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.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 159,
"column": 46
} | {
"line": 159,
"column": 57
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 159,
"column": 46
} | {
"line": 159,
"column": 57
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 213,
"column": 41
} | {
"line": 213,
"column": 52
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : SetLike σ A\ninst✝⁸ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝⁷ : GradedRing 𝒜\nO : Type u_3\ninst✝⁶ : CommRing O\ninst✝⁵ : IsDomain O\ninst✝⁴ : ValuationRing O\nK : Type u_4\ninst✝³ : Field K\ninst✝² : Algebra O K\ninst✝¹ : IsFractionRing O K\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 224,
"column": 35
} | {
"line": 224,
"column": 93
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : SetLike σ A\ninst✝⁸ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝⁷ : GradedRing 𝒜\nO : Type u_3\ninst✝⁶ : CommRing O\ninst✝⁵ : IsDomain O\ninst✝⁴ : ValuationRing O\nK : Type u_4\ninst✝³ : Field K\ninst✝² : Algebra O K\ninst✝¹ : IsFractionRing O K\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 88,
"column": 6
} | {
"line": 88,
"column": 30
} | [
{
"pp": "case refine_1\nP : MorphismProperty Scheme\ninst✝² : P.IsStableUnderBaseChange\ninst✝¹ : P.IsMultiplicative\nF : Schemeᵒᵖ ⥤ Type u_1\ninst✝ : IsZariskiLocalAtSource P\nx✝ :\n Presieve.IsSheaf zariskiTopology F ∧\n ∀ {R S : CommRingCat} (f : R ⟶ S),\n P (Spec.map f) → Surjective (Spec.map f) → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.CommSq | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 20
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\nA₀ : C\nz : A₀ ⟶ cokernel t\nhz : z ≫ cokernel.map t b l r ⋯ = 0\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₂ : A₁ ⟶ X₂\nhx₂ : π₁ ≫ z = x₂ ≫ cokernel.π t\nt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.CommSq | {
"line": 159,
"column": 4
} | {
"line": 159,
"column": 15
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPushout t l r b\nA₀ : C\nz : A₀ ⟶ kernel b\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₁ :\n A₁ ⟶\n { X₁ := X₁, X₂ := X₂ ⊞ X₃, X₃ := ⋯.cokernelCofork.pt, f ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.CommSq | {
"line": 161,
"column": 4
} | {
"line": 161,
"column": 15
} | [
{
"pp": "case refine_2.h\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPushout t l r b\nA₀ : C\nz : A₀ ⟶ kernel b\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₁ :\n A₁ ⟶\n { X₁ := X₁, X₂ := X₂ ⊞ X₃, X₃ := ⋯.cokernelCofork.pt, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Subcanonical | {
"line": 111,
"column": 2
} | {
"line": 112,
"column": 9
} | [
{
"pp": "case h.w.h.h.toFun.h\nC : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝ : J.Subcanonical\nP Q : Sheaf J (Type v)\nf g : P ⟶ Q\nh : ∀ (X : C) (p : J.yoneda.obj X ⟶ P), p ≫ f = p ≫ g\nX : Cᵒᵖ\nx : P.obj.obj X\n⊢ (ConcreteCategory.hom (f.hom.app X)).toFun x = (ConcreteCategory.hom ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Subcanonical | {
"line": 208,
"column": 2
} | {
"line": 209,
"column": 9
} | [
{
"pp": "case h.w.h.h.toFun.h\nC : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\ninst✝ : J.Subcanonical\nP Q : Sheaf J (Type (max v v'))\nf g : P ⟶ Q\nh : ∀ (X : C) (p : (uliftYoneda.{v', v, u} J).obj X ⟶ P), p ≫ f = p ≫ g\nX : Cᵒᵖ\nx : P.obj.obj X\n⊢ (ConcreteCategory.hom (f.hom.app X)).toFun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject | {
"line": 56,
"column": 62
} | {
"line": 56,
"column": 73
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nF : J ⥤ MonoOver X\ninst✝ : IsFiltered J\nc : Cocone (F ⋙ MonoOver.forget X ⋙ Over.forget X)\nhc : IsColimit c\nf : c.pt ⟶ X\nhf : ∀ (j : J), c.ι.app j ≫ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject | {
"line": 75,
"column": 10
} | {
"line": 76,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\ninst✝³ : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝² : SmallCategory J\nF : J ⥤ MonoOver X\ninst✝¹ : IsFiltered J\nc : Cocone (F ⋙ MonoOver.forget X ⋙ Over.forget X)\nhc : IsColimit c\nf✝ : c.pt ⟶ X\nhf : ∀ (j : J), c.ι.app j ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPredOrder | {
