module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 396,
"column": 73
} | {
"line": 396,
"column": 79
} | {
"line": 398,
"column": 0
} | [
{
"pp": "case inr\nk : Type u_1\ninst✝³ : Field k\nK : Type u_2\ninst✝² : Field K\ninst✝¹ : Algebra k K\nw : InfinitePlace K\ninst✝ : IsGalois k K\ne : Nat.card ↥(Stab w) = 2\n⊢ ¬2 = 1 ↔ 2 = 2",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 632,
"column": 6
} | {
"line": 632,
"column": 32
} | {
"line": 632,
"column": 32
} | [
{
"pp": "K : Type u_4\nL : Type u_5\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\nw : InfinitePlace L\nv : InfinitePlace K\ninst✝ : (↑w).LiesOver ↑v\nhw : w.IsReal\n⊢ v.IsReal",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NumberField.InfinitePlace.not_... | [
"K : Type u_4\nL : Type u_5\ninst✝³ : Field K\ninst✝² : Field L\ninst✝¹ : Algebra K L\nw : InfinitePlace L\nv : InfinitePlace K\ninst✝ : (↑w).LiesOver ↑v\nhw : ¬w.IsComplex\n⊢ ¬v.IsComplex"
] | ← not_isComplex_iff_isReal | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 544,
"column": 8
} | {
"line": 544,
"column": 24
} | {
"line": 544,
"column": 25
} | [
{
"pp": "case refine_3\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\n⊢ Fintype.card (index K) = Fintype.card (K →+* ℂ)",
"ppTerm": "?refine_3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instFintypeSum",
"congrArg",
"NumberField.InfinitePlace.IsComplex",
... | [
"case refine_3\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\n⊢ Fintype.card (index K) = finrank ℚ K"
] | Embeddings.card, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.IntegralClosure.IntegralRestrict | {
"line": 317,
"column": 2
} | {
"line": 317,
"column": 80
} | {
"line": 319,
"column": 0
} | [
{
"pp": "A : Type u_1\nB : Type u_6\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDomain B\ninst✝³ : IsIntegrallyClosed B\ninst✝² : Module.Finite A B\ninst✝¹ : IsTorsionFree A B\ninst✝ : Free A B\nx : B\nthis✝¹ : IsIntegralClosure... | [] | rw [Algebra.algebraMap_intTrace_fractionRing, Algebra.trace_localization A A⁰] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 382,
"column": 6
} | {
"line": 382,
"column": 25
} | {
"line": 382,
"column": 26
} | [
{
"pp": "case _a\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nN : ℕ\nhK : |discr K| ≤ ↑N\nthis : boundOfDiscBdd N - 1 < boundOfDiscBdd N\n⊢ ↑|discr K| ≤ ↑↑N",
"ppTerm": "?_a",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWit... | [
"case _a\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nN : ℕ\nhK : |discr K| ≤ ↑N\nthis : boundOfDiscBdd N - 1 < boundOfDiscBdd N\n⊢ ↑|discr K| ≤ ↑N"
] | NNReal.coe_natCast, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 434,
"column": 4
} | {
"line": 435,
"column": 84
} | {
"line": 436,
"column": 4
} | [
{
"pp": "case refine_3\nA : Type u_2\ninst✝¹ : Field A\ninst✝ : CharZero A\nN : ℕ\nD : ℕ := rankOfDiscrBdd N\nB : ℝ≥0 := boundOfDiscBdd N\nC : ℕ := ⌈max B 1 ^ D * ↑(D.choose (D / 2))⌉₊\nx✝¹ : { F // FiniteDimensional ℚ ↥F }\nK : IntermediateField ℚ A\nhK₀ : FiniteDimensional ℚ ↥K\nx✝ : ⟨K, hK₀⟩ ∈ {K | {w | w.Is... | [
"case refine_4\nA : Type u_2\ninst✝¹ : Field A\ninst✝ : CharZero A\nN : ℕ\nD : ℕ := rankOfDiscrBdd N\nB : ℝ≥0 := boundOfDiscBdd N\nC : ℕ := ⌈max B 1 ^ D * ↑(D.choose (D / 2))⌉₊\nx✝¹ : { F // FiniteDimensional ℚ ↥F }\nK : IntermediateField ℚ A\nhK₀ : FiniteDimensional ℚ ↥K\nx✝ : ⟨K, hK₀⟩ ∈ {K | {w | w.IsReal}.Nonemp... | · refine mem_rootSet.mpr ⟨minpoly.ne_zero hx, ?_⟩
exact (aeval_algebraMap_eq_zero_iff A (x : K) _).mpr (minpoly.aeval ℤ (x : K)) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.RamificationInertia.Galois | {
"line": 349,
"column": 2
} | {
"line": 361,
"column": 73
} | {
"line": 363,
"column": 0
} | [
{
"pp": "R : Type u_1\nK : Type u_2\nL : Type u_3\nS : Type u_4\ninst✝¹⁵ : CommRing R\ninst✝¹⁴ : CommRing S\ninst✝¹³ : Algebra R S\ninst✝¹² : Field K\ninst✝¹¹ : Field L\ninst✝¹⁰ : Algebra R K\ninst✝⁹ : IsFractionRing R K\ninst✝⁸ : Algebra S L\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra R L\ninst✝⁵ : IsScalarTower R... | [] | have : IsDomain S :=
(IsIntegralClosure.equiv R S L (integralClosure R L)).toMulEquiv.isDomain (integralClosure R L)
have := IsIntegralClosure.isDedekindDomain R K L S
have : Module.Finite R S := IsIntegralClosure.finite R K L S
have := hP₁.1
have := hP₁.2
have := hP₂.1
have := hP₂.2
have : IsFraction... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.RamificationInertia.Galois | {
"line": 349,
"column": 2
} | {
"line": 361,
"column": 73
} | {
"line": 363,
"column": 0
} | [
{
