nhxy : (x + a * y) * (x - a * y) = 1\n⊢ False",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Pell | {
"line": 553,
"column": 2
} | {
"line": 553,
"column": 75
} | [
{
"pp": "d : ℤ\na₁ : Solution₁ d\nh : IsFundamental a₁\na : Solution₁ d\nhax : 1 < a.x\nhay : 0 < a.y\n⊢ 0 ≤ (a * a₁⁻¹).y",
"usedConstants": [
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionM... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Pell | {
"line": 565,
"column": 35
} | {
"line": 565,
"column": 50
} | [
{
"pp": "d : ℤ\na₁ : Solution₁ d\nh : IsFundamental a₁\na : Solution₁ d\nhax : 1 < a.x\nhay : 0 < a.y\n⊢ d * a.y * (a.y * a₁.x) = (a.x ^ 2 - 1) * a₁.x",
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"Pell.Solution₁.x",
"HSub.hSub",
"id",
"Pell.Solution₁.prop... | rw [← a.prop_y] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.Rayleigh | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 25
} | [
{
"pp": "r s : ℝ\nhrs : r.HolderConjugate s\n⊢ ∀ ⦃a : ℤ⦄, a ∈ {x | ∃ k, beattySeq r k = x} → a ∉ {x | ∃ k, beattySeq' s k = x}",
"usedConstants": [
"Int"
]
}
] | intro j ⟨k, h₁⟩ ⟨m, h₂⟩ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.NumberTheory.Padics.HeightOneSpectrum | {
"line": 159,
"column": 12
} | {
"line": 159,
"column": 23
} | [
{
"pp": "R✝ : Type u_1\ninst✝⁷ : CommRing R✝\ninst✝⁶ : Algebra R✝ ℚ\ninst✝⁵ : IsIntegralClosure R✝ ℤ ℚ\nR : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : Algebra R ℚ\ninst✝² : IsIntegralClosure R ℤ ℚ\ninst✝¹ : IsDedekindDomain R\ninst✝ : IsFractionRing R ℚ\nv : HeightOneSpectrum R\nx✝ : UniformSpace.Completion (WithV... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.HeightOneSpectrum | {
"line": 162,
"column": 10
} | {
"line": 162,
"column": 21
} | [
{
"pp": "R✝ : Type u_1\ninst✝⁷ : CommRing R✝\ninst✝⁶ : Algebra R✝ ℚ\ninst✝⁵ : IsIntegralClosure R✝ ℤ ℚ\nR : Type u_2\ninst✝⁴ : CommRing R\ninst✝³ : Algebra R ℚ\ninst✝² : IsIntegralClosure R ℤ ℚ\ninst✝¹ : IsDedekindDomain R\ninst✝ : IsFractionRing R ℚ\nv : HeightOneSpectrum R\nx✝ : UniformSpace.Completion (WithV... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Rayleigh | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 46
} | [
{
"pp": "r s : ℝ\nhrs : r.HolderConjugate s\n⊢ {x | ∃ k, beattySeq' r k = x}ᶜ = {x | ∃ k, beattySeq s k = x}",
"usedConstants": [
"Eq.mpr",
"compl_compl",
"congrArg",
"Compl.compl",
"setOf",
"Real.HolderConjugate.symm",
"Exists",
"BooleanAlgebra.toCompl",
... | rw [← compl_beattySeq hrs.symm, compl_compl] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.Rayleigh | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 46
} | [
{
"pp": "r s : ℝ\nhrs : r.HolderConjugate s\n⊢ {x | ∃ k, beattySeq' r k = x}ᶜ = {x | ∃ k, beattySeq s k = x}",
"usedConstants": [
"Eq.mpr",
"compl_compl",
"congrArg",
"Compl.compl",
"setOf",
"Real.HolderConjugate.symm",
"Exists",
"BooleanAlgebra.toCompl",
... | rw [← compl_beattySeq hrs.symm, compl_compl] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Rayleigh | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 46
} | [
{
"pp": "r s : ℝ\nhrs : r.HolderConjugate s\n⊢ {x | ∃ k, beattySeq' r k = x}ᶜ = {x | ∃ k, beattySeq s k = x}",
"usedConstants": [
"Eq.mpr",
"compl_compl",
"congrArg",
"Compl.compl",
"setOf",
"Real.HolderConjugate.symm",
"Exists",
"BooleanAlgebra.toCompl",
... | rw [← compl_beattySeq hrs.symm, compl_compl] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.SelbergSieve | {
"line": 152,
"column": 8
} | {
"line": 152,
"column": 60
} | [
{
"pp": "case h_ne\ns : BoundingSieve\nd : ℕ\nhdP : d ∣ s.prodPrimes\nhd_ne_one : d ≠ 1\nhd_sq : Squarefree d\nthis : d ≠ 0\n⊢ d.primeFactors.Nonempty",
"usedConstants": [
"instOfNatNat",
"Nat",
"LT.lt",
"True",
"Finset.Nonempty",
"eq_true",
"of_eq_true",
"_pr... | simp only [nonempty_primeFactors, show 1 < d by lia] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.SelbergSieve | {
"line": 152,
"column": 8
} | {
"line": 152,
"column": 60
} | [
{
"pp": "case h_ne\ns : BoundingSieve\nd : ℕ\nhdP : d ∣ s.prodPrimes\nhd_ne_one : d ≠ 1\nhd_sq : Squarefree d\nthis : d ≠ 0\n⊢ d.primeFactors.Nonempty",
"usedConstants": [
"instOfNatNat",
"Nat",
"LT.lt",
"True",
"Finset.Nonempty",
"eq_true",
"of_eq_true",
"_pr... | simp only [nonempty_primeFactors, show 1 < d by lia] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.SelbergSieve | {
