module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicGeometry.Sites.Small | {
"line": 122,
"column": 4
} | {
"line": 125,
"column": 50
} | {
"line": 127,
"column": 0
} | [
{
"pp": "case mpr\nP : MorphismProperty Scheme\nS : Scheme\ninst✝² : P.IsStableUnderBaseChange\ninst✝¹ : P.IsMultiplicative\ninst✝ : P.RespectsIso\nX : Over S\nR : Sieve X\n⊢ R ∈ (overPretopology P S).toGrothendieck X → (Sieve.overEquiv X) R ∈ (grothendieckTopology P) X.left",
"ppTerm": "?mpr",
"assigne... | [] | rintro ⟨T, ⟨𝒰, h, rfl⟩, hT⟩
rw [mem_grothendieckTopology_iff]
use 𝒰
rwa [Cover.toPresieveOver_le_arrows_iff] at hT | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.ValuativeCriterion | {
"line": 198,
"column": 89
} | {
"line": 213,
"column": 24
} | {
"line": 215,
"column": 0
} | [
{
"pp": "X Y : Scheme\nf : X ⟶ Y\n⊢ Existence.IsStableUnderBaseChange",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"CategoryTheory.IsPullback.hom_ext",
"AlgebraicGeometry.ValuativeCommSq.algebra",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"AlgebraicGeometry... | [] | by
constructor
intro Y' X X' Y Y'_to_Y f X'_to_X f' hP hf commSq
let commSq' : ValuativeCommSq f :=
{ R := commSq.R
K := commSq.K
i₁ := commSq.i₁ ≫ X'_to_X
i₂ := commSq.i₂ ≫ Y'_to_Y
commSq := ⟨by simp only [Category.assoc, hP.w, reassoc_of% commSq.commSq.w]⟩ }
obtain ⟨l₀, hl₁, hl₂⟩ := (hf comm... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.Sites.Small | {
"line": 205,
"column": 2
} | {
"line": 206,
"column": 33
} | {
"line": 207,
"column": 2
} | [
{
"pp": "P Q : MorphismProperty Scheme\nS : Scheme\ninst✝⁵ : P.IsStableUnderBaseChange\ninst✝⁴ : P.IsMultiplicative\ninst✝³ : P.RespectsIso\ninst✝² : Q.IsStableUnderComposition\ninst✝¹ : Q.IsStableUnderBaseChange\ninst✝ : Q.HasOfPostcompProperty Q\nhPQ : P ≤ Q\nX : Q.Over ⊤ S\nR : Sieve X\n⊢ R ∈ (smallGrothendi... | [
"P Q : MorphismProperty Scheme\nS : Scheme\ninst✝⁵ : P.IsStableUnderBaseChange\ninst✝⁴ : P.IsMultiplicative\ninst✝³ : P.RespectsIso\ninst✝² : Q.IsStableUnderComposition\ninst✝¹ : Q.IsStableUnderBaseChange\ninst✝ : Q.HasOfPostcompProperty Q\nhPQ : P ≤ Q\nX : Q.Over ⊤ S\nR : Sieve X\nthis : (MorphismProperty.Over.for... | have : (MorphismProperty.Over.forget Q ⊤ S).LocallyCoverDense (overGrothendieckTopology P S) :=
locallyCoverDense_of_le S hPQ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 201,
"column": 8
} | {
"line": 201,
"column": 54
} | {
"line": 202,
"column": 8
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁵ : Category.{v₀, u₀} C₀\ninst✝⁴ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\ninst✝³ : IsDenseSubsite J₀ J F\ninst✝² : HasPullbacks C\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nS : C\nι : C → Type w\nU : (S : C) → ι S → C₀\nf : (S ... | [
"C₀ : Type u₀\nC : Type u\ninst✝⁵ : Category.{v₀, u₀} C₀\ninst✝⁴ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\ninst✝³ : IsDenseSubsite J₀ J F\ninst✝² : HasPullbacks C\ninst✝¹ : F.Full\ninst✝ : F.Faithful\nS : C\nι : C → Type w\nU : (S : C) → ι S → C₀\nf : (S : C) → (i : ... | rintro T _ ⟨Z, q, r, ⟨_, s, _, ⟨k⟩, fac⟩, rfl⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 122,
"column": 9
} | {
"line": 122,
"column": 33
} | {
"line": 122,
"column": 33
} | [
{
"pp": "case h₁\nσ : Type u_1\nA : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\ni j : (affineOpenCover 𝒜).openCover.I₀\ne₁ : pullback ((affineOpenCover 𝒜).f i ≫ toSpecZero 𝒜) ((affineOpenCover 𝒜).f j ≫ toSpecZero 𝒜) ≅\n Spec (CommR... | [
"case h₁\nσ : Type u_1\nA : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\ni j : (affineOpenCover 𝒜).openCover.I₀\ne₁ : pullback ((affineOpenCover 𝒜).f i ≫ toSpecZero 𝒜) ((affineOpenCover 𝒜).f j ≫ toSpecZero 𝒜) ≅\n Spec (CommRingCat.of (A... | pullbackAwayιIso_inv_snd | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.Sites.Etale | {
"line": 99,
"column": 4
} | {
"line": 99,
"column": 43
} | {
"line": 100,
"column": 4
} | [
{
"pp": "Ω : Type u\ninst✝¹ : Field Ω\ninst✝ : IsSepClosed Ω\nS : Scheme\nR : Sieve S\nhR : R ∈ etaleTopology S\nx : ↥S\na : S.residueField x ⟶ CommRingCat.of Ω\n⊢ ∃ Y f,\n ∃ (_ : R.arrows f),\n ∃ y,\n (ConcreteCategory.hom ((coyoneda.obj (Opposite.op (Spec (CommRingCat.of Ω)))).map f)) y =\n ... | [
