module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 286,
"column": 4
} | {
"line": 286,
"column": 67
} | {
"line": 286,
"column": 68
} | [
{
"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... | [
"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 ↥((opensDiagram D i U).ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 288,
"column": 34
} | {
"line": 288,
"column": 45
} | {
"line": 288,
"column": 46
} | [
{
"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... | [
"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 ↥((opensDiagram D i U).ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 288,
"column": 2
} | {
"line": 288,
"column": 58
} | {
"line": 288,
"column": 59
} | [
{
"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... | [
"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 ↥((opensDiagram D i U).ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sets.CompactOpenCovered | {
"line": 115,
"column": 6
} | {
"line": 115,
"column": 17
} | {
"line": 115,
"column": 18
} | [
{
"pp": "case refine_1.refine_2\nS : Type u_1\nι : Type u_2\nX : ι → Type u_3\nf : (i : ι) → X i → S\ninst✝¹ : (i : ι) → TopologicalSpace (X i)\ninst✝ : TopologicalSpace S\nU : Set S\nhU : IsCompact U\nUs : (x : S) → x ∈ U → Set S\nhU' : ∀ (x : S) (a : x ∈ U), Us x a ⊆ U\nhUx : ∀ (x : S) (a : x ∈ U), x ∈ Us x a... | [
"case refine_1.refine_2\nS : Type u_1\nι : Type u_2\nX : ι → Type u_3\nf : (i : ι) → X i → S\ninst✝¹ : (i : ι) → TopologicalSpace (X i)\ninst✝ : TopologicalSpace S\nU : Set S\nhU : IsCompact U\nUs : (x : S) → x ∈ U → Set S\nhU' : ∀ (x : S) (a : x ∈ U), Us x a ⊆ U\nhUx : ∀ (x : S) (a : x ∈ U), x ∈ Us x a\nhUo : ∀ (x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 302,
"column": 4
} | {
"line": 302,
"column": 65
} | {
"line": 302,
"column": 66
} | [
{
"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... | [
"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 : j₁ ⟶ i\ne₁ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 304,
"column": 4
} | {
"line": 304,
"column": 65
} | {
"line": 304,
"column": 66
} | [
{
"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... | [
"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 : j₁ ⟶ i\ne₁ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sets.CompactOpenCovered | {
"line": 164,
"column": 2
} | {
"line": 164,
"column": 13
} | {
"line": 164,
"column": 14
} | [
{
"pp": "S : Type u_1\nι : Type u_2\nX : ι → Type u_3\nf : (i : ι) → X i → S\ninst✝² : (i : ι) → TopologicalSpace (X i)\ninst✝¹ : Finite ι\ninst✝ : TopologicalSpace S\nhf : ∀ (i : ι), IsSpectralMap (f i)\nU : Set S\nhs : ∀ x ∈ U, ∃ i, x ∈ Set.range (f i)\nhU : IsOpen U\nhc : IsCompact U\ni : ι\ny : X i\nhx : f ... | [
"S : Type u_1\nι : Type u_2\nX : ι → Type u_3\nf : (i : ι) → X i → S\ninst✝² : (i : ι) → TopologicalSpace (X i)\ninst✝¹ : Finite ι\ninst✝ : TopologicalSpace S\nhf : ∀ (i : ι), IsSpectralMap (f i)\nU : Set S\nhs : ∀ x ∈ U, ∃ i, x ∈ Set.range (f i)\nhU : IsOpen U\nhc : IsCompact U\ni : ι\ny : X i\nhx : f i y ∈ U\n⊢ ∃... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sets.CompactOpenCovered | {
"line": 173,
"column": 2
} | {
"line": 173,
"column": 13
} | {
"line": 173,
"column": 14
} | [
{
"pp": "S : Type u_1\nι : Type u_2\nX : ι → Type u_3\nf : (i : ι) → X i → S\ninst✝² : (i : ι) → TopologicalSpace (X i)\ninst✝¹ : TopologicalSpace S\ninst✝ : ∀ (i : ι), PrespectralSpace (X i)\nhfc : ∀ (i : ι), Continuous (f i)\nh : ∀ (i : ι), IsOpenMap (f i)\nU : Set S\nhs : ∀ x ∈ U, ∃ i, x ∈ Set.range (f i)\nh... | [
"S : Type u_1\nι : Type u_2\nX : ι → Type u_3\nf : (i : ι) → X i → S\ninst✝² : (i : ι) → TopologicalSpace (X i)\ninst✝¹ : TopologicalSpace S\ninst✝ : ∀ (i : ι), PrespectralSpace (X i)\nhfc : ∀ (i : ι), Continuous (f i)\nh : ∀ (i : ι), IsOpenMap (f i)\nU : Set S\nhs : ∀ x ∈ U, ∃ i, x ∈ Set.range (f i)\nhU : IsOpen U... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Cover.QuasiCompact | {
"line": 55,
"column": 2
} | {
"line": 55,
"column": 13
} | {
"line": 55,
"column": 14
} | [
{
"pp": "S : Scheme\n𝒰 : PreZeroHypercover S\ninst✝ : QuasiCompactCover 𝒰\nU : S.Opens\nhU : IsCompact ↑U\nUs : Set (TopologicalSpace.Opens ↥S)\nhUs : Us ⊆ S.affineOpens\nhUf : Us.Finite\nhUc : U = sSup Us\n⊢ ∀ t ∈ SetLike.coe '' Us, IsCompactOpenCovered (fun x ↦ ⇑(𝒰.f x)) t",
"ppTerm": "?m.60",
"ass... | [
"S : Scheme\n𝒰 : PreZeroHypercover S\ninst✝ : QuasiCompactCover 𝒰\nU : S.Opens\nhU : IsCompact ↑U\nUs : Set (TopologicalSpace.Opens ↥S)\nhUs : Us ⊆ S.affineOpens\nhUf : Us.Finite\nhUc : U = sSup Us\n⊢ ∀ a ∈ Us, IsCompactOpenCovered (fun x ↦ ⇑(𝒰.f x)) ↑a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 348,
"column": 24
} | {
"line": 348,
"column": 66
} | {
"line": 348,
"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)\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 ... | [
"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 ↑(sSup s)\nt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 349,
"column": 58
} | {
"line": 349,
"column": 69
} | {
"line": 349,
"column": 70
} | [
{
"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 ... | [
"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 ↑(sSup s)\nt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EffectiveEpi.Comp | {
"line": 86,
"column": 9
} | {
"line": 86,
"column": 28
} | {
"line": 86,
"column": 29
} | [
{
"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 ... | [
"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 a₂ : I) (g₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.EffectiveEpi.Comp | {
"line": 86,
"column": 65
} | {
"line": 86,
"column": 84
} | {
"line": 86,
