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.GradedAlgebra.TensorProduct | {
"line": 39,
"column": 17
} | {
"line": 39,
"column": 19
} | {
"line": 40,
"column": 4
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nA : Type u_3\nS : Type u_4\ninst✝⁷ : CommSemiring R\ninst✝⁶ : CommSemiring S\ninst✝⁵ : Algebra R S\ninst✝⁴ : DecidableEq ι\ninst✝³ : AddMonoid ι\ninst✝² : Semiring A\ninst✝¹ : Algebra R A\n𝒜 : ι → Submodule R A\ninst✝ : GradedAlgebra 𝒜\ni j : ι\n⊢ ∀ {gi gj : S ⊗[R] A},\n ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Frobenius | {
"line": 207,
"column": 78
} | {
"line": 207,
"column": 80
} | {
"line": 208,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R S\nG : Type u_3\ninst✝² : Group G\ninst✝¹ : MulSemiringAction G S\ninst✝ : SMulCommClass G R S\nQ : Ideal S\nσ : G\nH : IsArithFrobAt R σ Q\nτ : G\nx : S\n⊢ Ideal.under R (Ideal.map ((MulSemiringAction.toRingEquiv ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.Frobenius | {
"line": 205,
"column": 88
} | {
"line": 205,
"column": 90
} | {
"line": 206,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁵ : CommRing R\ninst✝⁴ : CommRing S\ninst✝³ : Algebra R S\nG : Type u_3\ninst✝² : Group G\ninst✝¹ : MulSemiringAction G S\ninst✝ : SMulCommClass G R S\nQ : Ideal S\nσ : G\nH : IsArithFrobAt R σ Q\nτ : G\n⊢ IsArithFrobAt R (τ * σ * τ⁻¹) (τ • Q)",
"ppTerm": "?m.38",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.GradedAlgebra.TensorProduct | {
"line": 128,
"column": 50
} | {
"line": 128,
"column": 52
} | {
"line": 128,
"column": 53
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nS : Type u_3\nA : Type u_4\nB : Type u_5\ninst✝¹² : DecidableEq ι\ninst✝¹¹ : AddMonoid ι\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R A\ninst✝⁵ : Algebra S B\n𝒜 : ι → Submodule R A\nℬ : ι → Submodule S B\ni... | [] | by | [anonymous] | by |
Mathlib.RingTheory.GradedAlgebra.TensorProduct | {
"line": 123,
"column": 20
} | {
"line": 123,
"column": 22
} | {
"line": 124,
"column": 8
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nS : Type u_3\nA : Type u_4\nB : Type u_5\ninst✝¹² : DecidableEq ι\ninst✝¹¹ : AddMonoid ι\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R A\ninst✝⁵ : Algebra S B\n𝒜 : ι → Submodule R A\nℬ : ι → Submodule S B\ni... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Frobenius | {
"line": 233,
"column": 21
} | {
"line": 233,
"column": 23
} | {
"line": 234,
"column": 8
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁹ : CommRing R\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nG : Type u_3\ninst✝⁶ : Group G\ninst✝⁵ : MulSemiringAction G S\ninst✝⁴ : SMulCommClass G R S\nQ : Ideal S\ninst✝³ : Finite G\ninst✝² : Algebra.IsInvariant R S G\ninst✝¹ : Q.IsPrime\ninst✝ : Finite (S ⧸ Q)\nP : I... | [] | by | [anonymous] | by |
Mathlib.RingTheory.GradedAlgebra.TensorProduct | {
"line": 132,
"column": 42
} | {
"line": 132,
"column": 44
} | {
"line": 132,
"column": 45
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nS : Type u_3\nA : Type u_4\nB : Type u_5\ninst✝¹² : DecidableEq ι\ninst✝¹¹ : AddMonoid ι\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R A\ninst✝⁵ : Algebra S B\n𝒜 : ι → Submodule R A\nℬ : ι → Submodule S B\ni... | [] | by | [anonymous] | by |
Mathlib.RingTheory.GradedAlgebra.TensorProduct | {
"line": 133,
"column": 43
} | {
"line": 133,
"column": 45
} | {
"line": 133,
"column": 46
} | [
{
"pp": "ι : Type u_1\nR : Type u_2\nS : Type u_3\nA : Type u_4\nB : Type u_5\ninst✝¹² : DecidableEq ι\ninst✝¹¹ : AddMonoid ι\ninst✝¹⁰ : CommSemiring R\ninst✝⁹ : CommSemiring S\ninst✝⁸ : Semiring A\ninst✝⁷ : Semiring B\ninst✝⁶ : Algebra R A\ninst✝⁵ : Algebra S B\n𝒜 : ι → Submodule R A\nℬ : ι → Submodule S B\ni... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Frobenius | {
"line": 221,
"column": 91
} | {
"line": 221,
"column": 93
} | {
"line": 222,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁹ : CommRing R\ninst✝⁸ : CommRing S\ninst✝⁷ : Algebra R S\nG : Type u_3\ninst✝⁶ : Group G\ninst✝⁵ : MulSemiringAction G S\ninst✝⁴ : SMulCommClass G R S\nQ : Ideal S\ninst✝³ : Finite G\ninst✝² : Algebra.IsInvariant R S G\ninst✝¹ : Q.IsPrime\ninst✝ : Finite (S ⧸ Q)\n⊢ ∃ σ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Frobenius | {
"line": 245,
"column": 41
} | {
"line": 245,
"column": 43
} | {
"line": 246,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : CommRing R\ninst✝⁶ : CommRing S\ninst✝⁵ : Algebra R S\nG : Type u_3\ninst✝⁴ : Group G\ninst✝³ : MulSemiringAction G S\ninst✝² : SMulCommClass G R S\ninst✝¹ : Finite G\ninst✝ : Algebra.IsInvariant R S G\nP : Ideal R\nhP : ∃ Q, Finite (S ⧸ ↑Q)\n⊢ ∃ σ, (∀ (Q : ↑(P.prim... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Frobenius | {
"line": 275,
"column": 2
} | {
"line": 276,
"column": 38