"Ω : Type u\ninst✝¹ : Field Ω\ninst✝ : IsSepClosed Ω\nS : Scheme\nR : Sieve S\nhR : ∃ 𝒰, Presieve.ofArrows 𝒰.X 𝒰.f ≤ R.arrows\nx : ↥S\na : S.residueField x ⟶ CommRingCat.of Ω\n⊢ ∃ Y f,\n ∃ (_ : R.arrows f),\n ∃ y,\n (ConcreteCategory.hom ((coyoneda.obj (Opposite.op (Spec (CommRingCat.of Ω)))).map ... | rw [mem_grothendieckTopology_iff] at hR | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 487,
"column": 73
} | {
"line": 487,
"column": 84
} | {
"line": 487,
"column": 84
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [] | simp [← h₂] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 487,
"column": 73
} | {
"line": 487,
"column": 84
} | {
"line": 487,
"column": 84
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [] | simp [← h₂] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 487,
"column": 73
} | {
"line": 487,
"column": 84
} | {
"line": 487,
"column": 84
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [] | simp [← h₂] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 53,
"column": 10
} | {
"line": 53,
"column": 44
} | {
"line": 53,
"column": 44
} | [
{
"pp": "case refine_3.inr.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 (S... | [
"case refine_3.inr.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) →... | ← Presieve.isSheafFor_iff_generate | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 56,
"column": 41
} | {
"line": 56,
"column": 79
} | {
"line": 56,
"column": 79
} | [
{
"pp": "case refine_3.inr.refine_2\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 (S... | [
"case refine_3.inr.refine_2\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) →... | ← Presieve.isSeparatedFor_iff_generate | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 67,
"column": 12
} | {
"line": 67,
"column": 46
} | {
"line": 67,
"column": 46
} | [
{
"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) → ... | [
"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) → Presieve.IsS... | ← Presieve.isSheafFor_iff_generate | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 72,
"column": 12
} | {
"line": 72,
"column": 50
} | {
"line": 72,
"column": 50
} | [
{
"pp": "case refine_2\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) → ... | [
"case refine_2\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) → Presieve.IsS... | ← Presieve.isSeparatedFor_iff_generate | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 76,
"column": 6
} | {
"line": 76,
"column": 63
} | {
"line": 77,
"column": 6
} | [
{
"pp": "case inr\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) → Presi... | [
"case inr\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) → Presieve.IsSheafF... | refine f.isSheafFor_iff ?_ fun f ↦ (H _ f).isSeparatedFor | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 305,
"column": 58
} | {
"line": 310,
"column": 43
} | {
"line": 312,
"column": 0
} | [
{
"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\... | [] | by
· simp only [ψ, ← map_pow]
congr 2
rw [← pow_mul, ← pow_mul, ← mul_assoc, ← mul_assoc, ← mul_assoc,
Finset.univ.prod_erase_mul d (h := Finset.mem_univ _),
mul_comm _ a, mul_right_comm] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 363,
"column": 2
} | {
"line": 364,
"column": 55
} | {
"line": 366,
"column": 0
} | [
{
"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\n⊢ UniversallyClosed (toSpecZero 𝒜)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"GradedRing.t... | [] | rw [UniversallyClosed.eq_valuativeCriterion]
exact ⟨valuativeCriterion_existence 𝒜, inferInstance⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 363,
"column": 2
} | {
"line": 364,
"column": 55
} | {
"line": 366,
"column": 0
} | [
{
"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\n⊢ UniversallyClosed (toSpecZero 𝒜)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"GradedRing.t... | [] | rw [UniversallyClosed.eq_valuativeCriterion]
exact ⟨valuativeCriterion_existence 𝒜, inferInstance⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 92,
"column": 42
} | {
"line": 99,
"column": 48
} | {
"line": 101,
"column": 0
} | [
{
