module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.CategoryTheory.EffectiveEpi.Comp | {
"line": 86,
"column": 65
} | {
"line": 86,
"column": 84
} | [
{
"pp": "C✝ : Type u_1\ninst✝³ : Category.{v_1, u_1} C✝\nC : Type u_2\ninst✝² : Category.{v_2, u_2} C\nI : Type u_3\nZ Y : I → C\nX : C\ng : (i : I) → Z i ⟶ Y i\nf : (i : I) → Y i ⟶ X\ninst✝¹ : EffectiveEpiFamily Z fun i ↦ g i ≫ f i\ninst✝ : ∀ (i : I), Epi (g i)\nW : C\nφ : (a : I) → Y a ⟶ W\nh : ∀ {Z : C} (a₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EffectiveEpi.Preserves | {
"line": 48,
"column": 2
} | {
"line": 48,
"column": 13
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nD : Type u_2\ninst✝ : Category.{v_2, u_2} D\ne : C ≌ D\nB : C\nα : Type u_3\nX : α → C\nπ : (a : α) → X a ⟶ B\nW : D\nε : (a : α) → e.functor.obj (X a) ⟶ W\nh :\n ∀ {Z : D} (a₁ a₂ : α) (g₁ : Z ⟶ e.functor.obj (X a₁)) (g₂ : Z ⟶ e.functor.obj (X a₂)),\n g... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 119,
"column": 6
} | {
"line": 119,
"column": 46
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofilteredOrEmpty I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nZ : (i : I) → Set ↥(D.obj i)\nhZc : ∀ (i : I), IsClosed (Z i)\nhZne : ∀ (i : I), (Z i).Nonempty\nhZcpt : ∀ (i : I), IsCompact (Z i)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 13
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofilteredOrEmpty I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nZ : (i : I) → Set ↥(D.obj i)\nhZc : ∀ (i : I), IsClosed (Z i)\nhZne : ∀ (i : I), (Z i).Nonempty\nhZcpt : ∀ (i : I), IsCompact (Z i)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 168,
"column": 2
} | {
"line": 168,
"column": 31
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofilteredOrEmpty I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nj : I\nZ : (i : I) → (i ⟶ j) → Set ↥(D.obj i)\nhZc : ∀ (i : I) (hij : i ⟶ j), IsClosed (Z i hij)\nhZne : ∀ (i : I) (hij : i ⟶ j), (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 191,
"column": 44
} | {
"line": 191,
"column": 55
} | [
{
"pp": "I : Type u\ninst✝³ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝² : IsCofiltered I\ninst✝¹ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ninst✝ : ∀ (i : I), CompactSpace ↥(D.obj i)\ni : I\nU : (D.obj i).Opens\nhU : c.π.app i ⁻¹ᵁ U = ⊤\nH : ∀ (j : I) (fji : j ⟶ i), D.map fji ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 417,
"column": 18
} | {
"line": 417,
"column": 53
} | [
{
"pp": "case hab.h\nR₀ : Type u_1\ninst✝² : CommRing R₀\nn : ℕ\nR : Type u_6\ninst✝¹ : CommRing R\ninst✝ : Algebra R₀ R\nc : R\ni : Fin n\ne : InductionObj R n\nhi : c = (e.val i).leadingCoeff\nhc : c ≠ 0\nq₁ : R →ₐ[R₀] Localization.Away c := ⋯\nq₂ : R →ₐ[R₀] R ⧸ Ideal.span {c} := ⋯\nq₂_surjective : Surjective... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 280,
"column": 4
} | {
"line": 280,
"column": 67
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU V : (D.obj i).Opens\nhU : IsCompact ↑U\nH✝ : c.π.app i ⁻¹ᵁ U ≤ c.π.app i ⁻¹ᵁ V\nthis : ∀ (j : Over i), CompactSpace ↥((opensDiagr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 282,
"column": 34
} | {
"line": 282,
"column": 45
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU V : (D.obj i).Opens\nhU : IsCompact ↑U\nH✝ : c.π.app i ⁻¹ᵁ U ≤ c.π.app i ⁻¹ᵁ V\nthis : ∀ (j : Over i), CompactSpace ↥((opensDiagr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 58
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU V : (D.obj i).Opens\nhU : IsCompact ↑U\nH✝ : c.π.app i ⁻¹ᵁ U ≤ c.π.app i ⁻¹ᵁ V\nthis : ∀ (j : Over i), CompactSpace ↥((opensDiagr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 425,
"column": 8
} | {
"line": 425,
"column": 19
} | [
{
"pp": "R₀ : Type u_1\ninst✝² : CommRing R₀\nn : ℕ\nR : Type u_6\ninst✝¹ : CommRing R\ninst✝ : Algebra R₀ R\nc : R\ni : Fin n\ne : InductionObj R n\nhi : c = (e.val i).leadingCoeff\nhc : c ≠ 0\nq₁ : R →ₐ[R₀] Localization.Away c := IsScalarTower.toAlgHom R₀ R (Localization.Away c)\nq₂ : R →ₐ[R₀] R ⧸ Ideal.span ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 296,
"column": 4
} | {
"line": 296,
"column": 65
} | [
{
"pp": "case refine_1\nI : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU V : (D.obj i).Opens\nhU : IsCompact ↑U\nhV : IsCompact ↑V\nH : c.π.app i ⁻¹ᵁ U = c.π.app i ⁻¹ᵁ V\nj₁ : I\nfj₁i : j... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 298,
"column": 4
} | {
"line": 298,
"column": 65
} | [
{
"pp": "case refine_2\nI : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU V : (D.obj i).Opens\nhU : IsCompact ↑U\nhV : IsCompact ↑V\nH : c.π.app i ⁻¹ᵁ U = c.π.app i ⁻¹ᵁ V\nj₁ : I\nfj₁i : j... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 340,
"column": 24
} | {
"line": 340,
"column": 66
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : Set (TopologicalSpace.Opens ↥c.pt)\nhs : s ⊆ {x | ∃ i V, ∃ (_ : IsAffineOpen V), c.π.app i ⁻¹ᵁ V = x}\nhsf : s.Finite\nhU : IsCompact ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 341,
"column": 58
} | {
"line": 341,
"column": 69
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : Set (TopologicalSpace.Opens ↥c.pt)\nhs : s ⊆ {x | ∃ i V, ∃ (_ : IsAffineOpen V), c.π.app i ⁻¹ᵁ V = x}\nhsf : s.Finite\nhU : IsCompact ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 413,
