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.RingTheory.PowerSeries.Ideal | {
"line": 150,
"column": 58
} | {
"line": 150,
"column": 60
} | {
"line": 150,
"column": 61
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI : Ideal R⟦X⟧\ninst✝ : I.IsPrime\nhI : X ∉ I\nS : Set R\nhSI : span S = Ideal.map constantCoeff I\nhS : S.Finite\nthis : SurjOn (⇑constantCoeff) (↑I) S\nT : Set R⟦X⟧\nhTI : T ⊆ ↑I\nhinj : InjOn (⇑constantCoeff) T\nhT : ⇑constantCoeff '' T = S\nf✝ : R⟦X⟧\nhf✝ : consta... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Ideal | {
"line": 132,
"column": 56
} | {
"line": 132,
"column": 58
} | {
"line": 133,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI : Ideal R⟦X⟧\ninst✝ : I.IsPrime\nhI : X ∉ I\nS : Set R\nhSI : span S = Ideal.map constantCoeff I\nhS : S.Finite\n⊢ ∃ T, I = span T ∧ T.Finite ∧ T.ncard = S.ncard",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Ideal.span_le",
"Iff.... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 1076,
"column": 77
} | {
"line": 1076,
"column": 79
} | {
"line": 1077,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx : ↥(cycles₂ A)\n⊢ (ConcreteCategory.hom (H2π A)) x = 0 ↔ ↑x ∈ boundaries₂ A",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"groupHomology.d₃₂",
"Eq.mpr",
"Submodule",
"Rep.V",
"groupH... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 1087,
"column": 53
} | {
"line": 1087,
"column": 55
} | {
"line": 1088,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nx y : ↥(cycles₂ A)\n⊢ (ConcreteCategory.hom (H2π A)) x = (ConcreteCategory.hom (H2π A)) y ↔ ↑x - ↑y ∈ boundaries₂ A",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr"... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 1094,
"column": 41
} | {
"line": 1094,
"column": 43
} | {
"line": 1094,
"column": 44
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\nC : ↑(H2 A) → Prop\nx : ↑(H2 A)\nh : ∀ (x : ↥(cycles₂ A)), C ((ConcreteCategory.hom (H2π A)) x)\ny : ↑(cycles A 2)\n⊢ C ((ConcreteCategory.hom (π A 2)) y)",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Submod... | [] | by | [anonymous] | by |
Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | {
"line": 1107,
"column": 56
} | {
"line": 1107,
"column": 58
} | {
"line": 1108,
"column": 2
} | [
{
"pp": "k G : Type u\ninst✝¹ : CommRing k\ninst✝ : Group G\nA : Rep k G\n⊢ π A 2 ≫ (H2Iso A).hom = (isoCycles₂ A).hom ≫ (shortComplexH2 A).moduleCatLeftHomologyData.π",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Submodule",
"Rep.V",
"CategoryTheory.Functor",
"C... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Ideal | {
"line": 154,
"column": 72
} | {
"line": 154,
"column": 74
} | {
"line": 155,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI : Ideal R⟦X⟧\ninst✝ : I.IsPrime\nhI : X ∉ I\nhfg : I.FG\n⊢ spanFinrank I = spanFinrank (Ideal.map constantCoeff I)",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"le_refl",
"Submodule.spanFinrank_... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 62,
"column": 61
} | {
"line": 62,
"column": 63
} | {
"line": 63,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nthis : ∀ (i j : ℕ), ∃ k, I ^ k ≤ I ^ i ∧ I ^ k ≤ I ^ j\n⊢ ∀ (i j : ℕ), ∃ k, I ^ k • ⊤ ≤ I ^ i • ⊤ ⊓ I ^ j • ⊤",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"instHSMul",
"Semiring.toModu... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 61,
"column": 13
} | {
"line": 61,
"column": 15
} | {
"line": 62,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ∀ (i j : ℕ), ∃ k, I ^ k • ⊤ ≤ I ^ i • ⊤ ⊓ I ^ j • ⊤",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"le_max_right",
"Eq.mpr",
"Submodule",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 67,
"column": 61
} | {
"line": 67,
"column": 63
} | {
"line": 68,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nthis : ∀ (a : R) (i : ℕ), ∃ j, a • I ^ j ≤ I ^ i\n⊢ ∀ (a : R) (i : ℕ), ∃ j, a • I ^ j • ⊤ ≤ I ^ i • ⊤",
"ppTerm": "?m.119",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule.pointwiseDistribMulAction",
"Submodule",
... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 66,
"column": 15
} | {
"line": 66,
"column": 17
} | {
"line": 67,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ∀ (a : R) (i : ℕ), ∃ j, a • I ^ j • ⊤ ≤ I ^ i • ⊤",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule.pointwiseDistribMulAction",
"Submodule",
"Submodule.instAddCommMonoidWithOne",
"Ide... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 74,
"column": 84
} | {
"line": 74,
"column": 86
} | {
"line": 75,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nthis : ∀ (i : ℕ), ∃ j, ↑(I ^ j) * ↑(I ^ j) ⊆ ↑(I ^ i)\n⊢ ∀ (i : ℕ), ∃ j, ↑(I ^ j • ⊤) * ↑(I ^ j • ⊤) ⊆ ↑(I ^ i • ⊤)",
"ppTerm": "?m.195",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Ideal.smul_top_eq_map",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Ideal | {
"line": 171,
"column": 61
} | {
"line": 171,
"column": 63
} | {
"line": 172,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : Ideal R⟦X⟧\ninst✝ : P.IsPrime\n⊢ spanFinrank P ≤ spanFinrank (Ideal.map constantCoeff P) + 1",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"PowerSeries.spanFinrank_le_spanFinrank_map_constantCoeff_add_one_of_X_mem",
"Nat.zero_le... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 73,
"column": 11
} | {
"line": 73,
"column": 13
} | {
"line": 74,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ∀ (i : ℕ), ∃ j, ↑(I ^ j • ⊤) * ↑(I ^ j • ⊤) ⊆ ↑(I ^ i • ⊤)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Submodule",
"Ideal.smul_top_eq_map",
"instHSMul",
"Semiring.toModule",
"instSM... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 104,
"column": 34
} | {
"line": 104,
"column": 36
} | {
"line": 104,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nU : Set R\ni : ℕ\nh : id ↑((fun i ↦ toAddSubgroup (I ^ i • ⊤)) i) ⊆ U\n⊢ ↑(I ^ i) ⊆ U",
"ppTerm": "?m.77",
"assigned": true,
"usedConstants": [
"Submodule",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"AddGr... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 107,
"column": 36
} | {
"line": 107,
"column": 38
} | {
"line": 107,
"column": 39
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nU : Set R\ni : ℕ\nh : ↑(I ^ i) ⊆ U\n⊢ ↑(I ^ i) = ↑((fun i ↦ toAddSubgroup (I ^ i • ⊤)) i)",
"ppTerm": "?m.122",
"assigned": true,
"usedConstants": [
"Submodule",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Ideal | {
"line": 181,
"column": 61
} | {
"line": 181,
"column": 63
} | {
"line": 182,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nP : Ideal R⟦X⟧\ninst✝ : P.IsPrime\n⊢ P.FG ↔ (Ideal.map constantCoeff P).FG",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"Ideal.FG.map",
"Finset",
"... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 99,
"column": 3
} | {
"line": 99,
"column": 5
} | {
"line": 100,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\n⊢ ∀ (t : Set R), t ∈ 𝓝 0 ↔ ∃ i, True ∧ ↑(I ^ i) ⊆ t",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"instHSMul",
"Sem... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 111,
"column": 47
} | {
"line": 111,
"column": 49
} | {
"line": 112,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nI : Ideal R\nx : R\n⊢ (𝓝 x).HasBasis (fun _n ↦ True) fun n ↦ (fun y ↦ x + y) '' ↑(I ^ n)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 130,
"column": 34
} | {
"line": 130,
"column": 36
} | {
"line": 130,
"column": 37
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nI : Ideal R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nm : M\ni : ℕ\n⊢ ↑(I ^ i • ⊤) = ↑((fun i ↦ toAddSubgroup (I ^ i • ⊤)) i)",
"ppTerm": "?m.107",
"assigned": true,
"usedConstants": [
"Submodule",
"instHSMul",
"Semiring... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 131,
"column": 36
} | {
"line": 131,
"column": 38
} | {
"line": 131,
"column": 39
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nI : Ideal R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nm : M\ni : ℕ\na : R\na_in : a ∈ ↑(I ^ i • ⊤)\n⊢ a ∈ I ^ i",
"ppTerm": "?m.122",
"assigned": true,
"usedConstants": [
"SetLike.mem_coe._simp_1",