"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\n⊢ Epi (f y)",
"ppTerm": "?m.54",
... | [] | by
exact (colim.exact_mapShortComplex
((ShortComplex.mk _ _ (kernel.condition (g y))).exact_of_f_is_kernel
(kernelIsKernel (g y)))
(colimit.isColimit _) (isColimitConstCocone _ _)
((Functor.Final.isColimitWhiskerEquiv (Under.forget j₀) c).symm hc) (f y) 0
(fun j ↦ by simpa using! hf y j)
(fu... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 27,
"column": 19
} | {
"line": 27,
"column": 24
} | {
"line": 28,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx✝² x✝¹ : ↑(Iic j)\nx✝ : (fun j_1 ↦ ↑j_1) x✝² = (fun j_1 ↦ ↑j_1) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"id",
"Subtype.mk",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 27,
"column": 19
} | {
"line": 27,
"column": 24
} | {
"line": 28,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx✝² x✝¹ : ↑(Iic j)\nx✝ : (fun j_1 ↦ ↑j_1) x✝² = (fun j_1 ↦ ↑j_1) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"id",
"Subtype.mk",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 27,
"column": 19
} | {
"line": 27,
"column": 24
} | {
"line": 28,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx✝² x✝¹ : ↑(Iic j)\nx✝ : (fun j_1 ↦ ↑j_1) x✝² = (fun j_1 ↦ ↑j_1) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"id",
"Subtype.mk",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 28,
"column": 21
} | {
"line": 28,
"column": 26
} | {
"line": 29,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ {a b : ↑(Iic j)}, { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } a < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem",
"F... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 28,
"column": 21
} | {
"line": 28,
"column": 26
} | {
"line": 29,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ {a b : ↑(Iic j)}, { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } a < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } b ↔ a < b",
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"F... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
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} | {
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"column": 26
} | {
"line": 29,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ {a b : ↑(Iic j)}, { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } a < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
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"congrArg",
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"F... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 36,
"column": 19
} | {
"line": 36,
"column": 24
} | {
"line": 37,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx✝² x✝¹ : ↑(Iio j)\nx✝ : (fun j_1 ↦ ↑j_1) x✝² = (fun j_1 ↦ ↑j_1) x✝¹\n⊢ x✝² = x✝¹",
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"Set.Elem",
"id",
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... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 36,
"column": 19
} | {
"line": 36,
"column": 24
} | {
"line": 37,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx✝² x✝¹ : ↑(Iio j)\nx✝ : (fun j_1 ↦ ↑j_1) x✝² = (fun j_1 ↦ ↑j_1) x✝¹\n⊢ x✝² = x✝¹",
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"usedConstants": [
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"Set.Elem",
"id",
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... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 36,
"column": 19
} | {
"line": 36,
"column": 24
} | {
"line": 37,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx✝² x✝¹ : ↑(Iio j)\nx✝ : (fun j_1 ↦ ↑j_1) x✝² = (fun j_1 ↦ ↑j_1) x✝¹\n⊢ x✝² = x✝¹",
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"usedConstants": [
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"Set.Elem",
"id",
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... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 37,
"column": 21
} | {
"line": 37,
"column": 26
} | {
"line": 38,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ {a b : ↑(Iio j)}, { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } a < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem",
"F... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 37,
"column": 21
} | {