"line": 30,
"column": 58
} | {
"line": 30,
"column": 69
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : ¬IsMax i\nj : Fin (n + 1)\n⊢ ?m.68 ≠ last ?m.67",
"usedConstants": [
"id",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Fin.last",
"instAddNat",
"OfNat.ofNat",
"Fin"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPredOrder | {
"line": 33,
"column": 42
} | {
"line": 33,
"column": 53
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : IsMax i\n⊢ i = last n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPredOrder | {
"line": 58,
"column": 54
} | {
"line": 58,
"column": 65
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : ¬IsMin i\nj : Fin (n + 1)\n⊢ ?m.70 ≠ 0",
"usedConstants": [
"instNeZeroNatHAdd_1",
"id",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPredOrder | {
"line": 61,
"column": 33
} | {
"line": 61,
"column": 44
} | [
{
"pp": "n : ℕ\ni : Fin (n + 1)\nhi : IsMin i\n⊢ i = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 29,
"column": 32
} | {
"line": 29,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx : ↑(Iic j)\nk : α\nh : k < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ } x\n⊢ k ∈ range ⇑{ toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ }",
"usedConstants": [
"Eq.mpr",
"RelEmbedding.mk",
"Preorder.toLT",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 95,
"column": 16
} | {
"line": 95,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nj₀ : J\ny : X ⟶ Y.obj j₀\nhy : y ≫ c.ι.app j₀ = 0\ninst✝ : IsFiltered J\nj : Under j₀\n⊢ (colimit.cocone\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 96,
"column": 16
} | {
"line": 96,
"column": 27
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nj₀ : J\ny : X ⟶ Y.obj j₀\nhy : y ≫ c.ι.app j₀ = 0\ninst✝ : IsFiltered J\nx✝ : Under j₀\n⊢ (constCocone (Under j... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 121,
"column": 59
} | {
"line": 121,
"column": 70
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nκ : Cardinal.{w}\nhκ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhXκ : HasCardinalLT (Subobject X) κ\nj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 125,
"column": 2
} | {
"line": 126,
"column": 9
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nκ : Cardinal.{w}\nhκ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhXκ : HasCardinalLT (Subobject X) κ\nj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 133,
"column": 18
} | {
"line": 133,
"column": 70
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nκ : Cardinal.{w}\nhκ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhXκ : HasCardinalLT (Subobject X) κ\nj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Limit | {
"line": 42,
"column": 27
} | {
"line": 42,
"column": 38
} | [
{
"pp": "J : Type u\ninst✝ : LinearOrder J\nj : J\nm : ↑(Ici j)\nhm : Order.IsSuccLimit m\nb : J\nhb : b < ↑m\nhb' : b < j\nthis : ↑m ≤ j\nk : J\nhk : k ∈ Ici j\na✝ : ⟨k, hk⟩ ≤ m\n⊢ j ≤ ↑⟨k, hk⟩",
"usedConstants": [
"Set.Ici",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 319,
"column": 80
} | {
"line": 319,
"column": 91
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nO : Type u_2\ncommRing✝ : CommRing O\ndomain✝ : IsDomain O\nvaluationRing✝ : ValuationRing O\nK : Type u_2\nfield✝ : Field K\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 335,
"column": 72
} | {
"line": 335,
"column": 83
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nO : Type u_2\ncommRing✝ : CommRing O\ndomain✝ : IsDomain O\nvaluationRing✝ : ValuationRing O\nK : Type u_2\nfield✝ : Field K\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | {
"line": 85,
"column": 8
} | {
"line": 85,
"column": 32
} | [
{
"pp": "J : Type w\ninst✝⁶ : LinearOrder J\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : HasIterationOfShape J C\ninst✝³ : SuccOrder J\ninst✝² : WellFoundedLT J\nα : Type u_1\ninst✝¹ : PartialOrder α\nf : InitialSeg (fun x1 x2 ↦ x1 < x2) fun x1 x2 ↦ x1 < x2\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | {
"line": 90,
"column": 42
} | {
"line": 90,
"column": 64
} | [
{