"instHSMul",
"Semiring... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 130,
"column": 58
} | {
"line": 130,
"column": 60
} | {
"line": 131,
"column": 8
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nI : Ideal R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nm : M\ni : ℕ\na : R\na_in : a ∈ ↑(I ^ i • ⊤)\n⊢ a ∈ (fun x ↦ x • m) ⁻¹' ↑(I ^ i • ⊤)",
"ppTerm": "?m.110",
"assigned": true,
"usedConstants": [
"Submodule",
"SetLike.mem_co... | [] | by | [anonymous] | by |
Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
"line": 143,
"column": 69
} | {
"line": 143,
"column": 71
} | {
"line": 144,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nI : Ideal R\nM : Type u_2\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nn : ℕ\n⊢ OpenAddSubgroup R",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"RingSubgroupsBasis.topology",
"RingSubgroupsBasis.openAddSubgroup",
"Eq.mpr",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Ideal | {
"line": 202,
"column": 83
} | {
"line": 202,
"column": 85
} | {
"line": 203,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommRing R\nI : Ideal R⟦X⟧\nS : Set R\nP : Ideal R⟦X⟧\ninst✝² : P.IsPrime\ninst✝¹ : IsPrincipalIdealRing R\ninst✝ : IsDomain R\n⊢ UniqueFactorizationMonoid R⟦X⟧",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Submodule",
"_privat... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 31,
"column": 72
} | {
"line": 31,
"column": 74
} | {
"line": 32,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : TopologicalSpace R\nI : Ideal R\nhI : IsAdic I\n⊢ IsHausdorff I R ↔ T2Space R",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"Submodule",
"SetL... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 53,
"column": 68
} | {
"line": 53,
"column": 70
} | {
"line": 54,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝ : (𝓝 0).IsCountablyGenerated\nthis : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R\nhu : Ca... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 57,
"column": 37
} | {
"line": 57,
"column": 39
} | {
"line": 57,
"column": 40
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝ : (𝓝 0).IsCountablyGenerated\nthis : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R\nhu : Ca... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 57,
"column": 66
} | {
"line": 57,
"column": 68
} | {
"line": 57,
"column": 69
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝ : (𝓝 0).IsCountablyGenerated\nthis : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R\nhu : Ca... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 56,
"column": 4
} | {
"line": 57,
"column": 75
} | {
"line": 58,
"column": 4
} | [
{
"pp": "case mp\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝ : (𝓝 0).IsCountablyGenerated\nthis : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R... | [
"case mp\nR : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝ : (𝓝 0).IsCountablyGenerated\nthis : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R\nhu : Cauch... | obtain ⟨L, hL⟩ := H (fun i ↦ u ((Finset.Iic i).sup N))
fun _ ↦ hN _ _ (Finset.le_sup (by simpa)) _ (Finset.le_sup (by simp)) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 59,
"column": 52
} | {
"line": 59,
"column": 54
} | {
"line": 60,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝¹ : (𝓝 0).IsCountablyGenerated\nthis✝ : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R\nhu : ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 62,
"column": 73
} | {
"line": 62,
"column": 75
} | {
"line": 62,
"column": 76
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : UniformSpace R\ninst✝ : IsUniformAddGroup R\nI : Ideal R\nhI : IsAdic I\nthis✝ : (𝓝 0).IsCountablyGenerated\nthis : (𝓤 R).IsCountablyGenerated\nH : ∀ (f : ℕ → R), (∀ {m n : ℕ}, m ≤ n → f m - f n ∈ I ^ m) → ∃ L, ∀ (n : ℕ), f n - L ∈ I ^ n\nu : ℕ → R\nhu : Ca... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
"line": 63,
"column": 32
} | {
"line": 63,
"column": 34
} | {
"line": 63,
"column": 35
} | [
{