"line": 152,
"column": 8
} | {
"line": 152,
"column": 60
} | [
{
"pp": "case h_ne\ns : BoundingSieve\nd : ℕ\nhdP : d ∣ s.prodPrimes\nhd_ne_one : d ≠ 1\nhd_sq : Squarefree d\nthis : d ≠ 0\n⊢ d.primeFactors.Nonempty",
"usedConstants": [
"instOfNatNat",
"Nat",
"LT.lt",
"True",
"Finset.Nonempty",
"eq_true",
"of_eq_true",
"_pr... | simp only [nonempty_primeFactors, show 1 < d by lia] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Zsqrtd.GaussianInt | {
"line": 194,
"column": 56
} | {
"line": 194,
"column": 67
} | [
{
"pp": "x y : ℤ[i]\nthis : |2⁻¹| = 2⁻¹\n⊢ |(toComplex x / toComplex y).re - ↑(round (toComplex x / toComplex y).re)| ≤ 2⁻¹",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.GaussianInt | {
"line": 195,
"column": 56
} | {
"line": 195,
"column": 67
} | [
{
"pp": "x y : ℤ[i]\nthis : |2⁻¹| = 2⁻¹\n⊢ |(toComplex x / toComplex y).im - ↑(round (toComplex x / toComplex y).im)| ≤ 2⁻¹",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.GaussianInt | {
"line": 250,
"column": 4
} | {
"line": 250,
"column": 58
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : ¬Irreducible ↑p\nhpu : ¬IsUnit ↑p\n⊢ ∃ a b, ↑p = a * b ∧ ¬IsUnit a ∧ ¬IsUnit b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.GaussianInt | {
"line": 253,
"column": 91
} | {
"line": 254,
"column": 85
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : ¬Irreducible ↑p\nhpu : ¬IsUnit ↑p\nhab : ∃ a b, ↑p = a * b ∧ ¬IsUnit a ∧ ¬IsUnit b\na b : ℤ[i]\nhpab : ↑p = a * b\nhau : ¬IsUnit a\nhbu : ¬IsUnit b\n⊢ (norm a).natAbs * (norm b).natAbs = p ^ 2",
"usedConstants": [
"instPowNat",
"AddGroup.toSubtracti... | by
rw [← Int.natCast_inj, Int.natCast_pow, sq, ← @norm_natCast (-1), hpab]; simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Zsqrtd.GaussianInt | {
"line": 255,
"column": 32
} | {
"line": 255,
"column": 64
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : ¬Irreducible ↑p\nhpu : ¬IsUnit ↑p\nhab : ∃ a b, ↑p = a * b ∧ ¬IsUnit a ∧ ¬IsUnit b\na b : ℤ[i]\nhpab : ↑p = a * b\nhau : ¬IsUnit a\nhbu : ¬IsUnit b\nhnap : (norm a).natAbs = p\n⊢ a.re.natAbs ^ 2 + a.im.natAbs ^ 2 = p",
"usedConstants": [
"Eq.mpr",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumFourSquares | {
"line": 101,
"column": 6
} | {
"line": 101,
"column": 93
} | [
{
"pp": "m a b c d : ℤ\nh : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * m\nthis :\n ∀ (f : Fin 4 → ZMod 2),\n f 0 ^ 2 + f 1 ^ 2 + f 2 ^ 2 + f 3 ^ 2 = 0 →\n ∃ i, f i ^ 2 + f ((swap i 0) 1) ^ 2 = 0 ∧ f ((swap i 0) 2) ^ 2 + f ((swap i 0) 3) ^ 2 = 0\nf : Fin 4 → ℤ := ![a, b, c, d]\ni : Fin 4\nσ : Perm (Fin 4) := s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumFourSquares | {
"line": 104,
"column": 6
} | {
"line": 104,
"column": 66
} | [
{
"pp": "m a b c d : ℤ\nh : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * m\nthis :\n ∀ (f : Fin 4 → ZMod 2),\n f 0 ^ 2 + f 1 ^ 2 + f 2 ^ 2 + f 3 ^ 2 = 0 →\n ∃ i, f i ^ 2 + f ((swap i 0) 1) ^ 2 = 0 ∧ f ((swap i 0) 2) ^ 2 + f ((swap i 0) 3) ^ 2 = 0\nf : Fin 4 → ℤ := ![a, b, c, d]\ni : Fin 4\nσ : Perm (Fin 4) := s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 50,
"column": 36
} | {
"line": 57,
"column": 34
} | [
{
"pp": "K : Type u_1\nΓ : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\ninst✝¹ : DecidableEq K⟮X⟯\ninst✝ : IsTrivialOn K v\nhlt : 1 < v X\n⊢ v.IsEquiv (inftyValuation K)",
"usedConstants": [
"Int.instAddCommGroup",
"WithZero.instNontrivial",
... | by
refine isEquiv_iff_val_lt_one.mpr fun {f} ↦ ?_
rcases eq_or_ne f 0 with rfl | hf
· simp
· have hlt' : 1 < inftyValuation K X := by simp [← exp_zero]
rw [valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_X hlt hf,
valuation_eq_valuation_X_zpow_intDegree_of_one_lt_valuation_X hlt' hf]
g... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.SumFourSquares | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 61
} | [
{
"pp": "m a b c d : ℤ\nh : a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = 2 * m\nthis✝ :\n ∀ (f : Fin 4 → ZMod 2),\n f 0 ^ 2 + f 1 ^ 2 + f 2 ^ 2 + f 3 ^ 2 = 0 →\n ∃ i, f i ^ 2 + f ((swap i 0) 1) ^ 2 = 0 ∧ f ((swap i 0) 2) ^ 2 + f ((swap i 0) 3) ^ 2 = 0\nf : Fin 4 → ℤ := ![a, b, c, d]\ni : Fin 4\nσ : Perm (Fin 4) := ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumFourSquares | {
"line": 130,
"column": 20
} | {
"line": 130,
"column": 31
} | [
{