"pp": "J : Type w\ninst✝⁶ : LinearOrder J\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : HasIterationOfShape J C\ninst✝³ : SuccOrder J\ninst✝² : WellFoundedLT J\nα : Type u_1\ninst✝¹ : PartialOrder α\nf : InitialSeg (fun x1 x2 ↦ x1 < x2) fun x1 x2 ↦ x1 < x2\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.SuccOrder | {
"line": 31,
"column": 51
} | {
"line": 31,
"column": 62
} | [
{
"pp": "J : Type u_1\ninst✝¹ : PartialOrder J\ninst✝ : SuccOrder J\nj : J\ni : ↑(Iic j)\nhi : ¬IsMax i\n⊢ i ≠ ⊤",
"usedConstants": [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"id",
"Ne",
"OrderTop.toTop",
"Set.Iic.orderTop",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.SuccOrder | {
"line": 46,
"column": 60
} | {
"line": 46,
"column": 71
} | [
{
"pp": "J : Type u_1\ninst✝¹ : PartialOrder J\ninst✝ : PredOrder J\nj : J\ni : ↑(Ici j)\nhi : ¬IsMin i\n⊢ i ≠ ⊥",
"usedConstants": [
"Set.Ici",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"id",
"Ne",
"Bot.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 24
} | [
{
"pp": "case h\nC : Type u\ninst✝ : Category.{v, u} C\nα : Type t\nA B : α → C\ng : (a : α) → A a ⟶ B a\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nc : AttachCells g f\nZ : C\nφ φ' : X₂ ⟶ Z\nh₀ : f ≫ φ = f ≫ φ'\nh : ∀ (i : c.ι), c.cell i ≫ φ = c.cell i ≫ φ'\n⊢ ∀ (i : c.ι), c.cofan₂.inj i ≫ c.g₂ ≫ φ = c.cofan₂.inj i ≫ c.g₂ ≫ φ'",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition | {
"line": 255,
"column": 4
} | {
"line": 255,
"column": 15
} | [
{
"pp": "case isMin\nC : Type u\ninst✝⁵ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : WellFoundedLT J\nX Y : C\nf : X ⟶ Y\nhf : W.TransfiniteCompositionOfShape J f\ninst✝ : W.IsMultiplicative\nhJ :\n ∀ (J : Type w) [inst : L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 56,
"column": 14
} | {
"line": 56,
"column": 56
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\n⊢ ¬↑⟨Order.succ j, ⋯⟩ ≤ j",
"usedConstants": [
"Eq.mpr",
"Order.succ",
"congrArg",
"PartialOrder.toPreorder",
"Preo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 92,
"column": 18
} | {
"line": 92,
"column": 60
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\n⊢ ¬Order.succ j ≤ j",
"usedConstants": [
"Eq.mpr",
"Order.succ",
"congrArg",
"_private.Mathlib.Cate... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition | {
"line": 386,
"column": 2
} | {
"line": 387,
"column": 85
} | [
{
"pp": "case mpr\nC : Type u\ninst✝¹ : Category.{v, u} C\nP Q : MorphismProperty C\ninst✝ : Q.IsStableUnderTransfiniteComposition\n⊢ P ≤ Q → transfiniteCompositions.{w, v, u} P ≤ Q",
"usedConstants": [
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebr... | · intro h
exact (transfiniteCompositions_monotone.{w} h).trans Q.transfiniteCompositions_le | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 102,
"column": 20
} | {
"line": 102,
"column": 62
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\nhi : Order.succ j ≤ Order.succ j\nh₁ : ¬Order.succ j ≤ j\n⊢ ¬Order.succ j ≤ j",
"usedConstants": [
"Eq.mpr",
"_... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone | {
"line": 59,
"column": 45
} | {
"line": 59,
"column": 56
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : Type u\ninst✝ : LinearOrder J\nj : J\nF : ↑(Set.Iio j) ⥤ C\nc : Cocone F\ni₁ i₂ : J\nhi : i₁ ≤ i₂\nhi₂ : i₂ ≤ j\nh₂ : ¬i₂ < j\n⊢ j ≤ i₂",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone | {
"line": 63,
"column": 58
} | {
"line": 63,
"column": 69
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : Type u\ninst✝ : LinearOrder J\nj : J\nF : ↑(Set.Iio j) ⥤ C\nc : Cocone F\ni₁ i₂ : J\nhi : i₁ ≤ i₂\nhi₂ : i₂ ≤ j\nh₂ : ¬i₂ < j\nh₂' : i₂ = j\nh₁ : ¬i₁ < j\n⊢ j ≤ i₁",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Construction | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝¹ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝ : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\nx : FunctorObjIndex f πX\n⊢ f x.i ≫ Sigma.ι (functorObjTgtFamily... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 109,
"column": 2
} | {
"line": 111,
"column": 19
} | [
{
