module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | {
"line": 509,
"column": 19
} | {
"line": 509,
"column": 30
} | {
"line": 509,
"column": 31
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nf : InfinitePlace K → ℝ≥0\nI : (FractionalIdeal (𝓞 K)⁰ K)ˣ\nw₀ : { w // w.IsComplex }\nh : minkowskiBound K I < volume (convexBodyLT' K f w₀)\nh_fund :\n IsAddFundamentalDomain (↥(span ℤ (Set.range ⇑(fractionalIdealLatticeBasis K I))).toAddSubgro... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nf : InfinitePlace K → ℝ≥0\nI : (FractionalIdeal (𝓞 K)⁰ K)ˣ\nw₀ : { w // w.IsComplex }\nh : minkowskiBound K I < volume (convexBodyLT' K f w₀)\nh_fund :\n IsAddFundamentalDomain (↥(span ℤ (Set.range ⇑(fractionalIdealLatticeBasis K I))).toAddSubgroup)\n (fu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 607,
"column": 4
} | {
"line": 620,
"column": 27
} | {
"line": 622,
"column": 0
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (K →+* ℂ) → ℂ\nhx : ∀ (φ : K →+* ℂ), (starRingEnd ℂ) (x φ) = x (ComplexEmbedding.conjugate φ)\nc : { w // w.IsComplex } × Fin 2\n⊢ ↑(((stdBasis K).repr (fun w ↦ (x (↑w).embedding).re, fun w ↦ x (↑w).embedding)) (Sum.inr c)) =\n ∑ x... | [] | rcases c with ⟨w, j⟩
fin_cases j
· simp only [Fin.zero_eta, Fin.isValue, stdBasis_apply_isComplex_fst, re_eq_add_conj,
mul_neg, fromBlocks_apply₂₁, Matrix.zero_apply, zero_mul, sum_const_zero,
fromBlocks_apply₂₂, submatrix_apply, Prod.swap_prod_mk, blockDiagonal_apply, of_apply,
cons_val... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 607,
"column": 4
} | {
"line": 620,
"column": 27
} | {
"line": 622,
"column": 0
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nx : (K →+* ℂ) → ℂ\nhx : ∀ (φ : K →+* ℂ), (starRingEnd ℂ) (x φ) = x (ComplexEmbedding.conjugate φ)\nc : { w // w.IsComplex } × Fin 2\n⊢ ↑(((stdBasis K).repr (fun w ↦ (x (↑w).embedding).re, fun w ↦ x (↑w).embedding)) (Sum.inr c)) =\n ∑ x... | [] | rcases c with ⟨w, j⟩
fin_cases j
· simp only [Fin.zero_eta, Fin.isValue, stdBasis_apply_isComplex_fst, re_eq_add_conj,
mul_neg, fromBlocks_apply₂₁, Matrix.zero_apply, zero_mul, sum_const_zero,
fromBlocks_apply₂₂, submatrix_apply, Prod.swap_prod_mk, blockDiagonal_apply, of_apply,
cons_val... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 621,
"column": 14
} | {
"line": 621,
"column": 25
} | {
"line": 621,
"column": 26
} | [
{
"pp": "case inr\nK : 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\nhr : (mk (w.embedding.comp (algebraMap K L))).embedding = conjugate (w.embedding.comp (algebraMap K L))\n⊢ w.embedding.comp (algebraMap K L) = ... | [
"case inr\nK : 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\nhr : (mk (w.embedding.comp (algebraMap K L))).embedding = conjugate (w.embedding.comp (algebraMap K L))\n⊢ w.embedding.comp (algebraMap K L) = v.embedding ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 643,
"column": 12
} | {
"line": 643,
"column": 57
} | {
"line": 643,
"column": 58
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\n⊢ Function.Injective fun r ↦ r • 1",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceRealComplex",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\n⊢ Function.Injective fun r ↦ ↑r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 645,
"column": 8
} | {
"line": 645,
"column": 43
} | {
"line": 645,
"column": 44
} | [
{
"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 : IsUnramified K w\nhv : v.IsReal\n⊢ ¬(w.comap (algebraMap K L)).IsComplex",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
... | [
"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 : IsUnramified K w\nhv : v.IsReal\n⊢ v.IsReal"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 709,
"column": 20
} | {
"line": 709,
"column": 31
} | {
"line": 709,
"column": 32
} | [
{
"pp": "case inl\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nψ : L →+* ℂ\nh : ψ ∈ mixedEmbeddingsOver L v.embedding\nhl : (mk ψ).embedding = ψ\n⊢ ψ ∈ Sum.elim embedding (conjugate ∘ embedding) '' Set.sumEquiv.symm (ramifiedPlacesOver L v, ramifiedP... | [
"case inl\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nψ : L →+* ℂ\nh : ψ ∈ mixedEmbeddingsOver L v.embedding\nhl : (mk ψ).embedding = ψ\n⊢ (∃ a ∈ ramifiedPlacesOver L v, a.embedding = ψ) ∨ ∃ b ∈ ramifiedPlacesOver L v, conjugate b.embedding = ψ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 710,
"column": 20
} | {
"line": 710,
"column": 31
} | {
"line": 710,
"column": 32
} | [
{
"pp": "case inr\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nψ : L →+* ℂ\nh : ψ ∈ mixedEmbeddingsOver L v.embedding\nhr : (mk ψ).embedding = conjugate ψ\n⊢ ψ ∈ Sum.elim embedding (conjugate ∘ embedding) '' Set.sumEquiv.symm (ramifiedPlacesOver L v,... | [
"case inr\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nψ : L →+* ℂ\nh : ψ ∈ mixedEmbeddingsOver L v.embedding\nhr : (mk ψ).embedding = conjugate ψ\n⊢ (∃ a ∈ ramifiedPlacesOver L v, a.embedding = ψ) ∨ ∃ b ∈ ramifiedPlacesOver L v, conjugate b.embedding = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 740,
"column": 4
} | {
"line": 740,
"column": 45
} | {
"line": 740,
"column": 46
} | [
{
"pp": "case pos\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nw : InfinitePlace L\nleft✝ : w.LiesOver v\nhw : IsUnramified K w\nh : ComplexEmbedding.LiesOver w.embedding v.embedding\n⊢ v.embeddingConjugateIte w ∈ unmixedEmbeddingsOver L v.embedding"... | [
"case pos\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nw : InfinitePlace L\nleft✝ : w.LiesOver v\nhw : IsUnramified K w\nh : ComplexEmbedding.LiesOver w.embedding v.embedding\n⊢ w.embedding ∈ unmixedEmbeddingsOver L v.embedding"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 741,
"column": 4
} | {
"line": 741,
"column": 45
} | {
"line": 742,
"column": 6
} | [
{
"pp": "case neg\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nw : InfinitePlace L\nleft✝ : w.LiesOver v\nhw : IsUnramified K w\nh : ¬ComplexEmbedding.LiesOver w.embedding v.embedding\n⊢ v.embeddingConjugateIte w ∈ unmixedEmbeddingsOver L v.embedding... | [
"case neg\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nw : InfinitePlace L\nleft✝ : w.LiesOver v\nhw : IsUnramified K w\nh : ¬ComplexEmbedding.LiesOver w.embedding v.embedding\n⊢ conjugate w.embedding ∈ unmixedEmbeddingsOver L v.embedding"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | {
"line": 562,
"column": 23
} | {
"line": 562,
"column": 57
} | {
"line": 562,
"column": 57
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw₀ : InfinitePlace K\nhw₀ : w₀.IsComplex\nB : ℝ≥0\nhB : minkowskiBound K 1 < ↑(convexBodyLT'Factor K) * ↑B\nthis : minkowskiBound K 1 < volume (convexBodyLT' K (fun w ↦ if w = w₀ then NNReal.sqrt B else 1) ⟨w₀, hw₀⟩)\na : 𝓞 K\nh_nz : a ≠ 0\nh_le :... | [] | convert! if_neg h_ne ▸ h_le w h_ne | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | {
"line": 562,
"column": 23
} | {
"line": 562,
"column": 57
} | {
"line": 562,
"column": 57
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw₀ : InfinitePlace K\nhw₀ : w₀.IsComplex\nB : ℝ≥0\nhB : minkowskiBound K 1 < ↑(convexBodyLT'Factor K) * ↑B\nthis : minkowskiBound K 1 < volume (convexBodyLT' K (fun w ↦ if w = w₀ then NNReal.sqrt B else 1) ⟨w₀, hw₀⟩)\na : 𝓞 K\nh_nz : a ≠ 0\nh_le :... | [] | convert! if_neg h_ne ▸ h_le w h_ne | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | {
"line": 562,
"column": 23
} | {
"line": 562,
"column": 57
} | {
"line": 562,
"column": 57
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw₀ : InfinitePlace K\nhw₀ : w₀.IsComplex\nB : ℝ≥0\nhB : minkowskiBound K 1 < ↑(convexBodyLT'Factor K) * ↑B\nthis : minkowskiBound K 1 < volume (convexBodyLT' K (fun w ↦ if w = w₀ then NNReal.sqrt B else 1) ⟨w₀, hw₀⟩)\na : 𝓞 K\nh_nz : a ≠ 0\nh_le :... | [] | convert! if_neg h_ne ▸ h_le w h_ne | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 750,
"column": 4
} | {
"line": 750,
"column": 43
} | {
"line": 750,
"column": 44
} | [
{
"pp": "case inr\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nψ : L →+* ℂ\nh : ψ ∈ unmixedEmbeddingsOver L v.embedding\nhψ : (mk ψ).embedding = conjugate ψ\n⊢ v.embeddingConjugateIte (mk ψ) = ψ",
"ppTerm": "?inr",
"assigned": true,
"used... | [
"case inr\nK : Type u_4\nL : Type u_5\ninst✝² : Field K\ninst✝¹ : Field L\ninst✝ : Algebra K L\nv : InfinitePlace K\nψ : L →+* ℂ\nh : ψ ∈ unmixedEmbeddingsOver L v.embedding\nhψ : (mk ψ).embedding = conjugate ψ\n⊢ ComplexEmbedding.LiesOver (conjugate ψ) v.embedding → conjugate ψ = ψ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | {
"line": 776,
"column": 50
} | {
"line": 776,
"column": 61
} | {
"line": 776,
"column": 62
} | [
{
"pp": "K : Type u_4\nL : Type u_5\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Algebra K L\nv : InfinitePlace K\ninst✝¹ : NumberField K\ninst✝ : NumberField L\nthis : Algebra K ℂ := v.embedding.toAlgebra\nσ : L →ₐ[K] ℂ\nx✝ : σ ∈ ↑univ\n⊢ σ.toRingHom ∈ ↑⋯.toFinset",
"ppTerm": "?m.122",
"assigned": tru... | [
"K : Type u_4\nL : Type u_5\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Algebra K L\nv : InfinitePlace K\ninst✝¹ : NumberField K\ninst✝ : NumberField L\nthis : Algebra K ℂ := v.embedding.toAlgebra\nσ : L →ₐ[K] ℂ\nx✝ : σ ∈ ↑univ\n⊢ ComplexEmbedding.LiesOver (↑σ) v.embedding"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 877,
"column": 2
} | {
"line": 877,
"column": 36
} | {
"line": 878,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\n⊢ IsZLattice ℝ (euclidean.integerLattice K)",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceRealComplex",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\n⊢ IsZLattice ℝ (ZLattice.comap ℝ (mixedEmbedding.integerLattice K) ↑↑(toMixed K))"
] | simp_rw [euclidean.integerLattice] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | {
"line": 603,
"column": 20
} | {
"line": 603,
"column": 31
} | {
"line": 603,
"column": 32
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nI : (FractionalIdeal (𝓞 K)⁰ K)ˣ\nB : ℝ\nh : minkowskiBound K I ≤ volume (convexBodySum K B)\nhB : 0 ≤ B\nh1 : 0 < (↑(finrank ℚ K))⁻¹\nh2 : 0 ≤ B / ↑(finrank ℚ K)\nh_fund :\n IsAddFundamentalDomain (↥(span ℤ (Set.range ⇑(fractionalIdealLatticeBasi... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nI : (FractionalIdeal (𝓞 K)⁰ K)ˣ\nB : ℝ\nh : minkowskiBound K I ≤ volume (convexBodySum K B)\nhB : 0 ≤ B\nh1 : 0 < (↑(finrank ℚ K))⁻¹\nh2 : 0 ≤ B / ↑(finrank ℚ K)\nh_fund :\n IsAddFundamentalDomain (↥(span ℤ (Set.range ⇑(fractionalIdealLatticeBasis K I))).toA... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.IntegralClosure.IntegralRestrict | {
"line": 96,
"column": 4
} | {
"line": 98,
"column": 45
} | {
"line": 98,
"column": 46
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u_3\nL₂ : Type u_4\nL₃ : Type u_5\nB : Type u_6\nB₂ : Type u_7\nB₃ : Type u_8\ninst✝³¹ : CommRing A\ninst✝³⁰ : CommRing B\ninst✝²⁹ : CommRing B₂\ninst✝²⁸ : CommRing B₃\ninst✝²⁷ : Algebra A B\ninst✝²⁶ : Algebra A B₂\ninst✝²⁵ : Algebra A B₃\ninst✝²⁴ : Field K\ninst✝²³... | [
"A : Type u_1\nK : Type u_2\nL : Type u_3\nL₂ : Type u_4\nL₃ : Type u_5\nB : Type u_6\nB₂ : Type u_7\nB₃ : Type u_8\ninst✝³¹ : CommRing A\ninst✝³⁰ : CommRing B\ninst✝²⁹ : CommRing B₂\ninst✝²⁸ : CommRing B₃\ninst✝²⁷ : Algebra A B\ninst✝²⁶ : Algebra A B₂\ninst✝²⁵ : Algebra A B₃\ninst✝²⁴ : Field K\ninst✝²³ : Field L\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Invariant.Galois | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 17
} | {
"line": 53,
"column": 4
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u_3\nB : Type u_4\ninst✝¹⁵ : CommRing A\ninst✝¹⁴ : CommRing B\ninst✝¹³ : Field K\ninst✝¹² : Field L\ninst✝¹¹ : Algebra A K\ninst✝¹⁰ : Algebra B L\ninst✝⁹ : IsFractionRing A K\ninst✝⁸ : IsFractionRing B L\ninst✝⁷ : Algebra A B\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra ... | [
"A : Type u_1\nK : Type u_2\nL : Type u_3\nB : Type u_4\ninst✝¹⁵ : CommRing A\ninst✝¹⁴ : CommRing B\ninst✝¹³ : Field K\ninst✝¹² : Field L\ninst✝¹¹ : Algebra A K\ninst✝¹⁰ : Algebra B L\ninst✝⁹ : IsFractionRing A K\ninst✝⁸ : IsFractionRing B L\ninst✝⁷ : Algebra A B\ninst✝⁶ : Algebra K L\ninst✝⁵ : Algebra A L\ninst✝⁴ ... | rintro ⟨g, -⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.RingTheory.IntegralClosure.IntegralRestrict | {
"line": 388,
"column": 27
} | {
"line": 388,
"column": 38
} | {
"line": 388,
"column": 39
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u_3\nL₂ : Type u_4\nL₃ : Type u_5\nB : Type u_6\nB₂ : Type u_7\nB₃ : Type u_8\ninst✝⁴² : CommRing A\ninst✝⁴¹ : CommRing B\ninst✝⁴⁰ : CommRing B₂\ninst✝³⁹ : CommRing B₃\ninst✝³⁸ : Algebra A B\ninst✝³⁷ : Algebra A B₂\ninst✝³⁶ : Algebra A B₃\ninst✝³⁵ : Field K\ninst✝³⁴... | [
"A : Type u_1\nK : Type u_2\nL : Type u_3\nL₂ : Type u_4\nL₃ : Type u_5\nB : Type u_6\nB₂ : Type u_7\nB₃ : Type u_8\ninst✝⁴² : CommRing A\ninst✝⁴¹ : CommRing B\ninst✝⁴⁰ : CommRing B₂\ninst✝³⁹ : CommRing B₃\ninst✝³⁸ : Algebra A B\ninst✝³⁷ : Algebra A B₂\ninst✝³⁶ : Algebra A B₃\ninst✝³⁵ : Field K\ninst✝³⁴ : Field L\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 1116,
"column": 2
} | {
"line": 1116,
"column": 17
} | {
"line": 1116,
"column": 18
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw : InfinitePlace K\nA : AffineSubspace ℝ (realSpace K) := ↑{ carrier := {x | x w = 0}, add_mem' := ⋯, zero_mem' := ⋯, smul_mem' := ⋯ }\nh : A = ⊤\n⊢ False",
"ppTerm": "?m.57",
"assigned": false,
"usedConstants": [],