"column": 4
} | {
"line": 413,
"column": 15
} | [
{
"pp": "case inr\nI : Type u\ninst✝⁷ : Category.{u, u} I\nX : Scheme\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝⁶ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝⁵ : IsCofiltered I\ninst✝⁴ : IsAffine X\ninst✝³ : ∀ (i : I), IsAffine (D.obj i)\ninst✝² : IsAffine c.pt\ni : I\na : D.obj i ⟶ X\nj : I\nb : D.obj j... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Morphisms.Flat | {
"line": 308,
"column": 12
} | {
"line": 308,
"column": 23
} | [
{
"pp": "case h.e'_3.h\nX Y S T : Scheme\nf : T ⟶ S\ng : Y ⟶ X\niX : X ⟶ S\niY : Y ⟶ T\nH : IsPullback g iY iX f\nUS : S.Opens\nUT : T.Opens\nUX : X.Opens\nhUST : UT ≤ f ⁻¹ᵁ US\nhUSX : UX ≤ iX ⁻¹ᵁ US\nUY : Y.Opens\nhUY : UY = g ⁻¹ᵁ UX ⊓ iY ⁻¹ᵁ UT\nι : Type u_1\ninst✝ : Finite ι\nVX : ι → X.Opens\nhVU : iSup VX ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 430,
"column": 4
} | {
"line": 430,
"column": 15
} | [
{
"pp": "case inr\nI : Type u\ninst✝¹⁰ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝⁹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝⁸ : IsCofiltered I\ninst✝⁷ : ∀ (i : I), IsAffine (D.obj i)\ninst✝⁶ : IsAffine c.pt\ni j : I\nR : CommRingCat\nt : D ⟶ (Functor.const I).obj (Spec R)\ninst✝⁵ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 439,
"column": 10
} | {
"line": 439,
"column": 21
} | [
{
"pp": "I : Type u\ninst✝⁷ : Category.{u, u} I\ninst✝⁶ : IsCofiltered I\ni j : I\nR : CommRingCat\ninst✝⁵ : IsAffine (Spec R)\nS : CommRingCat\ninst✝⁴ : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝³ : LocallyOfFiniteType (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝² : ∀ (i : I)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 439,
"column": 52
} | {
"line": 439,
"column": 72
} | [
{
"pp": "I : Type u\ninst✝⁷ : Category.{u, u} I\ninst✝⁶ : IsCofiltered I\ni j : I\nR : CommRingCat\ninst✝⁵ : IsAffine (Spec R)\nS : CommRingCat\ninst✝⁴ : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝³ : LocallyOfFiniteType (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝² : ∀ (i : I)... | by ext : 2; simp [e] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 445,
"column": 30
} | {
"line": 445,
"column": 41
} | [
{
"pp": "I : Type u\ninst✝⁷ : Category.{u, u} I\ninst✝⁶ : IsCofiltered I\ni j : I\nR : CommRingCat\ninst✝⁵ : IsAffine (Spec R)\nS : CommRingCat\ninst✝⁴ : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝³ : LocallyOfFiniteType (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝² : ∀ (i : I)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 446,
"column": 30
} | {
"line": 446,
"column": 41
} | [
{
"pp": "I : Type u\ninst✝⁷ : Category.{u, u} I\ninst✝⁶ : IsCofiltered I\ni j : I\nR : CommRingCat\ninst✝⁵ : IsAffine (Spec R)\nS : CommRingCat\ninst✝⁴ : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝³ : LocallyOfFiniteType (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝² : ∀ (i : I)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 451,
"column": 40
} | {
"line": 451,
"column": 83
} | [
{
"pp": "I : Type u\ninst✝⁷ : Category.{u, u} I\ninst✝⁶ : IsCofiltered I\ni j : I\nR : CommRingCat\ninst✝⁵ : IsAffine (Spec R)\nS : CommRingCat\ninst✝⁴ : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝³ : LocallyOfFiniteType (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝² : ∀ (i : I)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 524,
"column": 2
} | {
"line": 524,
"column": 49
} | [
{
"pp": "I : Type u\ninst✝³ : Category.{u, u} I\nS X : Scheme\nD : I ⥤ Scheme\nt : D ⟶ (Functor.const I).obj S\nf : X ⟶ S\ninst✝² : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nA : ExistsHomHomCompEqCompAux D t f\n⊢ Set.range ⇑A.g ⊆ ↑(Schem... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 533,
"column": 16
} | {
"line": 534,
"column": 57
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nS X : Scheme\nD : I ⥤ Scheme\nt : D ⟶ (Functor.const I).obj S\nf : X ⟶ S\nc : Cone D\nhc : IsLimit c\ninst✝³ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝² : LocallyOfFiniteType f\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nA :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | {
"line": 148,
"column": 32
} | {
"line": 148,
"column": 51
} | [
{
"pp": "R : Type u\ninst✝ : CommRing R\nW✝ : WeierstrassCurve R\nC : VariableChange R\nW : WeierstrassCurve R\n⊢ { u := 1, r := 0, s := 0, t := 0 } • W = W",
"usedConstants": [
"WeierstrassCurve.VariableChange.r",
"Units.val",
"Eq.mpr",
"instHSMul",
"HMul.hMul",
"AddGrou... | variableChange_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 519,
"column": 20
} | {
"line": 519,
"column": 31
} | [
{
"pp": "case hxy\nR✝ : Type u_2\ninst✝³ : CommRing R✝\nn : ℕ\nR : Type u_2\ninst✝² : CommRing R\nc : InductionObj R n\ni j : Fin n\nhi : (c.val i).Monic\nhle : (c.val i).degree ≤ (c.val j).degree\nhne : i ≠ j\nH :\n ∀ {R₀ : Type u_1} [inst : CommRing R₀] [inst_1 : Algebra R₀ R],\n Statement R₀ R n { val :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 511,
"column": 8
} | {
"line": 519,
"column": 72
} | [
{