} | {
"line": 277,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nG : Type u_3\ninst✝⁸ : Group G\ninst✝⁷ : MulSemiringAction G S\ninst✝⁶ : SMulCommClass G R S\nQ : Ideal S\ninst✝⁵ : Finite G\ninst✝⁴ : Algebra.IsInvariant R S G\ninst✝³ : Q.IsPrime\ninst✝² : Finite (S ⧸ Q)\nQ'... | [
"R : Type u_1\nS : Type u_2\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nG : Type u_3\ninst✝⁸ : Group G\ninst✝⁷ : MulSemiringAction G S\ninst✝⁶ : SMulCommClass G R S\nQ : Ideal S\ninst✝⁵ : Finite G\ninst✝⁴ : Algebra.IsInvariant R S G\ninst✝³ : Q.IsPrime\ninst✝² : Finite (S ⧸ Q)\nQ' : Ideal S\n... | obtain ⟨P, hP, h₁, h₂⟩ : ∃ P : Ideal R, P.IsPrime ∧ P = Q.under R ∧ P = Q'.under R :=
⟨Q.under R, inferInstance, rfl, H⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.Frobenius | {
"line": 274,
"column": 86
} | {
"line": 274,
"column": 88
} | {
"line": 275,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹¹ : CommRing R\ninst✝¹⁰ : CommRing S\ninst✝⁹ : Algebra R S\nG : Type u_3\ninst✝⁸ : Group G\ninst✝⁷ : MulSemiringAction G S\ninst✝⁶ : SMulCommClass G R S\nQ : Ideal S\ninst✝⁵ : Finite G\ninst✝⁴ : Algebra.IsInvariant R S G\ninst✝³ : Q.IsPrime\ninst✝² : Finite (S ⧸ Q)\nQ'... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 84,
"column": 83
} | {
"line": 84,
"column": 85
} | {
"line": 85,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝² : CommRing R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nk : ℕ\nN₁ N₂ : G(k, M; R)\nh : N₁.toSubmodule = N₂.toSubmodule\n⊢ N₁ = N₂",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Module.Grassmannian",
"Submodule",
"Submodule.Quot... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 132,
"column": 76
} | {
"line": 132,
"column": 78
} | {
"line": 133,
"column": 10
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nk : ℕ\nA : Type w\ninst✝³ : CommRing A\ninst✝² : Algebra R A\nB : Type w\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\nf : A →ₐ[R] B\nN : G(k, A ⊗[R] M; A)\nthis✝ : Algebra A B := f.toAlgebra\nthis : IsScalarTower R... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 135,
"column": 56
} | {
"line": 135,
"column": 58
} | {
"line": 136,
"column": 10
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nk : ℕ\nA : Type w\ninst✝³ : CommRing A\ninst✝² : Algebra R A\nB : Type w\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\nf : A →ₐ[R] B\nN : G(k, A ⊗[R] M; A)\nthis✝ : Algebra A B := f.toAlgebra\nthis : IsScalarTower R... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 130,
"column": 24
} | {
"line": 130,
"column": 26
} | {
"line": 131,
"column": 6
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nk : ℕ\nA : Type w\ninst✝³ : CommRing A\ninst✝² : Algebra R A\nB : Type w\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\nf : A →ₐ[R] B\nN : G(k, A ⊗[R] M; A)\nthis✝ : Algebra A B := f.toAlgebra\nthis : IsScalarTower R... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 142,
"column": 65
} | {
"line": 142,
"column": 67
} | {
"line": 142,
"column": 68
} | [
{
"pp": "R : Type u\ninst✝⁶ : CommRing R\nM : Type v\ninst✝⁵ : AddCommGroup M\ninst✝⁴ : Module R M\nk : ℕ\nA : Type w\ninst✝³ : CommRing A\ninst✝² : Algebra R A\nB : Type w\ninst✝¹ : CommRing B\ninst✝ : Algebra R B\nf : A →ₐ[R] B\nN : G(k, A ⊗[R] M; A)\n⊢ (map f N).toSubmodule = (baseChangeMkQ B N.toSubmodule).... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 147,
"column": 27
} | {
"line": 147,
"column": 29
} | {
"line": 148,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝² : CommRing R\nM : Type v\ninst✝¹ : AddCommGroup M\ninst✝ : Module R M\nk : ℕ\nA : CommAlgCat R\nN : G(k, ↑A ⊗[R] M; ↑A)\n⊢ map (AlgHom.id R ↑A) N = N",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"TensorProduct.AlgebraTensorModule.cancelBaseChange",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 158,
"column": 31
} | {
"line": 158,
"column": 33
} | {
"line": 158,
"column": 34
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommRing R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nk : ℕ\nA : Type w\ninst✝⁵ : CommRing A\ninst✝⁴ : Algebra R A\nB : Type w\ninst✝³ : CommRing B\ninst✝² : Algebra R B\nf : A →ₐ[R] B\nC : Type w\ninst✝¹ : CommRing C\ninst✝ : Algebra R C\ng : B →ₐ[R] C\nN : G(k, A ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 169,
"column": 64
} | {
"line": 169,
"column": 66
} | {
"line": 170,
"column": 4
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommRing R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nk : ℕ\nA : Type w\ninst✝⁵ : CommRing A\ninst✝⁴ : Algebra R A\nB : Type w\ninst✝³ : CommRing B\ninst✝² : Algebra R B\nf : A →ₐ[R] B\nC : Type w\ninst✝¹ : CommRing C\ninst✝ : Algebra R C\ng : B →ₐ[R] C\nN : G(k, A ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 84,
"column": 49
} | {
