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Mathlib.RingTheory.PolynomialLaw.Basic | {
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Mathlib.RingTheory.PolynomialLaw.Basic | {
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Mathlib.RingTheory.PolynomialLaw.Basic | {
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Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
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Mathlib.RingTheory.Regular.ProjectiveDimension | {
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Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
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Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
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} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\n⊢ H.div 0 = 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"instHSMul",
"MvPowerSeries.instZero",
"Semiring.toModule",
"congrArg",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 394,
"column": 2
} | {
"line": 395,
"column": 47
} | {
"line": 397,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\nf f' : A⟦X⟧\ninst✝ : IsAdicComplete I A\nH1 : (f + f').IsWeierstrassDivisionAt g (H.div f + H.div f') (H.mod f + H.mod f') I\nH2 : (f + f').IsWeierstrassDivisionAt g (H.div (f + f')) (H.mod (f + f')) I\n⊢ H.mod (f... | [] | exact (H.eq_of_mul_add_eq_mul_add H2.degree_lt H1.degree_lt
(H2.eq_mul_add.symm.trans H1.eq_mul_add)).2 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 391,
"column": 78
} | {
"line": 391,
"column": 80
} | {
"line": 392,
"column": 2
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\nf f' : A⟦X⟧\ninst✝ : IsAdicComplete I A\n⊢ H.mod (f + f') = H.mod f + H.mod f'",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_a... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 401,
"column": 2
} | {
"line": 402,
"column": 47
} | {
"line": 404,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na : A\nf : A⟦X⟧\ninst✝ : IsAdicComplete I A\nH1 : (a • f).IsWeierstrassDivisionAt g (a • H.div f) (a • H.mod f) I\nH2 : (a • f).IsWeierstrassDivisionAt g (H.div (a • f)) (H.mod (a • f)) I\n⊢ H.mod (a • f) = a • H.... | [] | exact (H.eq_of_mul_add_eq_mul_add H2.degree_lt H1.degree_lt
(H2.eq_mul_add.symm.trans H1.eq_mul_add)).2 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 398,
"column": 71
} | {
"line": 398,
"column": 73
} | {
"line": 399,
"column": 2
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na : A\nf : A⟦X⟧\ninst✝ : IsAdicComplete I A\n⊢ H.mod (a • f) = a • H.mod f",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_add",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 405,
"column": 55
} | {
"line": 405,
"column": 57
} | {
"line": 406,
"column": 2
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\n⊢ H.mod 0 = 0",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"PowerSeries.IsWeierstrassDivisorAt.mod.congr_simp",
"instHSMul",
"MvPowerSeries.in... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PolynomialLaw.Basic | {
"line": 564,
"column": 45
} | {
"line": 564,
"column": 47
} | {
"line": 565,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nM : Type u_6\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nN : Type u_7\ninst✝³ : AddCommGroup N\ninst✝² : Module R N\nf : M →ₚₗ[R] N\nS : Type u_8\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\n⊢ toFun S (-f) = -1 • toFun S f",
"ppTerm": "?m.70",
"assigned": t... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PolynomialLaw.Basic | {
"line": 572,
"column": 58
} | {
"line": 572,
"column": 60
} | {
"line": 573,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommSemiring R\nM : Type u_3\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nN : Type u_4\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nr : R\nf : M →ₚₗ[R] N\nS : Type u_5\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\n⊢ toFun S (r • f) = r • toFun S f",