"pp": "case neg\nR✝ : Type u_2\ninst✝³ : CommRing R✝\nn : ℕ\nR : Type u_2\ninst✝² : CommRing R\nc : InductionObj R n\ni j : Fin n\nhi : (c.val i).Monic\nhle : (c.val i).degree ≤ (c.val j).degree\nhne : i ≠ j\nH :\n ∀ {R₀ : Type u_1} [inst : CommRing R₀] [inst_1 : Algebra R₀ R],\n Statement R₀ R n { val :=... | have deg_bound₂ : c'.degBound < c.degBound := by
dsimp [InductionObj.degBound, c']
apply Finset.sum_lt_sum ?_ ⟨j, Finset.mem_univ _, ?_⟩
· intro k _
rw [update_apply]
split_ifs with hkj
· subst hkj; gcongr; exact (degree_modByMonic_le _ hi).trans hle
... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 607,
"column": 6
} | {
"line": 607,
"column": 83
} | [
{
"pp": "I : Type u\ninst✝⁵ : Category.{u, u} I\nS X : Scheme\nD : I ⥤ Scheme\nt : D ⟶ (Functor.const I).obj S\nf : X ⟶ S\ninst✝⁴ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝³ : LocallyOfFiniteType f\ninst✝² : IsCofiltered I\ninst✝¹ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nA : ExistsHomHomCompEqCompAux ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | {
"line": 247,
"column": 36
} | {
"line": 247,
"column": 54
} | [
{
"pp": "R : Type u\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\nC : VariableChange R\ninst✝ : W.IsElliptic\n⊢ ↑C.u ^ 12 * ↑W.Δ'⁻¹ * (C • W).c₄ ^ 3 = W.j",
"usedConstants": [
"Units.val",
"Eq.mpr",
"instHSMul",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"W... | variableChange_c₄, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 34
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : Affine R\n⊢ W.polynomial.Monic",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Polynomial.instOne",
"congrArg",
"CommSemiring.toSemiring",
"WeierstrassCurve.Affine.polynomial_eq",
"AddGroupWithOne.toAddMonoidWithOne... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 609,
"column": 2
} | {
"line": 610,
"column": 76
} | [
{
"pp": "I : Type u\ninst✝⁵ : Category.{u, u} I\nS X : Scheme\nD : I ⥤ Scheme\nt : D ⟶ (Functor.const I).obj S\nf : X ⟶ S\ninst✝⁴ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝³ : LocallyOfFiniteType f\ninst✝² : IsCofiltered I\ninst✝¹ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\nA : ExistsHomHomCompEqCompAux ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 543,
"column": 36
} | {
"line": 543,
"column": 51
} | [
{
"pp": "R✝ : Type u_2\ninst✝³ : CommRing R✝\nn : ℕ\nR : Type u_2\ninst✝² : CommRing R\nc : InductionObj R n\ni j : Fin n\nhi : (c.val i).Monic\nhle : (c.val i).degree ≤ (c.val j).degree\nhne : i ≠ j\nH :\n ∀ {R₀ : Type u_1} [inst : CommRing R₀] [inst_1 : Algebra R₀ R],\n Statement R₀ R n { val := Function.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic | {
"line": 230,
"column": 84
} | {
"line": 234,
"column": 20
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : Affine R\nx y : R\n⊢ W.Nonsingular x y ↔ (toAffine ({ u := 1, r := x, s := 0, t := y } • W)).Nonsingular 0 0",
"usedConstants": [
"WeierstrassCurve.VariableChange.r",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero... | by
rw [nonsingular_iff', equation_iff_variableChange, equation_zero, ← neg_ne_zero, or_comm,
nonsingular_zero, variableChange_a₃, variableChange_a₄, inv_one, Units.val_one]
simp only [variableChange_def]
congr! 3 <;> ring1 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula | {
"line": 125,
"column": 52
} | {
"line": 128,
"column": 55
} | [
{
"pp": "F : Type u\ninst✝ : Field F\nW : Affine F\nx₁ x₂ y₁ y₂ : F\nh₁ : W.Equation x₁ y₁\nh₂ : W.Equation x₂ y₂\nhx : x₁ = x₂\n⊢ y₁ = y₂ ∨ y₁ = W.negY x₂ y₂",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid",
"Mathlib.Tactic.Ring.Common.neg_zero... | by
rw [equation_iff] at h₁ h₂
rw [← sub_eq_zero, ← sub_eq_zero (a := y₁), ← mul_eq_zero, negY]
linear_combination (norm := (rw [hx]; ring1)) h₁ - h₂ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 655,
"column": 16
} | {
"line": 655,
"column": 27
} | [
{
"pp": "k₁ k₂ : ℕ\nD₁ D₂ : ℕ → ℕ\nhk : k₁ ≤ k₂\nhD : ∀ i < 0, D₁ i ≤ D₂ i\n⊢ numBound k₁ D₁ 0 ≤ numBound k₂ D₂ 0",
"usedConstants": [
"Eq.mpr",
"ChevalleyThm.MvPolynomialC.numBound_zero",
"ChevalleyThm.MvPolynomialC.numBound",
"congrArg",
"id",
"instOfNatNat",
"LE.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Morphisms.Flat | {
"line": 415,
"column": 6
} | {
"line": 415,
"column": 17
} | [
{
"pp": "case right\nX Y S T : Scheme\nf : T ⟶ S\ng : Y ⟶ X\niX : X ⟶ S\niY : Y ⟶ T\nH : IsPullback g iY iX f\nUS : S.Opens\nUT : T.Opens\nUX : X.Opens\nhUST : UT ≤ f ⁻¹ᵁ US\nhUSX : UX ≤ iX ⁻¹ᵁ US\nUY : Y.Opens\nhUY : UY = g ⁻¹ᵁ UX ⊓ iY ⁻¹ᵁ UT\nι : Type u\ninst✝ : Finite ι\nVX : ι → X.Opens\nhVU : iSup VX = UX\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 686,
"column": 2
} | {
"line": 686,
"column": 13
} | [
{
"pp": "case h\nI : Type u\ninst✝⁴ : Category.{u, u} I\nS X : Scheme\nD : I ⥤ Scheme\nt : D ⟶ (Functor.const I).obj S\nf : X ⟶ S\nc : Cone D\nhc : IsLimit c\ninst✝³ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝² : LocallyOfFiniteType f\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 722,
"column": 28
} | {
"line": 722,
"column": 39
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ (i : I), IsAffine (D.obj i)\ni : I\ns : ↑Γ(D.obj i, ⊤)\nhs : (ConcreteCategory.hom (Scheme.Hom.appTop (c.π.app i))) s = 0\nthis : ∀ (i : Iᵒᵖ), IsAffine (Opposite.unop (D.op.obj i))\nj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 741,