"column": 85
} | [
{
"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 ... | [
"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 a₂ : I) (g₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 518,
"column": 20
} | {
"line": 518,
"column": 31
} | {
"line": 518,
"column": 32
} | [
{
"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 :=... | [
"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 := Function.up... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 510,
"column": 8
} | {
"line": 518,
"column": 72
} | {
"line": 519,
"column": 8
} | [
{
"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 :=... | [
"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 := Function.up... | 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.CategoryTheory.EffectiveEpi.Preserves | {
"line": 48,
"column": 2
} | {
"line": 48,
"column": 13
} | {
"line": 48,
"column": 14
} | [
{
"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... | [
"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 g₁ ≫ e.functo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 448,
"column": 53
} | {
"line": 448,
"column": 73
} | {
"line": 448,
"column": 73
} | [
{
"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.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 542,
"column": 36
} | {
"line": 542,
"column": 51
} | {
"line": 542,
"column": 52
} | [
{
"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.... | [
"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.update c.val... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 543,
"column": 16
} | {
"line": 544,
"column": 57
} | {
"line": 544,
"column": 58
} | [
{
"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 :... | [
"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 : ExistsHomHo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 654,
"column": 16
} | {
"line": 654,
"column": 27
} | {
"line": 654,
"column": 28
} | [
{
"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",
"ppTerm": "?m.100",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChevalleyThm.MvPolynomialC.numBound_zero",
"ChevalleyThm.MvPolynomialC.numBound",
"congrArg"... | [
"k₁ k₂ : ℕ\nD₁ D₂ : ℕ → ℕ\nhk : k₁ ≤ k₂\nhD : ∀ i < 0, D₁ i ≤ D₂ i\n⊢ k₁ ≤ k₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 34
} | {
"line": 121,
"column": 35
} | [
{
"pp": "R : Type r\ninst✝ : CommRing R\nW : Affine R\n⊢ W.polynomial.Monic",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Polynomial.instOne",
"congrArg",
"CommSemiring.toSemiring",
"WeierstrassCurve.Affine.polynomial_eq... | [
"R : Type r\ninst✝ : CommRing R\nW : Affine R\n⊢ { a := 0, b := 1, c := { a := 0, b := 0, c := W.a₁, d := W.a₃ }.toPoly,\n d := { a := -1, b := -W.a₂, c := -W.a₄, d := -W.a₆ }.toPoly }.toPoly.Monic"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Basic | {
"line": 230,
"column": 84
} | {
"line": 234,
"column": 20
} | {
"line": 236,
"column": 0
} | [
{
"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",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"WeierstrassCurve.VariableChange.r",
"Mathlib.Tactic.Ring.Common.mul_pf_left... | [] | 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.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 720,
"column": 10
} | {
"line": 720,
"column": 57
} | {
"line": 720,
"column": 58
} | [
{
"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... | [
"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 ℤ (degreesL... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | {
"line": 148,
"column": 32
} | {
"line": 148,
"column": 51
} | {
"line": 148,
"column": 52
} | [
{
"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",
"ppTerm": "?m.1392",
"assigned": true,
"usedConstants": [
"WeierstrassCurve.VariableChange.r",
"Units.val",
"Eq.mpr",
... | [
"R : Type u\ninst✝ : CommRing R\nW✝ : WeierstrassCurve R\nC : VariableChange R\nW : WeierstrassCurve R\n⊢ { a₁ := ↑{ u := 1, r := 0, s := 0, t := 0 }.u⁻¹ * (W.a₁ + 2 * { u := 1, r := 0, s := 0, t := 0 }.s),\n a₂ :=\n ↑{ u := 1, r := 0, s := 0, t := 0 }.u⁻¹ ^ 2 *\n (W.a₂ - { u := 1, r := 0, s :=... | variableChange_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Formula | {
"line": 125,
"column": 52
} | {
"line": 128,
"column": 55
} | {
"line": 130,
"column": 0
} | [
{
"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",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid... | [] | 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": 745,
"column": 6
} | {
"line": 745,
"column": 53
} | {
"line": 745,
"column": 54
} | [
{
"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.... | [
"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.restrictScal... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 699,
"column": 2
} | {
"line": 699,
"column": 13
} | {
"line": 699,
"column": 14
} | [
{
"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... | [
"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 f)\ni : I\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 736,
"column": 28
} | {
"line": 736,
"column": 39
} | {
"line": 736,
"column": 40
} | [
{
"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 ... | [
"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 : Iᵒᵖ\nf : O... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 756,
"column": 35
} | {
"line": 756,
"column": 46
} | {
"line": 756,
"column": 47
} | [
{
"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... | [
"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.obj i)\nU : To... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | {
"line": 247,
"column": 36
} | {
"line": 247,
