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.RingTheory.Ideal.AssociatedPrime.Finiteness | {
"line": 82,
"column": 68
} | {
"line": 82,
"column": 76
} | [
{
"pp": "A : Type u\ninst✝² : CommRing A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nN₁ N₂ : Submodule A M\nf : ↥N₂ ⧸ N₁.submoduleOf N₂ →ₗ[A] M ⧸ N₁ := (N₁.submoduleOf N₂).mapQ N₁ N₂.subtype ⋯\nhf₁ : f.ker = ⊥\nhf₂ : f.range = map N₁.mkQ N₂\nx✝ : ∃ x, (⊥.colon {N₁.mkQ x}).IsPrime ∧ N₂ = N₁ ⊔ A ∙ x... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness | {
"line": 82,
"column": 68
} | {
"line": 82,
"column": 76
} | [
{
"pp": "A : Type u\ninst✝² : CommRing A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nN₁ N₂ : Submodule A M\nf : ↥N₂ ⧸ N₁.submoduleOf N₂ →ₗ[A] M ⧸ N₁ := (N₁.submoduleOf N₂).mapQ N₁ N₂.subtype ⋯\nhf₁ : f.ker = ⊥\nhf₂ : f.range = map N₁.mkQ N₂\nx✝ : ∃ x, (⊥.colon {N₁.mkQ x}).IsPrime ∧ N₂ = N₁ ⊔ A ∙ x... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness | {
"line": 82,
"column": 68
} | {
"line": 82,
"column": 76
} | [
{
"pp": "A : Type u\ninst✝² : CommRing A\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module A M\nN₁ N₂ : Submodule A M\nf : ↥N₂ ⧸ N₁.submoduleOf N₂ →ₗ[A] M ⧸ N₁ := (N₁.submoduleOf N₂).mapQ N₁ N₂.subtype ⋯\nhf₁ : f.ker = ⊥\nhf₂ : f.range = map N₁.mkQ N₂\nx✝ : ∃ x, (⊥.colon {N₁.mkQ x}).IsPrime ∧ N₂ = N₁ ⊔ A ∙ x... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Ideal.AssociatedPrime.Basic | {
"line": 277,
"column": 8
} | {
"line": 277,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI J : Ideal R\nhI : I.IsPrimary\nhJ : J.IsPrime\nx : R\ne : J = (⊥.colon {(Ideal.Quotient.mkₐ R I) x}).radical\nthis : (Ideal.Quotient.mkₐ R I) x ≠ 0\ny : R\n⊢ y ∈ ⊥.colon {(Ideal.Quotient.mk I) x} ↔ (Ideal.Quotient.mk I) (y * x) = 0",
"usedConstants": [
"Eq.... | mem_colon_singleton, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness | {
"line": 209,
"column": 63
} | {
"line": 209,
"column": 88
} | [
{
"pp": "A : Type u\ninst✝² : CommRing A\ninst✝¹ : IsNoetherianRing A\nI : Ideal A\ninst✝ : FaithfulSMul A ↥I\nthis : ↑I ∩ ↑(nonZeroDivisors A) = ∅\n⊢ Module.annihilator A ↥I = ⊥",
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"Module.annihilator",
"congrArg",
"CommSemiring... | Module.annihilator_eq_bot | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.LinearAlgebra.PiTensorProduct | {
"line": 815,
"column": 6
} | {
"line": 817,
"column": 14
} | [
{
"pp": "ι : Type u_1\nι₂ : Type u_2\nι₃ : Type u_3\nR : Type u_4\ninst✝¹⁰ : CommSemiring R\nR₁ : Type u_5\nR₂ : Type u_6\ns : ι → Type u_7\ninst✝⁹ : (i : ι) → AddCommMonoid (s i)\ninst✝⁸ : (i : ι) → Module R (s i)\nM : Type u_8\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nE : Type u_9\ninst✝⁵ : AddCommMonoi... | ext f
have h : update (0 : (i : ι) → s i) i₀ (f i₀) = f := update_eq_self i₀ f
simp [h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.LinearAlgebra.PiTensorProduct | {
"line": 815,
"column": 6
} | {
"line": 817,
"column": 14
} | [
{
"pp": "ι : Type u_1\nι₂ : Type u_2\nι₃ : Type u_3\nR : Type u_4\ninst✝¹⁰ : CommSemiring R\nR₁ : Type u_5\nR₂ : Type u_6\ns : ι → Type u_7\ninst✝⁹ : (i : ι) → AddCommMonoid (s i)\ninst✝⁸ : (i : ι) → Module R (s i)\nM : Type u_8\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nE : Type u_9\ninst✝⁵ : AddCommMonoi... | ext f
have h : update (0 : (i : ι) → s i) i₀ (f i₀) = f := update_eq_self i₀ f
simp [h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.ClassGroup | {
"line": 114,
"column": 54
} | {
"line": 117,
"column": 5
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDomain R\nI : (FractionalIdeal R⁰ (FractionRing R))ˣ\n⊢ Quot.mk (⇑(QuotientGroup.leftRel (toPrincipalIdeal R (FractionRing R)).range)) I = (mk (FractionRing R)) I",
"usedConstants": [
"Eq.mpr",
"MonoidHom.range",
"FractionRing.field",
... | by
rw [ClassGroup.mk_def, canonicalEquiv_self, RingEquiv.coe_monoidHom_refl, Units.map_id,
MonoidHom.id_apply, QuotientGroup.mk'_apply]
rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.ClassGroup | {
"line": 433,
"column": 4
} | {
"line": 434,
"column": 58
} | [
{
"pp": "case h\nR : Type u_1\nK : Type u_2\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Algebra R K\ninst✝⁶ : IsFractionRing R K\ninst✝⁵ : IsDomain R\nS : Type u_3\nL : Type u_4\ninst✝⁴ : CommRing S\ninst✝³ : IsDomain S\ninst✝² : Field L\ninst✝¹ : Algebra S L\ninst✝ : IsFractionRing S L\nf : R ≃+* S\nI : (... | simp only [RingEquiv.toRingHom_eq_coe, Units.coe_map, MonoidHom.coe_coe, RingHom.coe_coe,
Units.coe_mapEquiv, ← huv, RingEquiv.coe_toMulEquiv] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.ZMod.ValMinAbs | {
"line": 68,
"column": 4
} | {
"line": 69,
"column": 61
} | [
{
"pp": "n : ℕ\na : ZMod (n + 1)\nh : ¬a.val ≤ n.succ / 2\n⊢ 2 * a.val = n + 1 → a.val ≤ n.succ / 2",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"instHDiv",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"Nat.instAt... | rw [mul_comm]
exact fun h => (Nat.le_div_iff_mul_le zero_lt_two).2 h.le | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ZMod.ValMinAbs | {
"line": 68,
"column": 4
} | {
"line": 69,
"column": 61
} | [
{
"pp": "n : ℕ\na : ZMod (n + 1)\nh : ¬a.val ≤ n.succ / 2\n⊢ 2 * a.val = n + 1 → a.val ≤ n.succ / 2",
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"instHDiv",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"Nat.instAt... | rw [mul_comm]