"pp": "case h\np : ℕ\nhp : Prime p\nthis : Fact (Prime p)\nnatAbs_iff :\n ∀ {a b c d : ℤ} {k : ℕ},\n a.natAbs ^ 2 + b.natAbs ^ 2 + c.natAbs ^ 2 + d.natAbs ^ 2 = k ↔ a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = ↑k\nhm : ∃ m < p, 0 < m ∧ ∃ a b c d, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = m * p\na b c d : ℕ\nhmin : ∀ m < 1, ¬(m ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 84,
"column": 4
} | {
"line": 84,
"column": 15
} | [
{
"pp": "K : Type u_1\nΓ : Type u_2\ninst✝¹ : Field K\ninst✝ : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\nhne : {p | v ↑p < 1 ∧ p ≠ 0}.Nonempty\na b : K[X]\nhab : v ↑(a * b) < 1 ∧ a ≠ 0 ∧ b ≠ 0\nhb : ¬IsUnit b\nπᵥ : K[X] := ⋯.min {p | v ↑p < 1 ∧ p ≠ 0} hne\nhπᵥ : πᵥ = a * b\nhbpos : 0 < ↑b.natDegre... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumFourSquares | {
"line": 161,
"column": 63
} | {
"line": 161,
"column": 86
} | [
{
"pp": "p : ℕ\nhp : Prime p\nthis✝ : Fact (Prime p)\nnatAbs_iff :\n ∀ {a b c d : ℤ} {k : ℕ},\n a.natAbs ^ 2 + b.natAbs ^ 2 + c.natAbs ^ 2 + d.natAbs ^ 2 = k ↔ a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = ↑k\nhm✝ : ∃ m < p, 0 < m ∧ ∃ a b c d, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = m * p\nm : ℕ\nhmin : ∀ m_1 < m, ¬(m_1 < p ∧ 0 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 13
} | [
{
"pp": "K : Type u_1\nΓ : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\ninst✝¹ : v.IsNontrivial\ninst✝ : IsTrivialOn K v\nhle : v X ≤ 1\n⊢ v ↑πᵥ < 1",
"usedConstants": [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"RatFunc.u... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 132,
"column": 15
} | {
"line": 132,
"column": 26
} | [
{
"pp": "K : Type u_1\nΓ : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\ninst✝¹ : v.IsNontrivial\ninst✝ : IsTrivialOn K v\nhle : v X ≤ 1\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity | {
"line": 57,
"column": 47
} | {
"line": 57,
"column": 82
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : Prime ↑p\nhp1 : p % 2 = 1\nhp3 : p % 4 ≠ 3\nk : ℕ\nk_lt_p : k < p\nhk : -1 = ↑k * ↑k\nhpk : p ∣ k ^ 2 + 1\nhkmul : ↑k ^ 2 + 1 = { re := ↑k, im := 1 } * { re := ↑k, im := -1 }\nhk₀ : k ≠ 0\nhkltp : 1 + k * k < p * p\nx✝ : ↑p ∣ { re := ↑k, im := -1 }\nx : ℤ[i]\nhx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity | {
"line": 60,
"column": 50
} | {
"line": 60,
"column": 67
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : Prime ↑p\nhp1 : p % 2 = 1\nhp3 : p % 4 ≠ 3\nk : ℕ\nk_lt_p : k < p\nhk : -1 = ↑k * ↑k\nhpk : p ∣ k ^ 2 + 1\nhkmul : ↑k ^ 2 + 1 = { re := ↑k, im := 1 } * { re := ↑k, im := -1 }\nhk₀ : k ≠ 0\nhkltp : 1 + k * k < p * p\nx✝ : ↑p ∣ { re := ↑k, im := -1 }\nx : ℤ[i]\nhx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity | {
"line": 65,
"column": 47
} | {
"line": 65,
"column": 82
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : Prime ↑p\nhp1 : p % 2 = 1\nhp3 : p % 4 ≠ 3\nk : ℕ\nk_lt_p : k < p\nhk : -1 = ↑k * ↑k\nhpk : p ∣ k ^ 2 + 1\nhkmul : ↑k ^ 2 + 1 = { re := ↑k, im := 1 } * { re := ↑k, im := -1 }\nhk₀ : k ≠ 0\nhkltp : 1 + k * k < p * p\nhpk₁ : ¬↑p ∣ { re := ↑k, im := -1 }\nx✝ : ↑p ∣ { ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Zsqrtd.QuadraticReciprocity | {
"line": 68,
"column": 49
} | {
"line": 68,
"column": 66
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nhpi : Prime ↑p\nhp1 : p % 2 = 1\nhp3 : p % 4 ≠ 3\nk : ℕ\nk_lt_p : k < p\nhk : -1 = ↑k * ↑k\nhpk : p ∣ k ^ 2 + 1\nhkmul : ↑k ^ 2 + 1 = { re := ↑k, im := 1 } * { re := ↑k, im := -1 }\nhk₀ : k ≠ 0\nhkltp : 1 + k * k < p * p\nhpk₁ : ¬↑p ∣ { re := ↑k, im := -1 }\nx✝ : ↑p ∣ { ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 94,
"column": 42
} | {
"line": 94,
"column": 53
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nncs : CauSeq ℤ_[p] norm\nF : Polynomial R\nhnorm : Tendsto (fun i ↦ ‖(Polynomial.aeval (↑ncs i)) F‖) atTop (𝓝 0)\n⊢ Tendsto (fun e ↦ ‖(Polynomial.aeval (↑ncs e)) F - 0‖) atTop (𝓝 0)",
"usedConstant... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 169,
"column": 4
} | {
"line": 170,
"column": 11
} | [
{
"pp": "case right\nK : Type u_1\nΓ : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\ninst✝¹ : v.IsNontrivial\ninst✝ : IsTrivialOn K v\nhle : v X ≤ 1\np : K[X]\nhp : p ≠ 0\nπ : K[X] := ⋯\nhne : {p | v ↑p < 1 ∧ p ≠ 0}.Nonempty\nhπirr : Irreducible π\nk : ℕ\nq : K[X]\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 174,