"pp": "case pos\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\ni₁ i₂ i₃ : J\nh₁₂ : i₁ ≤ i₂\nh₂₃ : i₂ ≤ i₃\nh : i₃ ≤ Order.succ j\nh₁ : i₃ ≤ j\n⊢ map hj F τ i₁ i₃ ⋯ h = map hj F τ i... | · rw [map_eq hj F τ i₁ i₂ _ (h₂₃.trans h₁), map_eq hj F τ i₂ i₃ _ h₁,
map_eq hj F τ i₁ i₃ _ h₁, assoc, assoc, Iso.inv_hom_id_assoc, ← Functor.map_comp_assoc,
homOfLE_comp] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.SmallObject.Construction | {
"line": 178,
"column": 31
} | {
"line": 178,
"column": 46
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝³ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝² : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\ninst✝¹ : LocallySmall.{t, v, u} C\ninst✝ : Small.{t, w} I\nφ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Construction | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 31
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝³ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝² : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\ninst✝¹ : LocallySmall.{t, v, u} C\ninst✝ : Small.{t, w} I\nφ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | {
"line": 45,
"column": 46
} | {
"line": 45,
"column": 57
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\nx✝ : J\nh₁ : Order.IsSuccLimit x✝\nh₂ : x✝ ≤ ⊥\n⊢ IsMin x✝",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | {
"line": 61,
"column": 8
} | {
"line": 61,
"column": 32
} | [
{
"pp": "case inl\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\nj : J\nhj : ¬IsMax j\niter : Φ.Iteration j\ni : J\nhi₁✝¹ : i < Order.succ j\nhi₁✝ : i ≤ j\n... | ← arrowSucc_def _ _ hi₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 97,
"column": 52
} | {
"line": 97,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : PartialOrder J\nj : J\nF : ↑(Set.Iic j) ⥤ C\ni : J\nhi : i ≤ j\nk₁ k₂ : ↑(Set.Iio i)\nφ : k₁ ⟶ k₂\n⊢ ⋯.functor.obj k₁ ≤ ⋯.functor.obj k₂",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Pr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 116,
"column": 52
} | {
"line": 116,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : PartialOrder J\nj : J\nF : ↑(Set.Iic j) ⥤ C\ni : J\nhi : i ≤ j\nk₁ k₂ : ↑(Set.Iic i)\nφ : k₁ ⟶ k₂\n⊢ ⋯.functor.obj k₁ ≤ ⋯.functor.obj k₂",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Set.initialSegIicIicOfLE",
"I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | {
"line": 154,
"column": 31
} | {
"line": 154,
"column": 42
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\ni : J\nhi : IsMin i\n⊢ i = ⊥",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteIteration | {
"line": 86,
"column": 8
} | {
"line": 86,
"column": 19
} | [
{
"pp": "case a\nC : Type u\ninst✝⁵ : Category.{v, u} C\nΦ : SuccStruct C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\ni : J\nhi : Order.IsSuccLimit i\nk₁ : J\nh₁ : k₁ ∈ Set.Iio i\nk₂ : J\nh₂ : k₂ ∈ Set.Iio i\nf : ⟨k₁,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 372,
"column": 32
} | {
"line": 372,
"column": 43
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj : J\nh : IsMin ⊥\niter₁ iter₂ : Φ.Iteration ⊥\nk₁ k₂ : J\nh₁₂ : k₁ ≤ k₂\nh₂ : k₂ ≤ ⊥\n⊢ k₂ = ⊥",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 373,
"column": 32
} | {
"line": 373,
"column": 43
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj : J\nh : IsMin ⊥\niter₁ iter₂ : Φ.Iteration ⊥\nk₁ : J\nh₁₂ : k₁ ≤ ⊥\nh₂ : ⊥ ≤ ⊥\n⊢ k₁ = ⊥",
"usedCons... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 402,
"column": 47
} | {
"line": 402,
"column": 58
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj✝ j : J\nh₁ : Order.IsSuccLimit j\nh₂ : ∀ b < j, ∀ (iter₁ iter₂ : Φ.Iteration b), iter₁.F = iter₂.F\niter₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.IsSmall | {
"line": 45,
"column": 2
} | {
"line": 45,
"column": 32
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nW : MorphismProperty C\nι : Type t\ninst✝ : Small.{w, t} ι\nA B : ι → C\nf : (i : ι) → A i ⟶ B i\nφ : ι → ↑(ofHoms f).toSet := fun i ↦ ⟨Arrow.mk (f i), ⋯⟩\nhφ : Function.Surjective φ\n⊢ IsSmall.{w, v, u} (ofHoms f)",
"usedConstants": [
"small_of_surject... | exact ⟨small_of_surjective hφ⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 408,
"column": 53
} | {
"line": 408,
"column": 64