"pp": "R : Type u_1\nK : Type u_2\nL : Type u_3\nS : Type u_4\ninst✝¹⁵ : CommRing R\ninst✝¹⁴ : CommRing S\ninst✝¹³ : Algebra R S\ninst✝¹² : Field K\ninst✝¹¹ : Field L\ninst✝¹⁰ : Algebra R K\ninst✝⁹ : IsFractionRing R K\ninst✝⁸ : Algebra S L\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra R L\ninst✝⁵ : IsScalarTower R... | [] | have : IsDomain S :=
(IsIntegralClosure.equiv R S L (integralClosure R L)).toMulEquiv.isDomain (integralClosure R L)
have := IsIntegralClosure.isDedekindDomain R K L S
have : Module.Finite R S := IsIntegralClosure.finite R K L S
have := hP₁.1
have := hP₁.2
have := hP₂.1
have := hP₂.2
have : IsFraction... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 481,
"column": 14
} | {
"line": 481,
"column": 33
} | {
"line": 481,
"column": 34
} | [
{
"pp": "case h₂\nA : Type u_2\ninst✝¹ : Field A\ninst✝ : CharZero A\nN : ℕ\nD : ℕ := ⋯\nB : ℝ≥0 := ⋯\nC : ℕ := ⋯\nx✝¹ : { F // FiniteDimensional ℚ ↥F }\nK : IntermediateField ℚ A\nhK₀ : FiniteDimensional ℚ ↥K\nx✝ : ⟨K, hK₀⟩ ∈ {K | {w | w.IsComplex}.Nonempty ∧ |discr ↥↑K| ≤ ↑N}\nhK₂ : |discr ↥↑⟨K, hK₀⟩| ≤ ↑N\nt... | [
"case h₂\nA : Type u_2\ninst✝¹ : Field A\ninst✝ : CharZero A\nN : ℕ\nD : ℕ := rankOfDiscrBdd N\nB : ℝ≥0 := boundOfDiscBdd N\nC : ℕ := ⌈max (sqrt (1 + B ^ 2)) 1 ^ D * ↑(D.choose (D / 2))⌉₊\nx✝¹ : { F // FiniteDimensional ℚ ↥F }\nK : IntermediateField ℚ A\nhK₀ : FiniteDimensional ℚ ↥K\nx✝ : ⟨K, hK₀⟩ ∈ {K | {w | w.IsC... | NNReal.coe_natCast, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 484,
"column": 4
} | {
"line": 485,
"column": 84
} | {
"line": 486,
"column": 4
} | [
{
"pp": "case refine_3\nA : Type u_2\ninst✝¹ : Field A\ninst✝ : CharZero A\nN : ℕ\nD : ℕ := rankOfDiscrBdd N\nB : ℝ≥0 := boundOfDiscBdd N\nC : ℕ := ⌈max (sqrt (1 + B ^ 2)) 1 ^ D * ↑(D.choose (D / 2))⌉₊\nx✝¹ : { F // FiniteDimensional ℚ ↥F }\nK : IntermediateField ℚ A\nhK₀ : FiniteDimensional ℚ ↥K\nx✝ : ⟨K, hK₀⟩... | [
"case refine_4\nA : Type u_2\ninst✝¹ : Field A\ninst✝ : CharZero A\nN : ℕ\nD : ℕ := rankOfDiscrBdd N\nB : ℝ≥0 := boundOfDiscBdd N\nC : ℕ := ⌈max (sqrt (1 + B ^ 2)) 1 ^ D * ↑(D.choose (D / 2))⌉₊\nx✝¹ : { F // FiniteDimensional ℚ ↥F }\nK : IntermediateField ℚ A\nhK₀ : FiniteDimensional ℚ ↥K\nx✝ : ⟨K, hK₀⟩ ∈ {K | {w |... | · refine mem_rootSet.mpr ⟨minpoly.ne_zero hx, ?_⟩
exact (aeval_algebraMap_eq_zero_iff A (x : K) _).mpr (minpoly.aeval ℤ (x : K)) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.FractionalIdeal.Extended | {
"line": 145,
"column": 2
} | {
"line": 155,
"column": 31
} | {
"line": 156,
"column": 2
} | [
{
"pp": "case refine_1\nA : Type u_1\ninst✝⁷ : CommRing A\nB : Type u_2\ninst✝⁶ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁵ : CommRing K\ninst✝⁴ : Algebra A K\ninst✝³ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝² : CommRing L\ninst✝¹ : Algebra B L\ninst✝ : IsLocalization N L\n... | [
"case refine_2\nA : Type u_1\ninst✝⁷ : CommRing A\nB : Type u_2\ninst✝⁶ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁵ : CommRing K\ninst✝⁴ : Algebra A K\ninst✝³ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝² : CommRing L\ninst✝¹ : Algebra B L\ninst✝ : IsLocalization N L\nhf : M ≤ Sub... | · rcases h with ⟨x, hx, rfl⟩
replace hx : x ∈ (I : Submodule A K) * (J : Submodule A K) := coe_mul I J ▸ hx
rw [Submodule.mul_eq_span_mul_set] at hx
refine span_induction (fun y hy ↦ ?_) (by simp) (fun y z _ _ hy hz ↦ ?_)
(fun a y _ hy ↦ ?_) hx
· rcases Set.mem_mul.mp hy with ⟨i, hi, j, hj, rfl⟩
... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.FractionalIdeal.Extended | {
"line": 166,
"column": 6
} | {
"line": 166,
"column": 27
} | {
"line": 166,
"column": 28
} | [
{
"pp": "A : Type u_1\ninst✝¹¹ : CommRing A\nB : Type u_2\ninst✝¹⁰ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁹ : CommRing K\ninst✝⁸ : Algebra A K\ninst✝⁷ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝⁶ : CommRing L\ninst✝⁵ : Algebra B L\ninst✝⁴ : IsLocalization N L\nhf : M ≤ Sub... | [
"A : Type u_1\ninst✝¹¹ : CommRing A\nB : Type u_2\ninst✝¹⁰ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁹ : CommRing K\ninst✝⁸ : Algebra A K\ninst✝⁷ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝⁶ : CommRing L\ninst✝⁵ : Algebra B L\ninst✝⁴ : IsLocalization N L\nhf : M ≤ Submonoid.comap... | ← coeToSubmodule_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.FractionalIdeal.Extended | {
"line": 186,
"column": 29
} | {
"line": 186,
"column": 50
} | {
"line": 186,
"column": 51
} | [
{
"pp": "A : Type u_1\ninst✝⁷ : CommRing A\nB : Type u_2\ninst✝⁶ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁵ : CommRing K\ninst✝⁴ : Algebra A K\ninst✝³ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝² : CommRing L\ninst✝¹ : Algebra B L\ninst✝ : IsLocalization N L\nhf : M ≤ Submon... | [