"column": 35
} | {
"line": 741,
"column": 46
} | [
{
"pp": "I : Type u\ninst✝³ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝² : IsCofiltered I\ninst✝¹ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\ninst✝ : CompactSpace ↥(D.obj i)\ns : ↑Γ(D.obj i, ⊤)\nhs : (ConcreteCategory.hom (Scheme.Hom.appTop (c.π.app i))) s = 0\nx : ↥(D.ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Morphisms.Flat | {
"line": 423,
"column": 8
} | {
"line": 423,
"column": 28
} | [
{
"pp": "case refine_2.pair\nX Y S T : Scheme\nf : T ⟶ S\ng : Y ⟶ X\niX : X ⟶ S\niY : Y ⟶ T\nH : IsPullback g iY iX f\nUS : S.Opens\nUT : T.Opens\nUX : X.Opens\nhUST : UT ≤ f ⁻¹ᵁ US\nhUSX : UX ≤ iX ⁻¹ᵁ US\nUY : Y.Opens\nhUY : UY = g ⁻¹ᵁ UX ⊓ iY ⁻¹ᵁ UT\nι : Type u\ninst✝ : Finite ι\nVX : ι → X.Opens\nhVU : iSup ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 721,
"column": 10
} | {
"line": 721,
"column": 57
} | [
{
"pp": "R : Type u_2\ninst✝ : CommRing R\nn✝ n : ℕ\nIH :\n ∀ {M : Submodule ℤ R},\n 1 ∈ M →\n ∀ (k : ℕ) (d : Multiset (Fin n)) (S : ConstructibleSetData (MvPolynomial (Fin n) R)),\n (∀ C ∈ S, C.n ≤ k) →\n (∀ C ∈ S, ∀ (j : Fin C.n), C.g j ∈ coeffsIn (Fin n) M ⊓ Submodule.restrictScalars... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 746,
"column": 6
} | {
"line": 746,
"column": 53
} | [
{
"pp": "case refine_1\nR : Type u_2\ninst✝ : CommRing R\nn✝ n : ℕ\nIH :\n ∀ {M : Submodule ℤ R},\n 1 ∈ M →\n ∀ (k : ℕ) (d : Multiset (Fin n)) (S : ConstructibleSetData (MvPolynomial (Fin n) R)),\n (∀ C ∈ S, C.n ≤ k) →\n (∀ C ∈ S, ∀ (j : Fin C.n), C.g j ∈ coeffsIn (Fin n) M ⊓ Submodule.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 793,
"column": 34
} | {
"line": 793,
"column": 45
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU : (D.obj i).Opens\nhU : IsCompact ↑U\ns : ↑Γ(D.obj i, U)\nhs : (ConcreteCategory.hom (Scheme.Hom.app (c.π.app i) U)) s = 0\nthis ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 809,
"column": 2
} | {
"line": 809,
"column": 27
} | [
{
"pp": "I : Type u\ninst✝² : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝¹ : IsCofiltered I\ninst✝ : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ni : I\nU : (D.obj i).Opens\nhU : IsCompact ↑U\ns t : ↑Γ(D.obj i, U)\nhs : (ConcreteCategory.hom (Scheme.Hom.app (c.π.app i) U)) s = (Concr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 836,
"column": 52
} | {
"line": 836,
"column": 63
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝³ : IsCofiltered I\ninst✝² : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : ↑Γ(c.pt, ⊤)\ninst✝¹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝ : ∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)\nthis✝ : CompactSpace ↥c.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 837,
"column": 57
} | {
"line": 837,
"column": 78
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝³ : IsCofiltered I\ninst✝² : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : ↑Γ(c.pt, ⊤)\ninst✝¹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝ : ∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)\nthis✝¹ : CompactSpace ↥c... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula | {
"line": 377,
"column": 2
} | {
"line": 377,
"column": 34
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Affine F\ninst✝ : DecidableEq F\nx₁ x₂ y₁ y₂ : F\nhx : x₁ ≠ x₂\n⊢ y₁ * (x₂ - (((y₁ - y₂) / (x₁ - x₂)) ^ 2 + W.a₁ * ((y₁ - y₂) / (x₁ - x₂)) - W.a₂ - x₁ - x₂)) +\n y₂ * (((y₁ - y₂) / (x₁ - x₂)) ^ 2 + W.a₁ * ((y₁ - y₂) / (x₁ - x₂)) - W.a₂ - x₁ - x₂ - x₁) +\n (... | simp [field, sub_ne_zero.mpr hx] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 860,
"column": 81
} | {
"line": 867,
"column": 9
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝³ : IsCofiltered I\ninst✝² : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : ↑Γ(c.pt, ⊤)\ninst✝¹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝ : ∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)\nthis : CompactSpace ↥c.p... | by
dsimp +instances [TopCat.Presheaf.restrictOpen, TopCat.Presheaf.restrict]
simp only [map_sub, sub_eq_zero, ← ConcreteCategory.comp_apply,
Scheme.Hom.app_eq_appLE, Scheme.Hom.appLE_map, Scheme.Hom.appLE_comp_appLE,
Cone.w]
simp_rw [Scheme.Hom.appLE, ConcreteCategory.comp_apply, ht, T... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 873,
"column": 4
} | {
"line": 874,
"column": 65
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝³ : IsCofiltered I\ninst✝² : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : ↑Γ(c.pt, ⊤)\ninst✝¹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝ : ∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)\nthis : CompactSpace ↥c.p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 861,
"column": 30
} | {
"line": 861,
"column": 73
} | [
{
"pp": "R : Type u_2\ninst✝ : CommRing R\nm n : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] MvPolynomial (Fin m) R\nk : ℕ\nd : Multiset (Fin m)\nS : ConstructibleSetData (MvPolynomial (Fin m) R)\nhSn : ∀ C ∈ S, C.n ≤ k\nhS : ∀ C ∈ S, ∀ (j : Fin C.n), (C.g j).degrees ≤ d\nhf : ∀ (i : Fin n), (f (MvPolynomial.X i)).degr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 862,
"column": 4
} | {
"line": 862,
"column": 15
} | [