exact fun h => (Nat.le_div_iff_mul_le zero_lt_two).2 h.le | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ZMod.ValMinAbs | {
"line": 128,
"column": 17
} | {
"line": 128,
"column": 31
} | [
{
"pp": "case inr.refine_2\nn : ℕ\na : ZMod n\nha : 2 * a.val ≠ n\nh : NeZero n\n⊢ -↑n < -(a.valMinAbs * 2)",
"usedConstants": [
"Int.instAddCommGroup",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | neg_lt_neg_iff | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Spectrum.Prime.FreeLocus | {
"line": 145,
"column": 4
} | {
"line": 146,
"column": 59
} | [
{
"pp": "R : Type uR\nM : Type uM\ninst✝² : CommRing R\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nS : Submonoid R\np : PrimeSpectrum (Localization S)\np' : Ideal R := Ideal.comap (algebraMap R (Localization S)) p.asIdeal\nhp' : S ≤ p'.primeCompl\nRₚ : Type uR := Localization.AtPrime p'\nMₚ : Type (max uR uM)... | have : IsLocalizedModule (Algebra.algebraMapSubmonoid (Localization S) p'.primeCompl) l :=
IsLocalizedModule.of_restrictScalars p'.primeCompl .. | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.RingTheory.Spectrum.Prime.FreeLocus | {
"line": 311,
"column": 51
} | {
"line": 311,
"column": 64
} | [
{
"pp": "R : Type uR\nM : Type uM\ninst✝⁴ : CommRing R\ninst✝³ : AddCommGroup M\ninst✝² : Module R M\ninst✝¹ : Flat R M\ninst✝ : Module.Finite R M\nh : rankAtStalk M = 0\np : PrimeSpectrum R\n⊢ 0 p = 0",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"congrArg",
"Pi.zero_apply"... | Pi.zero_apply | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.LocalRing.ResidueField.Fiber | {
"line": 46,
"column": 69
} | {
"line": 58,
"column": 57
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing S\ninst✝¹ : Algebra R S\np : Ideal R\ninst✝ : p.IsPrime\nx : S ⊗[R] p.ResidueField\n⊢ ∃ r ∉ p, ∃ s, r • x = s ⊗ₜ[R] 1",
"usedConstants": [
"_private.Mathlib.RingTheory.LocalRing.ResidueField.Fiber.0.Ideal.ResidueField.exists_s... | by
obtain ⟨t, r, a, hrt, e⟩ := RingHom.SurjectiveOnStalks.exists_mul_eq_tmul
p.surjectiveOnStalks_residueField x ⊥ isPrime_bot
obtain ⟨t, rfl⟩ := IsLocalRing.residue_surjective t
obtain ⟨⟨y, t⟩, rfl⟩ := IsLocalization.mk'_surjective p.primeCompl t
simp only [smul_def, Submodule.mem_bot, mul_eq_zero, algebra... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.LinearAlgebra.Quotient.Pi | {
"line": 111,
"column": 2
} | {
"line": 112,
"column": 32
} | [
{
"pp": "case e_a.H\nι : Type u_1\nR : Type u_2\ninst✝⁴ : CommRing R\nMs : ι → Type u_3\ninst✝³ : (i : ι) → AddCommGroup (Ms i)\ninst✝² : (i : ι) → Module R (Ms i)\np : (i : ι) → Submodule R (Ms i)\ninst✝¹ : Fintype ι\ninst✝ : DecidableEq ι\ni : ι\nx' : Ms i\nj : ι\n⊢ (quotientPiLift p (fun i ↦ (p i).mkQ) ⋯ ∘ₗ ... | rw [comp_apply, piQuotientLift_single, mapQ_apply,
quotientPiLift_mk, id_apply] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.PicardGroup | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 55
} | [
{
"pp": "R : Type u\nM : Type v\ninst✝³ : CommSemiring R\ninst✝² : AddCommMonoid M\ninst✝¹ : Module R M\ninst✝ : Module.Invertible R M\nN : Type (max v u) := Dual R M\ne : M ⊗[R] N ≃ₗ[R] R := TensorProduct.comm R M N ≪≫ₗ linearEquiv R M\nS : Finset (M × N)\nhS : e.symm 1 = ∑ i ∈ S, i.1 ⊗ₜ[R] i.2\nf : (↥S →₀ N) ... | rw [← LinearMap.range_eq_top, Ideal.eq_top_iff_one] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.FieldTheory.Finite.Basic | {
"line": 297,
"column": 10
} | {
"line": 299,
"column": 58
} | [
{
"pp": "case pos\nK : Type u_1\ninst✝² : Field K\ninst✝¹ : Fintype K\ninst✝ : DecidableEq K\ni : ℕ\nφ : Kˣ →* K := { toFun := fun x ↦ ↑x ^ i, map_one' := ⋯, map_mul' := ⋯ }\nthis✝ : Decidable (φ = 1)\nthis : q - 1 ∣ i ↔ φ = 1\nh✝ : φ = 1\n⊢ ↑(Fintype.card Kˣ) = -1",
"usedConstants": [
"Iff.mpr",
... | · rw [Fintype.card_units, Nat.cast_sub,
cast_card_eq_zero, Nat.cast_one, zero_sub]
show 1 ≤ q; exact Fintype.card_pos_iff.mpr ⟨0⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.FieldTheory.Finite.Basic | {
"line": 377,
"column": 45
} | {
"line": 377,
"column": 54
} | [
{
"pp": "K : Type u_1\ninst✝⁴ : Field K\ninst✝³ : Fintype K\nL : Type u_3\ninst✝² : Field L\ninst✝¹ : Algebra K L\ninst✝ : Finite L\nthis : Fintype L\nm : ℕ\nlt : m < Module.finrank K L\npos : 0 < m\neq : frobeniusAlgHom K L ^ m = 1\nx : L\nx✝ : x ∈ univ.val\n⊢ X ^ q ^ m - X ≠ 0 ∧ eval x (X ^ q ^ m) - eval x X ... | eval_pow, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.FieldTheory.Finite.Basic | {
"line": 454,
"column": 70
} | {
"line": 454,
"column": 79
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : Fintype K\naux : X ^ q - X ≠ 0\nx : K\n⊢ eval x (X ^ q) - eval x X = 0",
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"Polynomial.eval_pow",
"HSu... | eval_pow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.Finite.Basic | {
"line": 467,
"column": 60
} | {
"line": 467,
"column": 73
} | [
{
"pp": "K : Type u_1\ninst✝³ : Field K\ninst✝² : Fintype K\np : ℕ\ninst✝¹ : Fact (Nat.Prime p)\ninst✝ : CharP K p\nn : ℕ\nhcard : q = p ^ n\nx : K\n| x",
"usedConstants": [
"GroupWithZero.toMonoidWithZero",
"congrArg",
"DivisionSemiring.toGroupWithZero",
"Fintype.card",
"Field... | ← pow_card x, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.RingTheory.PicardGroup | {
"line": 617,
"column": 2
} | {