"ppTerm": "?m.57",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 411,
"column": 57
} | {
"line": 411,
"column": 59
} | {
"line": 412,
"column": 4
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na : A\nf✝ f'✝ : A⟦X⟧\ninst✝ : IsAdicComplete I A\nf f' : A⟦X⟧\nhf : f ≈ f'\n⊢ H.mod f = H.mod f'",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"MvPowerSeries.instAddCommGroup",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 419,
"column": 19
} | {
"line": 419,
"column": 21
} | {
"line": 420,
"column": 4
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na : A\nf✝ f'✝ : A⟦X⟧\ninst✝ : IsAdicComplete I A\nf f' : A⟦X⟧ ⧸ Ideal.span {g}\n⊢ Quotient.lift (fun f ↦ H.mod f) ⋯ (f + f') =\n Quotient.lift (fun f ↦ H.mod f) ⋯ f + Quotient.lift (fun f ↦ H.mod f) ⋯ f'",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 424,
"column": 4
} | {
"line": 425,
"column": 24
} | {
"line": 427,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na✝ : A\nf✝ f' : A⟦X⟧\ninst✝ : IsAdicComplete I A\na : A\nf : A⟦X⟧ ⧸ Ideal.span {g}\n⊢ Quotient.lift (fun f ↦ H.mod f) ⋯ (a • f) = (RingHom.id A) a • Quotient.lift (fun f ↦ H.mod f) ⋯ f",
"ppTerm": "?m.245",
... | [] | obtain ⟨f, rfl⟩ := Ideal.Quotient.mk_surjective f
exact H.mod_smul a f | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 424,
"column": 4
} | {
"line": 425,
"column": 24
} | {
"line": 427,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na✝ : A\nf✝ f' : A⟦X⟧\ninst✝ : IsAdicComplete I A\na : A\nf : A⟦X⟧ ⧸ Ideal.span {g}\n⊢ Quotient.lift (fun f ↦ H.mod f) ⋯ (a • f) = (RingHom.id A) a • Quotient.lift (fun f ↦ H.mod f) ⋯ f",
"ppTerm": "?m.245",
... | [] | obtain ⟨f, rfl⟩ := Ideal.Quotient.mk_surjective f
exact H.mod_smul a f | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 423,
"column": 19
} | {
"line": 423,
"column": 21
} | {
"line": 424,
"column": 4
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\na✝ : A\nf✝ f' : A⟦X⟧\ninst✝ : IsAdicComplete I A\na : A\nf : A⟦X⟧ ⧸ Ideal.span {g}\n⊢ Quotient.lift (fun f ↦ H.mod f) ⋯ (a • f) = (RingHom.id A) a • Quotient.lift (fun f ↦ H.mod f) ⋯ f",
"ppTerm": "?m.245",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 434,
"column": 68
} | {
"line": 434,
"column": 70
} | {
"line": 434,
"column": 71
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\nr : A[X]\nhr : r.degree < ↑((map (Ideal.Quotient.mk I)) g).order.toNat\nh1 : (H.mod ↑r).degree < ↑((map (Ideal.Quotient.mk I)) g).order.toNat\nh2 : ↑r = g * H.div ↑r + ↑(H.mod ↑r)\n⊢ g ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 432,
"column": 81
} | {
"line": 432,
"column": 83
} | {
"line": 433,
"column": 2
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\nr : A[X]\nhr : r.degree < ↑((map (Ideal.Quotient.mk I)) g).order.toNat\n⊢ H.div ↑r = 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 439,
"column": 68
} | {
"line": 439,
"column": 70
} | {
"line": 439,
"column": 71
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\nr : A[X]\nhr : r.degree < ↑((map (Ideal.Quotient.mk I)) g).order.toNat\nh1 : (H.mod ↑r).degree < ↑((map (Ideal.Quotient.mk I)) g).order.toNat\nh2 : ↑r = g * H.div ↑r + ↑(H.mod ↑r)\n⊢ g ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 437,
"column": 81
} | {
"line": 437,
"column": 83
} | {
"line": 438,
"column": 2
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\nr : A[X]\nhr : r.degree < ↑((map (Ideal.Quotient.mk I)) g).order.toNat\n⊢ H.mod ↑r = r",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"WithBot.instPreorder"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PolynomialLaw.Basic | {
"line": 588,
"column": 44
} | {
"line": 588,
"column": 46
} | {