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Mathlib.RingTheory.AdicCompletion.Topology | {
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{
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Mathlib.RingTheory.AdicCompletion.Topology | {
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{
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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} | {
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{
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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{
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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{
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Mathlib.RingTheory.AdicCompletion.Topology | {
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{
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Mathlib.RingTheory.AdicCompletion.Topology | {
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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{
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Mathlib.RingTheory.AdicCompletion.Topology | {
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Mathlib.RingTheory.AdicCompletion.Topology | {
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Mathlib.RingTheory.AdicCompletion.Topology | {
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
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{
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Mathlib.RingTheory.AdicCompletion.Topology | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.Topology | {
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} | {
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{
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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{
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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{
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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} | {
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{
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology | {
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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Mathlib.RingTheory.MvPowerSeries.Equiv | {
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"co... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 127,
"column": 15
} | {
"line": 127,
"column": 17
} | {
"line": 128,
"column": 4
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\n⊢ ∀ (r : R),\n optionFunLeft σ R ((algebraMap R (MvPowerSeries (Option σ) R)) r) =\n (algebraMap R (PowerSeries (MvPowerSeries σ R))) r",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"E... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 142,
"column": 67
} | {
"line": 142,
"column": 69
} | {
"line": 143,
"column": 4
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ni : σ\n⊢ optionElim 0 (single i 1) = single (Option.some i) 1",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"False",
"Nat.instMulZeroClass",
"Option.instDecidableEq",
"Finsup... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 141,
"column": 71
} | {
"line": 141,
"column": 73
} | {
"line": 142,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\ni : σ\n⊢ (optionEquivLeft σ R) (X (Option.some i)) = PowerSeries.C (X i)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"F... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 149,
"column": 79
} | {
"line": 149,
"column": 81
} | {
"line": 150,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\n⊢ (optionEquivLeft σ R) (X none) = PowerSeries.X",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Nat.instMulZe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 154,
"column": 87
} | {
"line": 154,
"column": 89
} | {
"line": 155,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝ : CommSemiring R\nr : R\n⊢ (optionEquivLeft σ R) (C r) = PowerSeries.C (C r)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Nat.instMulZeroClass",