"line": 617,
"column": 65
} | [
{
"pp": "case refine_2.a.h.h\nR : Type u_5\nM : Type u_6\ninst✝³ : CommRing R\ninst✝² : AddCommGroup M\ninst✝¹ : Module R M\ninst✝ : Module.Invertible R M\nf : (P : Ideal R) → [inst : P.IsMaximal] → M →ₗ[R] LocalizedModule P.primeCompl M :=\n fun P [P.IsMaximal] ↦ LocalizedModule.mkLinearMap P.primeCompl M\nff... | refine (congr e e ≪≫ₗ equivOfCompatibleSMul Rp ..).injective ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.FieldTheory.PrimitiveElement | {
"line": 95,
"column": 15
} | {
"line": 95,
"column": 17
} | [
{
"pp": "F : Type u_1\ninst✝² : Field F\ninst✝¹ : Infinite F\nE : Type u_2\ninst✝ : Field E\nϕ : F →+* E\nα β : E\nf g : F[X]\nsf : Multiset E := (Polynomial.map ϕ f).roots\nsg : Multiset E := (Polynomial.map ϕ g).roots\ns : Finset E := (sf.bind fun α' ↦ Multiset.map (fun β' ↦ -(α' - α) / (β' - β)) sg).toFinset... | s, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.Norm.Basic | {
"line": 193,
"column": 4
} | {
"line": 193,
"column": 46
} | [
{
"pp": "K : Type u_4\nL : Type u_5\nF : Type u_6\ninst✝¹¹ : Field K\ninst✝¹⁰ : Field L\ninst✝⁹ : Field F\ninst✝⁸ : Algebra K L\ninst✝⁷ : Algebra K F\nE : Type u_7\ninst✝⁶ : Field E\ninst✝⁵ : Algebra K E\ninst✝⁴ : Algebra L F\ninst✝³ : IsScalarTower K L F\ninst✝² : IsAlgClosed E\ninst✝¹ : Algebra.IsSeparable K ... | refine Finset.prod_congr rfl fun σ _ => ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.NumberTheory.RamificationInertia.Inertia | {
"line": 155,
"column": 13
} | {
"line": 155,
"column": 44
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\ninst✝³ : IsDedekindDomain R\ninst✝² : Free ℤ R\ninst✝¹ : Module.Finite ℤ R\np : ℤ\nP : Ideal R\ninst✝ : P.LiesOver (span {p})\nhp : Prime p\n⊢ (span {p}).IsPrime",
"usedConstants": [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"Prime",
... | span_singleton_prime hp.ne_zero | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.FieldTheory.PrimitiveElement | {
"line": 401,
"column": 71
} | {
"line": 408,
"column": 76
} | [
{
"pp": "F : Type u_3\nE : Type u_4\ninst✝⁶ : Field F\ninst✝⁵ : Field E\ninst✝⁴ : Algebra F E\ninst✝³ : FiniteDimensional F E\ninst✝² : Algebra.IsSeparable F E\nA : Type u_5\ninst✝¹ : Field A\ninst✝ : Algebra F A\nhA : ∀ (x : E), (Polynomial.map (algebraMap F A) (minpoly F x)).Splits\nα : E\nφ : E →ₐ[F] A\n⊢ F⟮... | by
refine ⟨fun h ψ hψ ↦ (Field.primitive_element_iff_algHom_eq_of_eval' F A hA α).mp h hψ,
fun h ↦ eq_of_le_of_finrank_eq' le_top ?_⟩
letI : Algebra F⟮α⟯ A := (φ.comp F⟮α⟯.val).toAlgebra
rw [IntermediateField.finrank_top, ← AlgHom.card_of_splits _ _ A, Fintype.card_eq_one_iff]
· exact ⟨{ __ := φ, commutes' ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.RamificationInertia.Ramification | {
"line": 199,
"column": 2
} | {
"line": 199,
"column": 10
} | [
{
"pp": "R : Type u\ninst✝³ : CommRing R\nS : Type v\ninst✝² : CommRing S\ninst✝¹ : Algebra R S\np : Ideal R\ninst✝ : IsDedekindDomain S\nh₁ : map f p ≠ ⊤\nh₂ : map f p ≠ ⊥\nh : map f p ≤ map f p ^ (1 + 1)\nthis✝ : map f p ^ 1 = map f p ^ 2\nthis : 1 = 2\n⊢ False",
"usedConstants": [
"False",
"F... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.Finset.Update | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 10
} | [
{
"pp": "case neg\nι : Type u_2\nπ : ι → Type u_3\ninst✝ : DecidableEq ι\nα : Type u_1\nf : ((i : ι) → π i) → α\ns : Set ι\nhf : DependsOn f s\nt : Finset ι\ny : (i : ↥t) → π ↑i\nx₁ x₂ : (i : ι) → π i\nh : ∀ i ∈ s \\ ↑t, x₁ i = x₂ i\ni : ι\nhi : i ∈ s\nh✝ : i ∉ t\n⊢ x₁ i = x₂ i",
"usedConstants": [
"S... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Module.Torsion.PrimaryComponent | {
"line": 100,
"column": 35
} | {
"line": 100,
"column": 43
} | [
{
"pp": "A : Type u_1\nM : Type u_2\ninst✝² : CommRing A\nI : Ideal A\ninst✝¹ : AddCommMonoid M\ninst✝ : Module A M\nJ : Ideal A\nhD : IsCoprime I J\nthis : ∀ (n : ℕ), Disjoint (torsionBySet A M ↑(I ^ n)) (torsionBySet A M ↑J)\nx : M\n⊢ x = 0 → (∃ n, ∀ a ∈ I ^ n, a • x = 0) ∧ ∀ a ∈ J, a • x = 0",
"usedConst... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Module.Torsion.PrimaryComponent | {
"line": 100,
"column": 35
} | {
"line": 100,
"column": 43
} | [
{
"pp": "A : Type u_1\nM : Type u_2\ninst✝² : CommRing A\nI : Ideal A\ninst✝¹ : AddCommMonoid M\ninst✝ : Module A M\nJ : Ideal A\nhD : IsCoprime I J\nthis : ∀ (n : ℕ), Disjoint (torsionBySet A M ↑(I ^ n)) (torsionBySet A M ↑J)\nx : M\n⊢ x = 0 → (∃ n, ∀ a ∈ I ^ n, a • x = 0) ∧ ∀ a ∈ J, a • x = 0",
"usedConst... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.Torsion.PrimaryComponent | {
"line": 100,
"column": 35
} | {
"line": 100,
"column": 43
} | [
{
"pp": "A : Type u_1\nM : Type u_2\ninst✝² : CommRing A\nI : Ideal A\ninst✝¹ : AddCommMonoid M\ninst✝ : Module A M\nJ : Ideal A\nhD : IsCoprime I J\nthis : ∀ (n : ℕ), Disjoint (torsionBySet A M ↑(I ^ n)) (torsionBySet A M ↑J)\nx : M\n⊢ x = 0 → (∃ n, ∀ a ∈ I ^ n, a • x = 0) ∧ ∀ a ∈ J, a • x = 0",
"usedConst... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Prod.TProd | {
"line": 160,
"column": 12
} | {
"line": 160,
"column": 32
} | [
{
"pp": "ι : Type u\nα : ι → Type v\ninst✝ : DecidableEq ι\nl : List ι\nhnd : l.Nodup\nh : ∀ (i : ι), i ∈ l\nt : (i : ι) → Set (α i)\nh2 : {i | i ∈ l} = univ\n⊢ TProd.elim' h ⁻¹' {i | i ∈ l}.pi t = Set.tprod l t",
"usedConstants": [
"Eq.mpr",
"Set.tprod",