"column": 54
} | {
"line": 247,
"column": 55
} | [
{
"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",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Units.val",
"Eq.mpr",
"instHSMul",
"HMul.hMul",
"congrAr... | [
"R : Type u\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\nC : VariableChange R\ninst✝ : W.IsElliptic\n⊢ ↑C.u ^ 12 * ↑W.Δ'⁻¹ * (↑C.u⁻¹ ^ 4 * W.c₄) ^ 3 = W.j"
] | variableChange_c₄, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 809,
"column": 34
} | {
"line": 809,
"column": 45
} | {
"line": 809,
"column": 46
} | [
{
"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 ... | [
"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 : CompactSpa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 824,
"column": 2
} | {
"line": 824,
"column": 27
} | {
"line": 824,
"column": 28
} | [
{
"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... | [
"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 = (ConcreteCategory.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 853,
"column": 52
} | {
"line": 853,
"column": 63
} | {
"line": 853,
"column": 64
} | [
{
"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.... | [
"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.pt\nx : ↥c.p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 854,
"column": 57
} | {
"line": 854,
"column": 78
} | {
"line": 854,
"column": 79
} | [
{
"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... | [
"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.pt\nx : ↥c.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 877,
"column": 81
} | {
"line": 884,
"column": 9
} | {
"line": 884,
"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": 890,
"column": 4
} | {
"line": 891,
"column": 65
} | {
"line": 891,
"column": 66
} | [
{
"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... | [
"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.pt\ni : ↥c.pt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 915,
"column": 8
} | {
"line": 915,
"column": 19
} | {
"line": 915,
"column": 20
} | [
{
"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... | [
"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.pt\ni : ↥c.pt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 860,
"column": 30
} | {
"line": 860,
"column": 73
} | {
"line": 860,
"column": 74
} | [
{
"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... | [
"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)).degrees ≤ d\ng :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 861,
"column": 4
} | {
"line": 861,
"column": 15
} | {
"line": 861,
"column": 16
} | [
{
"pp": "case e'_3\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 (MvPolynomial... | [
"case e'_3\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 (MvPolynomial.X i)).degre... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | {
"line": 879,
"column": 48
} | {
"line": 879,
"column": 59
} | {
"line": 879,
"column": 60
} | [
{
"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... | [
"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)).degrees ≤ d\ng :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 433,
"column": 12
} | {
"line": 437,
"column": 41
} | {
"line": 437,
"column": 42
} | [
{
"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... | [
"case e'_3.e'_4\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 • some dq + 3\nhdpq : (p... | 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.Affine.AddSubMap | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 32
} | {
"line": 110,
"column": 2
} | [
{
"pp": "case «6»\nR : Type u_1\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ (C (-12) * t ^ 2 + C (-(4 * W.b₂)) * t * u + C (W.b₂ ^ 2 - 32 * W.b₄) * u ^ 2).IsHomogeneous 2",
"ppTerm": "?«6»",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"NegZeroClass.toNeg",
"... | [] | exact CXX.add CXY |>.add CXX | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 32
} | {
"line": 110,
"column": 2
} | [
{
"pp": "case «6»\nR : Type u_1\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ (C (-12) * t ^ 2 + C (-(4 * W.b₂)) * t * u + C (W.b₂ ^ 2 - 32 * W.b₄) * u ^ 2).IsHomogeneous 2",
"ppTerm": "?«6»",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"NegZeroClass.toNeg",
"... | [] | exact CXX.add CXY |>.add CXX | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 32
} | {
"line": 110,
"column": 2
} | [
{
"pp": "case «6»\nR : Type u_1\ninst✝ : CommRing R\nW : WeierstrassCurve R\n⊢ (C (-12) * t ^ 2 + C (-(4 * W.b₂)) * t * u + C (W.b₂ ^ 2 - 32 * W.b₄) * u ^ 2).IsHomogeneous 2",
"ppTerm": "?«6»",
"assigned": true,
"usedConstants": [
"Finsupp.instAddZeroClass",
"NegZeroClass.toNeg",
"... | [] | exact CXX.add CXY |>.add CXX | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 444,
"column": 4
} | {
"line": 444,
"column": 39
} | {
"line": 444,
"column": 40
} | [
{
"pp": "case nat.succ.succ.succ\nR : Type u_1\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... | [
"case nat.succ.succ.succ\nR : Type u_1\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 c d (m +... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 672,
"column": 2
} | {
"line": 672,
"column": 33
} | {
"line": 672,
"column": 34
} | [
{
"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",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"WeierstrassCurve... | [
"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⊢ (if hxy : x₁ = x₂ ∧ y₁ = W.negY x₂ y₂ then 0\n else some (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂)) (W.addY x₁ x₂ y₁ (W.slope x₁ x₂ y₁ y₂)) ⋯)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 458,