"line": 84,
"column": 51
} | {
"line": 84,
"column": 52
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf₀ f₁ f₂ : MvPowerSeries σ R\nh₀ : PowerSeries.HasSubst f₀\nh₁ : PowerSeries.HasSubst f₁\nh₂ : PowerSeries.HasSubst f₂\naux₁ : HasSubst ![subst ![Y₀, Y₁] F.toPowerSeries, Y₂]\naux₂ : HasSubst ![Y₀, subst ![Y₁, Y₂] F.toPowerSeries]\ns : ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 171,
"column": 47
} | {
"line": 171,
"column": 49
} | {
"line": 172,
"column": 4
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommRing R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nk : ℕ\nA : Type w\ninst✝⁵ : CommRing A\ninst✝⁴ : Algebra R A\nB : Type w\ninst✝³ : CommRing B\ninst✝² : Algebra R B\nf : A →ₐ[R] B\nC : Type w\ninst✝¹ : CommRing C\ninst✝ : Algebra R C\ng : B →ₐ[R] C\nN : G(k, A ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 86,
"column": 94
} | {
"line": 86,
"column": 96
} | {
"line": 87,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf₀ f₁ f₂ : MvPowerSeries σ R\nh₀ : PowerSeries.HasSubst f₀\nh₁ : PowerSeries.HasSubst f₁\nh₂ : PowerSeries.HasSubst f₂\naux₁ : HasSubst ![subst ![Y₀, Y₁] F.toPowerSeries, Y₂]\naux₂ : HasSubst ![Y₀, subst ![Y₁, Y₂] F.toPowerSeries]\nthis... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 155,
"column": 42
} | {
"line": 155,
"column": 44
} | {
"line": 156,
"column": 2
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommRing R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nk : ℕ\nA : Type w\ninst✝⁵ : CommRing A\ninst✝⁴ : Algebra R A\nB : Type w\ninst✝³ : CommRing B\ninst✝² : Algebra R B\nf : A →ₐ[R] B\nC : Type w\ninst✝¹ : CommRing C\ninst✝ : Algebra R C\ng : B →ₐ[R] C\nN : G(k, A ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 191,
"column": 14
} | {
"line": 191,
"column": 16
} | {
"line": 191,
"column": 17
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommRing R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nk : ℕ\nA✝ : Type w\ninst✝⁵ : CommRing A✝\ninst✝⁴ : Algebra R A✝\nB : Type w\ninst✝³ : CommRing B\ninst✝² : Algebra R B\nf : A✝ →ₐ[R] B\nC : Type w\ninst✝¹ : CommRing C\ninst✝ : Algebra R C\ng : B →ₐ[R] C\nA : Com... | [] | by | [anonymous] | by |
Mathlib.RingTheory.Grassmannian | {
"line": 192,
"column": 18
} | {
"line": 192,
"column": 20
} | {
"line": 192,
"column": 21
} | [
{
"pp": "R : Type u\ninst✝⁸ : CommRing R\nM : Type v\ninst✝⁷ : AddCommGroup M\ninst✝⁶ : Module R M\nk : ℕ\nA : Type w\ninst✝⁵ : CommRing A\ninst✝⁴ : Algebra R A\nB : Type w\ninst✝³ : CommRing B\ninst✝² : Algebra R B\nf✝ : A →ₐ[R] B\nC : Type w\ninst✝¹ : CommRing C\ninst✝ : Algebra R C\ng✝ : B →ₐ[R] C\nX✝ Y✝ Z✝ ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 46,
"column": 87
} | {
"line": 46,
"column": 89
} | {
"line": 47,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : Ring R\nu : Rˣ\n⊢ constantCoeff (invUnitsSub u) = 1 /ₚ u",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMa... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 50,
"column": 90
} | {
"line": 50,
"column": 92
} | {
"line": 51,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : Ring R\nu : Rˣ\n⊢ invUnitsSub u * X = invUnitsSub u * C ↑u - 1",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"PowerSeries.coeff_mul_C",
"Units.val",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 56,
"column": 78
} | {
"line": 56,
"column": 80
} | {
"line": 57,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : Ring R\nu : Rˣ\n⊢ invUnitsSub u * (C ↑u - X) = 1",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"MvPowerSeries.instAddCommGroup",
"Units.val",
"HMul.hMul",
"Ring.toNonAssocRing",
"mul_sub",
"AddGroupWithOne.toAddGroup",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 60,
"column": 70
} | {
"line": 60,
"column": 72
} | {
"line": 61,
"column": 2
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝¹ : Ring R\ninst✝ : Ring S\nf : R →+* S\nu : Rˣ\n⊢ (map f) (invUnitsSub u) = invUnitsSub ((Units.map ↑f) u)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"RingHom.instRingHomClass",
"MonoidHom.instMo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 77,
"column": 67
} | {
"line": 77,
"column": 69
} | {
"line": 78,
"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\n⊢ mk 1 * (1 - X) = 1",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"False... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 90,
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} | {
"line": 90,
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} | {
"line": 91,
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} | [
{
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Mathlib.RingTheory.PowerSeries.WellKnown | {
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} | {
"line": 111,
"column": 17
} | {
"line": 112,