"A : Type u_1\ninst✝⁷ : CommRing A\nB : Type u_2\ninst✝⁶ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁵ : CommRing K\ninst✝⁴ : Algebra A K\ninst✝³ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝² : CommRing L\ninst✝¹ : Algebra B L\ninst✝ : IsLocalization N L\nhf : M ≤ Submonoid.comap f ... | ← coeToSubmodule_inj, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.PID | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 6
} | {
"line": 54,
"column": 2
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹ : CommRing R\nP : Ideal R\nhP : P.IsPrime\ninst✝ : IsDedekindDomain R\nx : R\nx_mem : x ∈ P\nhxP2 : x ∉ P ^ 2\nhxQ : ∀ (Q : Ideal R), Q.IsPrime → Q ≠ P → x ∉ Q\nhP0 : ¬P = ⊥\nhspan0 : span {x} ≠ ⊥\nQ : Ideal R\n⊢ (if Q = P then 1 else 0) = Multiset.count Q (normalizedFact... | [
"case neg\nR : Type u_1\ninst✝¹ : CommRing R\nP : Ideal R\nhP : P.IsPrime\ninst✝ : IsDedekindDomain R\nx : R\nx_mem : x ∈ P\nhxP2 : x ∉ P ^ 2\nhxQ : ∀ (Q : Ideal R), Q.IsPrime → Q ≠ P → x ∉ Q\nhP0 : ¬P = ⊥\nhspan0 : span {x} ≠ ⊥\nQ : Ideal R\n⊢ Multiset.count Q (normalizedFactors (span {x})) = if Q = P then 1 else ... | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 44
} | {
"line": 121,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝²⁴ : CommRing R\ninst✝²³ : IsDomain R\nS : Type u_3\ninst✝²² : CommRing S\ninst✝²¹ : IsDomain S\ninst✝²⁰ : IsIntegrallyClosed R\ninst✝¹⁹ : IsIntegrallyClosed S\ninst✝¹⁸ : Algebra R S\ninst✝¹⁷ : Module.Finite R S\ninst✝¹⁶ : IsTorsionFree R S\nI : Ideal S\nM : Submonoid R\nhM : M ≤ R⁰\... | [
"R : Type u_1\ninst✝²⁴ : CommRing R\ninst✝²³ : IsDomain R\nS : Type u_3\ninst✝²² : CommRing S\ninst✝²¹ : IsDomain S\ninst✝²⁰ : IsIntegrallyClosed R\ninst✝¹⁹ : IsIntegrallyClosed S\ninst✝¹⁸ : Algebra R S\ninst✝¹⁷ : Module.Finite R S\ninst✝¹⁶ : IsTorsionFree R S\nI : Ideal S\nM : Submonoid R\nhM : M ≤ R⁰\nRₘ : Type u... | algebraize [f, g, (algebraMap K L).comp f] | Mathlib.Tactic._aux_Mathlib_Tactic_Algebraize___elabRules_Mathlib_Tactic_tacticAlgebraize___1 | Mathlib.Tactic.tacticAlgebraize__ |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 389,
"column": 4
} | {
"line": 389,
"column": 75
} | {
"line": 390,
"column": 2
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : IsDomain R\nS : Type u_3\ninst✝⁹ : CommRing S\ninst✝⁸ : IsDomain S\ninst✝⁷ : IsIntegrallyClosed R\ninst✝⁶ : IsIntegrallyClosed S\ninst✝⁵ : Algebra R S\ninst✝⁴ : Module.Finite R S\ninst✝³ : IsTorsionFree R S\ninst✝² : IsDedekindDomain R\ninst✝¹ : I... | [] | rw [hp, eq_bot_of_liesOver_bot R P, relNorm_bot, bot_pow (one_ne_zero)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 460,
"column": 6
} | {
"line": 460,
"column": 41
} | {
"line": 460,
"column": 41
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹⁴ : CommRing R\ninst✝¹³ : IsDomain R\nS : Type u_3\ninst✝¹² : CommRing S\ninst✝¹¹ : IsDomain S\ninst✝¹⁰ : IsIntegrallyClosed R\ninst✝⁹ : IsIntegrallyClosed S\ninst✝⁸ : Algebra R S\ninst✝⁷ : Module.Finite R S\ninst✝⁶ : IsTorsionFree R S\ninst✝⁵ : IsDedekindDomain R\ninst✝⁴ ... | [
"case neg\nR : Type u_1\ninst✝¹⁴ : CommRing R\ninst✝¹³ : IsDomain R\nS : Type u_3\ninst✝¹² : CommRing S\ninst✝¹¹ : IsDomain S\ninst✝¹⁰ : IsIntegrallyClosed R\ninst✝⁹ : IsIntegrallyClosed S\ninst✝⁸ : Algebra R S\ninst✝⁷ : Module.Finite R S\ninst✝⁶ : IsTorsionFree R S\ninst✝⁵ : IsDedekindDomain R\ninst✝⁴ : IsDedekind... | ← prod_normalizedFactors_eq_self hI | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 278,
"column": 66
} | {
"line": 278,
"column": 72
} | {
"line": 278,
"column": 72
} | [
{
"pp": "k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2 ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (2 ^ (k + 1))\nthis : NumberField K\nh : hζ.toInteger - 1 = 0\n⊢ 1 < 2",
"ppTerm": "?m.102",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 278,
"column": 66
} | {
"line": 278,
"column": 72
} | {
"line": 278,
"column": 72
} | [
{
"pp": "k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2 ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (2 ^ (k + 1))\nthis : NumberField K\nh : hζ.toInteger - 1 = 0\n⊢ 1 < 2",
"ppTerm": "?m.102",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 278,
"column": 66
} | {
"line": 278,
"column": 72
} | {
"line": 278,
"column": 72
} | [
{
"pp": "k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2 ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (2 ^ (k + 1))\nthis : NumberField K\nh : hζ.toInteger - 1 = 0\n⊢ 1 < 2",
"ppTerm": "?m.102",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 347,
"column": 73
} | {
"line": 347,
"column": 79
} | {
"line": 347,
"column": 79
} | [
{
"pp": "k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2 ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (2 ^ (k + 1))\nthis : NumberField K\n⊢ 0 < 2",