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj✝ j : J\nh₁ : Order.IsSuccLimit j\nh₂ : ∀ b < j, ∀ (iter₁ iter₂ : Φ.Iteration b), iter₁.F = iter₂.F\niter₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 416,
"column": 48
} | {
"line": 416,
"column": 59
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj₁ j₂ : J\niter₁ : Φ.Iteration j₁\niter₂ : Φ.Iteration j₂\nk : J\nh₁ : k ≤ j₁\nh₂ : k ≤ j₂\nthis :\n ∀ {j₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 135,
"column": 29
} | {
"line": 135,
"column": 40
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : IsMin i\n⊢ i = ⊥",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 150,
"column": 4
} | {
"line": 159,
"column": 75
} | [
{
"pp": "case isSuccLimit\nJ : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : Order.IsSuccLimit i\nhi' : ∀ b < i, Subsingleton (d.Extension val₀ b)\n⊢ Subsingleton (d.Extension v... | refine Subsingleton.intro (fun e₁ e₂ ↦ val_injective ?_)
have h₁ := e₁.map_limit i hi (by rfl)
have h₂ := e₂.map_limit i hi (by rfl)
simp only [homOfLE_refl, op_id, map_id, id_apply, OrderHom.Subtype.val_coe, comp_obj, op_obj,
Monotone.functor_obj, homOfLE_leOfHom] at h₁ h₂
rw [h₁, h₂]
congr
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 150,
"column": 4
} | {
"line": 159,
"column": 75
} | [
{
"pp": "case isSuccLimit\nJ : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : Order.IsSuccLimit i\nhi' : ∀ b < i, Subsingleton (d.Extension val₀ b)\n⊢ Subsingleton (d.Extension v... | refine Subsingleton.intro (fun e₁ e₂ ↦ val_injective ?_)
have h₁ := e₁.map_limit i hi (by rfl)
have h₂ := e₂.map_limit i hi (by rfl)
simp only [homOfLE_refl, op_id, map_id, id_apply, OrderHom.Subtype.val_coe, comp_obj, op_obj,
Monotone.functor_obj, homOfLE_leOfHom] at h₁ h₂
rw [h₁, h₂]
congr
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 175,
"column": 29
} | {
"line": 175,
"column": 40
} | [
{
"pp": "J : Type u\ninst✝² : LinearOrder J\ninst✝¹ : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝ : OrderBot J\nval₀ : F.obj (op ⊥)\ni : J\nhi : Order.IsSuccLimit i\nhij : i ≤ ⊥\n⊢ i = ⊥",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 15
} | [
{
"pp": "J : Type u\ninst✝² : LinearOrder J\ninst✝¹ : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝ : OrderBot J\nval₀ : F.obj (op ⊥)\nhi : Order.IsSuccLimit ⊥\nhij : ⊥ ≤ ⊥\n⊢ (ConcreteCategory.hom (F.map (homOfLE hij).op)) val₀ =\n d.lift ⊥ hi\n ⟨fun x ↦\n match x with\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 221,
"column": 31
} | {
"line": 221,
"column": 62
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ⊥ < j",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 15
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ↑⟨fun x ↦\n match x with\n | op ⟨i,... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 222,
"column": 25
} | {
"line": 222,
"column": 56
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ⊥ < j",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 86,
"column": 4
} | {
"line": 86,
"column": 43
} | [
{
"pp": "case isMin\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 89,
"column": 6
} | {
"line": 89,
"column": 17
} | [
{
"pp": "case succ.h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 91,
"column": 6
} | {
"line": 91,
"column": 48
} | [
{
"pp": "case succ.h\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 94,
"column": 24
} | {
"line": 94,
"column": 35
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\nZ : C\nφ₁ φ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 15
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type w\ninst✝² : LinearOrder J\ninst✝¹ : OrderBot J\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\np : X ⟶ Y\nf : F.obj ⊥ ⟶ X\ng : c.pt ⟶ Y\ninst✝ : F.IsWellOrderContinuous\nj : J\nhj : Order.IsSuccLimit j\ns : ↑(⋯.functor.op ⋙ sqFunctor c p f g).sectio... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 257,
"column": 29
} | {
"line": 257,
"column": 40
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : IsMin i\n⊢ i = ⊥",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 227,
"column": 30
} | {
"line": 227,
"column": 41