"line": 589,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommSemiring R\nM : Type u_3\ninst✝⁵ : AddCommMonoid M\ninst✝⁴ : Module R M\nN : Type u_4\ninst✝³ : AddCommMonoid N\ninst✝² : Module R N\nf : M →ₚₗ[R] N\nS : Type u_5\ninst✝¹ : CommSemiring S\ninst✝ : Algebra R S\nx : M\n⊢ 1 ⊗ₜ[R] f.ground x = toFun S f (1 ⊗ₜ[R] x)",
"ppTerm": ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 443,
"column": 49
} | {
"line": 443,
"column": 51
} | {
"line": 444,
"column": 2
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng : A⟦X⟧\nI : Ideal A\nH : g.IsWeierstrassDivisorAt I\ninst✝ : IsAdicComplete I A\nf : A⟦X⟧ ⧸ Ideal.span {g}\n⊢ (Ideal.Quotient.mk (Ideal.span {g})) ↑(H.mod' f) = f",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"MvPowerSeries.instAddCommG... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PolynomialLaw.Basic | {
"line": 612,
"column": 69
} | {
"line": 612,
"column": 71
} | {
"line": 613,
"column": 4
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommSemiring R\nM : Type u_3\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nN : Type u_4\ninst✝⁵ : AddCommMonoid N\ninst✝⁴ : Module R N\nP : Type u_5\ninst✝³ : AddCommMonoid P\ninst✝² : Module R P\nf : M →ₚₗ[R] N\ng : N →ₚₗ[R] P\nS : Type u_7\ninst✝¹ : CommSemiring S\ninst✝ : Alge... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 464,
"column": 14
} | {
"line": 464,
"column": 16
} | {
"line": 464,
"column": 17
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\na : A[X]\nha : a ∈ Ideal.span {g}\nb : A[X]\nhb : b * g = a\n⊢ ↑b * ↑g = ↑a",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"HMul.hMul",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 460,
"column": 79
} | {
"line": 460,
"column": 81
} | {
"line": 461,
"column": 4
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\na : A[X]\nha : a ∈ Ideal.span {g}\n⊢ a ∈ Ideal.comap (Polynomial.coeToPowerSeries.algHom A) (Ideal.span {↑g})",
"ppTerm": "?m.86",
"assigned": true,
"use... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 471,
"column": 23
} | {
"line": 471,
"column": 25
} | {
"line": 472,
"column": 6
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nf : A[X] ⧸ Ideal.span {g}\nh✝ : Nontrivial A\n⊢ I ≠ ⊤",
"ppTerm": "?m.147",
"assigned": true,
"usedConstants": [
"False",
"Semiring.toModule"... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.PolynomialLaw.Basic | {
"line": 609,
"column": 57
} | {
"line": 609,
"column": 59
} | {
"line": 610,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommSemiring R\nM : Type u_3\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nN : Type u_4\ninst✝⁵ : AddCommMonoid N\ninst✝⁴ : Module R N\nP : Type u_5\ninst✝³ : AddCommMonoid P\ninst✝² : Module R P\nf : M →ₚₗ[R] N\ng : N →ₚₗ[R] P\nS : Type u_7\ninst✝¹ : CommSemiring S\ninst✝ : Alge... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PolynomialLaw.Basic | {
"line": 618,
"column": 56
} | {
"line": 618,
"column": 58
} | {
"line": 619,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommSemiring R\nM : Type u_3\ninst✝⁷ : AddCommMonoid M\ninst✝⁶ : Module R M\nN : Type u_4\ninst✝⁵ : AddCommMonoid N\ninst✝⁴ : Module R N\nP : Type u_5\ninst✝³ : AddCommMonoid P\ninst✝² : Module R P\nf : M →ₚₗ[R] N\ng : N →ₚₗ[R] P\nS : Type u_7\ninst✝¹ : CommSemiring S\ninst✝ : Alge... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 479,
"column": 21
} | {
"line": 479,
"column": 23
} | {
"line": 479,
"column": 24
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nh✝ : Nontrivial A\nhI : I ≠ ⊤\nthis : Nontrivial (A ⧸ I)\nf : A[X]\n⊢ f /ₘ g * g = f - f %ₘ g",
"ppTerm": "?m.262",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 475,
"column": 92
} | {
"line": 475,
"column": 94
} | {
"line": 476,
"column": 6