"ppTerm": "?m.160",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 347,
"column": 73
} | {
"line": 347,
"column": 79
} | {
"line": 347,
"column": 79
} | [
{
"pp": "k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2 ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (2 ^ (k + 1))\nthis : NumberField K\n⊢ 0 < 2",
"ppTerm": "?m.160",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 347,
"column": 73
} | {
"line": 347,
"column": 79
} | {
"line": 347,
"column": 79
} | [
{
"pp": "k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2 ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (2 ^ (k + 1))\nthis : NumberField K\n⊢ 0 < 2",
"ppTerm": "?m.160",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 273,
"column": 4
} | {
"line": 276,
"column": 27
} | {
"line": 279,
"column": 4
} | [
{
"pp": "case neg.hi.convert_2\nR : Type u\nK : Type v\nL : Type z\np : R\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : Algebra R K\ninst✝³ : IsScalarTower R K L\ninst✝² : IsDomain R\ninst✝¹ : IsFractionRing R K\ninst✝ : IsIntegrallyClosed R\nB : ... | [
"case neg.hi.convert_2\nR : Type u\nK : Type v\nL : Type z\np : R\ninst✝⁹ : CommRing R\ninst✝⁸ : Field K\ninst✝⁷ : Field L\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra R L\ninst✝⁴ : Algebra R K\ninst✝³ : IsScalarTower R K L\ninst✝² : IsDomain R\ninst✝¹ : IsFractionRing R K\ninst✝ : IsIntegrallyClosed R\nB : PowerBasis K... | have Hj : Q.natDegree + 1 = j + 1 + (Q.natDegree - j) := by
rw [← add_comm 1, ← add_comm 1, add_assoc, add_right_inj,
← Nat.add_sub_assoc (Nat.lt_of_succ_lt_succ (mem_range.1 hj)).le, add_comm,
Nat.add_sub_cancel] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 580,
"column": 10
} | {
"line": 580,
"column": 69
} | {
"line": 581,
"column": 6
} | [
{
"pp": "case neg\nn : ℕ\nhn✝ : 2 ≤ n\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nζ : K\np : ℕ\nhF : Fact (Nat.Prime p)\nhζ : IsPrimitiveRoot ζ n\nthis✝ : NeZero n\nμ : ↥ℚ⟮ζ⟯\nhμ✝ : IsPrimitiveRoot μ n\nhp : ↑p ∣ (Algebra.norm ℤ) (hμ✝.toInteger - 1) ^ Module.finrank (↥ℚ⟮ζ⟯) K\nh : (Algebra.norm ℤ) (... | [] | · rwa [hμ.norm_toInteger_sub_one_of_prime_ne_two hq'] at hp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 582,
"column": 33
} | {
"line": 582,
"column": 44
} | {
"line": 582,
"column": 44
} | [
{
"pp": "case neg\nn : ℕ\nhn✝ : 2 ≤ n\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nζ : K\np : ℕ\nhF : Fact (Nat.Prime p)\nhζ : IsPrimitiveRoot ζ n\nthis : NeZero n\nμ : ↥ℚ⟮ζ⟯\nhC : IsCyclotomicExtension {n} ℚ ↥ℚ⟮ζ⟯\nhμ : IsPrimitiveRoot μ n\nhp : p ∣ 1\nh✝ : (Algebra.norm ℤ) (hζ.toInteger - 1) = (Alg... | [
"case neg\nn : ℕ\nhn✝ : 2 ≤ n\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nζ : K\np : ℕ\nhF : Fact (Nat.Prime p)\nhζ : IsPrimitiveRoot ζ n\nthis : NeZero n\nμ : ↥ℚ⟮ζ⟯\nhC : IsCyclotomicExtension {n} ℚ ↥ℚ⟮ζ⟯\nhμ : IsPrimitiveRoot μ n\nhp : p = 1\nh✝ : (Algebra.norm ℤ) (hζ.toInteger - 1) = (Algebra.norm ℤ)... | Nat.dvd_one | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 693,
"column": 4
} | {
"line": 694,
"column": 51
} | {
"line": 695,
"column": 4
} | [
{
"pp": "case e_a.coprime\nn₁ n₂ : ℕ\nhn₁ : 1 < n₁\nhn₂ : 1 < n₂\nh : n₁.Coprime n₂\nhK₂ :\n ∀ (K : Type u) [inst : Field K] [inst_1 : CharZero K] [hn : NeZero n₂] [hK : IsCyclotomicExtension {n₂} ℚ K]\n (this : NumberField K), (NumberField.discr K).natAbs = n₂ ^ φ n₂ / ∏ p ∈ n₂.primeFactors, p ^ (φ n₂ / (p... | [
"case e_a.coprime\nn₁ n₂ : ℕ\nhn₁ : 1 < n₁\nhn₂ : 1 < n₂\nh : n₁.Coprime n₂\nhK₂ :\n ∀ (K : Type u) [inst : Field K] [inst_1 : CharZero K] [hn : NeZero n₂] [hK : IsCyclotomicExtension {n₂} ℚ K]\n (this : NumberField K), (NumberField.discr K).natAbs = n₂ ^ φ n₂ / ∏ p ∈ n₂.primeFactors, p ^ (φ n₂ / (p - 1))\nK : ... | have hζ₂' : IsPrimitiveRoot (AdjoinSimple.gen ℚ (ζ ^ n₁)) n₂ :=
IsPrimitiveRoot.coe_submonoidClass_iff.mp hζ₂ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | {
"line": 99,
"column": 56
} | {
"line": 99,
"column": 79
} | {
"line": 99,
"column": 80
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\nh : ∑ i, ↑(↑i).mult * Real.log (↑i ((algebraMap (𝓞 K) K) ↑x)) + ↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x)) = 0\n⊢ ∑ w, (logEmbedding K) (Additive.ofMul x) w = -↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x))",
"ppTerm... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\nh : ∑ i, ↑(↑i).mult * Real.log (↑i ((algebraMap (𝓞 K) K) ↑x)) = -(↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x)))\n⊢ ∑ w, (logEmbedding K) (Additive.ofMul x) w = -↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x))"