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\np : X ⟶ Y\nf : F.obj ⊥ ⟶ X\ng✝ : c.pt ⟶ Y\ninst✝² : F.IsWellOrderContinuous\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nhF : ∀ (j : J), ¬IsMax j → Has... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 277,
"column": 2
} | {
"line": 277,
"column": 13
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\nval₀ : F.obj (op ⊥)\n⊢ ↑(d.sectionsMk val₀) (op ⊥) = val₀",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 277,
"column": 2
} | {
"line": 277,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\n⊢ (coproducts.{w, v, u} W).pushouts.transfiniteCompositionsOfShape J ≤ W.rlp.llp",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 293,
"column": 2
} | {
"line": 293,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nW : MorphismProperty C\n⊢ transfiniteCompositions.{w, v, u} (coproducts.{w, v, u} W).pushouts ≤ W.rlp.llp",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.instIsStableUnderCoproductsLlp",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nj : κ.ord.ToType\n⊢ (succStruct I κ).prop ((iterationFunctor I κ).map (homOfLE ⋯))",
"usedConstants": [
"l... | have := hasIterationOfShape I κ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | {
"line": 314,
"column": 2
} | {
"line": 314,
"column": 33
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nX Y : C\nf : X ⟶ Y\n⊢ RelativeCellComplex (fun x ↦ I.homFamily) (ιObj I κ f)",
"usedConstants": [
"linearO... | have := hasIterationOfShape I κ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | {
"line": 349,
"column": 2
} | {
"line": 349,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nX Y : C\nf : X ⟶ Y\nj : κ.ord.ToType\n⊢ ιFunctorObj I.homFamily (((iterationFunctor I κ).obj j).obj (Arrow.mk f)).ho... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 216,
"column": 2
} | {
"line": 217,
"column": 54
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nn d : ℤ\nhqz : q ≠ 0\nqdf : q = n /. d\nhd : d ≠ 0\nc : ℤ\nhc1 : n = c * q.num\nhc2 : d = c * ↑q.den\n⊢ ↑(multiplicity (↑p) q.num) - ↑(multiplicity p q.den) =\n ↑(multiplicity (↑p) (c * q.num)) - ↑(multiplicity (↑p) (c * ↑q.den))",
"usedConstants": [
... | rw [multiplicity_mul (Nat.prime_iff_prime_int.1 hp.1),
multiplicity_mul (Nat.prime_iff_prime_int.1 hp.1)] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 43
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nn d : ℤ\nhqz : q ≠ 0\nqdf : q = n /. d\nhd : d ≠ 0\nc : ℤ\nhc1 : n = c * q.num\nhc2 : d = c * ↑q.den\n⊢ FiniteMultiplicity (↑p) (c * ↑q.den)",
"usedConstants": [
"Eq.mpr",
"False",
"IsDomain.to_noZeroDivisors",
"HMul.hMul",
"MulZe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 48
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nq : ℚ\nn d : ℤ\nhqz : q ≠ 0\nqdf : q = n /. d\nhd : d ≠ 0\nc : ℤ\nhc1 : n = c * q.num\nhc2 : d = c * ↑q.den\n⊢ FiniteMultiplicity (↑p) (c * q.num)",
"usedConstants": [
"Rat.instOfNat",
"Eq.mpr",
"False",
"Rat.num",
"IsDomain.to_noZeroDiv... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 228,
"column": 8
} | {
"line": 228,
"column": 25
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhq : q ≠ 0\nhr : r ≠ 0\n⊢ q * r = q.num * r.num /. (↑q.den * ↑r.den)",
"usedConstants": [
"Eq.mpr",
"Rat.instMul",
"Rat.num",
"Rat.mul_eq_mkRat",
"HMul.hMul",
"congrArg",
"Rat",
"Rat.divInt",
"Rat.den",
... | Rat.mul_eq_mkRat, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 280,
"column": 24
} | {
"line": 280,
"column": 40
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nhqr : q + r ≠ 0\nh : padicValRat p q ≤ padicValRat p r\nhq : q = 0\n⊢ padicValRat p q ≤ padicValRat p (q + r)",
"usedConstants": [
"Rat.instOfNat",
"Eq.mpr",
"padicValRat.zero",
"congrArg",
"AddMonoid.toAddZeroClass",
"Rat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives | {
"line": 134,
"column": 19
} | {
"line": 134,
"column": 30
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nG : C\ninst✝¹ : Abelian C\nhG : IsSeparator G\nX Y : C\np : X ⟶ Y\ninst✝ : Mono p\nf : G ⟶ Y\nhf : ∀ (x : G ⟶ X), ¬(ConcreteCategory.hom ((yoneda.map p).app (Opposite.op G))) x = f\nh : ∀ (T : C), Function.Bijective fun x ↦ x ≫ pushout.inl (pullback.fst p f) (pul... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 341,