"column": 27
} | {
"line": 174,
"column": 38
} | [
{
"pp": "K : Type u_1\nΓ : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\ninst✝¹ : v.IsNontrivial\ninst✝ : IsTrivialOn K v\nhle : v X ≤ 1\nf : K⟮X⟯\nhf : f ≠ 0\n⊢ v ↑πᵥ ≠ 0",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Linea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 116,
"column": 47
} | {
"line": 116,
"column": 58
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nF : Polynomial R\na : ℤ_[p]\nha : (Polynomial.aeval a) F = 0\nz' : ℤ_[p]\nhz' : (Polynomial.aeval z') F = 0\nhnormz' : ‖z' - a‖ < ‖(Polynomial.aeval a) (Polynomial.derivative F)‖\nh : ℤ_[p] := z' - a\nq ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RatFunc.Ostrowski | {
"line": 187,
"column": 27
} | {
"line": 187,
"column": 38
} | [
{
"pp": "K : Type u_1\nΓ : Type u_2\ninst✝³ : Field K\ninst✝² : LinearOrderedCommGroupWithZero Γ\nv : Valuation K⟮X⟯ Γ\ninst✝¹ : v.IsNontrivial\ninst✝ : IsTrivialOn K v\nhle : v X ≤ 1\nhv : v.IsRankOneDiscrete\n⊢ v ↑πᵥ ≠ 0",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 138,
"column": 72
} | {
"line": 139,
"column": 14
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nF : Polynomial R\na : ℤ_[p]\n⊢ T_gen p F a = ‖(Polynomial.aeval a) F‖ / ‖(Polynomial.aeval a) (Polynomial.derivative F)‖ ^ 2",
"usedConstants": [
"Polynomial.derivative",
"Norm.norm",
... | by
simp [T_gen] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 15
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nF : Polynomial R\na : ℤ_[p]\nhnorm : ‖(Polynomial.aeval a) F‖ < ‖(Polynomial.aeval a) (Polynomial.derivative F)‖ ^ 2\nz z' z1 : ℤ_[p]\nhz' : z' = z - z1\nn : ℕ\nhz : ih_gen n z\nh1 : ‖↑((Polynomial.aeval... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumFourSquares | {
"line": 191,
"column": 8
} | {
"line": 192,
"column": 30
} | [
{
"pp": "p : ℕ\nhp : Prime p\nthis✝² : Fact (Prime p)\nnatAbs_iff :\n ∀ {a b c d : ℤ} {k : ℕ},\n a.natAbs ^ 2 + b.natAbs ^ 2 + c.natAbs ^ 2 + d.natAbs ^ 2 = k ↔ a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = ↑k\nhm✝ : ∃ m < p, 0 < m ∧ ∃ a b c d, a ^ 2 + b ^ 2 + c ^ 2 + d ^ 2 = m * p\nm : ℕ\nhmin : ∀ m_1 < m, ¬(m_1 < p ∧ 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumTwoSquares | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 42
} | [
{
"pp": "m n : ℕ\nhc : m.Coprime n\nhm : IsSquare (-1)\nhn : IsSquare (-1)\nthis : IsSquare (-1)\n⊢ IsSquare (-1)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 226,
"column": 24
} | {
"line": 226,
"column": 73
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nF : Polynomial R\na : ℤ_[p]\nhnorm : ‖(Polynomial.aeval a) F‖ < ‖(Polynomial.aeval a) (Polynomial.derivative F)‖ ^ 2\nz z' z1 : ℤ_[p]\nhz' : z' = z - z1\nn : ℕ\nhz : ih_gen n z\nh1 : ‖↑((Polynomial.aeval... | by simp only [PadicInt.coe_neg, PadicInt.coe_mul] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 228,
"column": 15
} | {
"line": 228,
"column": 74
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nF : Polynomial R\na : ℤ_[p]\nhnorm : ‖(Polynomial.aeval a) F‖ < ‖(Polynomial.aeval a) (Polynomial.derivative F)‖ ^ 2\nz z' z1 : ℤ_[p]\nhz' : z' = z - z1\nn : ℕ\nhz : ih_gen n z\nh1 : ‖↑((Polynomial.aeval... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.SumTwoSquares | {
"line": 228,
"column": 4
} | {
"line": 228,
"column": 90
} | [
{
"pp": "case inr.refine_2\nn : ℕ\nhn₀ : n > 0\nH : ∀ q ∈ n.primeFactors, q % 4 = 3 → Even (padicValNat q n)\nb a : ℕ\nhb₀ : 0 < b\nha₀ : 0 < a\nhab : a ^ 2 * b = n\nhb : Squarefree b\nq : ℕ\nhq : q ∈ b.primeFactors\nhq4 : q % 4 = 3\nthis✝¹ : Fact (Prime q)\nthis✝ : n ≠ 0 → b.primeFactors ⊆ n.primeFactors\nthis... | grind [factorization_def, prime_of_mem_primeFactors, padicValNat.mul, padicValNat.pow] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleNumber | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 41
} | [
{
"pp": "m : ℕ\nhm : 2 ≤ m\nmZ1 : 1 < ↑m\nm1 : 1 < ↑m\nn p : ℕ\nhp : partialSum (↑m) n = ↑p / ↑m ^ n !\nhpos : 0 < remainder (↑m) n\n⊢ partialSum (↑m) n + remainder (↑m) n ≠ partialSum (↑m) n ∧\n |partialSum (↑m) n + remainder (↑m) n - partialSum (↑m) n| < 1 / (↑m ^ n !) ^ n",
"usedConstants": [
"E... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.Irrational | {