] | add_eq_zero_iff_eq_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | {
"line": 97,
"column": 62
} | {
"line": 100,
"column": 40
} | {
"line": 102,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\n⊢ ∑ w, (logEmbedding K) (Additive.ofMul x) w = -↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x))",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"NumberField.Infinite... | [] | by
have h := sum_mult_mul_log x
rw [Fintype.sum_eq_add_sum_subtype_ne _ w₀, add_comm, add_eq_zero_iff_eq_neg, ← neg_mul] at h
simpa [logEmbedding_component] using h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 40,
"column": 82
} | {
"line": 40,
"column": 88
} | {
"line": 40,
"column": 88
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\n⊢ 3 ≠ 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 40,
"column": 82
} | {
"line": 40,
"column": 88
} | {
"line": 40,
"column": 88
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\n⊢ 3 ≠ 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 40,
"column": 82
} | {
"line": 40,
"column": 88
} | {
"line": 40,
"column": 88
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\n⊢ 3 ≠ 0",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"Ne",
"instOfNatNat",
"Bool.true",
"Nat",
"Bool",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 55,
"column": 86
} | {
"line": 55,
"column": 92
} | {
"line": 55,
"column": 92
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 2 < 3",
"ppTerm": "?m.134",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 55,
"column": 86
} | {
"line": 55,
"column": 92
} | {
"line": 55,
"column": 92
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 2 < 3",
"ppTerm": "?m.134",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 55,
"column": 86
} | {
"line": 55,
"column": 92
} | {
"line": 55,
"column": 92
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 2 < 3",
"ppTerm": "?m.134",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 72,
"column": 75
} | {
"line": 72,
"column": 81
} | {
"line": 72,
"column": 81
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhrank : rank K = 0\nx : ↥(torsion K)\ne : Fin (rank K) → ℤ\nhxu : u = ↑x\nn : ℕ\nhnpos : 0 < n\nhn : (algebraMap (𝓞 K) K) ↑u ^ ↑⟨n, hnpos⟩ = 1\n⊢ Odd 3",
"pp... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 72,
"column": 75
} | {
"line": 72,
"column": 81
} | {
"line": 72,
"column": 81
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhrank : rank K = 0\nx : ↥(torsion K)\ne : Fin (rank K) → ℤ\nhxu : u = ↑x\nn : ℕ\nhnpos : 0 < n\nhn : (algebraMap (𝓞 K) K) ↑u ^ ↑⟨n, hnpos⟩ = 1\n⊢ Odd 3",
"pp... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 72,
"column": 75
} | {
"line": 72,
"column": 81
} | {
"line": 72,
"column": 81
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nu : (𝓞 K)ˣ\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhrank : rank K = 0\nx : ↥(torsion K)\ne : Fin (rank K) → ℤ\nhxu : u = ↑x\nn : ℕ\nhnpos : 0 < n\nhn : (algebraMap (𝓞 K) K) ↑u ^ ↑⟨n, hnpos⟩ = 1\n⊢ Odd 3",
"pp... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 86,
"column": 59
} | {
"line": 86,
"column": 65
} | {
"line": 86,
"column": 65
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 0 < 3",
"ppTerm": "?m.213",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 86,
"column": 59
} | {
"line": 86,
"column": 65
} | {
"line": 86,
"column": 65
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 0 < 3",
"ppTerm": "?m.213",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 86,
"column": 59
} | {
"line": 86,
"column": 65
} | {
"line": 86,
"column": 65
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 0 < 3",
"ppTerm": "?m.213",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 92,
"column": 44
} | {
"line": 92,
"column": 50
} | {
"line": 92,
"column": 50
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 0 < 3",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 92,
"column": 44
} | {
"line": 92,
"column": 50
} | {
"line": 92,
"column": 50
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 0 < 3",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 92,
"column": 44
} | {
"line": 92,
"column": 50
} | {
"line": 92,
"column": 50
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ 0 < 3",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 108,
"column": 63
} | {
"line": 108,
"column": 69
} | {
"line": 108,
"column": 69
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑⋯.unit - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.821",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 108,
"column": 63
} | {
"line": 108,
"column": 69
} | {
"line": 108,
"column": 69