"line": 37,
"column": 26
} | {
"line": 38,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ {a b : ↑(Iio j)}, { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } a < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem",
"F... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 37,
"column": 21
} | {
"line": 37,
"column": 26
} | {
"line": 38,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ {a b : ↑(Iio j)}, { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } a < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem",
"F... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 38,
"column": 27
} | {
"line": 38,
"column": 32
} | {
"line": 40,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ (b : α), b ∈ range ⇑{ toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ } ↔ b < j",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"RelEmbedding.mk",
"Preorder.toLT",
"congrArg",
"setOf",
"Membershi... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 38,
"column": 27
} | {
"line": 38,
"column": 32
} | {
"line": 40,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ (b : α), b ∈ range ⇑{ toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ } ↔ b < j",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"RelEmbedding.mk",
"Preorder.toLT",
"congrArg",
"setOf",
"Membershi... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 38,
"column": 27
} | {
"line": 38,
"column": 32
} | {
"line": 40,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\n⊢ ∀ (b : α), b ∈ range ⇑{ toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ } ↔ b < j",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"RelEmbedding.mk",
"Preorder.toLT",
"congrArg",
"setOf",
"Membershi... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 51,
"column": 19
} | {
"line": 51,
"column": 24
} | {
"line": 52,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\nx✝² x✝¹ : ↑(Iic i)\nx✝ : (fun k ↦ ⟨↑k, ⋯⟩) x✝² = (fun k ↦ ⟨↑k, ⋯⟩) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"Subtyp... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 51,
"column": 19
} | {
"line": 51,
"column": 24
} | {
"line": 52,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\nx✝² x✝¹ : ↑(Iic i)\nx✝ : (fun k ↦ ⟨↑k, ⋯⟩) x✝² = (fun k ↦ ⟨↑k, ⋯⟩) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"Subtyp... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 51,
"column": 19
} | {
"line": 51,
"column": 24
} | {
"line": 52,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\nx✝² x✝¹ : ↑(Iic i)\nx✝ : (fun k ↦ ⟨↑k, ⋯⟩) x✝² = (fun k ↦ ⟨↑k, ⋯⟩) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"Subtyp... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 52,
"column": 21
} | {
"line": 52,
"column": 26
} | {
"line": 53,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ {a b : ↑(Iic i)}, { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } a < { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 52,
"column": 21
} | {
"line": 52,
"column": 26
} | {
"line": 53,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ {a b : ↑(Iic i)}, { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } a < { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 52,
"column": 21
} | {
"line": 52,
"column": 26
} | {
"line": 53,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ {a b : ↑(Iic i)}, { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } a < { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.65",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"congrArg",
"Membership.mem"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 60,
"column": 19
} | {
"line": 60,
"column": 24
} | {
"line": 61,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\nx✝² x✝¹ : ↑(Iio i)\nx✝ : (fun k ↦ ⟨↑k, ⋯⟩) x✝² = (fun k ↦ ⟨↑k, ⋯⟩) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.42",
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"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"LT.lt.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 60,
"column": 19
} | {
"line": 60,
"column": 24
} | {
"line": 61,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\nx✝² x✝¹ : ↑(Iio i)\nx✝ : (fun k ↦ ⟨↑k, ⋯⟩) x✝² = (fun k ↦ ⟨↑k, ⋯⟩) x✝¹\n⊢ x✝² = x✝¹",