"line": 95,
"column": 4
} | {
"line": 95,
"column": 35
} | [
{
"pp": "x : ℝ\nhx : Irrational x\nn : ℕ\nε : ℝ\nH : ∀ k ≤ n, ∀ (m : ℤ), ε ≤ dist x (↑m / ↑k)\nr : ℚ\nhr : r.den ≤ n\n⊢ ε ≤ dist x ↑r",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Real.instLE",
"Real",
"Rat.num",
"instHDiv",
"congrArg",
"Real.instRatCast",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.Hensel | {
"line": 386,
"column": 4
} | {
"line": 386,
"column": 15
} | [
{
"pp": "p : ℕ\ninst✝² : Fact (Nat.Prime p)\nR : Type u_1\ninst✝¹ : CommSemiring R\ninst✝ : Algebra R ℤ_[p]\nF : Polynomial R\na : ℤ_[p]\nhnorm : ‖(Polynomial.aeval a) F‖ < ‖(Polynomial.aeval a) (Polynomial.derivative F)‖ ^ 2\nhnsol : (Polynomial.aeval a) F ≠ 0\nn : ℕ\nthis : (fun x ↦ 2 ^ x) 1 ≤ (fun x ↦ 2 ^ x)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart | {
"line": 179,
"column": 6
} | {
"line": 179,
"column": 26
} | [
{
"pp": "case h.right.refine_1\nf : ℤ[X]\nhf : eval 0 f ≠ 0\nc' : ℂ → ℝ\nc'0 : ∀ (s : ℂ), c' s ≥ 0\nPp'_le : ∀ (s : ℂ) (p : ℕ), p ≠ 0 → ‖P (map (algebraMap ℤ ℂ) (X ^ (p - 1) * f ^ p)) s‖ ≤ c' s ^ p\np : ℕ\np_gt : p > (eval 0 f).natAbs\nprime_p : Nat.Prime p\ngp' : ℤ[X]\nh' : eval 0 (sumIDeriv (X ^ (p - 1) * f ^... | add_tsub_cancel_left | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Transcendental.Liouville.Measure | {
"line": 54,
"column": 30
} | {
"line": 54,
"column": 40
} | [
{
"pp": "p : ℝ\nhp : p > 2\nn : ℕ\nhn : 2 + 1 / (↑n + 1) < p\nx : ℝ\nhxp : LiouvilleWith p x\nhx01 : x ∈ Ico 0 1\nb : ℕ\nhb : 1 ≤ b\na : ℤ\nhlt : |x - ↑a / ↑b| < (↑b ^ (2 + 1 / (↑n + 1)))⁻¹\n⊢ ∃ a ∈ Finset.Icc 0 ↑b, |x - ↑a / ↑b| < 1 / ↑b ^ (2 + 1 / ↑(n + 1))",
"usedConstants": [
"Int.cast",
"No... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Transcendental.Liouville.Measure | {
"line": 64,
"column": 4
} | {
"line": 64,
"column": 15
} | [
{
"pp": "p : ℝ\nhp : p > 2\nn : ℕ\nhn : 2 + 1 / (↑n + 1) < p\nx : ℝ\nhxp : LiouvilleWith p x\nhx01 : x ∈ Ico 0 1\nb : ℕ\na : ℤ\nhlt : |x - ↑a / ↑b| < 1 / ↑b ^ (2 + 1 / ↑n.succ)\nhb : 1 ≤ ↑b\nhb0 : 0 < ↑b\n⊢ 2 ≤ 2 + 1 / ↑(n + 1)",
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart | {
"line": 204,
"column": 4
} | {
"line": 204,
"column": 44
} | [
{
"pp": "f : ℤ[X]\nhf : eval 0 f ≠ 0\nc' : ℂ → ℝ\nc'0 : ∀ (s : ℂ), c' s ≥ 0\nPp'_le : ∀ (s : ℂ) (p : ℕ), p ≠ 0 → ‖P (map (algebraMap ℤ ℂ) (X ^ (p - 1) * f ^ p)) s‖ ≤ c' s ^ p\np : ℕ\np_gt : p > (eval 0 f).natAbs\nprime_p : Nat.Prime p\ngp' : ℤ[X]\nh' : eval 0 (sumIDeriv (X ^ (p - 1) * f ^ p)) = (p - 1)! • eval ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Liouville.Measure | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 72
} | [
{
"pp": "⊢ ∀ᵐ (x : ℝ), ∀ p > 2, ¬LiouvilleWith p x",
"usedConstants": [
"MeasureTheory.ae",
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"Iff.of_eq",
"congrArg",
"_private.Mathlib.NumberTheory.Transcendental.Liouville.Measure.0.ae_not_liouvilleWith._simp_1_3",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Liouville.Measure | {
"line": 119,
"column": 2
} | {
"line": 119,
"column": 46
} | [
{
"pp": "⊢ volume {x | Liouville x} = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Lindemann.AnalyticalPart | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 35
} | [
{
"pp": "case h.right.refine_2\nf : ℤ[X]\nhf : eval 0 f ≠ 0\nc' : ℂ → ℝ\nc'0 : ∀ (s : ℂ), c' s ≥ 0\nPp'_le : ∀ (s : ℂ) (p : ℕ), p ≠ 0 → ‖P (map (algebraMap ℤ ℂ) (X ^ (p - 1) * f ^ p)) s‖ ≤ c' s ^ p\np : ℕ\np_gt : p > (eval 0 f).natAbs\nprime_p : Nat.Prime p\ngp' : ℤ[X]\nh' : eval 0 (sumIDeriv (X ^ (p - 1) * f ^... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 39
} | [
{
"pp": "p x C : ℝ\nhC : ∃ᶠ (n : ℕ) in atTop, ∃ m, x ≠ ↑m / ↑n ∧ |x - ↑m / ↑n| < C / ↑n ^ p\nn : ℕ\nhle : 1 ≤ n\nm : ℤ\nhne : x ≠ ↑m / ↑n\nhlt : |x - ↑m / ↑n| < C / ↑n ^ p\n⊢ 1 ≤ n ∧ ∃ m, x ≠ ↑m / ↑n ∧ |x - ↑m / ↑n| < max C 1 / ↑n ^ p",
"usedConstants": [
"Int.cast",
"Real.instPow",
"Real"... | refine ⟨hle, m, hne, hlt.trans_le ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | {
"line": 101,
"column": 4
} | {
"line": 101,
"column": 48
} | [
{
"pp": "p q x : ℝ\nh : LiouvilleWith p x\nhlt : q < p\nC : ℝ\n_hC₀ : 0 < C\nhC : ∃ᶠ (n : ℕ) in atTop, 1 ≤ n ∧ ∃ m, x ≠ ↑m / ↑n ∧ |x - ↑m / ↑n| < C / ↑n ^ p\n⊢ ∀ᶠ (n : ℕ) in atTop, C < ↑n ^ (p - q)",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Wilson | {