"usedFVars": []... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nw : InfinitePlace K\nA : AffineSubspace ℝ (realSpace K) := ↑{ carrier := {x | x w = 0}, add_mem' := ⋯, zero_mem' := ⋯, smul_mem' := ⋯ }\nh : A = ⊤\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 1160,
"column": 41
} | {
"line": 1162,
"column": 35
} | {
"line": 1164,
"column": 0
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nx : mixedSpace K\nw : { w // w.IsComplex }\n⊢ normAtComplexPlaces x ↑w = ‖x.2 w‖",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Norm.norm",
"Eq.mpr",
"Real",
"congrArg",
"NumberField.InfinitePlace.IsCo... | [] | by
rw [normAtComplexPlaces, dif_neg (not_isReal_iff_isComplex.mpr w.prop),
normAtPlace_apply_of_isComplex] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 1219,
"column": 4
} | {
"line": 1220,
"column": 53
} | {
"line": 1220,
"column": 54
} | [
{
"pp": "case inl\nK : Type u_1\ninst✝ : Field K\nx y : mixedSpace K\nh : normAtComplexPlaces x = normAtComplexPlaces y\nw : InfinitePlace K\nhw : w.IsReal\n⊢ normAtAllPlaces x w = normAtAllPlaces y w",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"Real.... | [
"case inl\nK : Type u_1\ninst✝ : Field K\nx y : mixedSpace K\nh : normAtComplexPlaces x = normAtComplexPlaces y\nw : InfinitePlace K\nhw : w.IsReal\n⊢ |x.1 ⟨w, hw⟩| = |y.1 ⟨w, hw⟩|"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | {
"line": 1221,
"column": 4
} | {
"line": 1222,
"column": 56
} | {
"line": 1222,
"column": 57
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝ : Field K\nx y : mixedSpace K\nh : normAtComplexPlaces x = normAtComplexPlaces y\nw : InfinitePlace K\nhw : w.IsComplex\n⊢ normAtAllPlaces x w = normAtAllPlaces y w",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Eq.mpr",
... | [
"case inr\nK : Type u_1\ninst✝ : Field K\nx y : mixedSpace K\nh : normAtComplexPlaces x = normAtComplexPlaces y\nw : InfinitePlace K\nhw : w.IsComplex\n⊢ ‖x.2 ⟨w, hw⟩‖ = ‖y.2 ⟨w, hw⟩‖"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Invariant.Galois | {
"line": 111,
"column": 67
} | {
"line": 111,
"column": 78
} | {
"line": 111,
"column": 79
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹⁹ : CommRing A\ninst✝¹⁸ : CommRing B\ninst✝¹⁷ : Algebra A B\nG : Type u_3\ninst✝¹⁶ : Finite G\ninst✝¹⁵ : Group G\ninst✝¹⁴ : MulSemiringAction G B\ninst✝¹³ : Algebra.IsInvariant A B G\nP : Ideal A\nQ : Ideal B\ninst✝¹² : Q.LiesOver P\ninst✝¹¹ : P.IsPrime\ninst✝¹⁰ : Q.Is... | [
"A : Type u_1\nB : Type u_2\ninst✝¹⁹ : CommRing A\ninst✝¹⁸ : CommRing B\ninst✝¹⁷ : Algebra A B\nG : Type u_3\ninst✝¹⁶ : Finite G\ninst✝¹⁵ : Group G\ninst✝¹⁴ : MulSemiringAction G B\ninst✝¹³ : Algebra.IsInvariant A B G\nP : Ideal A\nQ : Ideal B\ninst✝¹² : Q.LiesOver P\ninst✝¹¹ : P.IsPrime\ninst✝¹⁰ : Q.IsPrime\nK : T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RamificationInertia.Galois | {
"line": 101,
"column": 20
} | {
"line": 105,
"column": 100
} | {
"line": 107,
"column": 0
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹⁶ : CommRing A\ninst✝¹⁵ : CommRing B\ninst✝¹⁴ : Algebra A B\np : Ideal A\nG : Type u_3\ninst✝¹³ : Group G\ninst✝¹² : MulSemiringAction G B\ninst✝¹¹ : SMulCommClass G A B\nK : Type u_4\nL : Type u_5\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : Algebra A K\ninst✝⁷ : Is... | [] | by
apply Subtype.val_inj.mp
change map _ Q.1 = map _ (map _ Q.1)
rw [map_mul]
exact (Q.1.map_map ((galRestrict A K L B) τ).toRingHom ((galRestrict A K L B) σ).toRingHom).symm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Invariant.Galois | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 47
} | {
"line": 117,
"column": 2
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹⁹ : CommRing A\ninst✝¹⁸ : CommRing B\ninst✝¹⁷ : Algebra A B\nG : Type u_3\ninst✝¹⁶ : Finite G\ninst✝¹⁵ : Group G\ninst✝¹⁴ : MulSemiringAction G B\ninst✝¹³ : Algebra.IsInvariant A B G\nP : Ideal A\nQ : Ideal B\ninst✝¹² : Q.LiesOver P\ninst✝¹¹ : P.IsPrime\ninst✝¹⁰ : Q.Is... | [] | exact MulSemiringAction.splits_charpoly G b | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.RamificationInertia.Galois | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 69
} | {
"line": 251,
"column": 70
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝²¹ : CommRing A\ninst✝²⁰ : CommRing B\ninst✝¹⁹ : Algebra A B\ninst✝¹⁸ : FaithfulSMul A B\np : Ideal A\nP : Ideal B\ninst✝¹⁷ : P.IsPrime\ninst✝¹⁶ : P.LiesOver p\nG : Type u_3\ninst✝¹⁵ : Group G\ninst✝¹⁴ : Finite G\ninst✝¹³ : MulSemiringAction G B\ninst✝¹² : IsGaloisGroup... | [
"A : Type u_1\nB : Type u_2\ninst✝²¹ : CommRing A\ninst✝²⁰ : CommRing B\ninst✝¹⁹ : Algebra A B\ninst✝¹⁸ : FaithfulSMul A B\np : Ideal A\nP : Ideal B\ninst✝¹⁷ : P.IsPrime\ninst✝¹⁶ : P.LiesOver p\nG : Type u_3\ninst✝¹⁵ : Group G\ninst✝¹⁴ : Finite G\ninst✝¹³ : MulSemiringAction G B\ninst✝¹² : IsGaloisGroup G A B\nC : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RamificationInertia.Galois | {
"line": 265,
"column": 41
} | {
"line": 265,
"column": 72
} | {
"line": 265,
"column": 73
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝¹⁹ : CommRing A\ninst✝¹⁸ : CommRing B\ninst✝¹⁷ : Algebra A B\ninst✝¹⁶ : FaithfulSMul A B\np : Ideal A\nP : Ideal B\ninst✝¹⁵ : P.IsPrime\ninst✝¹⁴ : P.LiesOver p\nG : Type u_3\ninst✝¹³ : Group G\ninst✝¹² : Finite G\ninst✝¹¹ : MulSemiringAction G B\ninst✝¹⁰ : IsGaloisGroup... | [
"A : Type u_1\nB : Type u_2\ninst✝¹⁹ : CommRing A\ninst✝¹⁸ : CommRing B\ninst✝¹⁷ : Algebra A B\ninst✝¹⁶ : FaithfulSMul A B\np : Ideal A\nP : Ideal B\ninst✝¹⁵ : P.IsPrime\ninst✝¹⁴ : P.LiesOver p\nG : Type u_3\ninst✝¹³ : Group G\ninst✝¹² : Finite G\ninst✝¹¹ : MulSemiringAction G B\ninst✝¹⁰ : IsGaloisGroup G A B\nC : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.ClassNumber | {
"line": 86,
"column": 8
} | {
"line": 86,
"column": 13
} | {
"line": 86,
"column": 14
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nC : ClassGroup (𝓞 K)\nJ : ↥(Ideal (𝓞 K))⁰\nhJ : ClassGroup.mk0 J = C⁻¹\na : 𝓞 K\nha : a ∈ ↑↑J\nh_nm :\n ↑|(Algebra.norm ℚ) ((Algebra.linearMap (𝓞 K) K) a)| ≤\n ↑(FractionalIdeal.absNorm ↑((FractionalIdeal.mk0 K) J)) * (4 / π) ^ nrComplexPla... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nC : ClassGroup (𝓞 K)\nJ : ↥(Ideal (𝓞 K))⁰\nhJ : ClassGroup.mk0 J = C⁻¹\na : 𝓞 K\nha : a ∈ ↑↑J\nh_nm :\n ↑|(Algebra.norm ℚ) ((Algebra.linearMap (𝓞 K) K) a)| ≤\n ↑(FractionalIdeal.absNorm ↑((FractionalIdeal.mk0 K) J)) * (4 / π) ^ nrComplexPlaces K * ↑(fi... | h_nz, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 424,
"column": 12
} | {
"line": 424,
"column": 64
} | {
"line": 424,
"column": 65
} | [
{
"pp": "case refine_2.refine_1\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 | ... | [
"case refine_2.refine_1\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.IsRea... | minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Ideal.Quotient.HasFiniteQuotients | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 42