"column": 4
} | {
"line": 458,
"column": 39
} | {
"line": 458,
"column": 40
} | [
{
"pp": "case nat.succ.succ\nR : Type u_1\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 * ... | [
"case nat.succ.succ\nR : Type u_1\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 Even n✝ t... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 743,
"column": 26
} | {
"line": 743,
"column": 57
} | {
"line": 743,
"column": 58
} | [
{
"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",
"ppTerm": "?m.92",
"assigned": true,
"usedConstants": [
"Eq.mpr",... | [
"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 (W.addX x₁ x₂ (W.slope x₁ x₂ y₁ y₂)) (W.addY x₁ x₂ y₁ (W.slope x₁ x₂ y₁ y₂)) ⋯ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | {
"line": 816,
"column": 4
} | {
"line": 816,
"column": 33
} | {
"line": 816,
"column": 34
} | [
{
"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\... | [
"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\ninst✝² : Al... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 754,
"column": 2
} | {
"line": 754,
"column": 29
} | {
"line": 756,
"column": 0
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing S\nF : Type u_3\ninst✝¹ : FunLike F R S\ninst✝ : RingHomClass F R S\nf : F\nb c d : R\nn : ℤ\n⊢ f (normEDS b c d n) = normEDS (f b) (f c) (f d) n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"HMul.hMul",
... | [] | simp [normEDS, apply_ite f] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 754,
"column": 2
} | {
"line": 754,
"column": 29
} | {
"line": 756,
"column": 0
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing S\nF : Type u_3\ninst✝¹ : FunLike F R S\ninst✝ : RingHomClass F R S\nf : F\nb c d : R\nn : ℤ\n⊢ f (normEDS b c d n) = normEDS (f b) (f c) (f d) n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"HMul.hMul",
... | [] | simp [normEDS, apply_ite f] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.EllipticDivisibilitySequence | {
"line": 754,
"column": 2
} | {
"line": 754,
"column": 29
} | {
"line": 756,
"column": 0
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝³ : CommRing R\ninst✝² : CommRing S\nF : Type u_3\ninst✝¹ : FunLike F R S\ninst✝ : RingHomClass F R S\nf : F\nb c d : R\nn : ℤ\n⊢ f (normEDS b c d n) = normEDS (f b) (f c) (f d) n",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"HMul.hMul",
... | [] | simp [normEDS, apply_ite f] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 27
} | {
"line": 127,
"column": 28
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nW : WeierstrassCurve R\ninst✝¹ : W.IsElliptic\ninst✝ : IsReduced R\nx : Fin 3 → R\nhx : (fun i ↦ (eval x) (W.addSubMap i)) = 0\ni : Fin 3\n⊢ x i = 0 i",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"CommSemiring.toSemiring",
"id",
... | [
"R : Type u_1\ninst✝² : CommRing R\nW : WeierstrassCurve R\ninst✝¹ : W.IsElliptic\ninst✝ : IsReduced R\nx : Fin 3 → R\nhx : (fun i ↦ (eval x) (W.addSubMap i)) = 0\ni : Fin 3\n⊢ x i = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms | {
"line": 351,
"column": 76
} | {
"line": 357,
"column": 7
} | {
"line": 359,
"column": 0
} | [
{
"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",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Mathlib.Tactic.Ring.Co... | [] | 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.DivisionPolynomial.Degree | {
"line": 207,
"column": 12
} | {
"line": 207,
"column": 41
} | {
"line": 207,
"column": 42
} | [
{
"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... | [
"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} ↦ natDegree_pow_l... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 208,
"column": 11
} | {
"line": 208,
"column": 39
} | {
"line": 208,
"column": 40
} | [
{
"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... | [
"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} ↦ natDegree_pow_le... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 209,
"column": 11
} | {
"line": 209,
"column": 39
} | {
"line": 209,
"column": 40
} | [
{
"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... | [
"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} ↦ natDegree_pow_le... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 210,
"column": 13
} | {
"line": 210,
"column": 43
} | {
"line": 210,
"column": 44
} | [
{
"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... | [
"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} ↦ natDegree_pow_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 211,
"column": 12
} | {
"line": 211,
"column": 41
} | {
"line": 211,
"column": 42
} | [
{
"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... | [
"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} ↦ natDegree_pow_l... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.AffineTransitionLimit | {
"line": 1196,
"column": 53
} | {
"line": 1196,
"column": 73
} | {
"line": 1196,
"column": 73
} | [
{
"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.AlgebraicGeometry.EllipticCurve.NormalForms | {
"line": 504,
"column": 59
} | {
"line": 506,
"column": 54
} | {
"line": 508,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝² : CommRing R\nW : WeierstrassCurve R\ninst✝¹ : W.IsCharTwoJNeZeroNF\ninst✝ : CharP R 2\n⊢ W.b₂ = 1",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"CharP.cast_eq_zero",
"AddGroup.toSubtractionMonoid",... | [] | by
rw [b₂_of_isCharTwoJNeZeroNF]
linear_combination 2 * W.a₂ * CharP.cast_eq_zero R 2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.IsomOfJ | {
"line": 196,
"column": 4
} | {
"line": 198,
"column": 30
} | {
"line": 199,
"column": 2
} | [
{