"line": 66,
"column": 6
} | {
"line": 66,
"column": 58
} | [
{
"pp": "case refine_3.refine_1\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nhp : 0 < p\nb : ℕ\nhb : b ≠ 0 ∧ b < p\nh : (↑b).val = val 0\n⊢ b = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Wilson | {
"line": 44,
"column": 2
} | {
"line": 68,
"column": 48
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ ↑(p - 1)! = -1",
"usedConstants": [
"Finset.mem_univ",
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.add_one_sub_one",
"MonoidHom.ins... | refine
calc
((p - 1)! : ZMod p) = ∏ x ∈ Ico 1 (succ (p - 1)), (x : ZMod p) := by
rw [← Finset.prod_Ico_id_eq_factorial, prod_natCast]
_ = ∏ x : (ZMod p)ˣ, (x : ZMod p) := ?_
_ = -1 := by
simp_rw [← Units.coeHom_apply, ← map_prod (Units.coeHom (ZMod p)),
prod_univ_units_id... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Wilson | {
"line": 44,
"column": 2
} | {
"line": 68,
"column": 48
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\n⊢ ↑(p - 1)! = -1",
"usedConstants": [
"Finset.mem_univ",
"Units.val",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.add_one_sub_one",
"MonoidHom.ins... | refine
calc
((p - 1)! : ZMod p) = ∏ x ∈ Ico 1 (succ (p - 1)), (x : ZMod p) := by
rw [← Finset.prod_Ico_id_eq_factorial, prod_natCast]
_ = ∏ x : (ZMod p)ˣ, (x : ZMod p) := ?_
_ = -1 := by
simp_rw [← Units.coeHom_apply, ← map_prod (Units.coeHom (ZMod p)),
prod_univ_units_id... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | {
"line": 131,
"column": 4
} | {
"line": 131,
"column": 91
} | [
{
"pp": "p x : ℝ\nr : ℚ\nhr : r ≠ 0\nh : LiouvilleWith p (x * ↑r)\n⊢ LiouvilleWith p x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | {
"line": 183,
"column": 15
} | {
"line": 183,
"column": 26
} | [
{
"pp": "p x : ℝ\nr : ℚ\nh : LiouvilleWith p (x + ↑r)\n⊢ LiouvilleWith p x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | {
"line": 275,
"column": 20
} | {
"line": 275,
"column": 30
} | [
{
"pp": "p : ℝ\nhp : 1 < p\nM : ℤ\nh : LiouvilleWith p ↑M\nn : ℕ\nhn : 0 < n\nm : ℤ\nhne : ↑M ≠ ↑m / ↑n\nhlt : |↑M - ↑m / ↑n| < ↑n ^ (-1)\nhn' : 0 < ↑n\n⊢ (↑n)⁻¹ ≤ |↑M - ↑m / ↑n|",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"MulOne.toOne",
"Real",
"DivInvMonoid.toInv",
"ins... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Bounds.Lattice | {
"line": 30,
"column": 2
} | {
"line": 31,
"column": 9
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\n⊢ GaloisConnection (⇑OrderDual.toDual ∘ upperBounds) (lowerBounds ∘ ⇑OrderDual.ofDual)",
"usedConstants": [
"OrderDual.instLE",
"OrderDual.toDual",
"Eq.mpr",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"lowerBounds",
"congrA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Transcendental.Liouville.LiouvilleWith | {
"line": 340,
"column": 36
} | {
"line": 340,
"column": 58
} | [
{
"pp": "x : ℝ\nH : ∀ (p : ℝ), LiouvilleWith p x\nn b : ℕ\nhb : 1 < b\na : ℤ\nhne : x ≠ ↑a / ↑b\nhlt : |x - ↑a / ↑b| < ↑b ^ (-↑n)\n⊢ |x - ↑a / ↑↑b| < 1 / ↑↑b ^ n",
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.WellApproximable | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 65
} | [
{
"pp": "A : Type u_1\ninst✝ : SeminormedCommGroup A\na : A\nn : ℕ\nδ : ℝ\nhn : 0 < n\nhan : ∀ {b : A}, orderOf b = n → orderOf (a * b) = n\nf : ↑{b | orderOf b = n} → ↑{b | orderOf b = n} := fun b ↦ ⟨a * ↑b, ⋯⟩\nhf : Surjective f\n⊢ ⋃ i, ⋃ (_ : orderOf i = n), ball (a * i) δ = ⋃ x, ⋃ (_ : orderOf x = n), ball ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Comparable | {
"line": 375,
"column": 2
} | {
"line": 375,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\na b : α\n⊢ a < b ∨ a = b ∨ b < a ∨ IncompRel (fun x1 x2 ↦ x1 ≤ x2) a b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Category.PartOrdEmb | {
"line": 233,
"column": 12
} | {
"line": 233,
"column": 37
} | [
{
"pp": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nx y : CoconePt hc\nj : J\nx₁ y₁ : ↑(F.obj j)\nhx₁ : (ConcreteCategory.hom (c.ι.app j)) x₁ = x\nhy₁ : (ConcreteCategory.hom (c.ι.app j)) y₁ = y\nh₁ : x₁ ≤ y₁\nk : J\ny₂ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Category.PartOrdEmb | {
"line": 234,
"column": 12
} | {
"line": 234,
"column": 37
} | [
{