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑⋯.unit - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.821",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 108,
"column": 63
} | {
"line": 108,
"column": 69
} | {
"line": 108,
"column": 69
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑⋯.unit - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.821",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 109,
"column": 63
} | {
"line": 109,
"column": 69
} | {
"line": 109,
"column": 69
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.829",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 109,
"column": 63
} | {
"line": 109,
"column": 69
} | {
"line": 109,
"column": 69
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.829",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 109,
"column": 63
} | {
"line": 109,
"column": 69
} | {
"line": 109,
"column": 69
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.829",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 115,
"column": 35
} | {
"line": 115,
"column": 41
} | {
"line": 115,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(⋯.unit ^ 2) - ↑n\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.877",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 115,
"column": 35
} | {
"line": 115,
"column": 41
} | {
"line": 115,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(⋯.unit ^ 2) - ↑n\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.877",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 115,
"column": 35
} | {
"line": 115,
"column": 41
} | {
"line": 115,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(⋯.unit ^ 2) - ↑n\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.877",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 116,
"column": 10
} | {
"line": 116,
"column": 16
} | {
"line": 116,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(⋯.unit ^ 2) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.885",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 116,
"column": 10
} | {
"line": 116,
"column": 16
} | {
"line": 116,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(⋯.unit ^ 2) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.885",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 116,
"column": 10
} | {
"line": 116,
"column": 16
} | {
"line": 116,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(⋯.unit ^ 2) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.885",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 117,
"column": 35
} | {
"line": 117,
"column": 41
} | {
"line": 117,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit ^ 2) - ↑n\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.892",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 117,
"column": 35
} | {
"line": 117,
"column": 41
} | {
"line": 117,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit ^ 2) - ↑n\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.892",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 117,
"column": 35
} | {
"line": 117,
"column": 41
} | {
"line": 117,
"column": 41
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit ^ 2) - ↑n\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.892",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 118,
"column": 10
} | {
"line": 118,
"column": 16
} | {
"line": 118,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit ^ 2) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.900",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 118,
"column": 10
} | {
"line": 118,
"column": 16
} | {
"line": 118,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit ^ 2) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.900",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 118,
"column": 10
} | {
"line": 118,
"column": 16
} | {
"line": 118,
"column": 16
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nhcong : ∃ n, 3 ∣ ↑(-⋯.unit ^ 2) - ↑n\n⊢ 3 ≠ 2",
"ppTerm": "?m.900",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 121,
"column": 36
} | {
"line": 121,
"column": 42
} | {
"line": 121,
"column": 42
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nn : ℤ\nx : 𝓞 K\nhx : ↑(-⋯.unit ^ 2) - ↑n = 3 * x\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.939",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_deci... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 121,
"column": 36
} | {
"line": 121,
"column": 42
} | {
"line": 121,
"column": 42
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nn : ℤ\nx : 𝓞 K\nhx : ↑(-⋯.unit ^ 2) - ↑n = 3 * x\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.939",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_deci... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 121,