"congrArg",
"setOf",
"... | ← mk_preimage_tprod, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Module.Torsion.PrimaryComponent | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 12
} | [
{
"pp": "case neg\nA : Type u_1\nM : Type u_2\ninst✝³ : CommRing A\ninst✝² : AddCommGroup M\ninst✝¹ : Module A M\ninst✝ : IsDedekindDomain A\nh : IsTorsion A M\na : A\nha : a ∈ A⁰\nha0 : span {a} ≠ ⊥\nthis✝ : Fintype ↑(mulSupport fun v ↦ v.maxPowDividing (span {a})) := Finite.fintype ⋯\nS : Finset (HeightOneSpe... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Module.Torsion.PrimaryComponent | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 12
} | [
{
"pp": "case neg\nA : Type u_1\nM : Type u_2\ninst✝³ : CommRing A\ninst✝² : AddCommGroup M\ninst✝¹ : Module A M\ninst✝ : IsDedekindDomain A\nh : IsTorsion A M\na : A\nha : a ∈ A⁰\nha0 : span {a} ≠ ⊥\nthis✝ : Fintype ↑(mulSupport fun v ↦ v.maxPowDividing (span {a})) := Finite.fintype ⋯\nS : Finset (HeightOneSpe... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.Torsion.PrimaryComponent | {
"line": 172,
"column": 4
} | {
"line": 172,
"column": 12
} | [
{
"pp": "case neg\nA : Type u_1\nM : Type u_2\ninst✝³ : CommRing A\ninst✝² : AddCommGroup M\ninst✝¹ : Module A M\ninst✝ : IsDedekindDomain A\nh : IsTorsion A M\na : A\nha : a ∈ A⁰\nha0 : span {a} ≠ ⊥\nthis✝ : Fintype ↑(mulSupport fun v ↦ v.maxPowDividing (span {a})) := Finite.fintype ⋯\nS : Finset (HeightOneSpe... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.RamificationInertia.Basic | {
"line": 148,
"column": 36
} | {
"line": 148,
"column": 43
} | [
{
"pp": "case f.h\nR : Type u\ninst✝¹⁶ : CommRing R\nS : Type v\ninst✝¹⁵ : CommRing S\ninst✝¹⁴ : Algebra R S\np : Ideal R\nK : Type u_1\ninst✝¹³ : Field K\ninst✝¹² : Algebra R K\nL : Type u_2\ninst✝¹¹ : Field L\ninst✝¹⁰ : Algebra S L\ninst✝⁹ : IsFractionRing S L\ninst✝⁸ : IsDomain R\ninst✝⁷ : IsDomain S\ninst✝⁶... | d_smul, | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 228,
"column": 42
} | {
"line": 228,
"column": 50
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nI : Ideal R\nh0 : I ≠ 0\nx : R\nh : ∀ (i : HeightOneSpectrum R), ¬i.maxPowDividing I = ⊤ → x ∈ i.maxPowDividing I\ni : HeightOneSpectrum R\nh✝ : i.maxPowDividing I = ⊤\n⊢ x ∈ i.maxPowDividing I",
"usedConstants": [
"Subm... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 228,
"column": 42
} | {
"line": 228,
"column": 50
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nI : Ideal R\nh0 : I ≠ 0\nx : R\nh : ∀ (i : HeightOneSpectrum R), ¬i.maxPowDividing I = ⊤ → x ∈ i.maxPowDividing I\ni : HeightOneSpectrum R\nh✝ : ¬i.maxPowDividing I = ⊤\n⊢ x ∈ i.maxPowDividing I",
"usedConstants": [
"Sub... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.MeasureTheory.MeasurableSpace.Constructions | {
"line": 451,
"column": 2
} | {
"line": 451,
"column": 10
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nm : MeasurableSpace α\nmβ : MeasurableSpace β\ns : Set α\nt : Set β\nx : α\ny : β\nhx : (x, y).1 ∈ s\nhy : (x, y).2 ∈ t\nhst : MeasurableSet (s ×ˢ t)\nthis✝ : MeasurableSet ((fun x ↦ (x, y)) ⁻¹' s ×ˢ t)\nthis : MeasurableSet (Prod.mk x ⁻¹' s ×ˢ t)\n⊢ MeasurableSet s ∧ Measur... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 387,
"column": 30
} | {
"line": 387,
"column": 66
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : CommRing R\nK : Type u_2\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nI I' : FractionalIdeal R⁰ K\nhI : I ≠ 0\nhI' : I' ≠ 0\nhv : Irreducible (Associates.mk v.asIdeal)\na : R\nJ : Ideal R\nha : a ≠ 0\nh... | mul_comm (J : FractionalIdeal R⁰ K), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 474,
"column": 2
} | {
"line": 475,
"column": 27
} | [
{
"pp": "case ofNat\nR : Type u_1\ninst✝⁴ : CommRing R\nK : Type u_2\ninst✝³ : Field K\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\ninst✝ : IsDedekindDomain R\nv : HeightOneSpectrum R\nI : FractionalIdeal R⁰ K\nn : ℕ\n⊢ count K v (I ^ ofNat n) = ofNat n * count K v I",
"usedConstants": [
"zpow_... | · rw [ofNat_eq_natCast, zpow_natCast]
exact count_pow K v n I | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated | {
"line": 111,
"column": 2
} | {
"line": 115,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : MeasurableSpace α\ns : Set α\n⊢ (𝓟 s).IsMeasurablyGenerated ↔ MeasurableSet s",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Filter.mem_principal_self",
"MeasurableSet",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | refine ⟨?_, fun hs => ⟨fun t ht => ⟨s, mem_principal_self s, hs, ht⟩⟩⟩
rintro ⟨hs⟩
rcases hs (mem_principal_self s) with ⟨t, ht, htm, hts⟩
have : t = s := hts.antisymm ht
rwa [← this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated | {
"line": 111,
"column": 2
} | {
"line": 115,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : MeasurableSpace α\ns : Set α\n⊢ (𝓟 s).IsMeasurablyGenerated ↔ MeasurableSet s",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Filter.mem_principal_self",
"MeasurableSet",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | refine ⟨?_, fun hs => ⟨fun t ht => ⟨s, mem_principal_self s, hs, ht⟩⟩⟩
rintro ⟨hs⟩
rcases hs (mem_principal_self s) with ⟨t, ht, htm, hts⟩
have : t = s := hts.antisymm ht
rwa [← this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.MeasurableSpace.MeasurablyGenerated | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 94