} | {
"line": 87,
"column": 43
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : HasFiniteQuotients R\nx : R\nhx : x ≠ 0\nthis✝ : Finite (R ⧸ Ideal.span {x})\nthis : {I | Ideal.comap (Ideal.Quotient.mk (Ideal.span {x})) ⊥ ≤ I}.Finite\n⊢ {I | x ∈ I}.Finite",
"ppTerm": "?m.67",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : HasFiniteQuotients R\nx : R\nhx : x ≠ 0\nthis✝ : Finite (R ⧸ Ideal.span {x})\nthis : {I | Ideal.comap (Ideal.Quotient.mk (Ideal.span {x})) ⊥ ≤ I}.Finite\n⊢ {I | x ∈ I}.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RamificationInertia.Galois | {
"line": 314,
"column": 2
} | {
"line": 314,
"column": 13
} | {
"line": 314,
"column": 14
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nG : Type u_3\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : Algebra R S\ninst✝⁷ : Group G\ninst✝⁶ : MulSemiringAction G S\ninst✝⁵ : IsGaloisGroup G R S\ninst✝⁴ : Finite G\np : Ideal R\ninst✝³ : p.IsPrime\nP : Ideal S\ninst✝² : P.LiesOver p\ninst✝¹ : P.IsPrime\ninst✝ : ... | [
"R : Type u_1\nS : Type u_2\nG : Type u_3\ninst✝¹⁰ : CommRing R\ninst✝⁹ : CommRing S\ninst✝⁸ : Algebra R S\ninst✝⁷ : Group G\ninst✝⁶ : MulSemiringAction G S\ninst✝⁵ : IsGaloisGroup G R S\ninst✝⁴ : Finite G\np : Ideal R\ninst✝³ : p.IsPrime\nP : Ideal S\ninst✝² : P.LiesOver p\ninst✝¹ : P.IsPrime\ninst✝ : PerfectField... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 424,
"column": 8
} | {
"line": 425,
"column": 59
} | {
"line": 426,
"column": 6
} | [
{
"pp": "case refine_2.refine_1\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 | ... | [] | rw [minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, coeff_map, eq_intCast,
Int.norm_cast_rat, Int.norm_eq_abs, Int.cast_abs] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 424,
"column": 8
} | {
"line": 425,
"column": 59
} | {
"line": 426,
"column": 6
} | [
{
"pp": "case refine_2.refine_1\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 | ... | [] | rw [minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, coeff_map, eq_intCast,
Int.norm_cast_rat, Int.norm_eq_abs, Int.cast_abs] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 424,
"column": 8
} | {
"line": 425,
"column": 59
} | {
"line": 426,
"column": 6
} | [
{
"pp": "case refine_2.refine_1\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 | ... | [] | rw [minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, coeff_map, eq_intCast,
Int.norm_cast_rat, Int.norm_eq_abs, Int.cast_abs] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.NumberField.ClassNumber | {
"line": 114,
"column": 2
} | {
"line": 114,
"column": 43
} | {
"line": 114,
"column": 44
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh :\n ∀ ⦃I : ↥(Ideal (𝓞 K))⁰⦄,\n ↑(absNorm ↑I) ≤ (4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|) →\n Submodule.IsPrincipal ↑I\nI : ↥(Ideal (𝓞 K))⁰\nhI : ↑(absNorm ↑I) ≤ (4 / π) ^ nrComplexPl... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh :\n ∀ ⦃I : ↥(Ideal (𝓞 K))⁰⦄,\n ↑(absNorm ↑I) ≤ (4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|) →\n Submodule.IsPrincipal ↑I\nI : ↥(Ideal (𝓞 K))⁰\nhI : ↑(absNorm ↑I) ≤ (4 / π) ^ nrComplexPlaces K * (↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Quotient.HasFiniteQuotients | {
"line": 167,
"column": 27
} | {
"line": 167,
"column": 38
} | {
"line": 167,
"column": 39
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nn : ℤ\nhI : ℤ ∙ n ≠ ⊥\n⊢ n ≠ 0",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"id",
"Ne",
"Int",
"Zero.toOfNat0",
"OfNat.ofNat",
"MulZeroClass.toZero",
"Int.instSemiring",
"instMulZeroClassOfSemirin... | [
"R : Type u_1\ninst✝ : CommRing R\nn : ℤ\nhI : ℤ ∙ n ≠ ⊥\n⊢ ¬n = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.ClassNumber | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 68
} | {
"line": 157,
"column": 69
} | [
{
"pp": "case inl\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh✝ :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / ... | [
"case inl\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh✝ :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / π) ^ nrCompl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.ClassNumber | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 68
} | {
"line": 157,
"column": 69
} | [
{
"pp": "case inr\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh✝ :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / ... | [
"case inr\nK : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh✝ :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / π) ^ nrCompl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.ClassNumber | {
"line": 162,
"column": 43
} | {
"line": 162,
"column": 54
} | {
"line": 162,
"column": 55
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / π) ^ nrComp... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / π) ^ nrComplexPlaces K ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.ClassNumber | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 69
} | {
"line": 164,
"column": 70
} | [
{
"pp": "K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / π) ^ nrComp... | [
"K : Type u_1\ninst✝¹ : Field K\ninst✝ : NumberField K\nh :\n ∀ p ∈ Finset.Icc 1 ⌊(4 / π) ^ nrComplexPlaces K * (↑(finrank ℚ K)! / ↑(finrank ℚ K) ^ finrank ℚ K * √|↑(discr K)|)⌋₊,\n Nat.Prime p →\n ∀ P ∈ (span {↑p}).primesOver (𝓞 K),\n p ^ P.inertiaDeg ℤ ≤\n ⌊(4 / π) ^ nrComplexPlaces K ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RamificationInertia.Unramified | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 38
} | {
"line": 105,
"column": 39
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\ninst✝⁴ : IsDomain R\ninst✝³ : IsDomain S\ninst✝² : Module.IsTorsionFree R S\ninst✝¹ : CharZero R\ninst✝ : Algebra.IsIntegral R S\n⊢ IsFractionRing S (Localization.AtPrime ⊥)",
"ppTerm": "?m.37",
"assigne... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\ninst✝⁴ : IsDomain R\ninst✝³ : IsDomain S\ninst✝² : Module.IsTorsionFree R S\ninst✝¹ : CharZero R\ninst✝ : Algebra.IsIntegral R S\n⊢ IsFractionRing S (Localization.AtPrime ⊥)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.RamificationInertia.Unramified | {
"line": 122,
"column": 2
} | {
"line": 122,
"column": 48
} | {
"line": 122,
"column": 49
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\ninst✝⁴ : IsDomain R\ninst✝³ : IsDomain S\ninst✝² : FaithfulSMul R S\ninst✝¹ : CharZero R\ninst✝ : Algebra.IsIntegral R S\nP : Ideal S\nx✝ : P.IsPrime\nhP : P.LiesOver ⊥\n⊢ IsUnramifiedAt R P",
"ppTerm": "?m.... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\ninst✝⁴ : IsDomain R\ninst✝³ : IsDomain S\ninst✝² : FaithfulSMul R S\ninst✝¹ : CharZero R\ninst✝ : Algebra.IsIntegral R S\nP : Ideal S\nx✝ : P.IsPrime\nhP : P.LiesOver ⊥\n⊢ IsUnramifiedAt R ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FractionalIdeal.Extended | {