"pp": "case of_j_ne_zero.of_j_eq_zero\nF : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE E' : WeierstrassCurve F\ninst✝⁴ : E.IsElliptic\ninst✝³ : E'.IsElliptic\ninst✝² : CharP F 3\nheq : E.j = E'.j\nC : VariableChange F\ninst✝¹ : (C • E).IsCharThreeJNeZeroNF\nC' : VariableChange F\ninst✝ : (C' • E').I... | [] | · have h := (C • E).j_ne_zero_of_isCharThreeJNeZeroNF_of_char_three
rw [variableChange_j, heq, ← variableChange_j E' C', j_of_isShortNF_of_char_three] at h
exact False.elim (h rfl) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.EllipticCurve.IsomOfJ | {
"line": 299,
"column": 4
} | {
"line": 299,
"column": 68
} | {
"line": 299,
"column": 69
} | [
{
"pp": "F : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE✝ E'✝ : WeierstrassCurve F\ninst✝⁴ : E✝.IsElliptic\ninst✝³ : E'✝.IsElliptic\np : ℕ\ninst✝² : CharP F p\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝³ : NeZero 2\nthis✝² : NeZero 4\nthis✝¹ : NeZero 6\nthis✝ : Invertible 2 := invertibleOfNonzero hchar2\nt... | [
"F : Type u_1\ninst✝⁶ : Field F\ninst✝⁵ : IsSepClosed F\nE✝ E'✝ : WeierstrassCurve F\ninst✝⁴ : E✝.IsElliptic\ninst✝³ : E'✝.IsElliptic\np : ℕ\ninst✝² : CharP F p\nhchar2 : 2 ≠ 0\nhchar3 : 3 ≠ 0\nthis✝³ : NeZero 2\nthis✝² : NeZero 4\nthis✝¹ : NeZero 6\nthis✝ : Invertible 2 := invertibleOfNonzero hchar2\nthis : Invert... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 316,
"column": 13
} | {
"line": 316,
"column": 42
} | {
"line": 316,
"column": 43
} | [
{
"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",
"ppTerm": "?nat",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"CommSemiring.toSemiring",
"id",
"Ne",
"Int",
... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 317,
"column": 16
} | {
"line": 318,
"column": 13
} | {
"line": 318,
"column": 14
} | [
{
"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",
"ppTerm": "?neg",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.instNeg",
"congrArg",
... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | {
"line": 447,
"column": 4
} | {
"line": 447,
"column": 33
} | {
"line": 447,
"column": 34
} | [
{
"pp": "case pos\nR : Type u\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\ninst✝ : Nontrivial R\nn : ℤ\nhn : n = 0\n⊢ W.Φ n ≠ 0",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.instOne",
"congrArg",
"CommSemiring.toSemiring",
"id",
... | [
"case pos\nR : Type u\ninst✝¹ : CommRing R\nW : WeierstrassCurve R\ninst✝ : Nontrivial R\nn : ℤ\nhn : n = 0\n⊢ 1 ≠ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | {
"line": 260,
"column": 4
} | {
"line": 260,
"column": 43
} | {
"line": 260,
"column": 43
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Jacobian F\ninst✝ : DecidableEq F\nP Q : Fin 3 → F\nhP : W.Equation P\nhQ : W.Equation Q\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\nhy : P y * Q z ^ 3 ≠ W.negY Q * P z ^ 3\n⊢ W.dblXYZ P =\n W.dblZ P •\n ![W.toAffine.addX (P x / P z ^ 2) ... | [
"F : Type u\ninst✝¹ : Field F\nW : Jacobian F\ninst✝ : DecidableEq F\nP Q : Fin 3 → F\nhP : W.Equation P\nhQ : W.Equation Q\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 = Q x * P z ^ 2\nhy : P y * Q z ^ 3 ≠ W.negY Q * P z ^ 3\n⊢ W.dblZ P •\n ![W.toAffine.addX (P x / P z ^ 2) (Q x / Q z ^ 2)\n (W.... | dblXYZ_of_Z_ne_zero hP hQ hPz hQz hx hy | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 458,
"column": 30
} | {
"line": 458,
"column": 64
} | {
"line": 458,
"column": 64
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Jacobian F\ninst✝ : DecidableEq F\nP Q : Fin 3 → F\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 ≠ Q x * P z ^ 2\n⊢ P x / P z ^ 2 ≠ Q x / Q z ^ 2",
"ppTerm": "?m.244",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"HMul.hM... | [] | by rwa [ne_eq, ← X_eq_iff hPz hQz] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 458,
"column": 2
} | {
"line": 460,
"column": 14
} | {
"line": 462,
"column": 0
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Jacobian F\ninst✝ : DecidableEq F\nP Q : Fin 3 → F\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 ≠ Q x * P z ^ 2\n⊢ W.toAffine.slope (P x / P z ^ 2) (Q x / Q z ^ 2) (P y / P z ^ 3) (Q y / Q z ^ 3) =\n (P y * Q z ^ 3 - Q y * P z ^ 3) / (P z * Q z * addZ P Q)",
... | [] | rw [Affine.slope_of_X_ne <| by rwa [ne_eq, ← X_eq_iff hPz hQz],
div_sub_div _ _ (pow_ne_zero 2 hPz) (pow_ne_zero 2 hQz), mul_comm <| _ ^ 2, addZ]
simp [field] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | {
"line": 458,
"column": 2
} | {
"line": 460,
"column": 14
} | {
"line": 462,
"column": 0
} | [
{
"pp": "F : Type u\ninst✝¹ : Field F\nW : Jacobian F\ninst✝ : DecidableEq F\nP Q : Fin 3 → F\nhPz : P z ≠ 0\nhQz : Q z ≠ 0\nhx : P x * Q z ^ 2 ≠ Q x * P z ^ 2\n⊢ W.toAffine.slope (P x / P z ^ 2) (Q x / Q z ^ 2) (P y / P z ^ 3) (Q y / Q z ^ 3) =\n (P y * Q z ^ 3 - Q y * P z ^ 3) / (P z * Q z * addZ P Q)",
... | [] | rw [Affine.slope_of_X_ne <| by rwa [ne_eq, ← X_eq_iff hPz hQz],
div_sub_div _ _ (pow_ne_zero 2 hPz) (pow_ne_zero 2 hQz), mul_comm <| _ ^ 2, addZ]
simp [field] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.Nonarchimedean.Bases | {
"line": 63,
"column": 58
} | {
"line": 63,
"column": 85
} | {
"line": 63,
"column": 86
} | [
{
"pp": "A : Type u_3\nι : Type u_4\ninst✝ : CommRing A\nB : ι → AddSubgroup A\ninter : ∀ (i j : ι), ∃ k, B k ≤ B i ⊓ B j\nmul : ∀ (i : ι), ∃ j, ↑(B j) * ↑(B j) ⊆ ↑(B i)\nleftMul : ∀ (x : A) (i : ι), ∃ j, ↑(B j) ⊆ (fun y ↦ x * y) ⁻¹' ↑(B i)\nx : A\ni j : ι\nhj : ↑(B j) ⊆ (fun y ↦ x * y) ⁻¹' ↑(B i)\n⊢ ↑(B j) ⊆ (... | [