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} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd✝ d : ℕ\n⊢ (mk fun n ↦ ↑((d + n).choose d)) * (1 - X) ^ (d + 1) = 1",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 113,
"column": 15
} | {
"line": 113,
"column": 17
} | {
"line": 114,
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} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd✝ d : ℕ\n⊢ ((1 - X) ^ (d + 1) * mk fun n ↦ ↑((d + n).choose d)) = 1",
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Mathlib.RingTheory.PowerSeries.WellKnown | {
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} | {
"line": 119,
"column": 11
} | {
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} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\n⊢ (match 0 with\n | 0 => 1\n | d.succ => { val := mk fun n ↦ ↑((d + n).choose d), inv := (1 - X) ^ (d + 1), val_inv := ⋯, inv_val := ⋯ }) =\n 1",
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"CommSemiring.toSemiring",
"Units",... | [] | simp only | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 117,
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} | {
"line": 117,
"column": 54
} | {
"line": 118,
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} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\n⊢ invOneSubPow S 0 = 1",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 122,
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} | {
"line": 122,
"column": 86
} | {
"line": 123,
"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd : ℕ\nh : 0 < d\n⊢ ↑(invOneSubPow S d) = mk fun n ↦ ↑((d - 1 + n).choose (d - 1))",
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"Units.val",
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"Nat.instOrderedSub",
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"Nat.instIsOrderedAddMonoid... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 95,
"column": 13
} | {
"line": 95,
"column": 15
} | {
"line": 96,
"column": 6
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf₀ f₁ f₂ : MvPowerSeries σ R\nh₀ : PowerSeries.HasSubst f₀\nh₁ : PowerSeries.HasSubst f₁\nh₂ : PowerSeries.HasSubst f₂\naux₁ : HasSubst ![subst ![Y₀, Y₁] F.toPowerSeries, Y₂]\naux₂ : HasSubst ![Y₀, subst ![Y₁, Y₂] F.toPowerSeries]\nthis... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 129,
"column": 53
} | {
"line": 129,
"column": 55
} | {
"line": 130,
"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\n⊢ ↑(invOneSubPow S 1) = invUnitsSub 1",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 80,
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} | {
"line": 80,
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} | {
"line": 81,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_3\nF : FormalGroup R\nf₀ f₁ f₂ : MvPowerSeries σ R\nh₀ : PowerSeries.HasSubst f₀\nh₁ : PowerSeries.HasSubst f₁\nh₂ : PowerSeries.HasSubst f₂\n⊢ subst ![subst ![f₀, f₁] F.toPowerSeries, f₂] F.toPowerSeries =\n subst ![f₀, subst ![f₁, f₂] F.toPowerSeries] F... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 109,
"column": 82
} | {
"line": 109,
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} | {
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} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nσ : Type u_3\nF : FormalGroup R\ninst✝ : F.IsComm\nf g : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\nhg : PowerSeries.HasSubst g\n⊢ ∀ (s : Fin (Nat.succ 0).succ), IsNilpotent (constantCoeff (![f, g] s))",
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Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
"line": 56,
"column": 55
} | {
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} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\nhx : ¬0 < x.orderTop\nf : PowerSeries R\n⊢ powerSeriesFamily x f = powerSeriesFamily 0 f",
"ppTer... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 145,
"column": 72
} | {
"line": 145,
"column": 74
} | {
"line": 146,
"column": 8
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd✝ d : ℕ\na✝ : invOneSubPow S d = (Units.mkOfMulEqOne (1 - X) (mk 1) ⋯)⁻¹ ^ d\n⊢ Units.mkOfMulEqOne (1 - X) (mk 1) ⋯ ^ (d + 1) * invOneSubPow S (d + 1) = 1",
"ppTerm": "?m.62",
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Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
"line": 62,
"column": 53
} | {
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} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\nhx : 0 < x.orderTop\nf : PowerSeries R\nn : ℕ\n⊢ (powerSeriesFamily x f) n = (PowerSeries.coeff n) f ... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
"line": 70,
"column": 43
} | {
"line": 70,
"column": 44
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nf : PowerSeries R\ng : Γ\nhg : g = 0\nn : ℕ\nhn : n ≠ 0\n⊢ ((powerSeriesFamily 0 f) n).coeff 0 = 0",