{
"pp": "case h.e'_3.h.e'_4\nR : Type u_2\ninst✝ : CommRing R\nm n : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] MvPolynomial (Fin m) R\nk : ℕ\nd : Multiset (Fin m)\nS : ConstructibleSetData (MvPolynomial (Fin m) R)\nhSn : ∀ C ∈ S, C.n ≤ k\nhS : ∀ C ∈ S, ∀ (j : Fin C.n), (C.g j).degrees ≤ d\nhf : ∀ (i : Fin n), (f (MvP... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 32
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW' : Affine R\n⊢ (CoordinateRing.basis W') 0 = 1",
"usedConstants": [
"Eq.mpr",
"WeierstrassCurve.Affine.monic_polynomial",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"AdjoinRoot",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 32
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW' : Affine R\n⊢ (CoordinateRing.basis W') 1 = (mk W') Y",
"usedConstants": [
"Eq.mpr",
"WeierstrassCurve.Affine.monic_polynomial",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"WeierstrassCurve.Affine... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 880,
"column": 48
} | {
"line": 880,
"column": 59
} | [
{
"pp": "R : Type u_2\ninst✝ : CommRing R\nm n : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] MvPolynomial (Fin m) R\nk : ℕ\nd : Multiset (Fin m)\nS : ConstructibleSetData (MvPolynomial (Fin m) R)\nhSn : ∀ C ∈ S, C.n ≤ k\nhS : ∀ C ∈ S, ∀ (j : Fin C.n), (C.g j).degrees ≤ d\nhf : ∀ (i : Fin n), (f (MvPolynomial.X i)).degr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 898,
"column": 8
} | {
"line": 898,
"column": 19
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝³ : IsCofiltered I\ninst✝² : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ns : ↑Γ(c.pt, ⊤)\ninst✝¹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝ : ∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)\nthis : CompactSpace ↥c.p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 911,
"column": 4
} | {
"line": 912,
"column": 11
} | [
{
"pp": "case refine_2\nR : Type u_2\ninst✝ : CommRing R\nm n : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] MvPolynomial (Fin m) R\nk : ℕ\nd : Multiset (Fin m)\nS : ConstructibleSetData (MvPolynomial (Fin m) R)\nhSn : ∀ C ∈ S, C.n ≤ k\nhS : ∀ C ∈ S, ∀ (j : Fin C.n), (C.g j).degrees ≤ d\nhf : ∀ (i : Fin n), (f (MvPolyno... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 39
} | [
{
"pp": "case nat.succ.succ.succ\nR : Type u\ninst✝ : CommRing R\nb c d : R\nm : ℕ\n⊢ preNormEDS b c d ↑(2 * (m + 1 + 2)) =\n preNormEDS b c d ↑(m + 1 + 1) ^ 2 * preNormEDS b c d ↑(m + 1 + 2) * preNormEDS b c d ↑(m + 1 + 2 + 2) -\n preNormEDS b c d ↑(m + 1) * preNormEDS b c d ↑(m + 1 + 2) * preNormEDS b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 233,
"column": 4
} | {
"line": 233,
"column": 39
} | [
{
"pp": "case nat.succ.succ\nR : Type u\ninst✝ : CommRing R\nb c d : R\nn✝ : ℕ\n⊢ preNormEDS b c d ↑(2 * (n✝ + 1 + 1) + 1) =\n (preNormEDS b c d ↑(n✝ + 1 + 1 + 2) * preNormEDS b c d ↑(n✝ + 1 + 1) ^ 3 * if Even n✝ then b else 1) -\n preNormEDS b c d ↑(n✝ + 1) * preNormEDS b c d ↑(n✝ + 1 + 1 + 1) ^ 3 * if... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 455,
"column": 4
} | {
"line": 455,
"column": 37
} | [
{
"pp": "case nat.succ\nR : Type u\ninst✝ : CommRing R\nb c d : R\nk : ℤ\nn✝ : ℕ\n⊢ complEDS b c d k ↑(2 * (n✝ + 1)) = complEDS b c d k ↑(n✝ + 1) * complEDS₂ b c d (↑(n✝ + 1) * k)",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 466,
"column": 4
} | {
"line": 466,
"column": 37
} | [
{
"pp": "case nat.succ\nR : Type u\ninst✝ : CommRing R\nb c d : R\nk : ℤ\nn✝ : ℕ\n⊢ complEDS b c d k ↑(2 * (n✝ + 1) + 1) =\n complEDS b c d k ↑(n✝ + 1) ^ 2 * normEDS b c d (↑(n✝ + 1 + 1) * k + 1) * normEDS b c d (↑(n✝ + 1 + 1) * k - 1) -\n complEDS b c d k ↑(n✝ + 1 + 1) ^ 2 * normEDS b c d (↑(n✝ + 1) * ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 531,
"column": 2
} | {
"line": 531,
"column": 29
} | [
{
"pp": "R : Type u\ninst✝¹ : CommRing R\nb c d : R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\nn : ℤ\n⊢ f (normEDS b c d n) = normEDS (f b) (f c) (f d) n",
"usedConstants": [
"RingHom.instRingHomClass",
"HMul.hMul",
"map_preNormEDS",
"congrArg",
"CommSemiring.toSemiring",
... | simp [normEDS, apply_ite f] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 531,
"column": 2
} | {
"line": 531,
"column": 29
} | [
{
"pp": "R : Type u\ninst✝¹ : CommRing R\nb c d : R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\nn : ℤ\n⊢ f (normEDS b c d n) = normEDS (f b) (f c) (f d) n",
"usedConstants": [
"RingHom.instRingHomClass",
"HMul.hMul",
"map_preNormEDS",
"congrArg",
"CommSemiring.toSemiring",
... | simp [normEDS, apply_ite f] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 531,
"column": 2
} | {
"line": 531,
"column": 29
} | [
{
"pp": "R : Type u\ninst✝¹ : CommRing R\nb c d : R\nS : Type v\ninst✝ : CommRing S\nf : R →+* S\nn : ℤ\n⊢ f (normEDS b c d n) = normEDS (f b) (f c) (f d) n",
"usedConstants": [
"RingHom.instRingHomClass",
"HMul.hMul",
"map_preNormEDS",
"congrArg",
"CommSemiring.toSemiring",
... | simp [normEDS, apply_ite f] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 207,
"column": 12
} | {
"line": 207,
"column": 41
} | [
{