"A : Type u_3\nι : Type u_4\ninst✝ : CommRing A\nB : ι → AddSubgroup A\ninter : ∀ (i j : ι), ∃ k, B k ≤ B i ⊓ B j\nmul : ∀ (i : ι), ∃ j, ↑(B j) * ↑(B j) ⊆ ↑(B i)\nleftMul : ∀ (x : A) (i : ι), ∃ j, ↑(B j) ⊆ (fun y ↦ x * y) ⁻¹' ↑(B i)\nx : A\ni j : ι\nhj : ↑(B j) ⊆ (fun y ↦ x * y) ⁻¹' ↑(B i)\n⊢ ↑(B j) ⊆ (fun x_1 ↦ x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Nonarchimedean.Bases | {
"line": 172,
"column": 8
} | {
"line": 172,
"column": 19
} | {
"line": 172,
"column": 20
} | [
{
"pp": "case h.right\nA : Type u_1\nι : Type u_2\ninst✝¹ : Ring A\ninst✝ : Nonempty ι\nB : ι → AddSubgroup A\nhB : RingSubgroupsBasis B\na : A\ns : Set A\ni : ι\nhi : {b | b - a ∈ B i} ⊆ s\nb : A\nb_in : b ∈ ↑(B i)\n⊢ (fun y ↦ a + y) b ∈ {b | b - a ∈ B i}",
"ppTerm": "?h.right",
"assigned": true,
"... | [
"case h.right\nA : Type u_1\nι : Type u_2\ninst✝¹ : Ring A\ninst✝ : Nonempty ι\nB : ι → AddSubgroup A\nhB : RingSubgroupsBasis B\na : A\ns : Set A\ni : ι\nhi : {b | b - a ∈ B i} ⊆ s\nb : A\nb_in : b ∈ ↑(B i)\n⊢ b ∈ B i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Nonarchimedean.Bases | {
"line": 185,
"column": 6
} | {
"line": 185,
"column": 17
} | {
"line": 185,
"column": 18
} | [
{
"pp": "case right\nA : Type u_1\nι : Type u_2\ninst✝¹ : Ring A\ninst✝ : Nonempty ι\nB : ι → AddSubgroup A\nhB : RingSubgroupsBasis B\ni : ι\nx✝ : TopologicalSpace A := hB.topology\na : A\na_in : a ∈ (B i).carrier\nb : A\nb_in : b ∈ {b | b - a ∈ B i}\n⊢ b ∈ (B i).carrier",
"ppTerm": "?right",
"assigned... | [
"case right\nA : Type u_1\nι : Type u_2\ninst✝¹ : Ring A\ninst✝ : Nonempty ι\nB : ι → AddSubgroup A\nhB : RingSubgroupsBasis B\ni : ι\nx✝ : TopologicalSpace A := hB.topology\na : A\na_in : a ∈ (B i).carrier\nb : A\nb_in : b ∈ {b | b - a ∈ B i}\n⊢ b ∈ B i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 31
} | {
"line": 51,
"column": 32
} | [
{
"pp": "case inr.inl\nK : Type u\ninst✝² : DivisionRing K\nΓ₀ : Type v\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : MulArchimedean Γ₀\nv : Valuation K Γ₀\nx : K\nhx : v x ≠ 0\nr : Γ₀ˣ\nhr : ↑r ≠ 0\nh : ∀ (x : K), v x ≠ 0 → ↑r < v x\nH : Units.mk0 (v x) hx = 1\n⊢ v x = 1",
"ppTerm": "?inr.inl",
... | [
"case inr.inl\nK : Type u\ninst✝² : DivisionRing K\nΓ₀ : Type v\ninst✝¹ : LinearOrderedCommGroupWithZero Γ₀\ninst✝ : MulArchimedean Γ₀\nv : Valuation K Γ₀\nx : K\nhx : v x ≠ 0\nr : Γ₀ˣ\nhr : ↑r ≠ 0\nh : ∀ (x : K), v x ≠ 0 → ↑r < v x\nH : Units.mk0 (v x) hx = 1\n⊢ v x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 192,
"column": 2
} | {
"line": 192,
"column": 13
} | {
"line": 192,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : R\n⊢ 0 ≤ᵥ x",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : R\n⊢ 0 ≤ᵥ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 386,
"column": 2
} | {
"line": 389,
"column": 13
} | {
"line": 391,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : ↥(posSubmonoid R)\n⊢ ↑x ≠ 0",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"ValuativeRel.vlt",
"False",
"congrArg",
"Mathlib.Tactic.Contrapose.contrapose₃",
"ValuativeRel.not_vlt_zero._sim... | [] | have := x.prop
rw [posSubmonoid_def] at this
contrapose this
simp [this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 386,
"column": 2
} | {
"line": 389,
"column": 13
} | {
"line": 391,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : ↥(posSubmonoid R)\n⊢ ↑x ≠ 0",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"ValuativeRel.vlt",
"False",
"congrArg",
"Mathlib.Tactic.Contrapose.contrapose₃",
"ValuativeRel.not_vlt_zero._sim... | [] | have := x.prop
rw [posSubmonoid_def] at this
contrapose this
simp [this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 406,
"column": 8
} | {
"line": 406,
"column": 19
} | {
"line": 406,
"column": 20
} | [
{
"pp": "case left\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z r : R\nu : ↥(posSubmonoid R)\ns : R\nv : ↥(posSubmonoid R)\nt : R\nw : ↥(posSubmonoid R)\nh1 : r * ↑v ≤ᵥ s * ↑u\nh2 : s * ↑u ≤ᵥ r * ↑v\nh3 : s * ↑w ≤ᵥ t * ↑v\nh4 : t * ↑v ≤ᵥ s * ↑w\nthis✝ : r * ↑v * ↑w ≤ᵥ s * ↑w * ↑u\nthi... | [
"case left\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z r : R\nu : ↥(posSubmonoid R)\ns : R\nv : ↥(posSubmonoid R)\nt : R\nw : ↥(posSubmonoid R)\nh1 : r * ↑v ≤ᵥ s * ↑u\nh2 : s * ↑u ≤ᵥ r * ↑v\nh3 : s * ↑w ≤ᵥ t * ↑v\nh4 : t * ↑v ≤ᵥ s * ↑w\nthis✝ : r * ↑v * ↑w ≤ᵥ s * ↑w * ↑u\nthis : r * ↑w *... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 411,
"column": 8
} | {
"line": 411,
"column": 19
} | {
"line": 411,
"column": 20
} | [
{
"pp": "case right\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z r : R\nu : ↥(posSubmonoid R)\ns : R\nv : ↥(posSubmonoid R)\nt : R\nw : ↥(posSubmonoid R)\nh1 : r * ↑v ≤ᵥ s * ↑u\nh2 : s * ↑u ≤ᵥ r * ↑v\nh3 : s * ↑w ≤ᵥ t * ↑v\nh4 : t * ↑v ≤ᵥ s * ↑w\nthis✝ : t * ↑v * ↑u ≤ᵥ s * ↑u * ↑w\nth... | [
"case right\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z r : R\nu : ↥(posSubmonoid R)\ns : R\nv : ↥(posSubmonoid R)\nt : R\nw : ↥(posSubmonoid R)\nh1 : r * ↑v ≤ᵥ s * ↑u\nh2 : s * ↑u ≤ᵥ r * ↑v\nh3 : s * ↑w ≤ᵥ t * ↑v\nh4 : t * ↑v ≤ᵥ s * ↑w\nthis✝ : t * ↑v * ↑u ≤ᵥ s * ↑u * ↑w\nthis : t * ↑u ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 482,
"column": 15
} | {
"line": 482,
"column": 26
} | {
"line": 482,
"column": 27
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : R\ny : ↥(posSubmonoid R)\nh : ValueGroupWithZero.mk x y = 0\n⊢ x ≤ᵥ 0",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : R\ny : ↥(posSubmonoid R)\nh : ValueGroupWithZero.mk x y = 0\n⊢ x ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 483,
"column": 42
} | {
"line": 483,
"column": 53
} | {
"line": 483,
"column": 54
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : R\ny : ↥(posSubmonoid R)\nh : x ≤ᵥ 0\n⊢ x * ↑1 ≤ᵥ 0 * ↑y",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"MulZeroClass.zero_mul",