"line": 94,
"column": 46
} | {
"line": 94,
"column": 78
} | {
"line": 94,
"column": 79
} | [
{
"pp": "A : Type u_1\ninst✝⁸ : CommRing A\nB : Type u_2\ninst✝⁷ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁶ : CommRing K\ninst✝⁵ : Algebra A K\ninst✝⁴ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝³ : CommRing L\ninst✝² : Algebra B L\ninst✝¹ : IsLocalization N L\nhf : M ≤ Submo... | [
"A : Type u_1\ninst✝⁸ : CommRing A\nB : Type u_2\ninst✝⁷ : CommRing B\nf : A →+* B\nK : Type u_3\nM : Submonoid A\ninst✝⁶ : CommRing K\ninst✝⁵ : Algebra A K\ninst✝⁴ : IsLocalization M K\nL : Type u_4\nN : Submonoid B\ninst✝³ : CommRing L\ninst✝² : Algebra B L\ninst✝¹ : IsLocalization N L\nhf : M ≤ Submonoid.comap f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.FractionalIdeal.Extended | {
"line": 113,
"column": 45
} | {
"line": 113,
"column": 56
} | {
"line": 113,
"column": 57
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 473,
"column": 12
} | {
"line": 473,
"column": 64
} | {
"line": 473,
"column": 65
} | [
{
"pp": "case refine_2.refine_1\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✝ :... | [
"case refine_2.refine_1\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⟩ ∈ ... | minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 473,
"column": 8
} | {
"line": 474,
"column": 59
} | {
"line": 475,
"column": 6
} | [
{
"pp": "case refine_2.refine_1\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✝ :... | [] | rw [minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, coeff_map, eq_intCast,
Int.norm_cast_rat, Int.norm_eq_abs, Int.cast_abs] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 473,
"column": 8
} | {
"line": 474,
"column": 59
} | {
"line": 475,
"column": 6
} | [
{
"pp": "case refine_2.refine_1\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✝ :... | [] | rw [minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, coeff_map, eq_intCast,
Int.norm_cast_rat, Int.norm_eq_abs, Int.cast_abs] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.NumberField.Discriminant.Basic | {
"line": 473,
"column": 8
} | {
"line": 474,
"column": 59
} | {
"line": 475,
"column": 6
} | [
{
"pp": "case refine_2.refine_1\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✝ :... | [] | rw [minpoly.isIntegrallyClosed_eq_field_fractions' ℚ hx, coeff_map, eq_intCast,
Int.norm_cast_rat, Int.norm_eq_abs, Int.cast_abs] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Ideal.Int | {
"line": 99,
"column": 47
} | {
"line": 99,
"column": 58
} | {
"line": 99,
"column": 59
} | [
{
"pp": "S : Type u_2\ninst✝² : CommRing S\ninst✝¹ : IsDedekindDomain S\ninst✝ : Module.Free ℤ S\nI : Ideal S\nh✝ : Finite (S ⧸ I)\nthis : Fintype (S ⧸ I)\nd : ℕ\nh : ∀ (x : S ⧸ I), (Ideal.Quotient.mk I) ↑d * x = 0\n⊢ (Ideal.Quotient.mk I) ↑d = 0",
"ppTerm": "?m.93",
"assigned": true,
"usedConstants... | [
"S : Type u_2\ninst✝² : CommRing S\ninst✝¹ : IsDedekindDomain S\ninst✝ : Module.Free ℤ S\nI : Ideal S\nh✝ : Finite (S ⧸ I)\nthis : Fintype (S ⧸ I)\nd : ℕ\nh : ∀ (x : S ⧸ I), (Ideal.Quotient.mk I) ↑d * x = 0\n⊢ ↑d = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Int | {
"line": 110,
"column": 6
} | {
"line": 110,
"column": 31
} | {
"line": 110,
"column": 32
} | [
{
"pp": "S : Type u_2\ninst✝ : CommRing S\nI : Ideal S\nx : ℕ\n⊢ (Ideal.Quotient.mk I) ↑x = 0 ↔ absNorm (under ℤ I) ∣ x",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"Nat.instMulZeroOneClass",
"Submodule.Quotient.instZeroQuotient"... | [
"S : Type u_2\ninst✝ : CommRing S\nI : Ideal S\nx : ℕ\n⊢ ↑x ∈ I ↔ absNorm (under ℤ I) ∣ x"
] | Quotient.eq_zero_iff_mem, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.Instances | {
"line": 128,
"column": 21
} | {
"line": 128,
"column": 32
} | {
"line": 128,
"column": 33
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\ninst✝⁶ : CommRing T\ninst✝⁵ : IsDomain R\ninst✝⁴ : IsDomain S\ninst✝³ : IsDomain T\ninst✝² : Algebra R S\nP : Ideal R\ninst✝¹ : P.IsPrime\ninst✝ : FaithfulSMul R S\nx✝ : ↥P.primeCompl\nx : R\nhx : x ∈ P.primeCompl\n⊢ fa... | [
"R : Type u_1\nS : Type u_2\nT : Type u_3\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\ninst✝⁶ : CommRing T\ninst✝⁵ : IsDomain R\ninst✝⁴ : IsDomain S\ninst✝³ : IsDomain T\ninst✝² : Algebra R S\nP : Ideal R\ninst✝¹ : P.IsPrime\ninst✝ : FaithfulSMul R S\nx✝ : ↥P.primeCompl\nx : R\nhx : x ∈ P.primeCompl\n⊢ ¬x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 63,
"column": 67
} | {
"line": 63,
"column": 78
} | {
"line": 63,
"column": 79
} | [
{
"pp": "R : Type u_1\ninst✝⁸ : CommRing R\ninst✝⁷ : IsDomain R\nS : Type u_3\ninst✝⁶ : CommRing S\ninst✝⁵ : IsDomain S\ninst✝⁴ : IsIntegrallyClosed R\ninst✝³ : IsIntegrallyClosed S\ninst✝² : Algebra R S\ninst✝¹ : Module.Finite R S\ninst✝ : IsTorsionFree R S\nx : R\nhx : x ∈ ⇑(Algebra.intNorm R S) '' ↑⊥\n⊢ x = ... | [
"R : Type u_1\ninst✝⁸ : CommRing R\ninst✝⁷ : IsDomain R\nS : Type u_3\ninst✝⁶ : CommRing S\ninst✝⁵ : IsDomain S\ninst✝⁴ : IsIntegrallyClosed R\ninst✝³ : IsIntegrallyClosed S\ninst✝² : Algebra R S\ninst✝¹ : Module.Finite R S\ninst✝ : IsTorsionFree R S\nx : R\nhx : x ∈ ⇑(Algebra.intNorm R S) '' ↑⊥\n⊢ x = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Discriminant.Different | {
"line": 52,
"column": 10
} | {
"line": 52,
"column": 21
} | {
"line": 52,
"column": 22
} | [
{
"pp": "K : Type u_1\n𝒪 : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : NumberField K\ninst✝⁵ : CommRing 𝒪\ninst✝⁴ : Algebra 𝒪 K\ninst✝³ : IsFractionRing 𝒪 K\ninst✝² : IsDedekindDomain 𝒪\ninst✝¹ : CharZero 𝒪\ninst✝ : Module.Finite ℤ 𝒪\n⊢ ↑(differentIdeal ℤ 𝒪) ≤ 1⁻¹",
"ppTerm": "?m.147",
"assigned": true... | [
"K : Type u_1\n𝒪 : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : NumberField K\ninst✝⁵ : CommRing 𝒪\ninst✝⁴ : Algebra 𝒪 K\ninst✝³ : IsFractionRing 𝒪 K\ninst✝² : IsDedekindDomain 𝒪\ninst✝¹ : CharZero 𝒪\ninst✝ : Module.Finite ℤ 𝒪\n⊢ ↑(differentIdeal ℤ 𝒪) ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Discriminant.Different | {
"line": 61,
"column": 4
} | {
"line": 61,
"column": 45
} | {
"line": 61,
"column": 46
} | [
{
"pp": "K : Type u_1\n𝒪 : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : NumberField K\ninst✝⁵ : CommRing 𝒪\ninst✝⁴ : Algebra 𝒪 K\ninst✝³ : IsFractionRing 𝒪 K\ninst✝² : IsDedekindDomain 𝒪\ninst✝¹ : CharZero 𝒪\ninst✝ : Module.Finite ℤ 𝒪\nthis✝ :\n (↥↑1 ⧸ Submodule.comap (↑1).subtype ↑↑(differentIdeal ℤ 𝒪)) ≃ₗ[𝒪... | [
"K : Type u_1\n𝒪 : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : NumberField K\ninst✝⁵ : CommRing 𝒪\ninst✝⁴ : Algebra 𝒪 K\ninst✝³ : IsFractionRing 𝒪 K\ninst✝² : IsDedekindDomain 𝒪\ninst✝¹ : CharZero 𝒪\ninst✝ : Module.Finite ℤ 𝒪\nthis✝ :\n (↥↑1 ⧸ Submodule.comap (↑1).subtype ↑↑(differentIdeal ℤ 𝒪)) ≃ₗ[𝒪]\n ↥↑(↑(... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Discriminant.Different | {