} | [
{
"pp": "β : Type u_2\nγ : Type u_3\nδ : Type u_4\nx✝ : MeasurableSpace β\ninst✝³ : MeasurableSpace γ\ninst✝² : Countable δ\nl : Filter δ\ninst✝¹ : l.IsCountablyGenerated\nl' : Filter γ\ninst✝ : l'.IsCountablyGenerated\nhl' : l'.IsMeasurablyGenerated\nf : δ → β → γ\nhf : ∀ (i : δ), Measurable (f i)\nu : ℕ → Set... | simp only [hu.tendsto_iff hv.toHasBasis, true_imp_iff, true_and, setOf_forall, setOf_exists] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.CauSeq.Completion | {
"line": 378,
"column": 76
} | {
"line": 378,
"column": 79
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : Field α\ninst✝⁴ : LinearOrder α\ninst✝³ : IsStrictOrderedRing α\nβ : Type u_2\ninst✝² : Field β\nabv : β → α\ninst✝¹ : IsAbsoluteValue abv\ninst✝ : IsComplete β abv\nf✝ : CauSeq β abv\nhf✝ : ¬f✝.LimZero\nhl : f✝.lim ≠ 0\ng f : CauSeq β abv\nhf : ¬f.LimZero\nh₂ : g - f * f.inv hf ... | h₂, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 48
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → β\nhf : IsCauSeq abv f\ni : ℕ\nh : ∀ j ≥ i, abv (f j - f i) < 1\nR : ℕ → α := Nat.rec (abv (f 0)) fun i c ↦ max c (abv (f i.... | exact (this i _ hji).trans_lt (lt_add_one _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 650,
"column": 65
} | {
"line": 650,
"column": 73
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nJ I : Ideal R\nhIJ : J * I ≤ J\nhJ : ¬J = 0\nhI : ¬I = 0\ns : Finset (HeightOneSpectrum R) := ⋯.toFinset\nthis : ∀ p ∈ s, J * ∏ q ∈ s, q.asIdeal < J * ∏ q ∈ s \\ {p}, q.asIdeal\na : HeightOneSpectrum R → R\nha : ∀ p ∈ s, a p ∈ J * ∏ q ∈ s \... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 48
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → β\nhf : IsCauSeq abv f\ni : ℕ\nh : ∀ j ≥ i, abv (f j - f i) < 1\nR : ℕ → α := Nat.rec (abv (f 0)) fun i c ↦ max c (abv (f i.... | exact (this i _ hji).trans_lt (lt_add_one _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 48
} | [
{
"pp": "case inl\nα : Type u_1\nβ : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → β\nhf : IsCauSeq abv f\ni : ℕ\nh : ∀ j ≥ i, abv (f j - f i) < 1\nR : ℕ → α := Nat.rec (abv (f 0)) fun i c ↦ max c (abv (f i.... | exact (this i _ hji).trans_lt (lt_add_one _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 650,
"column": 65
} | {
"line": 650,
"column": 73
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nJ I : Ideal R\nhIJ : J * I ≤ J\nhJ : ¬J = 0\nhI : ¬I = 0\ns : Finset (HeightOneSpectrum R) := ⋯.toFinset\nthis : ∀ p ∈ s, J * ∏ q ∈ s, q.asIdeal < J * ∏ q ∈ s \\ {p}, q.asIdeal\na : HeightOneSpectrum R → R\nha : ∀ p ∈ s, a p ∈ J * ∏ q ∈ s \... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 650,
"column": 65
} | {
"line": 650,
"column": 73
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nJ I : Ideal R\nhIJ : J * I ≤ J\nhJ : ¬J = 0\nhI : ¬I = 0\ns : Finset (HeightOneSpectrum R) := ⋯.toFinset\nthis : ∀ p ∈ s, J * ∏ q ∈ s, q.asIdeal < J * ∏ q ∈ s \\ {p}, q.asIdeal\na : HeightOneSpectrum R → R\nha : ∀ p ∈ s, a p ∈ J * ∏ q ∈ s \... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 148,
"column": 74
} | {
"line": 149,
"column": 57
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → β\n⊢ IsCauSeq abv (-f) ↔ IsCauSeq abv f",
"usedConstants": [
"NegZeroClass.toNeg",
"IsDomain.to_noZeroDivisors",
... | by
simp only [IsCauSeq, Pi.neg_apply, ← neg_sub', abv_neg] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 454,
"column": 71
} | {
"line": 454,
"column": 89
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : Field α\ninst✝³ : LinearOrder α\ninst✝² : IsStrictOrderedRing α\ninst✝¹ : Ring β\nabv : β → α\ninst✝ : IsAbsoluteValue abv\nf : ℕ → β\ng : CauSeq β abv\nh : ∀ ε > 0, ∃ i, ∀ j ≥ i, abv (f j - ↑g j) < ε\nε : α\nε0 : ε > 0\ni : ℕ\nhi : ∀ j ≥ i, abv (f j - ↑g j) < ε / 2... | sub_add_sub_cancel | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.Factorization | {
"line": 668,
"column": 4
} | {
"line": 668,
"column": 26
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsDedekindDomain R\nJ I : Ideal R\nhIJ : J * I ≤ J\nhJ : ¬J = 0\nhI : ¬I = 0\ns : Finset (HeightOneSpectrum R) := ⋯.toFinset\nthis✝ : ∀ p ∈ s, J * ∏ q ∈ s, q.asIdeal < J * ∏ q ∈ s \\ {p}, q.asIdeal\na : HeightOneSpectrum R → R\nha : ∀ p ∈ s, a p ∈ J ... | convert! sub_mem H₁ H₂ | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 835,
"column": 6
} | {
"line": 835,
"column": 40
} | [
{
"pp": "case inl.inl\nα : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b c : CauSeq α abs\nha : a < c\nhb : b < c\n⊢ a ⊔ b ≤ c",
"usedConstants": [
"CauSeq.instLTAbs._proof_1",
"CauSeq.instLTAbs",
"CauSeq.sup_lt",
"AddGroupWithOne.toAddGroup",... | exact Or.inl (CauSeq.sup_lt ha hb) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 835,
"column": 6
} | {
"line": 835,
"column": 40
} | [
{
"pp": "case inl.inl\nα : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b c : CauSeq α abs\nha : a < c\nhb : b < c\n⊢ a ⊔ b ≤ c",
"usedConstants": [
"CauSeq.instLTAbs._proof_1",
"CauSeq.instLTAbs",
"CauSeq.sup_lt",
"AddGroupWithOne.toAddGroup",... | exact Or.inl (CauSeq.sup_lt ha hb) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.CauSeq.Basic | {
"line": 835,
"column": 6
} | {
"line": 835,
"column": 40
} | [
{
"pp": "case inl.inl\nα : Type u_1\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\na b c : CauSeq α abs\nha : a < c\nhb : b < c\n⊢ a ⊔ b ≤ c",