"ppTer... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
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"column": 72
} | {
"line": 140,
"column": 74
} | {
"line": 141,
"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd : ℕ\n⊢ invOneSubPow S d = (Units.mkOfMulEqOne (1 - X) (mk 1) ⋯)⁻¹ ^ d",
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"usedConstants": [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
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"Eq.mpr",
"MulOne.toOne",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 150,
"column": 51
} | {
"line": 150,
"column": 53
} | {
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"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd : ℕ\n⊢ (invOneSubPow S d).inv = (1 - X) ^ d",
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"AddGroupWithOne.toAddGroup",
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"HSub.hSub",
"MvPo... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
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"column": 69
} | {
"line": 155,
"column": 71
} | {
"line": 156,
"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\n⊢ (invOneSubPow S 0).inv = 1",
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
"line": 73,
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} | {
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} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nf : PowerSeries R\ng : Γ\nhg : ¬g = 0\nn : ℕ\n⊢ ((powerSeriesFamily 0 f) n).coeff g = 0",
"ppTerm": "?m.85"... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 164,
"column": 68
} | {
"line": 164,
"column": 70
} | {
"line": 165,
"column": 2
} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd e : ℕ\n⊢ invOneSubPow S (d + e) = invOneSubPow S d * invOneSubPow S e",
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"MulOne.toOne",
"NonUnitalCommRi... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
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"column": 69
} | {
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"column": 71
} | {
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} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nσ : Type u_3\nF : FormalGroup R\ninst✝ : F.IsComm\nf g : MvPowerSeries σ R\nhf : PowerSeries.HasSubst f\nhg : PowerSeries.HasSubst g\n⊢ subst ![f, g] F.toPowerSeries = subst ![g, f] F.toPowerSeries",
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"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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} | {
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"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nf : PowerSeries R\n⊢ (powerSeriesFamily 0 f).hsum = PowerSeries.constantCoeff f • 1",
"ppTerm": "?m.33",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
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"column": 75
} | {
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} | {
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} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd e : ℕ\n⊢ (1 - X) ^ e * ↑(invOneSubPow S (d + e)) = ↑(invOneSubPow S d)",
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"usedConstants": [
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"MulOne.toOne",
"Semigroup.t... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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} | {
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} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\nx y : F.Point σ\n⊢ HasSubst ![↑x, ↑y]",
"ppTerm": "?m.42",
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"usedConstants": [
"congrArg",
"CommSemiring.toSemiring",
"and_se... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
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"column": 91
} | {
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} | {
"line": 135,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝ : CommRing R\nσ : Type u_5\nF : FormalGroup R\nx y : F.Point σ\n⊢ ↑(x + y) = subst ![↑x, ↑y] F.toPowerSeries",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"PowerSeries.HasSubst",
"MvPowerSeries",
"instHAdd",
"FormalGroup.instAddPoint",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
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"column": 64
} | {
"line": 172,
"column": 66
} | {
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} | [
{
"pp": "S : Type u_1\ninst✝ : CommRing S\nd e : ℕ\n⊢ (1 - X) ^ (d + e) * ↑(invOneSubPow S e) = (1 - X) ^ d",
"ppTerm": "?m.49",
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"MulOne.toOne",
"Semigroup.toMul",
"PowerSeries.invOneSubPow_inv_eq_one_sub_pow",