"line": 70,
"column": 4
} | {
"line": 70,
"column": 98
} | {
"line": 71,
"column": 4
} | [
{
"pp": "case refine_3\nK : Type u_1\n𝒪 : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : NumberField K\ninst✝⁵ : CommRing 𝒪\ninst✝⁴ : Algebra 𝒪 K\ninst✝³ : IsFractionRing 𝒪 K\ninst✝² : IsDedekindDomain 𝒪\ninst✝¹ : CharZero 𝒪\ninst✝ : Module.Finite ℤ 𝒪\nthis✝ :\n (↥↑1 ⧸ Submodule.comap (↑1).subtype ↑↑(differentIde... | [
"case refine_3\nK : Type u_1\n𝒪 : Type u_2\ninst✝⁷ : Field K\ninst✝⁶ : NumberField K\ninst✝⁵ : CommRing 𝒪\ninst✝⁴ : Algebra 𝒪 K\ninst✝³ : IsFractionRing 𝒪 K\ninst✝² : IsDedekindDomain 𝒪\ninst✝¹ : CharZero 𝒪\ninst✝ : Module.Finite ℤ 𝒪\nthis✝ :\n (↥↑1 ⧸ Submodule.comap (↑1).subtype ↑↑(differentIdeal ℤ 𝒪)) ≃ₗ... | rw [AddSubgroup.toIntSubmodule_closure, ← LinearMap.BilinForm.dualSubmodule_span_of_basis, hb] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 285,
"column": 2
} | {
"line": 285,
"column": 32
} | {
"line": 285,
"column": 33
} | [
{
"pp": "R : Type u_1\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : IsDomain S\ninst✝⁶ : IsIntegrallyClosed R\ninst✝⁵ : IsIntegrallyClosed S\ninst✝⁴ : Algebra R S\ninst✝³ : Module.Finite R S\ninst✝² : IsTorsionFree R S\ninst✝¹ : IsDedekindDomain R\ninst✝ : IsDedekindDom... | [
"R : Type u_1\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : IsDomain S\ninst✝⁶ : IsIntegrallyClosed R\ninst✝⁵ : IsIntegrallyClosed S\ninst✝⁴ : Algebra R S\ninst✝³ : Module.Finite R S\ninst✝² : IsTorsionFree R S\ninst✝¹ : IsDedekindDomain R\ninst✝ : IsDedekindDomain S\n⊢ (re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 289,
"column": 2
} | {
"line": 289,
"column": 31
} | {
"line": 289,
"column": 32
} | [
{
"pp": "R : Type u_1\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : IsDomain S\ninst✝⁶ : IsIntegrallyClosed R\ninst✝⁵ : IsIntegrallyClosed S\ninst✝⁴ : Algebra R S\ninst✝³ : Module.Finite R S\ninst✝² : IsTorsionFree R S\ninst✝¹ : IsDedekindDomain R\ninst✝ : IsDedekindDom... | [
"R : Type u_1\ninst✝¹⁰ : CommRing R\ninst✝⁹ : IsDomain R\nS : Type u_3\ninst✝⁸ : CommRing S\ninst✝⁷ : IsDomain S\ninst✝⁶ : IsIntegrallyClosed R\ninst✝⁵ : IsIntegrallyClosed S\ninst✝⁴ : Algebra R S\ninst✝³ : Module.Finite R S\ninst✝² : IsTorsionFree R S\ninst✝¹ : IsDedekindDomain R\ninst✝ : IsDedekindDomain S\n⊢ (re... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Ideal.Norm.RelNorm | {
"line": 388,
"column": 2
} | {
"line": 390,
"column": 75
} | {
"line": 391,
"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... | [
"case neg\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 : IsDedekindDom... | · refine ⟨1, ?_⟩
have : P.LiesOver ⊥ := hp ▸ hPp
rw [hp, eq_bot_of_liesOver_bot R P, relNorm_bot, bot_pow (one_ne_zero)] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 108,
"column": 8
} | {
"line": 108,
"column": 30
} | {
"line": 108,
"column": 31
} | [
{
"pp": "case refine_2.succ\np : ℕ\nhp : Fact (Nat.Prime p)\nn i k : ℕ\nhi : p * k < p * (p ^ n * (p - 1))\nhk : i = p * k\nhn : (Polynomial.map (Int.castRingHom (ZMod p)) ((cyclotomic (p ^ (n + 1)) ℤ).comp (X + C 1))).coeff k = 0\n⊢ ((cyclotomic (p ^ (n + 1)) (ZMod p)).comp (X + 1)).coeff k = 0",
"ppTerm":... | [
"case refine_2.succ\np : ℕ\nhp : Fact (Nat.Prime p)\nn i k : ℕ\nhi : p * k < p * (p ^ n * (p - 1))\nhk : i = p * k\nhn : (Polynomial.map (Int.castRingHom (ZMod p)) ((cyclotomic (p ^ (n + 1)) ℤ).comp (X + C 1))).coeff k = 0\n⊢ ((cyclotomic (p ^ (n + 1)) (ZMod p)).comp (X + 1)).coeff k = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Prime | {
"line": 70,
"column": 57
} | {
"line": 70,
"column": 78
} | {
"line": 70,
"column": 79
} | [
{
"pp": "α : Type u_1\ninst✝ : CommRing α\np : α\nh1 : p ≠ 0\nh2 : ¬IsUnit p\nh3 : ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b\n⊢ ∀ (a b : α), -p ∣ a * b → -p ∣ a ∨ -p ∣ b",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Semigroup.toMul",
... | [
"α : Type u_1\ninst✝ : CommRing α\np : α\nh1 : p ≠ 0\nh2 : ¬IsUnit p\nh3 : ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b\n⊢ ∀ (a b : α), p ∣ a * b → p ∣ a ∨ p ∣ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.LinearDisjoint | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 55
} | {
"line": 52,
"column": 56
} | [
{
"pp": "A : Type u_1\nB : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝³⁴ : CommRing A\ninst✝³³ : Field K\ninst✝³² : Algebra A K\ninst✝³¹ : IsFractionRing A K\ninst✝³⁰ : CommRing B\ninst✝²⁹ : Field L\ninst✝²⁸ : Algebra B L\ninst✝²⁷ : Algebra A L\ninst✝²⁶ : Algebra K L\ninst✝²⁵ : FiniteDimensional K L\ninst✝²⁴ : ... | [
"A : Type u_1\nB : Type u_2\nK : Type u_3\nL : Type u_4\ninst✝³⁴ : CommRing A\ninst✝³³ : Field K\ninst✝³² : Algebra A K\ninst✝³¹ : IsFractionRing A K\ninst✝³⁰ : CommRing B\ninst✝²⁹ : Field L\ninst✝²⁸ : Algebra B L\ninst✝²⁷ : Algebra A L\ninst✝²⁶ : Algebra K L\ninst✝²⁵ : FiniteDimensional K L\ninst✝²⁴ : IsScalarTowe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 101,
"column": 47
} | {
"line": 101,
"column": 58
} | {
"line": 101,
"column": 59
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn : ℕ\nhcycl : IsCyclotomicExtension {p ^ 0} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ 0)\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ B.gen\nthis : Fi... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn : ℕ\nhcycl : IsCyclotomicExtension {p ^ 0} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ 0)\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ B.gen\nthis : FiniteDimensio... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 122,
"column": 56
} | {
"line": 122,
"column": 67
} | {
"line": 122,
"column": 68
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn n✝ : ℕ\nhcycl : IsCyclotomicExtension {p ^ (n✝ + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (n✝ + 1))\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nx : K\nh : IsIntegral ℤ x\nu : ℤˣ\nn n✝ : ℕ\nhcycl : IsCyclotomicExtension {p ^ (n✝ + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (n✝ + 1))\nB : PowerBasis ℚ K := IsPrimitiveRoot.subOnePowerBasis ℚ hζ\nhint : IsIntegral ℤ B.gen\nthis... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 265,
"column": 4
} | {
"line": 265,
"column": 15
} | {
"line": 265,
"column": 16
} | [
{
"pp": "case refine_1\np k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\nthis : NumberField K := numberField {p ^ (k + 1)} ℚ K\nh : hζ.toInteger = 1\n⊢ ζ ^ 1 = 1",
... | [
"case refine_1\np k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\nthis : NumberField K := numberField {p ^ (k + 1)} ℚ K\nh : hζ.toInteger = 1\n⊢ ζ = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 244,