"pp": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nx y : CoconePt hc\nj : J\nx₁ y₁ : ↑(F.obj j)\nhx₁ : (ConcreteCategory.hom (c.ι.app j)) x₁ = x\nhy₁ : (ConcreteCategory.hom (c.ι.app j)) y₁ = y\nh₁ : x₁ ≤ y₁\nk : J\ny₂ x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Category.PartOrdEmb | {
"line": 261,
"column": 8
} | {
"line": 261,
"column": 34
} | [
{
"pp": "J : Type u\ninst✝¹ : SmallCategory J\ninst✝ : IsFiltered J\nF : J ⥤ PartOrdEmb\nc : Cocone (F ⋙ forget PartOrdEmb)\nhc : IsColimit c\nj : J\nx y : ↑(F.1 j)\nk : J\nx' y' : ↑(F.obj k)\nhx : (ConcreteCategory.hom (c.ι.app k)) x' = (ConcreteCategory.hom (c.ι.app j)) x\nhy : (ConcreteCategory.hom (c.ι.app ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteSublattice | {
"line": 69,
"column": 30
} | {
"line": 69,
"column": 41
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\nL : CompleteSublattice α\n⊢ ⊤ ∈ L",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteSublattice | {
"line": 71,
"column": 30
} | {
"line": 71,
"column": 41
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\nL : CompleteSublattice α\n⊢ ⊥ ∈ L",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteSublattice | {
"line": 104,
"column": 12
} | {
"line": 104,
"column": 22
} | [
{
"pp": "α : Type u_1\ninst✝ : CompleteLattice α\nL : CompleteSublattice α\nι : Sort u_3\nf : ι → ↥L\n⊢ ↑(sSup (range f)) = ⨆ i, ↑(f i)",
"usedConstants": [
"Eq.mpr",
"CompleteSublattice.instSupSet",
"congrArg",
"iSup",
"Membership.mem",
"CompleteLattice.toConditionallyCo... | coe_sSup', | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.CompleteSublattice | {
"line": 152,
"column": 4
} | {
"line": 152,
"column": 62
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nf : CompleteLatticeHom α β\nL✝ : CompleteSublattice α\nL : CompleteSublattice β\ns : Set α\nhs : s ⊆ ⇑f ⁻¹' ↑L\n⊢ sSup s ∈ ⇑f ⁻¹' ↑L",
"usedConstants": [
"Eq.mpr",
"sSupHomClass.map_sSup",
"congrArg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteSublattice | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 62
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : CompleteLattice α\ninst✝ : CompleteLattice β\nf : CompleteLatticeHom α β\nL✝ : CompleteSublattice α\nL : CompleteSublattice β\ns : Set α\nhs : s ⊆ ⇑f ⁻¹' ↑L\n⊢ sInf s ∈ ⇑f ⁻¹' ↑L",
"usedConstants": [
"sInfHomClass.map_sInf",
"Eq.mpr",
"congrArg... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.WellApproximable | {
"line": 331,
"column": 6
} | {
"line": 331,
"column": 42
} | [
{
"pp": "case refine_1\nA : Type u_1\ninst✝⁵ : NormedAddCommGroup A\ninst✝⁴ : CompactSpace A\ninst✝³ : PreconnectedSpace A\ninst✝² : MeasurableSpace A\ninst✝¹ : BorelSpace A\nμ : Measure A\ninst✝ : μ.IsAddHaarMeasure\nξ : A\nn : ℕ\nhn : 0 < n\nδ : ℝ\nhδ : μ univ ≤ (n + 1) • μ (closedBall 0 (δ / 2))\nB : ↑(Icc 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Completion | {
"line": 89,
"column": 13
} | {
"line": 89,
"column": 45
} | [
{
"pp": "case h\nα : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : Preorder β\na x✝ : α\n⊢ x✝ ∈ Iic a ↔ x✝ ∈ (ofObject (fun x1 x2 ↦ x1 ≤ x2) a).extent",
"usedConstants": [
"Eq.mpr",
"Concept.ofObject",
"Set.Ici",
"lowerBounds",
"congrArg",
"Preorder.toLE",
"S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Completion | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 13
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\n⊢ principal a ≤ principal b ↔ a ≤ b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Concept | {
"line": 418,
"column": 2
} | {
"line": 418,
"column": 95
} | [
{
"pp": "α : Type u_2\nr' : α → α → Prop\nc' : Concept α α r'\ninst✝¹ : Std.Trichotomous r'\ninst✝ : IsTrans α r'\nx : α\nx✝ : x ∈ ⊤\nhx : x ∉ c'.extent\ny : α\nhy : y ∈ c'.extent\n⊢ r' y x",
"usedConstants": [
"Concept.mem_extent_of_rel_extent",
"Not.imp_symm",
"Eq",
"Std.Trichotomo... | apply Not.imp_symm <| Std.Trichotomous.trichotomous x y (hx <| mem_extent_of_rel_extent · hy) | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Order.Completion | {
"line": 166,
"column": 2
} | {
"line": 170,
"column": 6
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : CompleteLattice α\ninst✝ : PartialOrder β\nf : β ↪o α\nx : β\n⊢ (factorEmbedding f) (principal x) = f x",
"usedConstants": [
"sSup_le_iff._simp_2",
"Eq.mpr",
"instReflLe",
"congrArg",
"Set.mem_image._simp_1",
"PartialOrder.toP... | rw [factorEmbedding_apply]
apply le_antisymm (by simp)
rw [le_sSup_iff]
refine fun y hy ↦ hy ?_