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"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"LT.lt.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 60,
"column": 19
} | {
"line": 60,
"column": 24
} | {
"line": 61,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\nx✝² x✝¹ : ↑(Iio i)\nx✝ : (fun k ↦ ⟨↑k, ⋯⟩) x✝² = (fun k ↦ ⟨↑k, ⋯⟩) x✝¹\n⊢ x✝² = x✝¹",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"Subtype.casesOn",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"LT.lt.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 61,
"column": 21
} | {
"line": 61,
"column": 26
} | {
"line": 62,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ {a b : ↑(Iio i)}, { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } a < { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.43",
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"usedConstants": [
"Preorder.toLT",
"congrArg",
"Set.principalSe... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 61,
"column": 21
} | {
"line": 61,
"column": 26
} | {
"line": 62,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ {a b : ↑(Iio i)}, { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } a < { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.43",
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"usedConstants": [
"Preorder.toLT",
"congrArg",
"Set.principalSe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 61,
"column": 21
} | {
"line": 61,
"column": 26
} | {
"line": 62,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ {a b : ↑(Iio i)}, { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } a < { toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯ } b ↔ a < b",
"ppTerm": "?m.43",
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"usedConstants": [
"Preorder.toLT",
"congrArg",
"Set.principalSe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 62,
"column": 27
} | {
"line": 62,
"column": 32
} | {
"line": 64,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ (b : ↑(Iic j)), b ∈ range ⇑{ toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯, map_rel_iff' := ⋯ } ↔ b < ⟨i, h⟩",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"RelEmbedding.mk",
"Preorder.to... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 62,
"column": 27
} | {
"line": 62,
"column": 32
} | {
"line": 64,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ (b : ↑(Iic j)), b ∈ range ⇑{ toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯, map_rel_iff' := ⋯ } ↔ b < ⟨i, h⟩",
"ppTerm": "?m.44",
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"Eq.mpr",
"RelEmbedding.mk",
"Preorder.to... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 62,
"column": 27
} | {
"line": 62,
"column": 32
} | {
"line": 64,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j : α\nh : i ≤ j\n⊢ ∀ (b : ↑(Iic j)), b ∈ range ⇑{ toFun := fun k ↦ ⟨↑k, ⋯⟩, inj' := ⋯, map_rel_iff' := ⋯ } ↔ b < ⟨i, h⟩",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"RelEmbedding.mk",
"Preorder.to... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | {
"line": 84,
"column": 6
} | {
"line": 85,
"column": 63
} | {
"line": 86,
"column": 6
} | [
{
"pp": "case neg.succ\nJ : 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 : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSe... | [
"case neg.succ\nJ : 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 : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSeg hf\na : α\... | obtain ⟨a, rfl⟩ := (s.mem_range_iff_rel (b := i)).2 (by
simpa only [← hi₀] using Order.lt_succ_of_not_isMax hi) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | {
"line": 90,
"column": 39
} | {
"line": 90,
"column": 75
} | {
"line": 90,
"column": 75
} | [
{
"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 : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSeg hf\na : α\nhi... | [] | by simpa only [hi₀] using s.lt_top b | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 368,
"column": 34
} | {
"line": 368,
"column": 39
} | {
"line": 369,
"column": 4
} | [
{
"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\niter₁ iter₂ : Φ.Iteration j\nthis : iter₁.F = iter₂.F\n⊢ iter₁ = iter₂",