"column": 43
} | {
"line": 244,
"column": 64
} | {
"line": 244,
"column": 65
} | [
{
"pp": "R : 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 L\nhp : _r... | [
"R : 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 L\nhp : _root_.Prime p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 383,
"column": 2
} | {
"line": 383,
"column": 38
} | {
"line": 384,
"column": 4
} | [
{
"pp": "p k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\n⊢ (Algebra.norm ℤ) (hζ.toInteger - 1) = ↑p",
"ppTerm": "?m.50",
"assigned": false,
"usedConstants"... | [
"p k : ℕ\nK : Type u\ninst✝² : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\nhζ : IsPrimitiveRoot ζ (p ^ (k + 1))\nhodd : p ≠ 2\n⊢ (Algebra.norm ℤ) (hζ.toInteger - 1) = ↑p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 13
} | {
"line": 393,
"column": 14
} | [
{
"pp": "K : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2} ℚ K\nhζ✝ : IsPrimitiveRoot ζ 2\nhζ : IsPrimitiveRoot ζ (2 ^ (0 + 1))\n⊢ (Algebra.norm ℤ) (hζ✝.toInteger - 1) = -2",
"ppTerm": "?m.64",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"K : Type u\ninst✝² : Field K\nζ : K\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {2} ℚ K\nhζ✝ : IsPrimitiveRoot ζ 2\nhζ : IsPrimitiveRoot ζ (2 ^ (0 + 1))\n⊢ (Algebra.norm ℤ) (hζ✝.toInteger - 1) = -2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 399,
"column": 55
} | {
"line": 399,
"column": 66
} | {
"line": 399,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Com... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 400,
"column": 53
} | {
"line": 400,
"column": 64
} | {
"line": 400,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.86",
"assigned": true,
"used... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nh : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 427,
"column": 55
} | {
"line": 427,
"column": 66
} | {
"line": 427,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.57",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 428,
"column": 53
} | {
"line": 428,
"column": 64
} | {
"line": 428,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.87",
"assigned": true,
"u... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 121,
"column": 74
} | {
"line": 121,
"column": 87
} | {
"line": 122,
"column": 6
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTowe... | [
"case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTower A B L\nb :... | true_implies, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 125,
"column": 4
} | {
"line": 125,
"column": 21
} | {
"line": 125,
"column": 22
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTowe... | [
"case neg\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁰ : CommRing A\ninst✝⁹ : Field K\ninst✝⁸ : CommRing B\ninst✝⁷ : Field L\ninst✝⁶ : Algebra A K\ninst✝⁵ : Algebra B L\ninst✝⁴ : Algebra A B\ninst✝³ : Algebra K L\ninst✝² : Algebra A L\ninst✝¹ : IsScalarTower A K L\ninst✝ : IsScalarTower A B L\nb c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 485,
"column": 55
} | {
"line": 485,
"column": 66
} | {
"line": 485,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 486,
"column": 53
} | {
"line": 486,
"column": 64
} | {
"line": 486,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.83",
"assigned": true,
"u... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nhodd : p ≠ 2\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 501,
"column": 55
} | {
"line": 501,
"column": 66
} | {
"line": 501,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CommRing",
... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 502,
"column": 53
} | {
"line": 502,
"column": 64
} | {
"line": 502,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants":... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 194,
"column": 4
} | {
"line": 194,
"column": 29
} | {
"line": 194,
"column": 30
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : Field K\ninst✝¹⁵ : CommRing B\ninst✝¹⁴ : Field L\ninst✝¹³ : Algebra A K\ninst✝¹² : Algebra B L\ninst✝¹¹ : Algebra A B\ninst✝¹⁰ : Algebra K L\ninst✝⁹ : Algebra A L\ninst✝⁸ : IsScalarTower A K L\ninst✝⁷ : IsScalarTower ... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : Field K\ninst✝¹⁵ : CommRing B\ninst✝¹⁴ : Field L\ninst✝¹³ : Algebra A K\ninst✝¹² : Algebra B L\ninst✝¹¹ : Algebra A B\ninst✝¹⁰ : Algebra K L\ninst✝⁹ : Algebra A L\ninst✝⁸ : IsScalarTower A K L\ninst✝⁷ : IsScalarTower A B L\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 531,
"column": 55
} | {
"line": 531,
"column": 66
} | {
"line": 531,
"column": 67
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p ^ (0 + 1)} ℚ K",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CommRing",
... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\n⊢ IsCyclotomicExtension {p} ℚ K"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 532,
"column": 53
} | {
"line": 532,
"column": 64
} | {
"line": 532,
"column": 65
} | [
{
"pp": "p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ (p ^ (0 + 1))",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants":... | [
"p : ℕ\nK : Type u\ninst✝¹ : Field K\nζ : K\nhp : Fact (Nat.Prime p)\ninst✝ : CharZero K\nhcycl : IsCyclotomicExtension {p} ℚ K\nhζ : IsPrimitiveRoot ζ p\nthis : IsCyclotomicExtension {p ^ (0 + 1)} ℚ K\n⊢ IsPrimitiveRoot ζ p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Basic | {
"line": 648,
"column": 2
} | {
"line": 648,
"column": 53
} | {
"line": 648,
"column": 54
} | [
{
"pp": "p k : ℕ\nK : Type u\ninst✝² : Field K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\n⊢ NumberField.discr K = (-1) ^ (p ^ k * (p - 1) / 2) * ↑p ^ (p ^ k * ((p - 1) * (k + 1) - 1))",
"ppTerm": "?m.107",
"assigned": false,
"usedConstants": [],
... | [
"p k : ℕ\nK : Type u\ninst✝² : Field K\nhp : Fact (Nat.Prime p)\ninst✝¹ : CharZero K\ninst✝ : IsCyclotomicExtension {p ^ (k + 1)} ℚ K\n⊢ NumberField.discr K = (-1) ^ (p ^ k * (p - 1) / 2) * ↑p ^ (p ^ k * ((p - 1) * (k + 1) - 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 423,
"column": 2
} | {
"line": 423,
"column": 13
} | {
"line": 423,
"column": 14
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝³⁸ : CommRing A\ninst✝³⁷ : Field K\ninst✝³⁶ : CommRing B\ninst✝³⁵ : Field L\ninst✝³⁴ : Algebra A K\ninst✝³³ : Algebra B L\ninst✝³² : Algebra A B\ninst✝³¹ : Algebra K L\ninst✝³⁰ : Algebra A L\ninst✝²⁹ : IsScalarTower A K L\ninst✝²⁸ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝³⁸ : CommRing A\ninst✝³⁷ : Field K\ninst✝³⁶ : CommRing B\ninst✝³⁵ : Field L\ninst✝³⁴ : Algebra A K\ninst✝³³ : Algebra B L\ninst✝³² : Algebra A B\ninst✝³¹ : Algebra K L\ninst✝³⁰ : Algebra A L\ninst✝²⁹ : IsScalarTower A K L\ninst✝²⁸ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 437,
"column": 2
} | {