"pp": "case zero\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\ndm : ∀ {m n : ℕ} {p q : R[X]}, p.natDegree ≤ m → q.natDegree ≤ n → (p * q).natDegree ≤ m + n :=\n fun {m n} {p q} ↦ natDegree_mul_le_of_le\ndp : ∀ {m n : ℕ} {p : R[X]}, p.natDegree ≤ m → (p ^ n).natDegree ≤ n * m := fun {m n} {p} ↦ nat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 208,
"column": 11
} | {
"line": 208,
"column": 39
} | [
{
"pp": "case one\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\ndm : ∀ {m n : ℕ} {p q : R[X]}, p.natDegree ≤ m → q.natDegree ≤ n → (p * q).natDegree ≤ m + n :=\n fun {m n} {p q} ↦ natDegree_mul_le_of_le\ndp : ∀ {m n : ℕ} {p : R[X]}, p.natDegree ≤ m → (p ^ n).natDegree ≤ n * m := fun {m n} {p} ↦ natD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 209,
"column": 11
} | {
"line": 209,
"column": 39
} | [
{
"pp": "case two\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\ndm : ∀ {m n : ℕ} {p q : R[X]}, p.natDegree ≤ m → q.natDegree ≤ n → (p * q).natDegree ≤ m + n :=\n fun {m n} {p q} ↦ natDegree_mul_le_of_le\ndp : ∀ {m n : ℕ} {p : R[X]}, p.natDegree ≤ m → (p ^ n).natDegree ≤ n * m := fun {m n} {p} ↦ natD... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 210,
"column": 13
} | {
"line": 210,
"column": 43
} | [
{
"pp": "case three\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\ndm : ∀ {m n : ℕ} {p q : R[X]}, p.natDegree ≤ m → q.natDegree ≤ n → (p * q).natDegree ≤ m + n :=\n fun {m n} {p q} ↦ natDegree_mul_le_of_le\ndp : ∀ {m n : ℕ} {p : R[X]}, p.natDegree ≤ m → (p ^ n).natDegree ≤ n * m := fun {m n} {p} ↦ na... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 211,
"column": 12
} | {
"line": 211,
"column": 41
} | [
{
"pp": "case four\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\ndm : ∀ {m n : ℕ} {p q : R[X]}, p.natDegree ≤ m → q.natDegree ≤ n → (p * q).natDegree ≤ m + n :=\n fun {m n} {p q} ↦ natDegree_mul_le_of_le\ndp : ∀ {m n : ℕ} {p : R[X]}, p.natDegree ≤ m → (p ^ n).natDegree ≤ n * m := fun {m n} {p} ↦ nat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | {
"line": 351,
"column": 76
} | {
"line": 357,
"column": 7
} | [
{
"pp": "F : Type u_2\ninst✝³ : Field F\nW : WeierstrassCurve F\ninst✝² : W.IsElliptic\ninst✝¹ : W.IsCharThreeJNeZeroNF\ninst✝ : CharP F 3\n⊢ W.j = -W.a₂ ^ 3 / W.a₆",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Units.val",
"Eq.... | by
have h := W.Δ'.ne_zero
rw [coe_Δ', Δ_of_isCharThreeJNeZeroNF_of_char_three] at h
rw [j, Units.val_inv_eq_inv_val, ← div_eq_inv_mul, coe_Δ',
c₄_of_isCharThreeJNeZeroNF_of_char_three, Δ_of_isCharThreeJNeZeroNF_of_char_three,
div_eq_div_iff h (right_ne_zero_of_mul h)]
ring1 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 435,
"column": 12
} | {
"line": 439,
"column": 41
} | [
{
"pp": "case neg.some.some.inl\nR : Type r\ninst✝¹ : CommRing R\nW' : Affine R\ninst✝ : IsDomain R\np q : R[X]\nhp : ¬p.degree = ⊥\nhq : ¬q.degree = ⊥\ndp : ℕ\nhdp : (p ^ 2).degree = 2 • some dp\nhp' : p.degree = some dp\ndq : ℕ\nhdq : (q ^ 2 * (X ^ 3 + C W'.a₂ * X ^ 2 + C W'.a₄ * X + C W'.a₆)).degree = 2 • so... | convert!
(degree_sub_eq_right_of_degree_lt <|
(degree_sub_le _ _).trans_lt <|
max_lt_iff.mpr ⟨hdp.trans_lt _, hdpq.trans_lt _⟩).trans
(max_eq_right_of_lt _).symm | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | {
"line": 504,
"column": 59
} | {
"line": 506,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nW : WeierstrassCurve R\ninst✝¹ : W.IsCharTwoJNeZeroNF\ninst✝ : CharP R 2\n⊢ W.b₂ = 1",
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"CharP.cast_eq_zero",
"AddGroup.toSubtractionMonoid",
"Mathlib.Tactic.Ring.Common.neg_zero",... | by
rw [b₂_of_isCharTwoJNeZeroNF]
linear_combination 2 * W.a₂ * CharP.cast_eq_zero R 2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.FieldTheory.Minpoly.Finite | {
"line": 35,
"column": 46
} | {
"line": 35,
"column": 57
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝³ : CommRing A\ninst✝² : Ring B\ninst✝¹ : Algebra A B\ninst✝ : Module.Finite A B\nx : B\nf : A[X]\nf_monic : f.Monic\nf_deg : f.natDegree = ⊤.spanFinrank\nf_aeval : (Algebra.lmul A B) ((Polynomial.aeval x) f) = 0\n⊢ (Algebra.lmul A B) ((Polynomial.aeval x) f) = (Algebra... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Minpoly.Finite | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 53
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : Ring B\ninst✝² : Algebra A B\ninst✝¹ : Module.Finite A B\nx : B\ninst✝ : Module.Free A B\na✝ : Nontrivial A\n⊢ (minpoly A x).natDegree ≤ Module.finrank A B",
"usedConstants": [
"Eq.mpr",
"Submodule",
"Ring.toNonAssocRing",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.Solvable | {
"line": 211,
"column": 40
} | {
"line": 220,
"column": 38
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : IsSimpleGroup G\nx✝ : IsSolvable G\nn : ℕ\nhn : derivedSeries G n = ⊥\n⊢ ∀ (a b : G), a * b = b * a",
"usedConstants": [
"commutatorSet",
"Eq.mpr",
"Semigroup.toMul",
"DivInvMonoid.toInv",
"InvOneClass.toOne",
"HMul.hMul",
... | by
cases n
· intro a b
refine (mem_bot.1 ?_).trans (mem_bot.1 ?_).symm <;>
· rw [← hn]
exact mem_top _
· rw [IsSimpleGroup.derivedSeries_succ] at hn
intro a b
rw [← mul_inv_eq_one, mul_inv_rev, ← mul_assoc, ← mem_bot, ← hn, commutator_eq_closure]
exact subset_closur... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 674,