"ppTerm": "?m.42",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 368,
"column": 34
} | {
"line": 368,
"column": 39
} | {
"line": 369,
"column": 4
} | [
{
"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\niter₁ iter₂ : Φ.Iteration j\nthis : iter₁.F = iter₂.F\n⊢ iter₁ = iter₂",
"ppTerm": "?m.42",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 368,
"column": 34
} | {
"line": 368,
"column": 39
} | {
"line": 369,
"column": 4
} | [
{
"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\niter₁ iter₂ : Φ.Iteration j\nthis : iter₁.F = iter₂.F\n⊢ iter₁ = iter₂",
"ppTerm": "?m.42",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone | {
"line": 164,
"column": 78
} | {
"line": 166,
"column": 68
} | {
"line": 168,
"column": 0
} | [
{
"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\ni : J\nhi : i < j\n⊢ arrowMap (ofCocone c) i j ⋯ ⋯ = Arrow.mk (c.ι.app ⟨i, hi⟩)",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Catego... | [] | by
rw [arrowMap, ofCocone_map_to_top _ _ hi]
exact Arrow.ext (ofCocone_obj_eq _ _ _) (ofCocone_obj_eq_pt _) rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 51
} | {
"line": 395,
"column": 0
} | [
{
"pp": "p b : ℕ\nhp : Fact (Nat.Prime p)\ndvd : p ∣ b\n⊢ padicValNat p (b / p) = padicValNat p b - 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"congrArg",
"HSub.hSub",
"id",
"padicValNat",
"HDiv.hDiv",
"instSubNat... | [] | rw [padicValNat.div_of_dvd dvd, padicValNat_self] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 51
} | {
"line": 395,
"column": 0
} | [
{
"pp": "p b : ℕ\nhp : Fact (Nat.Prime p)\ndvd : p ∣ b\n⊢ padicValNat p (b / p) = padicValNat p b - 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"congrArg",
"HSub.hSub",
"id",
"padicValNat",
"HDiv.hDiv",
"instSubNat... | [] | rw [padicValNat.div_of_dvd dvd, padicValNat_self] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 393,
"column": 2
} | {
"line": 393,
"column": 51
} | {
"line": 395,
"column": 0
} | [
{
"pp": "p b : ℕ\nhp : Fact (Nat.Prime p)\ndvd : p ∣ b\n⊢ padicValNat p (b / p) = padicValNat p b - 1",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instHDiv",
"congrArg",
"HSub.hSub",
"id",
"padicValNat",
"HDiv.hDiv",
"instSubNat... | [] | rw [padicValNat.div_of_dvd dvd, padicValNat_self] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Padics.PadicVal.Basic | {
"line": 491,
"column": 6
} | {
"line": 491,
"column": 66
} | {
"line": 491,
"column": 67
} | [
{
"pp": "p n : ℕ\nhp : Fact (Nat.Prime p)\nhn : n ≠ 0\n⊢ log p n = padicValNat p n ↔ n < p ^ (padicValNat p n + 1)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"instPowNat",
"Eq.mpr",
"congrArg",
"Nat.instMonoid",
"_private.Mathlib.NumberTheory.Padics.Padic... | [
"p n : ℕ\nhp : Fact (Nat.Prime p)\nhn : n ≠ 0\n⊢ p ^ padicValNat p n ≤ n ∧ n < p ^ (padicValNat p n + 1) ↔ n < p ^ (padicValNat p n + 1)"
] | Nat.log_eq_iff (Or.inr ⟨(Nat.Prime.one_lt' p).out, by lia⟩), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 264,
"column": 8
} | {
"line": 264,
"column": 17
} | {
"line": 264,
"column": 18
} | [
{
"pp": "case h\np : ℕ\nhp : Fact (Nat.Prime p)\nε : ℝ\nhε : 0 < ε\nk : ℕ\nhk : ε⁻¹ < ↑k\n⊢ ε⁻¹ < (↑p ^ (-↑k))⁻¹",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"GroupWithZero.toDivisionMonoid",
"Group... | [
"case h\np : ℕ\nhp : Fact (Nat.Prime p)\nε : ℝ\nhε : 0 < ε\nk : ℕ\nhk : ε⁻¹ < ↑k\n⊢ ε⁻¹ < (↑p ^ ↑k)⁻¹⁻¹"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicIntegers | {
"line": 490,
"column": 49
} | {
"line": 490,
"column": 78
} | {
"line": 491,
"column": 4
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\na : ℤ\n⊢ ↑(p ^ n) ∣ ↑a ↔ ‖↑a‖ ≤ ↑p ^ (-↑n)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Norm.norm",
"Int.cast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.instLE",
"Real",
"Dvd.dvd... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℕ\na : ℤ\n⊢ ↑(p ^ n) ∣ ↑a ↔ ↑a ∈ Ideal.span {↑p ^ n}"
] | norm_le_pow_iff_mem_span_pow, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Sites.Point.Conservative | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 83
} | {
"line": 227,
"column": 2