"usedConstants": [
"CauSeq.instLTAbs._proof_1",
"CauSeq.instLTAbs",
"CauSeq.sup_lt",
"AddGroupWithOne.toAddGroup",... | exact Or.inl (CauSeq.sup_lt ha hb) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Real.Basic | {
"line": 195,
"column": 42
} | {
"line": 195,
"column": 75
} | [
{
"pp": "case a\nx a b c : ℝ\n⊢ (a + b + c).cauchy = (a + (b + c)).cauchy",
"usedConstants": [
"Real",
"Real.cauchy",
"AddMonoid.toAddSemigroup",
"abs",
"congrArg",
"add_assoc",
"IsAbsoluteValue.abs_isAbsoluteValue",
"Rat",
"CauSeq.Completion.Cauchy",
... | simp only [cauchy_add, add_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Real.Basic | {
"line": 199,
"column": 36
} | {
"line": 199,
"column": 65
} | [
{
"pp": "case a\nx a : ℝ\n⊢ (1 * a).cauchy = a.cauchy",
"usedConstants": [
"Real",
"Real.cauchy",
"HMul.hMul",
"abs",
"congrArg",
"IsAbsoluteValue.abs_isAbsoluteValue",
"Rat",
"CauSeq.Completion.Cauchy",
"Rat.linearOrder",
"CauSeq.Completion.instMu... | simp [cauchy_mul, cauchy_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Real.Basic | {
"line": 198,
"column": 36
} | {
"line": 198,
"column": 65
} | [
{
"pp": "case a\nx a : ℝ\n⊢ (a * 1).cauchy = a.cauchy",
"usedConstants": [
"Real",
"Real.cauchy",
"HMul.hMul",
"abs",
"congrArg",
"IsAbsoluteValue.abs_isAbsoluteValue",
"Rat",
"CauSeq.Completion.Cauchy",
"Rat.linearOrder",
"CauSeq.Completion.instMu... | simp [cauchy_mul, cauchy_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Real.Basic | {
"line": 200,
"column": 21
} | {
"line": 200,
"column": 71
} | [
{
"pp": "x a b : ℝ\n⊢ a * b = b * a",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.cauchy",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Real.ext_cauchy",
"abs",... | apply ext_cauchy; simp only [cauchy_mul, mul_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Real.Basic | {
"line": 200,
"column": 21
} | {
"line": 200,
"column": 71
} | [
{
"pp": "x a b : ℝ\n⊢ a * b = b * a",
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.cauchy",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Real.ext_cauchy",
"abs",... | apply ext_cauchy; simp only [cauchy_mul, mul_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Real.Basic | {
"line": 544,
"column": 54
} | {
"line": 544,
"column": 72
} | [
{
"pp": "case h.h\nx : ℝ\nf y✝ : CauSeq ℚ abs\nh : ∃ i, ∀ j ≥ i, mk y✝ ≤ ↑(↑f j)\nK : ℚ\nK0 : K > 0\nhK : ∃ i, ∀ j ≥ i, K ≤ ↑(y✝ - f) j\ni : ℕ\nH : ∀ j ≥ i, mk y✝ ≤ ↑(↑f j) ∧ K ≤ ↑(y✝ - f) j ∧ ∀ k ≥ j, |↑f k - ↑f j| < K / 2\nj : ℕ\nij : j ≥ i\nthis : K / 2 ≤ ↑y✝ j - ↑f j + (↑f j - ↑f i)\n⊢ K / 2 ≤ ↑(y✝ - const ... | sub_add_sub_cancel | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Real.Archimedean | {
"line": 216,
"column": 2
} | {
"line": 216,
"column": 24
} | [
{
"pp": "case pos\ns : Set ℝ\nhn : s.Nonempty\nhb : BddBelow s\n⊢ sSup (-s) = -sInf s",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Real",
"congrArg",
"covariant_swap_add_of_covariant_add",
"PartialOrder.toPreorder",
"Pr... | · rw [csSup_neg hn hb] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.RamificationInertia.Basic | {
"line": 661,
"column": 49
} | {
"line": 661,
"column": 87
} | [
{
"pp": "R : Type u\ninst✝¹⁷ : CommRing R\nS : Type v\ninst✝¹⁶ : CommRing S\ninst✝¹⁵ : Algebra R S\ninst✝¹⁴ : IsDedekindDomain S\nK : Type u_1\nL : Type u_2\ninst✝¹³ : Field K\ninst✝¹² : Field L\ninst✝¹¹ : IsDedekindDomain R\ninst✝¹⁰ : Algebra R K\ninst✝⁹ : IsFractionRing R K\ninst✝⁸ : Algebra S L\ninst✝⁷ : IsF... | IsLocalRing.primesOverFinset_eq S hp0, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.ENNReal.Basic | {
"line": 648,
"column": 2
} | {
"line": 648,
"column": 74
} | [
{
"pp": "⊢ ⋂ n, Ici ↑n = {∞}",
"usedConstants": [
"ENNReal.iUnion_Iio_coe_nat",
"Set.Ici",
"compl_compl",
"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat._simp_1_2",
"congrArg",
"Set.iInter",
"Compl.compl",
"PartialOrder.toPreorder",
"S... | simp only [← compl_Iio, ← compl_iUnion, iUnion_Iio_coe_nat, compl_compl] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.ENNReal.Basic | {
"line": 648,
"column": 2
} | {
"line": 648,
"column": 74
} | [
{
"pp": "⊢ ⋂ n, Ici ↑n = {∞}",
"usedConstants": [
"ENNReal.iUnion_Iio_coe_nat",
"Set.Ici",
"compl_compl",
"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat._simp_1_2",
"congrArg",
"Set.iInter",
"Compl.compl",
"PartialOrder.toPreorder",
"S... | simp only [← compl_Iio, ← compl_iUnion, iUnion_Iio_coe_nat, compl_compl] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.ENNReal.Basic | {
"line": 648,
"column": 2
} | {
"line": 648,
"column": 74
} | [
{
"pp": "⊢ ⋂ n, Ici ↑n = {∞}",
"usedConstants": [
"ENNReal.iUnion_Iio_coe_nat",
"Set.Ici",
"compl_compl",
"_private.Mathlib.Data.ENNReal.Basic.0.ENNReal.iInter_Ici_coe_nat._simp_1_2",
"congrArg",
"Set.iInter",
"Compl.compl",
"PartialOrder.toPreorder",
"S... | simp only [← compl_Iio, ← compl_iUnion, iUnion_Iio_coe_nat, compl_compl] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNReal.Defs | {
"line": 803,
"column": 38
} | {
"line": 803,
"column": 58
} | [
{
"pp": "x y : ℝ\nhx : 0 ≤ x\n⊢ (x * y⁻¹).toNNReal = x.toNNReal * y.toNNReal⁻¹",
"usedConstants": [
"Eq.mpr",
"Real",
"DivInvMonoid.toInv",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"Monoid.toMulOneClass",
"congrArg",
"Real.instInv",