"HMul.hMu... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 147,
"column": 24
} | {
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"column": 26
} | {
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} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 148,
"column": 17
} | {
"line": 148,
"column": 19
} | {
"line": 148,
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} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 149,
"column": 17
} | {
"line": 149,
"column": 19
} | {
"line": 149,
"column": 20
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
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"column": 44
} | {
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"column": 46
} | {
"line": 195,
"column": 2
} | [
{
"pp": "A : Type u_1\nA' : Type u_2\ninst✝³ : Ring A\ninst✝² : Ring A'\ninst✝¹ : Algebra ℚ A\ninst✝ : Algebra ℚ A'\nf : A →+* A'\n⊢ (map f) (sin A) = sin A'",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"RingHom.instRingHomClass",
"instHDiv",
"Se... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 151,
"column": 81
} | {
"line": 151,
"column": 83
} | {
"line": 151,
"column": 84
} | [
{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
"ppTerm": "?m.60",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.WellKnown | {
"line": 199,
"column": 44
} | {
"line": 199,
"column": 46
} | {
"line": 200,
"column": 2
} | [
{
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"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"RingHom.instRingHomClass",
"instHDiv",
"Se... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
"line": 152,
"column": 82
} | {
"line": 152,
"column": 84
} | {
"line": 152,
"column": 85
} | [
{
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Mathlib.RingTheory.HahnSeries.HEval | {
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"column": 83
} | {
"line": 77,
"column": 85
} | {
"line": 78,
"column": 2
} | [
{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
"line": 82,
"column": 89
} | {
"line": 82,
"column": 91
} | {
"line": 83,
"column": 2
} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\nf : PowerSeries R\nr : R\n⊢ powerSeriesFamily x (r • f) = (HahnSeries.single 0) r • powerSeriesFamily... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Binomial | {
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"column": 46
} | {
"line": 57,
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} | {
"line": 58,
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} | [
{
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"ppTerm": "?m.16",
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"usedConstants": [
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"MulOne.toOne",
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Binomial | {
"line": 62,
"column": 74
} | {
"line": 62,
"column": 76
} | {
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{
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Mathlib.RingTheory.PowerSeries.Binomial | {
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{
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Mathlib.RingTheory.PowerSeries.Binomial | {
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{
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Mathlib.RingTheory.PowerSeries.Binomial | {
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{
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Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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{
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Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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} | {
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{
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"CommRing",
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Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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{
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"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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} | {
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{
"pp": "R : Type u_1\ninst✝¹ : CommRing R\nS : Type u_2\ninst✝ : CommRing S\nσ✝ : Type u_3\nτ : Type u_4\nσ : Type u_5\nF : FormalGroup R\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
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"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.PowerSeries.Binomial | {
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} | {
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} | {
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{
"pp": "A : Type u_2\ninst✝ : CommRing A\nd : ℕ\n⊢ (rescale (-1)) ↑(invOneSubPow A d) = binomialSeries A (-↑d)",