"Membership.mem",
... | [
"R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx : R\ny : ↥(posSubmonoid R)\nh : x ≤ᵥ 0\n⊢ x ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 540,
"column": 2
} | {
"line": 540,
"column": 13
} | {
"line": 540,
"column": 14
} | [
{
"pp": "case mk.mk\nR : Type u_1\ninst✝² : Semiring R\ninst✝¹ : ValuativeRel R\nα : Type u_2\ninst✝ : Mul α\nf : R → ↥(posSubmonoid R) → α\nhf : ∀ (x y : R) (t s : ↥(posSubmonoid R)), x * ↑t ≤ᵥ y * ↑s → y * ↑s ≤ᵥ x * ↑t → f x s = f y t\nhdist : ∀ (a b : R) (r s : ↥(posSubmonoid R)), f (a * b) (r * s) = f a r *... | [
"case mk.mk\nR : Type u_1\ninst✝² : Semiring R\ninst✝¹ : ValuativeRel R\nα : Type u_2\ninst✝ : Mul α\nf : R → ↥(posSubmonoid R) → α\nhf : ∀ (x y : R) (t s : ↥(posSubmonoid R)), x * ↑t ≤ᵥ y * ↑s → y * ↑s ≤ᵥ x * ↑t → f x s = f y t\nhdist : ∀ (a b : R) (r s : ↥(posSubmonoid R)), f (a * b) (r * s) = f a r * f b s\nx✝¹ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 100,
"column": 8
} | {
"line": 100,
"column": 19
} | {
"line": 100,
"column": 20
} | [
{
"pp": "case h\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx : R\nγ : (ofClass v).ValueGroup₀ˣ\nγx : Γ₀ˣ\nHx : v x = ↑γx\nu : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu_def : u = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\n... | [
"case h\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx : R\nγ : (ofClass v).ValueGroup₀ˣ\nγx : Γ₀ˣ\nHx : v x = ↑γx\nu : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu_def : u = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu : embeddi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.WithZeroTopology | {
"line": 166,
"column": 6
} | {
"line": 166,
"column": 63
} | {
"line": 166,
"column": 64
} | [
{
"pp": "case inr\nα : Type u_1\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ γ₁ γ₂ : Γ₀\nl : Filter α\nf : α → Γ₀\nx y : Γ₀\nthis✝ : ∀ (x y : Γ₀), x ≤ y → Tendsto (fun p ↦ p.1 * p.2) (𝓝 (x, y)) (𝓝 ((x, y).1 * (x, y).2))\nhle : ¬x ≤ y\nthis : Tendsto ((fun p ↦ p.1 * p.2) ∘ Prod.swap) (𝓝 (x, y)... | [
"case inr\nα : Type u_1\nΓ₀ : Type u_2\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nγ γ₁ γ₂ : Γ₀\nl : Filter α\nf : α → Γ₀\nx y : Γ₀\nthis✝ : ∀ (x y : Γ₀), x ≤ y → Tendsto (fun p ↦ p.1 * p.2) (𝓝 (x, y)) (𝓝 ((x, y).1 * (x, y).2))\nhle : ¬x ≤ y\nthis : Tendsto ((fun p ↦ p.1 * p.2) ∘ Prod.swap) (𝓝 (x, y)) (𝓝 ((y, x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 543,
"column": 21
} | {
"line": 547,
"column": 20
} | {
"line": 548,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx x' y y' z : R\na b c : ValueGroupWithZero R\n⊢ a * b * c = a * (b * c)",
"ppTerm": "?m.72",
"assigned": true,
"usedConstants": [
"Semigroup.toMul",
"Submonoid.mul",
"HMul.hMul",
"MulMemClass.toSemigroup",
... | [] | by
induction a using ValueGroupWithZero.ind
induction b using ValueGroupWithZero.ind
induction c using ValueGroupWithZero.ind
simp [mul_assoc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 116,
"column": 8
} | {
"line": 116,
"column": 19
} | {
"line": 116,
"column": 20
} | [
{
"pp": "case h\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx : R\nγ : (ofClass v).ValueGroup₀ˣ\nγx : Γ₀ˣ\nHx : v x = ↑γx\nu : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu_def : u = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\n... | [
"case h\nR : Type u\ninst✝¹ : Ring R\nΓ₀ : Type v\ninst✝ : LinearOrderedCommGroupWithZero Γ₀\nv : Valuation R Γ₀\nx : R\nγ : (ofClass v).ValueGroup₀ˣ\nγx : Γ₀ˣ\nHx : v x = ↑γx\nu : (ofClass v).ValueGroup₀ˣ := Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu_def : u = Units.mk0 ((restrict₀ (ofClass v)) x) ⋯\nhu : embeddi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 595,
"column": 6
} | {
"line": 595,
"column": 17
} | {
"line": 595,
"column": 18
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z✝ x y z w : R\nt s u v : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nh₃ : z * ↑u ≤ᵥ w * ↑v\nh₄ : w * ↑v ≤ᵥ z * ↑u\nhw : w ≤ᵥ 0\nhz : ¬z ≤ᵥ 0\n⊢ z * ↑u ≤ᵥ 0 * ↑u",
"ppTerm": "?neg✝",
"assigned"... | [
"case neg\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z✝ x y z w : R\nt s u v : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nh₃ : z * ↑u ≤ᵥ w * ↑v\nh₄ : w * ↑v ≤ᵥ z * ↑u\nhw : w ≤ᵥ 0\nhz : ¬z ≤ᵥ 0\n⊢ z * ↑u ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 598,
"column": 6
} | {
"line": 598,
"column": 17
} | {
"line": 598,
"column": 18
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z✝ x y z w : R\nt s u v : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nh₃ : z * ↑u ≤ᵥ w * ↑v\nh₄ : w * ↑v ≤ᵥ z * ↑u\nhw : ¬w ≤ᵥ 0\nhz : z ≤ᵥ 0\n⊢ w * ↑v ≤ᵥ 0 * ↑v",
"ppTerm": "?pos✝",
"assigned"... | [
"case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z✝ x y z w : R\nt s u v : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nh₃ : z * ↑u ≤ᵥ w * ↑v\nh₄ : w * ↑v ≤ᵥ z * ↑u\nhw : ¬w ≤ᵥ 0\nhz : z ≤ᵥ 0\n⊢ w * ↑v ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 599,
"column": 6
} | {
"line": 599,
"column": 47
} | {
"line": 600,
"column": 6
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z✝ x y z w : R\nt s u v : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nh₃ : z * ↑u ≤ᵥ w * ↑v\nh₄ : w * ↑v ≤ᵥ z * ↑u\nhw : ¬w ≤ᵥ 0\nhz : ¬z ≤ᵥ 0\n⊢ (x * ↑v ≤ᵥ z * ↑s) = (y * ↑u ≤ᵥ w * ↑t)",
"ppTerm":... | [
"case neg.refine_1\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z✝ x y z w : R\nt s u v : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nh₃ : z * ↑u ≤ᵥ w * ↑v\nh₄ : w * ↑v ≤ᵥ z * ↑u\nhw : ¬w ≤ᵥ 0\nhz : ¬z ≤ᵥ 0\nh : x * ↑v ≤ᵥ z * ↑s\n⊢ y * ↑u ≤ᵥ w * ↑t",