"Semiring.toModule",
"congrArg",
"CommSemirin... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 164,
"column": 93
} | {
"line": 164,
"column": 95
} | {
"line": 165,
"column": 2
} | [
{
"pp": "M : Type u_3\ninst✝ : AddCommMonoid M\nn : ℕ\ni : M\nx : Fin n →₀ M\n⊢ embDomain (finSuccEquiv n).toEmbedding (Finsupp.cons i x) = optionElim i x",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"instNeZeroNatHAdd_1",
"Equiv.instEquivLike",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 176,
"column": 70
} | {
"line": 176,
"column": 72
} | {
"line": 176,
"column": 73
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\np : MvPowerSeries (Fin (n + 1)) R\nk : ℕ\nx : Fin n →₀ ℕ\nthis :\n (coeff x) ((PowerSeries.coeff k) ((optionEquivLeft (Fin n) R) ((rename ⇑(_root_.finSuccEquiv n)) p))) =\n (coeff (Finsupp.cons k x)) p\n⊢ (coeff x) ((PowerSeries.coeff k) ((finSuccEquiv R... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 174,
"column": 79
} | {
"line": 174,
"column": 81
} | {
"line": 175,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\np : MvPowerSeries (Fin (n + 1)) R\nk : ℕ\nx : Fin n →₀ ℕ\n⊢ (coeff x) ((PowerSeries.coeff k) ((finSuccEquiv R n) p)) = (coeff (Finsupp.cons k x)) p",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroCl... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 187,
"column": 27
} | {
"line": 187,
"column": 29
} | {
"line": 187,
"column": 30
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn k : ℕ\nx : Fin n →₀ ℕ\nh1 : ¬(x = 0 ∧ k = 1)\nh3 : k = 1\n⊢ ¬x = 0",
"ppTerm": "?m.85",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"False.elim",
"instOfNatNat",
"Or.casesOn",
"And",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 181,
"column": 61
} | {
"line": 181,
"column": 63
} | {
"line": 182,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\n⊢ (finSuccEquiv R n) (X 0) = PowerSeries.X",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"MvPowerSeries.coeff_zero",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instNeZeroNatHAdd_1",
"False",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 197,
"column": 25
} | {
"line": 197,
"column": 27
} | {
"line": 197,
"column": 28
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nj : Fin n\nk : ℕ\nx : Fin n →₀ ℕ\nh1 : ¬(x = single j 1 ∧ k = 0)\nh3 : k = 0\n⊢ ¬x = single j 1",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"False.elim",
"instOfNatNat",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 191,
"column": 84
} | {
"line": 191,
"column": 86
} | {
"line": 192,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nj : Fin n\n⊢ (finSuccEquiv R n) (X j.succ) = PowerSeries.C (X j)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"MvPowerSeries.coeff_zero",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Na... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 68,
"column": 45
} | {
"line": 68,
"column": 47
} | {
"line": 69,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI m : Ideal R\ninst✝ : m.IsMaximal\nle : I ≤ m\nfg : I.FG\n⊢ Ideal.map (algebraMap R (AdicCompletion I R)) m = comap (evalOneₐ I).toRingHom (Ideal.map (Ideal.Quotient.mk I) m)",
"ppTerm": "?m.67",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 74,
"column": 78
} | {
"line": 74,
"column": 80
} | {
"line": 74,
"column": 81
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI m : Ideal R\ninst✝ : m.IsMaximal\nle : I ≤ m\nfg : I.FG\nmapeq :\n Ideal.map (algebraMap R (AdicCompletion I R)) m = comap (evalOneₐ I).toRingHom (Ideal.map (Ideal.Quotient.mk I) m)\n⊢ RingHom.ker (Ideal.Quotient.mk I) ≤ m",
"ppTerm": "?m.151",
"assigned": ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 66,
"column": 61
} | {
"line": 66,
"column": 63
} | {
"line": 67,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nI m : Ideal R\ninst✝ : m.IsMaximal\nle : I ≤ m\nfg : I.FG\n⊢ (Ideal.map (algebraMap R (AdicCompletion I R)) m).IsMaximal",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"RingHom.instRingHomClass",