"column": 2
} | {
"line": 674,
"column": 33
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Affine F\ninst✝ : DecidableEq F\nx₁ x₂ y₁ y₂ : F\nh₁ : W.Nonsingular x₁ y₁\nh₂ : W.Nonsingular x₂ y₂\nhx : x₁ = x₂\nhy : y₁ = W.negY x₂ y₂\n⊢ some x₁ y₁ h₁ + some x₂ y₂ h₂ = 0",
"usedConstants": [
"WeierstrassCurve.Affine.Point.instZero",
"id",
"F... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 745,
"column": 26
} | {
"line": 745,
"column": 57
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Affine F\ninst✝ : DecidableEq F\nx₁ y₁ : F\nh✝¹ : W.Nonsingular x₁ y₁\nx₂ y₂ : F\nh✝ : W.Nonsingular x₂ y₂\nhxy : ¬(x₁ = x₂ ∧ y₁ = W.negY x₂ y₂)\n⊢ ¬some x₁ y₁ h✝¹ + some x₂ y₂ h✝ = 0",
"usedConstants": [
"Eq.mpr",
"WeierstrassCurve.Affine.Point.instZer... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 292,
"column": 13
} | {
"line": 293,
"column": 11
} | [
{
"pp": "case nat\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℕ\nh : ↑↑n ≠ 0\n⊢ (W.preΨ ↑n).coeff (((↑n).natAbs ^ 2 - if Even ↑n then 4 else 1) / 2) ≠ 0",
"usedConstants": [
"Eq.mpr",
"instHDiv",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"H... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 294,
"column": 16
} | {
"line": 295,
"column": 13
} | [
{
"pp": "case neg\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nih : ∀ (n : ℕ), ↑↑n ≠ 0 → (W.preΨ ↑n).coeff (((↑n).natAbs ^ 2 - if Even ↑n then 4 else 1) / 2) ≠ 0\nn : ℕ\nh : ↑(-↑n) ≠ 0\n⊢ (W.preΨ (-↑n)).coeff (((-↑n).natAbs ^ 2 - if Even (-↑n) then 4 else 1) / 2) ≠ 0",
"usedConstants": [
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 305,
"column": 13
} | {
"line": 305,
"column": 42
} | [
{
"pp": "case nat\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nn : ℕ\nhn : 2 < (↑n).natAbs\nh : ↑↑n ≠ 0\n⊢ 0 < (W.preΨ ↑n).natDegree",
"usedConstants": [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"Pol... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 306,
"column": 16
} | {
"line": 307,
"column": 13
} | [
{
"pp": "case neg\nR : Type u\ninst✝ : CommRing R\nW : WeierstrassCurve R\nih : ∀ (n : ℕ), 2 < (↑n).natAbs → ↑↑n ≠ 0 → 0 < (W.preΨ ↑n).natDegree\nn : ℕ\nhn : 2 < (-↑n).natAbs\nh : ↑(-↑n) ≠ 0\n⊢ 0 < (W.preΨ (-↑n)).natDegree",
"usedConstants": [
"Eq.mpr",
"Polynomial.instNeg",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 316,
"column": 13
} | {
"line": 316,
"column": 42
} | [
{
"pp": "case nat\nR : Type u\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\ninst✝ : Nontrivial R\nn : ℕ\nh : ↑↑n ≠ 0\n⊢ W.preΨ ↑n ≠ 0",
"usedConstants": [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"id",
"Ne",
"Int",
"Nat.cast",
"Polynomial",
"Weie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 317,
"column": 16
} | {
"line": 318,
"column": 13
} | [
{
"pp": "case neg\nR : Type u\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\ninst✝ : Nontrivial R\nih : ∀ (n : ℕ), ↑↑n ≠ 0 → W.preΨ ↑n ≠ 0\nn : ℕ\nh : ↑(-↑n) ≠ 0\n⊢ W.preΨ (-↑n) ≠ 0",
"usedConstants": [
"Eq.mpr",
"Polynomial.instNeg",
"congrArg",
"CommSemiring.toSemiring",
"id",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 798,
"column": 6
} | {
"line": 798,
"column": 95
} | [
{
"pp": "case neg\nR : Type r\nS : Type s\nA F : Type u\nB K : Type v\nL : Type w\ninst✝¹⁹ : CommRing R\ninst✝¹⁸ : CommRing S\ninst✝¹⁷ : CommRing A\ninst✝¹⁶ : CommRing B\ninst✝¹⁵ : Field F\ninst✝¹⁴ : Field K\ninst✝¹³ : Field L\nW' : Affine R\nW : Affine F\ninst✝¹² : DecidableEq F\ninst✝¹¹ : DecidableEq K\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 818,
"column": 4
} | {
"line": 818,
"column": 33
} | [
{
"pp": "case some.some\nR : Type r\nS : Type s\nF : Type u\nK : Type v\ninst✝¹² : CommRing R\ninst✝¹¹ : CommRing S\ninst✝¹⁰ : Field F\ninst✝⁹ : Field K\nW' : Affine R\ninst✝⁸ : DecidableEq F\ninst✝⁷ : DecidableEq K\ninst✝⁶ : Algebra R S\ninst✝⁵ : Algebra R F\ninst✝⁴ : Algebra S F\ninst✝³ : IsScalarTower R S F\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1076,
"column": 37
} | {
"line": 1076,
"column": 48
} | [
{
"pp": "I : Type u\ninst✝⁴ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝³ : IsCofiltered I\ninst✝² : ∀ {i j : I} (f : i ⟶ j), IsAffineHom (D.map f)\ninst✝¹ : ∀ (i : I), CompactSpace ↥(D.obj i)\ninst✝ : ∀ (i : I), QuasiSeparatedSpace ↥(D.obj i)\nJ : Type u_1\nU : J → c.pt.Opens\nhU : Is... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Normal.Basic | {
"line": 106,
"column": 8
} | {
"line": 106,
"column": 40
} | [
{
"pp": "case refine_2\nF : Type u_1\nK : Type u_2\ninst✝² : Field F\ninst✝¹ : Field K\ninst✝ : Algebra F K\nι : Type u_3\nt : ι → IntermediateField F K\nh : ∀ (i : ι), Normal F ↥(t i)\nx : ↥(⨆ i, t i)\ns : Finset ((i : ι) × ↥(t i))\nhx : ↑x ∈ ⨆ i ∈ s, adjoin F ((minpoly F i.snd).rootSet K)\nE : IntermediateFie... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1101,
"column": 24
} | {
"line": 1101,
"column": 35
} | [
{
"pp": "I : Type u\ninst✝⁵ : Category.{u, u} I\nS X : Scheme\nD : I ⥤ Scheme\nt : D ⟶ (Functor.const I).obj S\nf : X ⟶ S\nc : Cone D\nhc : IsLimit c\ninst✝⁴ : IsCofiltered I\ninst✝³ : LocallyOfFinitePresentation f\ninst✝² : IsAffine S\ninst✝¹ : IsAffine X\ninst✝ : ∀ (i : I), IsAffine (D.obj i)\na : c.pt ⟶ X\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1106,
"column": 36