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Completion | {
"line": 166,
"column": 2
} | {
"line": 170,
"column": 6
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : CompleteLattice α\ninst✝ : PartialOrder β\nf : β ↪o α\nx : β\n⊢ (factorEmbedding f) (principal x) = f x",
"usedConstants": [
"sSup_le_iff._simp_2",
"Eq.mpr",
"instReflLe",
"congrArg",
"Set.mem_image._simp_1",
"PartialOrder.toP... | rw [factorEmbedding_apply]
apply le_antisymm (by simp)
rw [le_sSup_iff]
refine fun y hy ↦ hy ?_
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Concept | {
"line": 517,
"column": 2
} | {
"line": 517,
"column": 13
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nr : α → β → Prop\ns : Set α\nc : Concept α β r\nh : c.extent ⊆ s\n⊢ c ≤ ofObjects r s",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Concept | {
"line": 527,
"column": 2
} | {
"line": 527,
"column": 13
} | [
{
"pp": "α : Type u_2\nβ : Type u_3\nr : α → β → Prop\nt : Set β\nc : Concept α β r\nh : c.intent ⊆ t\n⊢ c.intent ⊆ (ofAttributes r t).intent",
"usedConstants": [
"Concept.ofAttributes",
"Concept.intent",
"id",
"HasSubset.Subset",
"Set.instHasSubset",
"Set"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.WellApproximable | {
"line": 351,
"column": 2
} | {
"line": 351,
"column": 13
} | [
{
"pp": "A : Type u_1\ninst✝⁵ : NormedAddCommGroup A\ninst✝⁴ : CompactSpace A\ninst✝³ : PreconnectedSpace A\ninst✝² : MeasurableSpace A\ninst✝¹ : BorelSpace A\nμ : Measure A\ninst✝ : μ.IsAddHaarMeasure\nξ : A\nn : ℕ\nhn : 0 < n\nδ : ℝ\nB : ↑(Icc 0 n) → Set A := fun j ↦ closedBall (↑j • ξ) (δ / 2)\nhB : ∀ (j : ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Rank | {
"line": 48,
"column": 2
} | {
"line": 56,
"column": 42
} | [
{
"pp": "α : Type u\na : α\nr : α → α → Prop\no : Ordinal.{u}\nha : Acc r a\nho : o ≤ ha.rank\n⊢ ∃ b, ∃ (hb : Acc r b), hb.rank = o",
"usedConstants": [
"Acc.rank_eq",
"LE.le.eq_or_lt",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Order.succ",
"Ordinal.partialOrder",
... | obtain rfl | ho := ho.eq_or_lt
· exact ⟨a, ha, rfl⟩
· revert ho
refine ha.recOn fun a ha IH ho ↦ ?_
rw [rank_eq, Ordinal.lt_iSup_iff] at ho
obtain ⟨⟨b, hb⟩, ho⟩ := ho
rw [Order.lt_succ_iff] at ho
obtain rfl | ho := ho.eq_or_lt
exacts [⟨b, ha b hb, rfl⟩, IH _ hb ho] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Rank | {
"line": 48,
"column": 2
} | {
"line": 56,
"column": 42
} | [
{
"pp": "α : Type u\na : α\nr : α → α → Prop\no : Ordinal.{u}\nha : Acc r a\nho : o ≤ ha.rank\n⊢ ∃ b, ∃ (hb : Acc r b), hb.rank = o",
"usedConstants": [
"Acc.rank_eq",
"LE.le.eq_or_lt",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Order.succ",
"Ordinal.partialOrder",
... | obtain rfl | ho := ho.eq_or_lt
· exact ⟨a, ha, rfl⟩
· revert ho
refine ha.recOn fun a ha IH ho ↦ ?_
rw [rank_eq, Ordinal.lt_iSup_iff] at ho
obtain ⟨⟨b, hb⟩, ho⟩ := ho
rw [Order.lt_succ_iff] at ho
obtain rfl | ho := ho.eq_or_lt
exacts [⟨b, ha b hb, rfl⟩, IH _ hb ho] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Partial | {
"line": 130,
"column": 4
} | {
"line": 131,
"column": 11
} | [
{
"pp": "case mp\nα : Type u\nβ : Type v\nr : SetRel α β\nl₁ : Filter α\nl₂ : Filter β\n⊢ (∀ s ∈ l₂.sets, r.core s ∈ l₁) → l₁ ≤ rcomap r l₂",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Filter.mem_sets._simp_1",
"SetRel",
"congrArg",
"PartialOrder.toPreorder",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Partial | {
"line": 132,
"column": 4
} | {
"line": 133,
"column": 11
} | [
{
"pp": "case mpr\nα : Type u\nβ : Type v\nr : SetRel α β\nl₁ : Filter α\nl₂ : Filter β\n⊢ l₁ ≤ rcomap r l₂ → ∀ s ∈ l₂.sets, r.core s ∈ l₁",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Filter.mem_sets._simp_1",
"SetRel",
"congrArg",
"PartialOrder.toPreorder",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.Partial | {
"line": 163,
"column": 6
} | {
"line": 163,
"column": 57
} | [
{
"pp": "case mp\nα : Type u\nβ : Type v\nγ : Type w\nr : SetRel α β\ns : SetRel β γ\nl : Filter γ\nt : Set α\nu : Set β\nh : r.preimage u ⊆ t\nv : Set γ\nvsets : v ∈ l\nhv : s.preimage v ⊆ u\n⊢ ∃ t_1 ∈ l, r.preimage (s.preimage t_1) ⊆ t",
"usedConstants": [
"Filter.instMembership",
"PartialOrde... | exact ⟨v, vsets, (SetRel.preimage_mono hv).trans h⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
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