"Lattice.toSemilattic... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 79,
"column": 55
} | {
"line": 79,
"column": 57
} | {
"line": 80,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsLocalRing R\nfg : (maximalIdeal R).FG\n⊢ IsLocalRing (AdicCompletion (maximalIdeal R) R)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"le_refl",
"Semiring.toModule",
"Algebra.algebraMap",
"CommSemiring.toSemir... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 105,
"column": 80
} | {
"line": 105,
"column": 82
} | {
"line": 106,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsNoetherianRing R\ninst✝ : IsLocalRing R\nx : AdicCompletion (maximalIdeal R) R\n⊢ (eval (maximalIdeal R) R 1).ker = maximalIdeal R • ⊤",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"Ideal.fg_of_isNoetherianRing",
"NonAsso... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 103,
"column": 72
} | {
"line": 103,
"column": 74
} | {
"line": 104,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\ninst✝¹ : IsNoetherianRing R\ninst✝ : IsLocalRing R\nx : AdicCompletion (maximalIdeal R) R\n⊢ x ∈ maximalIdeal (AdicCompletion (maximalIdeal R) R) ↔ ↑x 1 = 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Ideal.fg_of_isNoetherianRing",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 111,
"column": 69
} | {
"line": 111,
"column": 71
} | {
"line": 112,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsLocalRing R\nfg : (maximalIdeal R).FG\n⊢ IsLocalHom (algebraMap R (AdicCompletion (maximalIdeal R) R))",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"RingHom.instRingHomClass",
"Semiring.toModule",
"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 208,
"column": 25
} | {
"line": 208,
"column": 27
} | {
"line": 208,
"column": 28
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nr : R\nk : ℕ\nx : Fin n →₀ ℕ\nh1 : ¬(k = 0 ∧ x = 0)\nh3 : k = 0\n⊢ ¬x = 0",
"ppTerm": "?m.89",
"assigned": true,
"usedConstants": [
"False",
"Nat.instMulZeroClass",
"False.elim",
"instDecidableEqFin",
"Finsupp.instDe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 123,
"column": 45
} | {
"line": 123,
"column": 47
} | {
"line": 124,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsLocalRing R\nfg : (maximalIdeal R).FG\n⊢ IsAdicComplete (maximalIdeal (AdicCompletion (maximalIdeal R) R)) (AdicCompletion (maximalIdeal R) R)",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 201,
"column": 83
} | {
"line": 201,
"column": 85
} | {
"line": 202,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\nr : R\n⊢ (finSuccEquiv R n) (C r) = PowerSeries.C (C r)",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"MvPowerSeries.coeff_zero",
"Eq.mpr",
"False",
"Nat.instMulZeroClass",
"MvPowerSeries.instZero",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 212,
"column": 62
} | {
"line": 212,
"column": 64
} | {
"line": 213,
"column": 2
} | [
{
"pp": "R : Type u_2\ninst✝ : CommSemiring R\nn : ℕ\n⊢ (finSuccEquiv R n).symm.toRingEquiv.toRingHom.comp (PowerSeries.C.comp C) = C",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"AlgEquiv.symm",
"congrArg",
"CommSemiring.toSemiring",
"MvPowerSeries.finSuccEquiv_... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 217,
"column": 91
} | {
"line": 217,
"column": 93
} | {
"line": 218,
"column": 2
} | [
{
"pp": "S : Type u_3\ninst✝¹ : CommRing S\ninst✝ : IsNoetherianRing S\nn : ℕ\n⊢ IsNoetherianRing (MvPowerSeries (Fin n) S)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Nat.recAux",
"CommSemiring.toSemiring",
"MvPowerSeries",
"Algebra.id",
"Distrib.toAdd",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 225,
"column": 79
} | {
"line": 225,
"column": 81
} | {
"line": 226,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝³ : CommSemiring R\nn : ℕ\nS : Type u_3\ninst✝² : CommRing S\ninst✝¹ : IsNoetherianRing S\ninst✝ : Finite σ\n⊢ IsNoetherianRing (MvPowerSeries σ S)",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"CommSemiring.toSemiring",
"MvPowerSeries... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 245,