"line": 438,
"column": 47
} | {
"line": 438,
"column": 48
} | [
{
"pp": "case h\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝⁴⁰ : CommRing A\ninst✝³⁹ : Field K\ninst✝³⁸ : CommRing B\ninst✝³⁷ : Field L\ninst✝³⁶ : Algebra A K\ninst✝³⁵ : Algebra B L\ninst✝³⁴ : Algebra A B\ninst✝³³ : Algebra K L\ninst✝³² : Algebra A L\ninst✝³¹ : IsScalarTower A K L\ninst✝³⁰ : IsS... | [
"case h\nA : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_5\ninst✝⁴⁰ : CommRing A\ninst✝³⁹ : Field K\ninst✝³⁸ : CommRing B\ninst✝³⁷ : Field L\ninst✝³⁶ : Algebra A K\ninst✝³⁵ : Algebra B L\ninst✝³⁴ : Algebra A B\ninst✝³³ : Algebra K L\ninst✝³² : Algebra A L\ninst✝³¹ : IsScalarTower A K L\ninst✝³⁰ : IsScalarTower A... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 491,
"column": 6
} | {
"line": 491,
"column": 16
} | {
"line": 491,
"column": 17
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝... | [
"A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝ : FiniteDim... | ← one_div, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 493,
"column": 4
} | {
"line": 493,
"column": 70
} | {
"line": 493,
"column": 71
} | [
{
"pp": "A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝... | [
"A : Type u_1\nB : Type u_3\ninst✝⁹ : CommRing A\ninst✝⁸ : CommRing B\ninst✝⁷ : Algebra A B\ninst✝⁶ : IsDomain A\ninst✝⁵ : IsIntegrallyClosed A\ninst✝⁴ : IsDedekindDomain B\ninst✝³ : IsTorsionFree A B\ninst✝² : Algebra.IsIntegral A B\ninst✝¹ : Algebra.IsSeparable (FractionRing A) (FractionRing B)\ninst✝ : FiniteDim... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 624,
"column": 6
} | {
"line": 624,
"column": 71
} | {
"line": 625,
"column": 6
} | [
{
"pp": "case neg\nA : Type u_1\nK : Type u_2\nL : Type u\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : Algebra A K\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra A L\ninst✝⁵ : IsScalarTower A K L\ninst✝⁴ : IsDomain A\ninst✝³ : IsFractionRing A K\ninst✝² : FiniteDimensional K L\ninst✝¹ : Algebra... | [
"case neg\nA : Type u_1\nK : Type u_2\nL : Type u\ninst✝¹¹ : CommRing A\ninst✝¹⁰ : Field K\ninst✝⁹ : Field L\ninst✝⁸ : Algebra A K\ninst✝⁷ : Algebra K L\ninst✝⁶ : Algebra A L\ninst✝⁵ : IsScalarTower A K L\ninst✝⁴ : IsDomain A\ninst✝³ : IsFractionRing A K\ninst✝² : FiniteDimensional K L\ninst✝¹ : Algebra.IsSeparable... | rw [Function.comp_apply, coeff_eq_zero_of_natDegree_lt, mul_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral | {
"line": 369,
"column": 12
} | {
"line": 369,
"column": 23
} | {
"line": 369,
"column": 24
} | [
{
"pp": "case zero\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... | [
"case zero\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 L\nhp : _ro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | {
"line": 100,
"column": 2
} | {
"line": 100,
"column": 38
} | {
"line": 100,
"column": 39
} | [
{
"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))\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, ↑(↑w).mult * Real.log (↑w ((algebraMap (𝓞 K) K) ↑x)) = -(↑w₀.mult * Real.log (w₀ ((algebraMap (𝓞 K) K) ↑x)))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 697,
"column": 42
} | {
"line": 697,
"column": 59
} | {
"line": 697,
"column": 60
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Fintype | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 45
} | {
"line": 66,
"column": 46
} | [
{
"pp": "M₀ : Type u_1\ninst✝² : MonoidWithZero M₀\ninst✝¹ : Nontrivial M₀\ninst✝ : Finite M₀\nthis : Fintype M₀\n⊢ Nat.card M₀ˣ < Nat.card M₀",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"M₀ : Type u_1\ninst✝² : MonoidWithZero M₀\ninst✝¹ : Nontrivial M₀\ninst✝ : Finite M₀\nthis : Fintype M₀\n⊢ Nat.card M₀ˣ < Nat.card M₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 719,
"column": 49
} | {
"line": 719,
"column": 60
} | {
"line": 719,
"column": 61
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 721,
"column": 59
} | {
"line": 721,
"column": 70
} | {
"line": 721,
"column": 71
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.DedekindDomain.Different | {
"line": 722,
"column": 74
} | {
"line": 722,
"column": 85
} | {
"line": 722,
"column": 86
} | [
{
"pp": "A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTow... | [
"A : Type u_1\nK : Type u_2\nL : Type u\nB : Type u_3\ninst✝²¹ : CommRing A\ninst✝²⁰ : Field K\ninst✝¹⁹ : CommRing B\ninst✝¹⁸ : Field L\ninst✝¹⁷ : Algebra A K\ninst✝¹⁶ : Algebra B L\ninst✝¹⁵ : Algebra A B\ninst✝¹⁴ : Algebra K L\ninst✝¹³ : Algebra A L\ninst✝¹² : IsScalarTower A K L\ninst✝¹¹ : IsScalarTower A B L\nin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 87,
"column": 22
} | {
"line": 87,
"column": 33
} | {
"line": 87,
"column": 34
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ (algebraMap (𝓞 K) K) ↑η ^ 2 + (algebraMap (𝓞 K) K) ↑η + 1 - 3 * (algebraMap (𝓞 K) K) ↑η =\n 0 - 3 * (algebraMap (𝓞 K) K) ↑η",
"ppTerm": "?m.169",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_is... | [
"K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ ζ ^ 2 + ζ + 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 94,
"column": 7
} | {
"line": 94,
"column": 18
} | {
"line": 94,
"column": 19
} | [
{
"pp": "K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ ↑(↑⋯.unit ^ 2 + ↑⋯.unit + 1) = ↑0",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"AddGroup.toSubtractionMonoid",
"Units.val",
"Eq.mpr",
"No... | [
"K : Type u_1\ninst✝ : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\n⊢ ζ ^ 2 + ζ + 1 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 13
} | {
"line": 147,
"column": 14
} | [
{
"pp": "p : ℕ\nh : Prime p\ns : Finset ℕ\nhs : s ⊆ {1}\n⊢ ∑ i ∈ s, i ≤ 1",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : ℕ\nh : Prime p\ns : Finset ℕ\nhs : s ⊆ {1}\n⊢ ∑ i ∈ s, i ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.FactorisationProperties | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 15
} | {
"line": 155,
"column": 16
} | [
{
"pp": "case inl\nn : ℕ\nh : Prime n\n⊢ (n ^ 0).Deficient",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Nat.instMonoid",
"id",
"instOfNatNat",
"NPow.toPow",
"pow_zero",
... | [
"case inl\nn : ℕ\nh : Prime n\n⊢ Deficient 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.NumberField.Cyclotomic.Three | {
"line": 195,
"column": 4
} | {
"line": 195,
"column": 29
} | {
"line": 196,
"column": 2
} | [
{
"pp": "K : Type u_1\ninst✝² : Field K\nζ : K\nhζ : IsPrimitiveRoot ζ 3\ninst✝¹ : NumberField K\ninst✝ : IsCyclotomicExtension {3} ℚ K\nx : 𝓞 K\nh : λ ∣ x + 1\n⊢ -x - 1 = -(x + 1)",
"ppTerm": "?m.163",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"NumberField.instCommRing... | [] | exact (neg_add' x 1).symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
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