"case neg.refin... | refine propext ⟨fun h => ?_, fun h => ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 170,
"column": 2
} | {
"line": 170,
"column": 30
} | {
"line": 170,
"column": 31
} | [
{
"pp": "case e'_2\nR : Type u_1\ninst✝⁵ : Ring R\ninst✝⁴ : ValuativeRel R\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ns : Set R\nx : R\n⊢ (∃ γ, {z | v.restrict (z - x) < ↑γ} ⊆ s) ↔ ∃ γ, (fun x... | [
"case e'_2\nR : Type u_1\ninst✝⁵ : Ring R\ninst✝⁴ : ValuativeRel R\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ns : Set R\nx : R\n⊢ (∃ γ, {z | v.restrict (z - x) < ↑γ} ⊆ s) ↔ ∃ γ, {a | (valuation R)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Valued.ValuationTopology | {
"line": 212,
"column": 44
} | {
"line": 212,
"column": 55
} | {
"line": 212,
"column": 56
} | [
{
"pp": "K : Type u\ninst✝³ : DivisionRing K\nΓ₀ : Type v\ninst✝² : LinearOrderedCommGroupWithZero Γ₀\ninst✝¹ : MulArchimedean Γ₀\ninst✝ : Valued K Γ₀\nr : Γ₀\nhr : r ≠ 0\nh : ∀ (x : K), v x ≠ 0 → r < v x\n⊢ ∀ (x : K), x ≠ 0 → v x = 1",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"... | [
"K : Type u\ninst✝³ : DivisionRing K\nΓ₀ : Type v\ninst✝² : LinearOrderedCommGroupWithZero Γ₀\ninst✝¹ : MulArchimedean Γ₀\ninst✝ : Valued K Γ₀\nr : Γ₀\nhr : r ≠ 0\nh : ∀ (x : K), v x ≠ 0 → r < v x\n⊢ ∀ (x : K), ¬x = 0 → v x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 209,
"column": 45
} | {
"line": 209,
"column": 56
} | {
"line": 209,
"column": 57
} | [
{
"pp": "R : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\nx z : R\nγ : (ofClass... | [
"R : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\nx z : R\nγ : (ofClass (valuation ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 214,
"column": 75
} | {
"line": 214,
"column": 86
} | {
"line": 214,
"column": 87
} | [
{
"pp": "R : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_add : ContinuousC... | [
"R : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_add : ContinuousConstVAdd R R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 216,
"column": 4
} | {
"line": 216,
"column": 30
} | {
"line": 216,
"column": 31
} | [
{
"pp": "case refine_4\nR : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_ad... | [
"case refine_4\nR : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_add : Continuo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 217,
"column": 4
} | {
"line": 217,
"column": 30
} | {
"line": 217,
"column": 31
} | [
{
"pp": "case refine_5\nR : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_ad... | [
"case refine_5\nR : Type u_1\ninst✝⁷ : Ring R\ninst✝⁶ : ValuativeRel R\nK : Type u_2\ninst✝⁵ : DivisionRing K\ninst✝⁴ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝³ : LinearOrderedCommGroupWithZero Γ₀\ninst✝² : TopologicalSpace R\nv : Valuation R Γ₀\ninst✝¹ : v.Compatible\ninst✝ : IsValuativeTopology R\ncts_add : Continuo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 683,
"column": 6
} | {
"line": 683,
"column": 17
} | {
"line": 683,
"column": 18
} | [
{
"pp": "case neg\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : x ≤ᵥ 0\nhy : ¬y ≤ᵥ 0\n⊢ y * ↑s ≤ᵥ 0 * ↑s",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"H... | [
"case neg\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : x ≤ᵥ 0\nhy : ¬y ≤ᵥ 0\n⊢ y * ↑s ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 686,
"column": 6
} | {
"line": 686,
"column": 17
} | {
"line": 686,
"column": 18
} | [
{
"pp": "case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : ¬x ≤ᵥ 0\nhy : y ≤ᵥ 0\n⊢ x * ↑t ≤ᵥ 0 * ↑t",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"H... | [
"case pos\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : ¬x ≤ᵥ 0\nhy : y ≤ᵥ 0\n⊢ x * ↑t ≤ᵥ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 690,
"column": 8
} | {
"line": 690,
"column": 19
} | {
"line": 690,
"column": 20
} | [
{
"pp": "case neg.h₁\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : ¬x ≤ᵥ 0\nhy : ¬y ≤ᵥ 0\n⊢ ↑⟨y, hy⟩ * ↑s ≤ᵥ x * ↑t",
"ppTerm": "?neg.h₁✝",
"assigned": true,
"usedConstants": [
"HMu... | [
"case neg.h₁\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : ¬x ≤ᵥ 0\nhy : ¬y ≤ᵥ 0\n⊢ y * ↑s ≤ᵥ x * ↑t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.ValuativeRel.Basic | {
"line": 692,
"column": 8
} | {
"line": 692,
"column": 30
} | {
"line": 692,
"column": 31
} | [
{
"pp": "case h₂\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : ¬x ≤ᵥ 0\nhy : ¬y ≤ᵥ 0\n⊢ ↑⟨x, hx⟩ * ↑t ≤ᵥ y * ↑s",
"ppTerm": "?h₂",
"assigned": true,
"usedConstants": [
"HMul.hMul",
... | [
"case h₂\nR : Type u_1\ninst✝¹ : Semiring R\ninst✝ : ValuativeRel R\nx✝ x' y✝ y' z x y : R\nt s : ↥(posSubmonoid R)\nh₁ : x * ↑t ≤ᵥ y * ↑s\nh₂ : y * ↑s ≤ᵥ x * ↑t\nhx : ¬x ≤ᵥ 0\nhy : ¬y ≤ᵥ 0\n⊢ x * ↑t ≤ᵥ y * ↑s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | {
"line": 288,
"column": 46
} | {
"line": 288,
"column": 57
} | {
"line": 288,
"column": 58
} | [
{
"pp": "K : Type u_2\ninst✝⁶ : DivisionRing K\ninst✝⁵ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝⁴ : LinearOrderedCommGroupWithZero Γ₀\ninst✝³ : TopologicalSpace K\ninst✝² : IsValuativeTopology K\ninst✝¹ : MulArchimedean Γ₀\nv : Valuation K Γ₀\ninst✝ : v.Compatible\nr : Γ₀\nhr : r ≠ 0\nh : ∀ (x : K), v x ≠ 0 → r < ... | [
"K : Type u_2\ninst✝⁶ : DivisionRing K\ninst✝⁵ : ValuativeRel K\nΓ₀ : Type u_3\ninst✝⁴ : LinearOrderedCommGroupWithZero Γ₀\ninst✝³ : TopologicalSpace K\ninst✝² : IsValuativeTopology K\ninst✝¹ : MulArchimedean Γ₀\nv : Valuation K Γ₀\ninst✝ : v.Compatible\nr : Γ₀\nhr : r ≠ 0\nh : ∀ (x : K), v x ≠ 0 → r < v x\n⊢ ∀ (x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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