} | {
"line": 1106,
"column": 67
} | [
{
"pp": "I : Type u\ninst✝⁵ : Category.{u, u} I\nX : Scheme\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝⁴ : IsCofiltered I\ninst✝³ : IsAffine X\ninst✝² : ∀ (i : I), IsAffine (D.obj i)\na : c.pt ⟶ X\nR : CommRingCat\nt : D ⟶ (Functor.const I).obj (Spec R)\nf✝ : X ⟶ Spec R\ninst✝¹ : LocallyOfFinitePresentat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.FixedPoints | {
"line": 96,
"column": 14
} | {
"line": 96,
"column": 25
} | [
{
"pp": "α : Type u_1\nG : Type u_2\ninst✝¹ : Group G\ninst✝ : MulAction G α\ng : G\na : α\nh : ∀ (j : ℤ), a ∈ fixedBy α (g ^ j)\n⊢ a ∈ fixedBy α g",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"MulAction.fixedBy",
"Membership.mem",
"id",
"DivInvMonoid.toMonoid",
"Gro... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1116,
"column": 24
} | {
"line": 1116,
"column": 35
} | [
{
"pp": "I : Type u\ninst✝⁷ : Category.{u, u} I\nD : I ⥤ Scheme\nc : Cone D\nhc : IsLimit c\ninst✝⁶ : IsCofiltered I\ninst✝⁵ : ∀ (i : I), IsAffine (D.obj i)\nR : CommRingCat\nt : D ⟶ (Functor.const I).obj (Spec R)\ninst✝⁴ : IsAffine (Spec R)\nS : CommRingCat\ninst✝³ : IsAffine (Spec S)\na : c.pt ⟶ Spec S\nφ : R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.FixedPoints | {
"line": 296,
"column": 2
} | {
"line": 296,
"column": 13
} | [
{
"pp": "G : Type u_1\nA : Type u_2\nB : Type u_3\ninst✝² : Monoid G\ninst✝¹ : MulAction G A\ninst✝ : MulAction G B\nf : A →ₑ[id] B\ng : G\na : A\nha : a ∈ MulAction.fixedBy A g\n⊢ f a ∈ MulAction.fixedBy B g",
"usedConstants": [
"Eq.mpr",
"instHSMul",
"MulAction.fixedBy",
"Membershi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Normal.Closure | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 68
} | [
{
"pp": "case refine_1\nF : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁵ : Field F\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Algebra F K\ninst✝¹ : Algebra F L\ninst✝ : Algebra.IsAlgebraic F K\nx✝ : IsNormalClosure F K L\nsplits : ∀ (x : K), (Polynomial.map (algebraMap F L) (minpoly F x)).Splits\nh : ⨆ x, In... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.FieldTheory.Normal.Closure | {
"line": 96,
"column": 4
} | {
"line": 96,
"column": 68
} | [
{
"pp": "case refine_2\nF : Type u_1\nK : Type u_2\nL : Type u_3\ninst✝⁵ : Field F\ninst✝⁴ : Field K\ninst✝³ : Field L\ninst✝² : Algebra F K\ninst✝¹ : Algebra F L\ninst✝ : Algebra.IsAlgebraic F K\nx✝ : (∀ (x : K), (Polynomial.map (algebraMap F L) (minpoly F x)).Splits) ∧ normalClosure F K L = ⊤\nsplits : ∀ (x :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.GroupTheory.GroupAction.FixingSubgroup | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 82
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns : Set α\nx✝ : M\nhx : x✝ ∈ (fixingSubmonoid M s).carrier\nz : ↑s\n⊢ x✝⁻¹ • ↑z = ↑z",
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"inv_smul_eq_iff",
"DivInvOneMonoid.toInvOneClass... | rw [inv_smul_eq_iff, hx z] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.GroupTheory.GroupAction.FixingSubgroup | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 82
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns : Set α\nx✝ : M\nhx : x✝ ∈ (fixingSubmonoid M s).carrier\nz : ↑s\n⊢ x✝⁻¹ • ↑z = ↑z",
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"inv_smul_eq_iff",
"DivInvOneMonoid.toInvOneClass... | rw [inv_smul_eq_iff, hx z] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.GroupTheory.GroupAction.FixingSubgroup | {
"line": 114,
"column": 56
} | {
"line": 114,
"column": 82
} | [
{
"pp": "M : Type u_1\nα : Type u_2\ninst✝¹ : Group M\ninst✝ : MulAction M α\ns : Set α\nx✝ : M\nhx : x✝ ∈ (fixingSubmonoid M s).carrier\nz : ↑s\n⊢ x✝⁻¹ • ↑z = ↑z",
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHSMul",
"inv_smul_eq_iff",
"DivInvOneMonoid.toInvOneClass... | rw [inv_smul_eq_iff, hx z] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1124,
"column": 10
} | {
"line": 1124,
"column": 21
} | [
{
"pp": "I : Type u\ninst✝⁵ : Category.{u, u} I\ninst✝⁴ : IsCofiltered I\nR : CommRingCat\ninst✝³ : IsAffine (Spec R)\nS : CommRingCat\ninst✝² : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝¹ : LocallyOfFinitePresentation (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝ : ∀ (i : I), ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1124,
"column": 52
} | {
"line": 1124,
"column": 72
} | [
{
"pp": "I : Type u\ninst✝⁵ : Category.{u, u} I\ninst✝⁴ : IsCofiltered I\nR : CommRingCat\ninst✝³ : IsAffine (Spec R)\nS : CommRingCat\ninst✝² : IsAffine (Spec S)\nφ : R ⟶ S\ninst✝¹ : LocallyOfFinitePresentation (Spec.map φ)\nD : I ⥤ CommRingCatᵒᵖ\nc : Cone (D ⋙ Scheme.Spec)\nhc : IsLimit c\ninst✝ : ∀ (i : I), ... | by ext : 2; simp [e] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.FieldTheory.Normal.Closure | {
"line": 310,
"column": 4
} | {
"line": 310,
"column": 37
} | [
{
"pp": "case refine_1\nF : Type u_1\nL : Type u_3\ninst✝⁴ : Field F\ninst✝³ : Field L\ninst✝² : Algebra F L\ninst✝¹ : Normal F L\nK₁ K₂ : IntermediateField F L\ninst✝ : Normal F ↥K₂\nh : ∀ (f : ↥K₁ →ₐ[F] L), f.fieldRange ≤ K₂\n⊢ K₁ ≤ K₂",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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