"column": 36
} | {
"line": 121,
"column": 42
} | {
"line": 121,
"column": 42
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nn : ℤ\nx : 𝓞 K\nhx : ↑(-⋯.unit ^ 2) - ↑n = 3 * x\n⊢ Nat.Coprime 2 3",
"ppTerm": "?m.939",
"assigned": true,
"usedConstants": [
"Nat.Coprime",
"of_deci... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 131,
"column": 51
} | {
"line": 131,
"column": 57
} | {
"line": 131,
"column": 57
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 1 < 3",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 131,
"column": 51
} | {
"line": 131,
"column": 57
} | {
"line": 131,
"column": 57
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 1 < 3",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 131,
"column": 51
} | {
"line": 131,
"column": 57
} | {
"line": 131,
"column": 57
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\n⊢ 1 < 3",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 138,
"column": 53
} | {
"line": 138,
"column": 59
} | {
"line": 138,
"column": 59
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nthis✝ : Finite (𝓞 K ⧸ Ideal.span {λ})\nx✝² : Fintype (𝓞 K ⧸ Ideal.span {λ}) := Fintype.ofFinite (𝓞 K ⧸ Ideal.span {λ})\nx✝¹ : Ring (𝓞 K ⧸ Ideal.span {λ}) := (Ide... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 138,
"column": 53
} | {
"line": 138,
"column": 59
} | {
"line": 138,
"column": 59
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nthis✝ : Finite (𝓞 K ⧸ Ideal.span {λ})\nx✝² : Fintype (𝓞 K ⧸ Ideal.span {λ}) := Fintype.ofFinite (𝓞 K ⧸ Ideal.span {λ})\nx✝¹ : Ring (𝓞 K ⧸ Ideal.span {λ}) := (Ide... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 138,
"column": 53
} | {
"line": 138,
"column": 59
} | {
"line": 138,
"column": 59
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nthis✝ : Finite (𝓞 K ⧸ Ideal.span {λ})\nx✝² : Fintype (𝓞 K ⧸ Ideal.span {λ}) := Fintype.ofFinite (𝓞 K ⧸ Ideal.span {λ})\nx✝¹ : Ring (𝓞 K ⧸ Ideal.span {λ}) := (Ide... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | {
"line": 313,
"column": 6
} | {
"line": 313,
"column": 23
} | {
"line": 313,
"column": 24
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw₁ : InfinitePlace K\nB : ℕ\nhB : minkowskiBound K 1 < ↑(convexBodyLTFactor K) * ↑B\nn : ℕ\n⊢ Ideal.span {↑(seq K w₁ hB n)} ∈ {I | Ideal.absNorm I ≤ B}",
"ppTerm": "?m.335",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Na... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw₁ : InfinitePlace K\nB : ℕ\nhB : minkowskiBound K 1 < ↑(convexBodyLTFactor K) * ↑B\nn : ℕ\n⊢ Ideal.absNorm (Ideal.span {↑(seq K w₁ hB n)}) ≤ B"
] | Set.mem_setOf_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 6
} | {
"line": 160,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\n⊢ x ^ 3 - 1 = (x - 1) * (x - ↑⋯.unit) * (x - ↑⋯.unit ^ 2)",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"Units.val",
"HMul.hMul",
"Numbe... | [
"K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\nx : 𝓞 K\n⊢ (x - 1) * (x - ↑⋯.unit) * (x - ↑⋯.unit ^ 2) = x ^ 3 - 1"
] | symm | Lean.Elab.Tactic.evalSymm | Lean.Parser.Tactic.symm |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 8
} | {
"line": 87,
"column": 0
} | [
{
"pp": "⊢ ¬Deficient 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfN... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 8
} | {
"line": 87,
"column": 0
} | [
{
"pp": "⊢ ¬Deficient 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 85,
"column": 2
} | {
"line": 85,
"column": 8
} | {
"line": 87,
"column": 0
} | [
{
"pp": "⊢ ¬Deficient 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfN... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 8
} | {
"line": 90,
"column": 0
} | [
{
"pp": "⊢ Deficient 1",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 8
} | {
"line": 90,
"column": 0
} | [
{
"pp": "⊢ Deficient 1",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 8
} | {
"line": 90,
"column": 0
} | [
{
"pp": "⊢ Deficient 1",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 8
} | {
"line": 93,
"column": 0
} | [
{
"pp": "⊢ Deficient 2",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 8
} | {
"line": 93,
"column": 0
} | [
{
"pp": "⊢ Deficient 2",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 8
} | {
"line": 93,
"column": 0
} | [
{
"pp": "⊢ Deficient 2",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 8
} | {
"line": 96,
"column": 0
} | [
{
"pp": "⊢ Deficient 3",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 8
} | {
"line": 96,
"column": 0
} | [
{
"pp": "⊢ Deficient 3",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 94,
"column": 2
} | {
"line": 94,
"column": 8
} | {
"line": 96,
"column": 0
} | [
{