"Real.instDivInvM... | ← Real.toNNReal_inv, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.NNReal.Defs | {
"line": 945,
"column": 12
} | {
"line": 945,
"column": 20
} | [
{
"pp": "case inl\nmotive : ℝ → Prop\nnonneg : ∀ (x : ℝ≥0), motive ↑x\nnonpos : ∀ (x : ℝ≥0), motive ↑x → motive (-↑x)\nr : ℝ≥0\n⊢ motive ↑r",
"usedConstants": [
"NNReal",
"eq_true",
"of_eq_true",
"NNReal.toReal"
]
}
] | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.NNReal.Defs | {
"line": 945,
"column": 12
} | {
"line": 945,
"column": 20
} | [
{
"pp": "case inl\nmotive : ℝ → Prop\nnonneg : ∀ (x : ℝ≥0), motive ↑x\nnonpos : ∀ (x : ℝ≥0), motive ↑x → motive (-↑x)\nr : ℝ≥0\n⊢ motive ↑r",
"usedConstants": [
"NNReal",
"eq_true",
"of_eq_true",
"NNReal.toReal"
]
}
] | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.NNReal.Defs | {
"line": 945,
"column": 12
} | {
"line": 945,
"column": 20
} | [
{
"pp": "case inl\nmotive : ℝ → Prop\nnonneg : ∀ (x : ℝ≥0), motive ↑x\nnonpos : ∀ (x : ℝ≥0), motive ↑x → motive (-↑x)\nr : ℝ≥0\n⊢ motive ↑r",
"usedConstants": [
"NNReal",
"eq_true",
"of_eq_true",
"NNReal.toReal"
]
}
] | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNReal.Defs | {
"line": 945,
"column": 12
} | {
"line": 945,
"column": 20
} | [
{
"pp": "case inr\nmotive : ℝ → Prop\nnonneg : ∀ (x : ℝ≥0), motive ↑x\nnonpos : ∀ (x : ℝ≥0), motive ↑x → motive (-↑x)\nr : ℝ≥0\n⊢ motive (-↑r)",
"usedConstants": [
"Real",
"instInhabitedTrue",
"Eq.mp",
"id",
"NNReal",
"implies_congr",
"instNonemptyOfInhabited",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.NNReal.Defs | {
"line": 945,
"column": 12
} | {
"line": 945,
"column": 20
} | [
{
"pp": "case inr\nmotive : ℝ → Prop\nnonneg : ∀ (x : ℝ≥0), motive ↑x\nnonpos : ∀ (x : ℝ≥0), motive ↑x → motive (-↑x)\nr : ℝ≥0\n⊢ motive (-↑r)",
"usedConstants": [
"Real",
"instInhabitedTrue",
"Eq.mp",
"id",
"NNReal",
"implies_congr",
"instNonemptyOfInhabited",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.NNReal.Defs | {
"line": 945,
"column": 12
} | {
"line": 945,
"column": 20
} | [
{
"pp": "case inr\nmotive : ℝ → Prop\nnonneg : ∀ (x : ℝ≥0), motive ↑x\nnonpos : ∀ (x : ℝ≥0), motive ↑x → motive (-↑x)\nr : ℝ≥0\n⊢ motive (-↑r)",
"usedConstants": [
"Real",
"instInhabitedTrue",
"Eq.mp",
"id",
"NNReal",
"implies_congr",
"instNonemptyOfInhabited",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inl\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\n⊢ motive 0",
"usedConstants": []
}
] | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inl\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\n⊢ motive 0",
"usedConstants": []
}
] | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inl\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\n⊢ motive 0",
"usedConstants": []
}
] | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inr.inl\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\nr : ℝ≥0\nhr : 0 < r\n⊢ motive ↑r",
"usedConstants": [
"Preorder.toLT",
"PartialOrder.toPreorder",
"NNReal",
"NNReal.instZero",
"... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inr.inl\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\nr : ℝ≥0\nhr : 0 < r\n⊢ motive ↑r",
"usedConstants": [
"Preorder.toLT",
"PartialOrder.toPreorder",
"NNReal",
"NNReal.instZero",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inr.inl\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\nr : ℝ≥0\nhr : 0 < r\n⊢ motive ↑r",
"usedConstants": [
"Preorder.toLT",
"PartialOrder.toPreorder",
"NNReal",
"NNReal.instZero",
"... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inr.inr\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\nr : ℝ≥0\nhr : 0 < r\n⊢ motive (-↑r)",
"usedConstants": [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"instInhabitedTrue",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inr.inr\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\nr : ℝ≥0\nhr : 0 < r\n⊢ motive (-↑r)",
"usedConstants": [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"instInhabitedTrue",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.NNReal.Defs | {
"line": 953,
"column": 12
} | {
"line": 953,
"column": 20
} | [
{
"pp": "case inr.inr\nmotive : ℝ → Prop\nzero : motive 0\npos : ∀ (x : ℝ≥0), 0 < x → motive ↑x\nneg : ∀ (x : ℝ≥0), 0 < x → motive ↑x → motive (-↑x)\nr : ℝ≥0\nhr : 0 < r\n⊢ motive (-↑r)",
"usedConstants": [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"instInhabitedTrue",
... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.ENNReal.Operations | {
"line": 213,
"column": 2
} | {
"line": 213,
"column": 74
} | [
{
"pp": "case mpr\na b : ℝ≥0∞\n⊢ a < ∞ ∧ b < ∞ ∨ a = 0 ∨ b = 0 → a * b < ∞",
"usedConstants": [
"Preorder.toLT",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"MulZeroClass.zero_mul",
"PartialOrder.toPreorder",
"ENNReal.instCommSemiring",
"Or.casesOn",
... | · rintro (⟨ha, hb⟩ | rfl | rfl) <;> [exact mul_lt_top ha hb; simp; simp] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.Interval.Set.OrdConnectedComponent | {
"line": 135,
"column": 67
} | {
"line": 141,
"column": 57
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\ns : Set α\nx y : α\nhx : x ∈ s.ordConnectedSection\nhy : y ∈ s.ordConnectedSection\nh : [[x, y]] ⊆ s\n⊢ x = y",
"usedConstants": [
"Iff.mpr",
"Set.mem_ordConnectedComponent_trans",
"Set.mem_ordConnectedComponent_ordConnectedProj",