"column": 63
} | {
"line": 245,
"column": 65
} | {
"line": 245,
"column": 66
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : Finite σ\nl m n : ℕ\nh : l ≤ m\nh' : l ≤ n\np : MvPowerSeries σ R\nx : σ →₀ ℕ\nhx : degree x < l\n⊢ degree x < m",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"_private.Mathlib.RingTheory.MvPowerSeries.Equiv.0.MvPowe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 246,
"column": 24
} | {
"line": 246,
"column": 26
} | {
"line": 246,
"column": 27
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : Finite σ\nl m n : ℕ\nh : l ≤ m\nh' : l ≤ n\np : MvPowerSeries σ R\nx : σ →₀ ℕ\nhx : degree x < l\n⊢ degree x < n",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"_private.Mathlib.RingTheory.MvPowerSeries.Equiv.0.MvPowe... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 243,
"column": 42
} | {
"line": 243,
"column": 44
} | {
"line": 244,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\ninst✝¹ : CommRing R\ninst✝ : Finite σ\nl m n : ℕ\nh : l ≤ m\nh' : l ≤ n\np : MvPowerSeries σ R\n⊢ (truncTotal m) p - (truncTotal n) p ∈ MvPolynomial.idealOfVars σ R ^ l",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"MvPowerSeries.truncTotal",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 250,
"column": 42
} | {
"line": 250,
"column": 44
} | {
"line": 251,
"column": 2
} | [
{
"pp": "σ : Type u_1\nR : Type u_2\nn : ℕ\ninst✝¹ : CommRing R\ninst✝ : Finite σ\np q : MvPowerSeries σ R\n⊢ (truncTotal n) (p * q) - (truncTotal n) p * (truncTotal n) q ∈ MvPolynomial.idealOfVars σ R ^ n",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"MvPowerSeries.truncTotal",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 263,
"column": 14
} | {
"line": 263,
"column": 16
} | {
"line": 264,
"column": 4
} | [
{
"pp": "σ✝ : Type u_1\nR✝ : Type u_2\nn✝ : ℕ\ninst✝³ : CommRing R✝\ninst✝² : Finite σ✝\nσ : Type u_3\nR : Type u_4\ninst✝¹ : Finite σ\ninst✝ : CommRing R\nn : ℕ\n⊢ (Ideal.Quotient.mk (MvPolynomial.idealOfVars σ R ^ n)) ((truncTotal n) 1) = 1",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 269,
"column": 18
} | {
"line": 269,
"column": 20
} | {
"line": 270,
"column": 4
} | [
{
"pp": "σ✝ : Type u_1\nR✝ : Type u_2\nn✝ : ℕ\ninst✝³ : CommRing R✝\ninst✝² : Finite σ✝\nσ : Type u_3\nR : Type u_4\ninst✝¹ : Finite σ\ninst✝ : CommRing R\nn : ℕ\np q : MvPowerSeries σ R\n⊢ (Ideal.Quotient.mk (MvPolynomial.idealOfVars σ R ^ n)) ((truncTotal n) (p * q)) =\n (Ideal.Quotient.mk (MvPolynomial.id... | [] | by | [anonymous] | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 272,
"column": 15
} | {
"line": 272,
"column": 17
} | {
"line": 272,
"column": 18
} | [
{
"pp": "σ✝ : Type u_1\nR✝ : Type u_2\nn✝ : ℕ\ninst✝³ : CommRing R✝\ninst✝² : Finite σ✝\nσ : Type u_3\nR : Type u_4\ninst✝¹ : Finite σ\ninst✝ : CommRing R\nn : ℕ\n⊢ (Ideal.Quotient.mk (MvPolynomial.idealOfVars σ R ^ n)) ((truncTotal n) 0) = 0",
"ppTerm": "?m.117",
"assigned": true,
"usedConstants": ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.AdicCompletion.LocalRing | {
"line": 145,
"column": 84
} | {
"line": 145,
"column": 86
} | {
"line": 146,
"column": 4
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\ninst✝ : IsLocalRing R\nfg : (maximalIdeal R).FG\nthis : IsLocalRing (AdicCompletion (maximalIdeal R) R)\nx : IsLocalRing.ResidueField (AdicCompletion (maximalIdeal R) R)\ny : AdicCompletion (maximalIdeal R) R\nhy : (residue (AdicCompletion (maximalIdeal R) R)) y = x\n... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.MvPowerSeries.Equiv | {
"line": 273,
"column": 18
} | {
"line": 273,
"column": 20
} | {
"line": 273,
"column": 21
} | [
{
"pp": "σ✝ : Type u_1\nR✝ : Type u_2\nn✝ : ℕ\ninst✝³ : CommRing R✝\ninst✝² : Finite σ✝\nσ : Type u_3\nR : Type u_4\ninst✝¹ : Finite σ\ninst✝ : CommRing R\nn : ℕ\nx✝¹ x✝ : MvPowerSeries σ R\n⊢ (Ideal.Quotient.mk (MvPolynomial.idealOfVars σ R ^ n)) ((truncTotal n) (x✝¹ + x✝)) =\n (Ideal.Quotient.mk (MvPolynom... | [] | by | [anonymous] | by |
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