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝² : Category.{v, u} C\nJ : GrothendieckTopology C\nP : ObjectProperty J.Point\ninst✝¹ : LocallySmall.{w, v, u} C\nhP :\n ∀ ⦃X : C⦄ (S : Sieve X),\n (∀ (Φ : P.FullSubcategory) (x : Φ.obj.fiber.obj X),\n ∃ Y g, ∃ (_ : S.arrows g), ∃ y, (ConcreteCategory.hom (Φ.o... | [
"case refine_2\nC : Type u\ninst✝² : Category.{v, u} C\nJ : GrothendieckTopology C\nP : ObjectProperty J.Point\ninst✝¹ : LocallySmall.{w, v, u} C\nhP :\n ∀ ⦃X : C⦄ (S : Sieve X),\n (∀ (Φ : P.FullSubcategory) (x : Φ.obj.fiber.obj X),\n ∃ Y g, ∃ (_ : S.arrows g), ∃ y, (ConcreteCategory.hom (Φ.obj.fiber.map... | · simpa using (shrinkYoneda_obj_map_shrinkYonedaObjObjEquiv_symm t.op (𝟙 _)).symm | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 503,
"column": 2
} | {
"line": 522,
"column": 46
} | {
"line": 524,
"column": 0
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfgne : f.norm ≠ g.norm\n⊢ (f + g).norm = max f.norm g.norm",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"padicNorm.instIsAbsoluteValueRat",
"Iff.mpr",
"Rat.instOfNat",
"CauSeq.addGroup",
"Eq.mpr",
... | [] | have hfg : ¬f + g ≈ 0 := mt norm_eq_of_add_equiv_zero hfgne
exact if hf : f ≈ 0 then by
have : LimZero (f - 0) := hf
have : f + g ≈ g := show LimZero (f + g - g) by simpa only [sub_zero, add_sub_cancel_right]
have h1 : (f + g).norm = g.norm := norm_equiv this
have h2 : f.norm = 0 := (norm_zero_iff _).... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 503,
"column": 2
} | {
"line": 522,
"column": 46
} | {
"line": 524,
"column": 0
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf g : PadicSeq p\nhfgne : f.norm ≠ g.norm\n⊢ (f + g).norm = max f.norm g.norm",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"padicNorm.instIsAbsoluteValueRat",
"Iff.mpr",
"Rat.instOfNat",
"CauSeq.addGroup",
"Eq.mpr",
... | [] | have hfg : ¬f + g ≈ 0 := mt norm_eq_of_add_equiv_zero hfgne
exact if hf : f ≈ 0 then by
have : LimZero (f - 0) := hf
have : f + g ≈ g := show LimZero (f + g - g) by simpa only [sub_zero, add_sub_cancel_right]
have h1 : (f + g).norm = g.norm := norm_equiv this
have h2 : f.norm = 0 := (norm_zero_iff _).... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicGeometry.Sites.EtalePoint | {
"line": 120,
"column": 54
} | {
"line": 120,
"column": 69
} | {
"line": 120,
"column": 69
} | [
{
"pp": "S : Scheme\nΩ : Type u\ninst✝¹ : Field Ω\ninst✝ : IsSepClosed Ω\nX : S.Etale\nt : ↥S\na : S.residueField t ⟶ CommRingCat.of Ω\ny : ↥(Hom.fiber X.hom t)\nhs₀ : ((SpecToEquivOfField Ω S).symm ⟨t, a⟩) default = t\n⊢ (Hom.fiberToSpecResidueField X.hom t) y = (Spec.map a) default",
"ppTerm": "?m.117",
... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 795,
"column": 4
} | {
"line": 795,
"column": 20
} | {
"line": 797,
"column": 0
} | [
{
"pp": "p : ℕ\ninst✝ : Fact (Nat.Prime p)\nx✝ y✝ : ℚ_[p]\nh : ↑(padicNormE (x✝ - y✝)) = 0\n⊢ padicNormE (x✝ - y✝) = 0",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Real.partialOrder",
"Real",
"padicNormE",
"FloorRing.toFloorSemiring",
"Real.instZero",
... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 855,
"column": 2
} | {
"line": 858,
"column": 22
} | {
"line": 860,
"column": 0
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑p‖ = (↑p)⁻¹",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Rat.instOfNat",
"Norm.norm",
"Eq.mpr",
"False",
"Real.partialOrder",
"Real",
"Rat.num",
"Nat.Prime",
... | [] | rw [← @Rat.cast_natCast ℝ _ p]
rw [← @Rat.cast_natCast ℚ_[p] _ p]
simp [hp.1.ne_zero, norm, padicNorm, padicValRat, padicValInt, zpow_neg,
-Rat.cast_natCast] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 855,
"column": 2
} | {
"line": 858,
"column": 22
} | {
"line": 860,
"column": 0
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\n⊢ ‖↑p‖ = (↑p)⁻¹",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Rat.instOfNat",
"Norm.norm",
"Eq.mpr",
"False",
"Real.partialOrder",
"Real",
"Rat.num",
"Nat.Prime",
... | [] | rw [← @Rat.cast_natCast ℝ _ p]
rw [← @Rat.cast_natCast ℚ_[p] _ p]
simp [hp.1.ne_zero, norm, padicNorm, padicValRat, padicValInt, zpow_neg,
-Rat.cast_natCast] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 866,
"column": 25
} | {
"line": 866,
"column": 34
} | {
"line": 866,