"column": 2
} | {
"line": 350,
"column": 45
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nF : ℕ → ℚ\nhF : ∀ i < n, 0 < padicValRat p (F i)\nhn0 : ∑ i ∈ Finset.range n, F i ≠ 0\n⊢ 0 < padicValRat p (∑ i ∈ Finset.range n, F i)",
"usedConstants": [
"Rat.addCommMonoid",
"Rat.instOfNat",
"Eq.mpr",
"Nat.recAux",
"Nat.instIsO... | induction n with
| zero => exact False.elim (hn0 rfl)
| succ d hd =>
rw [Finset.sum_range_succ] at hn0 ⊢
by_cases h : ∑ x ∈ Finset.range d, F x = 0
· rw [h, zero_add]
exact hF d (lt_add_one _)
· refine lt_of_lt_of_le ?_ (min_le_padicValRat_add hn0)
refine lt_min (hd (fun i hi => ?_) h) (... | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 341,
"column": 2
} | {
"line": 350,
"column": 45
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nF : ℕ → ℚ\nhF : ∀ i < n, 0 < padicValRat p (F i)\nhn0 : ∑ i ∈ Finset.range n, F i ≠ 0\n⊢ 0 < padicValRat p (∑ i ∈ Finset.range n, F i)",
"usedConstants": [
"Rat.addCommMonoid",
"Rat.instOfNat",
"Eq.mpr",
"Nat.recAux",
"Nat.instIsO... | induction n with
| zero => exact False.elim (hn0 rfl)
| succ d hd =>
rw [Finset.sum_range_succ] at hn0 ⊢
by_cases h : ∑ x ∈ Finset.range d, F x = 0
· rw [h, zero_add]
exact hF d (lt_add_one _)
· refine lt_of_lt_of_le ?_ (min_le_padicValRat_add hn0)
refine lt_min (hd (fun i hi => ?_) h) (... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 341,
"column": 2
} | {
"line": 350,
"column": 45
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nF : ℕ → ℚ\nhF : ∀ i < n, 0 < padicValRat p (F i)\nhn0 : ∑ i ∈ Finset.range n, F i ≠ 0\n⊢ 0 < padicValRat p (∑ i ∈ Finset.range n, F i)",
"usedConstants": [
"Rat.addCommMonoid",
"Rat.instOfNat",
"Eq.mpr",
"Nat.recAux",
"Nat.instIsO... | induction n with
| zero => exact False.elim (hn0 rfl)
| succ d hd =>
rw [Finset.sum_range_succ] at hn0 ⊢
by_cases h : ∑ x ∈ Finset.range d, F x = 0
· rw [h, zero_add]
exact hF d (lt_add_one _)
· refine lt_of_lt_of_le ?_ (min_le_padicValRat_add hn0)
refine lt_min (hd (fun i hi => ?_) h) (... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives | {
"line": 143,
"column": 8
} | {
"line": 143,
"column": 56
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nG : C\ninst✝¹ : Abelian C\nhG : IsSeparator G\nX A✝ : C\nf : A✝ ⟶ X\ninst✝ : Mono f\nhA : Subobject.mk f ≠ ⊤\n⊢ ¬IsIso f",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.IsIso",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 392,
"column": 2
} | {
"line": 392,
"column": 49
} | [
{
"pp": "p a : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\nha : a ≠ 0\n⊢ padicValNat p (a ^ n) = n * padicValNat p a",
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"Nat.instMonoid",
"Rat",
"AddGroupWithOne.toAddMonoidWithOn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives | {
"line": 202,
"column": 16
} | {
"line": 202,
"column": 62
} | [
{
"pp": "C : Type u\ninst✝⁶ : Category.{v, u} C\nG : C\ninst✝⁵ : Abelian C\nhG : IsSeparator G\nX : C\ninst✝⁴ : IsGrothendieckAbelian.{w, v, u} C\nA₀ : Subobject X\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nhJ : HasCardinalLT (Subobject X) (Cardinal.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 446,
"column": 56
} | {
"line": 447,
"column": 86
} | [
{
"pp": "p q : ℕ\nhp : Fact (Nat.Prime p)\nhq : Fact (Nat.Prime q)\nn : ℕ\nne : p ≠ q\n⊢ padicValNat p (q ^ n) = 0",
"usedConstants": [
"Eq.mpr",
"Nat.instMulZeroClass",
"Nat.Prime",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"Nat.instMonoid",
"padicValNat... | by
rw [padicValNat.pow _ <| Nat.Prime.ne_zero hq.elim, padicValNat_primes ne, mul_zero] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Padics.PadicNorm | {
"line": 164,
"column": 43
} | {
"line": 164,
"column": 60
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nq r : ℚ\nh : padicValRat p q ≤ padicValRat p r\nhnqp : padicNorm p q ≥ 0\nhnrp : padicNorm p r ≥ 0\nhq : ¬q = 0\nhr : ¬r = 0\nhqr : q + r = 0\n⊢ padicNorm p (q + r) ≤ padicNorm p q",
"usedConstants": [
"Rat.instOfNat",
"Eq.mpr",
"congrArg",
"R... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives | {
"line": 321,
"column": 37
} | {
"line": 321,
"column": 48
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nG : C\ninst✝¹ : Abelian C\ninst✝ : IsGrothendieckAbelian.{w, v, u} C\nκ : Cardinal.{w}\nhκ' : κ.IsRegular\nhκ : HasCardinalLT (Subobject G) κ\nthis : Fact κ.IsRegular\n⊢ Nonempty κ.ord.ToType",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.EnoughInjectives | {
"line": 369,
"column": 2
} | {
"line": 370,
"column": 44
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nG : C\ninst✝¹ : Abelian C\ninst✝ : IsGrothendieckAbelian.{w, v, u} C\nX : C\nfac : (monomorphisms C).MapFactorizationData (monomorphisms C).rlp 0 := monoMapFactorizationDataRlp 0\n⊢ Injective (monoMapFactorizationDataRlp 0).Z",
"usedConstants": [
"Categ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 66
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ IsOpen {y | ‖y‖ ≤ 1}",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 249,
"column": 32
} | {
"line": 249,
"column": 60
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℤ_[p]\nf : CauSeq ℤ_[p] norm\nx✝ : ℝ\nhε : x✝ > 0\n⊢ ∃ i, ∀ j ≥ i, (fun a ↦ ‖a‖) ((fun n ↦ ↑(↑f n)) j - (fun n ↦ ↑(↑f n)) i) < x✝",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Eq.mpr",
"Real.instLE",
"Real",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 258,
"column": 6
} | {
"line": 258,
"column": 34
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℤ_[p]\nf : CauSeq ℤ_[p] norm\nhqn : ‖(cauSeq_to_rat_cauSeq f).lim‖ ≤ 1\nε : ℝ\n⊢ ε > 0 → ∃ i, ∀ j ≥ i, ‖↑(f - CauSeq.const norm ⟨(cauSeq_to_rat_cauSeq f).lim, hqn⟩) j‖ < ε",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Eq.mp... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 331,
"column": 8
} | {
"line": 331,
"column": 37
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nx y : ℤ_[p]\nhxy : x + y ≠ 0\n⊢ min ↑x.valuation ↑y.valuation ≤ ↑(x + y).valuation",
"usedConstants": [
"Norm.norm",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.instLE",
"Real",
"instAddPadic",
"Lattice.toSemil... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 386,
"column": 2
} | {
"line": 386,
"column": 13
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nz : ℤ_[p]\n⊢ ¬IsUnit z ↔ ‖z‖ < 1",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 464,
"column": 4
} | {
"line": 464,
"column": 51
} | [
{
"pp": "case mpr\np : ℕ\nhp : Fact (Nat.Prime p)\nx : ℤ_[p]\nhx : x ≠ 0\nn : ℕ\n⊢ n ≤ x.valuation → ↑p ^ n ∣ ↑(unitCoeff hx) * ↑p ^ x.valuation",
"usedConstants": [
"NormedCommRing.toNormedRing",
"Units.val",
"Eq.mpr",
"Dvd.dvd",
"NormedRing.toRing",
"HMul.hMul",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 217,
"column": 4
} | {
"line": 217,
"column": 18
} | [
{
"pp": "case mp\np : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nh : (if hf : f ≈ 0 then 0 else padicNorm p (↑f (stationaryPoint hf))) = 0\nhf : ¬f ≈ 0\n⊢ False",
"usedConstants": [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"Rat.instOfNat",
"NormedRing.to... | split_ifs at h | Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1 | Mathlib.Tactic.splitIfs |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 238,
"column": 20
} | {
"line": 238,
"column": 35
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf g : PadicSeq p\nh : ∀ (k : ℕ), padicNorm p (↑f k) = padicNorm p (↑g k)\nhf : f ≈ 0\nε : ℚ\nhε : ε > 0\ni : ℕ\nhi : ∀ j ≥ i, padicNorm p (↑(f - 0) j) < ε\nj : ℕ\nhj : j ≥ i\n⊢ padicNorm p (↑(g - 0) j) < ε",
"usedConstants": [
"padicNorm.instIsAbsoluteValueR... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 247,
"column": 42
} | {
"line": 247,
"column": 57
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nf : PadicSeq p\nhf : ¬f ≈ 0\nheq : f.norm = padicNorm p (↑f (stationaryPoint hf))\nh : ↑f (stationaryPoint hf) = 0\n⊢ f.norm = 0",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 254,
"column": 51
} | {
"line": 254,
"column": 62
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nq : ℚ\nhq : q ≠ 0\nh : (const (padicNorm p) q - 0).LimZero\n⊢ (const (padicNorm p) q).LimZero",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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