"Member... | by
rcases hx with ⟨x, rfl⟩; rcases hy with ⟨y, rfl⟩
exact
ordConnectedProj_eq.2
(mem_ordConnectedComponent_trans
(mem_ordConnectedComponent_trans (ordConnectedProj_mem_ordConnectedComponent _ _) h)
(mem_ordConnectedComponent_ordConnectedProj _ _)) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.EReal.Basic | {
"line": 411,
"column": 4
} | {
"line": 411,
"column": 40
} | [
{
"pp": "case neg\nx : EReal\nh : x ≠ ⊥\nh' : ¬x = ⊤\n⊢ ↑x.toReal ≤ x",
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"LE.le",
"EReal.coe_toReal",
"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le._simp_1_2",
"True"... | simp only [le_refl, coe_toReal h' h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.EReal.Basic | {
"line": 411,
"column": 4
} | {
"line": 411,
"column": 40
} | [
{
"pp": "case neg\nx : EReal\nh : x ≠ ⊥\nh' : ¬x = ⊤\n⊢ ↑x.toReal ≤ x",
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"LE.le",
"EReal.coe_toReal",
"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le._simp_1_2",
"True"... | simp only [le_refl, coe_toReal h' h] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Basic | {
"line": 411,
"column": 4
} | {
"line": 411,
"column": 40
} | [
{
"pp": "case neg\nx : EReal\nh : x ≠ ⊥\nh' : ¬x = ⊤\n⊢ ↑x.toReal ≤ x",
"usedConstants": [
"congrArg",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"LE.le",
"EReal.coe_toReal",
"_private.Mathlib.Data.EReal.Basic.0.EReal.coe_toReal_le._simp_1_2",
"True"... | simp only [le_refl, coe_toReal h' h] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Basic | {
"line": 629,
"column": 6
} | {
"line": 629,
"column": 39
} | [
{
"pp": "x : ℝ≥0∞\n⊢ ↑x = 0 ↔ x = 0",
"usedConstants": [
"Eq.mpr",
"congrArg",
"EReal",
"EReal.coe_ennreal_eq_coe_ennreal_iff",
"id",
"instZeroEReal",
"Iff",
"ENNReal.toEReal",
"ENNReal",
"propext",
"Zero.toOfNat0",
"ENNReal.instZero",
... | ← coe_ennreal_eq_coe_ennreal_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.EReal.Basic | {
"line": 633,
"column": 6
} | {
"line": 633,
"column": 39
} | [
{
"pp": "x : ℝ≥0∞\n⊢ ↑x = 1 ↔ x = 1",
"usedConstants": [
"Eq.mpr",
"congrArg",
"EReal",
"EReal.coe_ennreal_eq_coe_ennreal_iff",
"id",
"Iff",
"ENNReal.toEReal",
"ENNReal",
"propext",
"One.toOfNat1",
"ENNReal.instOne",
"OfNat.ofNat",
... | ← coe_ennreal_eq_coe_ennreal_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.EReal.Basic | {
"line": 723,
"column": 2
} | {
"line": 723,
"column": 34
} | [
{
"pp": "x : EReal\n⊢ x.toENNReal = 0 ↔ x ≤ 0",
"usedConstants": [
"False",
"Real.instLE",
"Real",
"ENNReal.top_ne_zero._simp_1",
"LinearOrder.toDecidableEq",
"bot_ne_top._simp_2",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._s... | induction x <;> simp [toENNReal] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.EReal.Basic | {
"line": 723,
"column": 2
} | {
"line": 723,
"column": 34
} | [
{
"pp": "x : EReal\n⊢ x.toENNReal = 0 ↔ x ≤ 0",
"usedConstants": [
"False",
"Real.instLE",
"Real",
"ENNReal.top_ne_zero._simp_1",
"LinearOrder.toDecidableEq",
"bot_ne_top._simp_2",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._s... | induction x <;> simp [toENNReal] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.EReal.Basic | {
"line": 723,
"column": 2
} | {
"line": 723,
"column": 34
} | [
{
"pp": "x : EReal\n⊢ x.toENNReal = 0 ↔ x ≤ 0",
"usedConstants": [
"False",
"Real.instLE",
"Real",
"ENNReal.top_ne_zero._simp_1",
"LinearOrder.toDecidableEq",
"bot_ne_top._simp_2",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._s... | induction x <;> simp [toENNReal] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case bot.bot\nhx hy : 0 ≤ ⊥\n⊢ ⊥.toENNReal = ⊥.toENNReal ↔ ⊥ = ⊥",
"usedConstants": [
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
"Bot.bot",
"instZeroEReal",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case bot.coe\nhx : 0 ≤ ⊥\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ ⊥.toENNReal = (↑a✝).toENNReal ↔ ⊥ = ↑a✝",
"usedConstants": [
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
"Bot.bot",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case bot.top\nhx : 0 ≤ ⊥\nhy : 0 ≤ ⊤\n⊢ ⊥.toENNReal = ⊤.toENNReal ↔ ⊥ = ⊤",
"usedConstants": [
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
"instTopEReal",
"Bot.b... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case coe.bot\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊥\n⊢ (↑a✝).toENNReal = ⊥.toENNReal ↔ ↑a✝ = ⊥",
"usedConstants": [
"False",
"EReal.toENNReal",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Eq.mp",
"Bot.bot",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case coe.coe\na✝¹ : ℝ\nhx : 0 ≤ ↑a✝¹\na✝ : ℝ\nhy : 0 ≤ ↑a✝\n⊢ (↑a✝¹).toENNReal = (↑a✝).toENNReal ↔ ↑a✝¹ = ↑a✝",
"usedConstants": [
"EReal.coe_nonneg._simp_1",
"False",
"Real.instLE",
"Real",
"EReal.toENNReal_of_ne_top",
"Real.instZero",
"ENNReal.ofReal",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Data.EReal.Basic | {
"line": 764,
"column": 34
} | {
"line": 764,
"column": 42
} | [
{
"pp": "case coe.top\na✝ : ℝ\nhx : 0 ≤ ↑a✝\nhy : 0 ≤ ⊤\n⊢ (↑a✝).toENNReal = ⊤.toENNReal ↔ ↑a✝ = ⊤",
"usedConstants": [
"False",
"EReal.toENNReal_of_ne_top",
"ENNReal.ofReal",
"congrArg",
"EReal.coe_ne_top._simp_1",
"EReal.toENNReal",
"EReal",
"instTopEReal",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
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