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nf : A[X] ⧸ Ideal.span {g}\nh✝ : Nontrivial A\nhI : I ≠ ⊤\nthis : Nontrivial (A ⧸ I)\n⊢ ∃ r, r.degree < g.degree ∧ (Ideal.Quotient.mk (Ideal.span {g})) r = f",
"p... | [] | by | [anonymous] | by |
Mathlib.RingTheory.RingInvo | {
"line": 69,
"column": 30
} | {
"line": 69,
"column": 32
} | {
"line": 70,
"column": 4
} | [
{
"pp": "F : Type u_1\nR : Type u_2\ninst✝¹ : Semiring R\ninst✝ : EquivLike F R Rᵐᵒᵖ\ne f : RingInvo R\nh₁ : e.toFun = f.toFun\nh₂ : e.invFun = f.invFun\n⊢ e = f",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"RingInvo.mk",
"RingEquiv.toEquiv",
"Function.LeftInverse",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 482,
"column": 44
} | {
"line": 482,
"column": 46
} | {
"line": 482,
"column": 47
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nh✝ : Nontrivial A\nhI : I ≠ ⊤\nthis : Nontrivial (A ⧸ I)\nf : A[X]\nhfdeg : f.degree < g.degree\n⊢ constantCoeff 1 ∉ I",
"ppTerm": "?m.312",
"assigned": true... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 483,
"column": 11
} | {
"line": 483,
"column": 13
} | {
"line": 483,
"column": 14
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nh✝ : Nontrivial A\nhI : I ≠ ⊤\nthis : Nontrivial (A ⧸ I)\nf : A[X]\nhfdeg : f.degree < g.degree\n⊢ ↑g = ↑g * 1",
"ppTerm": "?m.313",
"assigned": true,
"u... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 480,
"column": 79
} | {
"line": 480,
"column": 81
} | {
"line": 481,
"column": 6
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nh✝ : Nontrivial A\nhI : I ≠ ⊤\nthis : Nontrivial (A ⧸ I)\nf : A[X]\nhfdeg : f.degree < g.degree\n⊢ g.degree = ↑((map (Ideal.Quotient.mk I)) ↑g).order.toNat",
"pp... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Regular.ProjectiveDimension | {
"line": 95,
"column": 37
} | {
"line": 95,
"column": 39
} | {
"line": 96,
"column": 4
} | [
{
"pp": "R : Type u\ninst✝⁴ : CommRing R\ninst✝³ : Small.{v, u} R\ninst✝² : IsLocalRing R\ninst✝¹ : IsNoetherianRing R\nM : ModuleCat R\ninst✝ : Module.Finite R ↑M\nx : R\nreg : IsSMulRegular (↑M) x\nmem : x ∈ maximalIdeal R\nsub : Subsingleton ↑M ↔ Subsingleton (QuotSMulTop x ↑M)\nn : ℕ\n⊢ projectiveDimension ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 487,
"column": 14
} | {
"line": 487,
"column": 16
} | {
"line": 487,
"column": 17
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nh✝ : Nontrivial A\nhI : I ≠ ⊤\nthis : Nontrivial (A ⧸ I)\nf : A[X]\nhfdeg : f.degree < g.degree\nh1 : g.degree = ↑((map (Ideal.Quotient.mk I)) ↑g).order.toNat\n⊢ 0 *... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 466,
"column": 16
} | {
"line": 466,
"column": 18
} | {
"line": 467,
"column": 4
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nf : A[X] ⧸ Ideal.span {g}\n⊢ (⇑(Ideal.Quotient.mk (Ideal.span {g})) ∘ ⇑⋯.mod')\n ((↑↑(Ideal.quotientMapₐ (Ideal.span {↑g}) (Polynomial.coeToPowerSeries.algHom A... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 488,
"column": 17
} | {
"line": 488,
"column": 19
} | {
"line": 488,
"column": 20
} | [
{
"pp": "A : Type u_1\ninst✝¹ : CommRing A\ng✝ : A⟦X⟧\nI✝ : Ideal A\ng : A[X]\nI : Ideal A\nH : g.IsDistinguishedAt I\ninst✝ : IsAdicComplete I A\nf : A⟦X⟧ ⧸ Ideal.span {↑g}\n⊢ (↑↑(Ideal.quotientMapₐ (Ideal.span {↑g}) (Polynomial.coeToPowerSeries.algHom A) ⋯).toRingHom).toFun\n ((⇑(Ideal.Quotient.mk (Ideal... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WeierstrassPreparation | {
"line": 536,
"column": 31
} | {
"line": 536,
"column": 33
} | {
"line": 536,
"column": 34
} | [
{
"pp": "A : Type u_1\ninst✝² : CommRing A\ninst✝¹ : IsLocalRing A\nf : A⟦X⟧\ninst✝ : IsPrecomplete (IsLocalRing.maximalIdeal A) A\n⊢ ¬(map (IsLocalRing.residue A)) 0 ≠ 0",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"RingHom.instRingHomClass",
"False",
"MvPowerSeries.i... | [] | by | [anonymous] | by |
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