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Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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} | {
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{
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"ppTerm": "?m.51",
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"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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} | {
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{
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"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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} | [
{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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{
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"ppTerm":... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.FormalGroup.Basic | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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} | {
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} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\na b : PowerSeries R\ng : Γ\nh : ¬0 < x.orderTop\nn : ℕ\nhn : ((powerSeriesFamily x (a * b)) n).coeff ... | [] | by | Lean.Elab.Tactic.evalWithAnnotateState | by |
Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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} | [
{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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} | [
{
"pp": "Γ : Type u_1\nR : Type u_2\nA : Type u_3\ninst✝⁶ : LinearOrder Γ\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : IsOrderedCancelAddMonoid Γ\ninst✝³ : CommRing R\ninst✝² : BinomialRing R\ninst✝¹ : CommRing A\ninst✝ : Algebra R A\nx : A⟦Γ⟧\nhx : 0 < (x - 1).orderTop\nr : R\nh✝ : Nontrivial A\nthis : ((binomialFamily... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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} | {
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} | [
{
"pp": "Γ : Type u_1\nR : Type u_3\nV : Type u_4\ninst✝⁵ : AddCommMonoid Γ\ninst✝⁴ : LinearOrder Γ\ninst✝³ : IsOrderedCancelAddMonoid Γ\ninst✝² : CommRing R\ninst✝¹ : CommRing V\ninst✝ : Algebra R V\nx : V⟦Γ⟧\na b : PowerSeries R\ng : Γ\n⊢ ((powerSeriesFamily x (a * b)).coeff g).support ⊆\n image (fun i ↦ i... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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"as... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Binomial | {
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} | {
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} | {
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{
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"ppTerm": "?m.98",... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Binomial | {
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{
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.HEval | {
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} | {
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{
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Mathlib.RingTheory.HahnSeries.Summable | {
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} | {
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} | {
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{
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"usedConstants":... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
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} | {
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} | {
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{
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"ppTerm":... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
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} | {
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} | {
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{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\n⊢ (⋃ a, (0 a).support).IsPWO",
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"usedConstants": [
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... | [] | by | [anonymous] | by |
Mathlib.RingTheory.HahnSeries.Summable | {
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} | {
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} | {
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} | [
{
"pp": "Γ : Type u_1\nΓ' : Type u_2\nR : Type u_3\nV : Type u_4\nα : Type u_5\nβ : Type u_6\ninst✝¹ : PartialOrder Γ\ninst✝ : AddCommMonoid R\n⊢ ∀ (g : Γ), {a | (0 a).coeff g ≠ 0}.Finite",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"Set.ofPred",
... | [] | by | [anonymous] | by |
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