"pp": "⊢ Deficient 3",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Deficient",
"Nat.instDecidableDeficient",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 8
} | {
"line": 99,
"column": 0
} | [
{
"pp": "⊢ ¬Abundant 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 8
} | {
"line": 99,
"column": 0
} | [
{
"pp": "⊢ ¬Abundant 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 8
} | {
"line": 99,
"column": 0
} | [
{
"pp": "⊢ ¬Abundant 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 8
} | {
"line": 102,
"column": 0
} | [
{
"pp": "⊢ Abundant 12",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.d... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 8
} | {
"line": 102,
"column": 0
} | [
{
"pp": "⊢ Abundant 12",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.d... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 8
} | {
"line": 102,
"column": 0
} | [
{
"pp": "⊢ Abundant 12",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.d... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 8
} | {
"line": 105,
"column": 0
} | [
{
"pp": "⊢ ¬Weird 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Nat.Weird",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidableWeird",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 8
} | {
"line": 105,
"column": 0
} | [
{
"pp": "⊢ ¬Weird 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Nat.Weird",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidableWeird",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 8
} | {
"line": 105,
"column": 0
} | [
{
"pp": "⊢ ¬Weird 0",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Nat.Weird",
"of_decide_eq_true",
"id",
"instOfNatNat",
"Nat.instDecidableWeird",
"Bool.true",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
... | [] | decide | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 205,
"column": 43
} | {
"line": 212,
"column": 65
} | {
"line": 214,
"column": 0
} | [
{
"pp": "n m : ℕ\nhn : n ≠ 0\nhd : m ∣ n\n⊢ m.abundancyIndex ≤ n.abundancyIndex",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZ... | [] | by
obtain ⟨k, hk⟩ := hd
have hk0 : k ≠ 0 := by grind
rw [abundancyIndex, abundancyIndex, hk, cast_mul, div_mul_eq_div_div_swap]
refine div_le_div_of_nonneg_right ?_ m.cast_nonneg
rw [le_div_iff₀ (by grind [cast_pos]), ← cast_mul, cast_le, sum_mul]
exact (sum_image (f := fun i ↦ i) (mul_left_injective₀ hk0).... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 226,
"column": 30
} | {
"line": 226,
"column": 36
} | {
"line": 227,
"column": 2
} | [
{
"pp": "a : ℕ\n⊢ Abundant 12",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"of_decide_eq_true",
"Nat.instDecidableAbundant",
"id",
"instOfNatNat",
"Bool.true",
"Nat.Abundant",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Dec... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 60,
"column": 12
} | {
"line": 60,
"column": 18
} | {
"line": 62,
"column": 0
} | [
{
"pp": "⊢ ∀ {n : ZMod 9}, (castHom ⋯ (ZMod 3)) n ≠ 0 → n ^ 3 = 1 ∨ n ^ 3 = 8",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"Dvd.dvd",
"of_decide_eq_true",
"ZMod.commRing",
"CommSemiring.toSemiring",
"ZMod.fintype",
"Nat.instA... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | {
"line": 510,
"column": 8
} | {
"line": 510,
"column": 31
} | {
"line": 510,
"column": 32
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\nζ : (𝓞 K)ˣ := x * (∏ i, fundSystem K i ^ ((basisModTorsion K).repr (Additive.ofMul ↑x)) i)⁻¹\n⊢ Additive.ofMul ↑x +\n -∑ x_1,\n ((basisModTorsion K).repr (Additive.ofMul ↑x)) x_1 •\n Additive.ofMul (Additive.t... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (𝓞 K)ˣ\nζ : (𝓞 K)ˣ := x * (∏ i, fundSystem K i ^ ((basisModTorsion K).repr (Additive.ofMul ↑x)) i)⁻¹\n⊢ Additive.ofMul ↑x =\n -\n -∑ x_1,\n ((basisModTorsion K).repr (Additive.ofMul ↑x)) x_1 • Additive.ofMul (Additive.toMul ((basisModTor... | add_eq_zero_iff_eq_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inl.inl.inl\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 1\nhb : ↑b ^ 3 = 1\nhc : ↑c ^ 3 = 1\n⊢ ¬1 + 1 = 1",
"ppTerm": "?inl.inl.inl",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
Mathlib.NumberTheory.FLT.Three | {
"line": 76,
"column": 22
} | {
"line": 76,
"column": 28
} | {
"line": 78,
"column": 0
} | [
{
"pp": "case inl.inl.inr\na b c : ℤ\nhdvd : (¬3 ∣ a ∧ ¬3 ∣ b) ∧ ¬3 ∣ c\nha : ↑a ^ 3 = 1\nhb : ↑b ^ 3 = 1\nhc : ↑c ^ 3 = 8\n⊢ ¬1 + 1 = 8",
"ppTerm": "?inl.inl.inr",
"assigned": true,
"usedConstants": [
"instDecidableNot",
"of_decide_eq_true",
"ZMod.commRing",
"AddMonoid.toAdd... | [] | decide | Lean.Elab.Tactic.evalDecide | Lean.Parser.Tactic.decide |
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