"column": 35
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\n⊢ (↑p)⁻¹ ^ n = ↑p ^ (-n)",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"Real.instInv",
"Real.ins... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\n⊢ (↑p)⁻¹ ^ n = (↑p ^ n)⁻¹"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 912,
"column": 68
} | {
"line": 912,
"column": 77
} | {
"line": 912,
"column": 78
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\nd : ℕ\nhn : d ≠ 0\nhd : n.natAbs.Coprime d\nhq : ¬p ∣ d\nhnz : ¬n = 0\nhnz' : { num := n, den := d, den_nz := hn, reduced := hd } ≠ 0\n⊢ ↑p ^ (-↑(padicValInt p { num := n, den := d, den_nz := hn, reduced := hd }.num)) ≤ 1",
"ppTerm": "?m.85",
"assigned": t... | [
"p : ℕ\nhp : Fact (Nat.Prime p)\nn : ℤ\nd : ℕ\nhn : d ≠ 0\nhd : n.natAbs.Coprime d\nhq : ¬p ∣ d\nhnz : ¬n = 0\nhnz' : { num := n, den := d, den_nz := hn, reduced := hd } ≠ 0\n⊢ (↑p ^ ↑(padicValInt p { num := n, den := d, den_nz := hn, reduced := hd }.num))⁻¹ ≤ 1"
] | zpow_neg, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 979,
"column": 2
} | {
"line": 979,
"column": 28
} | {
"line": 981,
"column": 0
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nz1 z2 : ℚ_[p]\nh : ‖z1 - z2‖ < ‖z2‖\n⊢ ‖z1 + -z2‖ < ‖-z2‖",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NegZeroClass.toNeg",
"NormedCommRing.t... | [] | simp [← sub_eq_add_neg, h] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 999,
"column": 6
} | {
"line": 999,
"column": 22
} | {
"line": 1002,
"column": 4
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] norm\nε : ℚ\nhε : ε > 0\nh : ∃ i, ∀ j ≥ i, ↑(padicNormE (↑f j - ↑f i)) < ↑ε\n⊢ ∃ i, ∀ j ≥ i, padicNormE (↑f j - ↑f i) < ε",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Real",
"Preorder.toLT",
"padicNormE",
... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.NumberTheory.Padics.PadicNumbers | {
"line": 1014,
"column": 4
} | {
"line": 1014,
"column": 20
} | {
"line": 1016,
"column": 0
} | [
{
"pp": "p : ℕ\nhp : Fact (Nat.Prime p)\nf : CauSeq ℚ_[p] norm\ncau_seq_norm_e : IsCauSeq ⇑padicNormE ↑f\nq : ℚ_[p]\nhq : ∀ ε > 0, ∃ N, ∀ i ≥ N, padicNormE (↑⟨↑f, cau_seq_norm_e⟩ i - q) < ε\nε : ℝ\nhε : ε > 0\nε' : ℚ\nhε' : 0 < ε' ∧ ↑ε' < ε\nN : ℕ\nhN : ∀ i ≥ N, padicNormE (↑⟨↑f, cau_seq_norm_e⟩ i - q) < ε'\ni ... | [] | exact mod_cast h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.MorphismProperty.Representable | {
"line": 643,
"column": 2
} | {
"line": 645,
"column": 38
} | {
"line": 646,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝⁹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁸ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝⁷ : HasBinaryProducts C\ninst✝⁶ : HasPullbacks D\ninst✝⁵ : HasBinaryProducts D\ninst✝⁴ : HasTerminal D\ninst✝³ : F.Full\ninst✝² : PreservesLimitsOfShape (Discrete WalkingPair) F\ninst✝¹ : HasPullbacks ... | [
"C : Type u₁\ninst✝⁹ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝⁸ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝⁷ : HasBinaryProducts C\ninst✝⁶ : HasPullbacks D\ninst✝⁵ : HasBinaryProducts D\ninst✝⁴ : HasTerminal D\ninst✝³ : F.Full\ninst✝² : PreservesLimitsOfShape (Discrete WalkingPair) F\ninst✝¹ : HasPullbacks C\ninst✝ : P... | obtain ⟨_, ⟨bot⟩⟩ := IsPullback.of_iso_pullback ⟨by rw [assoc]; simp [pullback.condition]⟩
(pbRepr.isoPullback ≪≫ (pullbackDiagonalMapIdIso (g ≫ pullback.fst _ _) (g ≫ pullback.snd _ _)
(terminal.from X)).symm) rfl rfl | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.DoldKan.Degeneracies | {
"line": 48,
"column": 10
} | {
"line": 48,
"column": 80
} | {
"line": 48,
"column": 80
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nY : C\nX : SimplicialObject C\nn b q : ℕ\nφ : Y ⟶ X _⦋n + 1⦌\nv : HigherFacesVanish q φ\nhnbq : n + 1 = b + q\n⊢ b < n + 1 + 1",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopo... | [] | simp only [hnbq, Nat.lt_add_one_iff, le_add_iff_nonneg_right, zero_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.DoldKan.Degeneracies | {
"line": 48,
"column": 10
} | {
"line": 48,
"column": 80
} | {
"line": 48,
"column": 80
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nY : C\nX : SimplicialObject C\nn b q : ℕ\nφ : Y ⟶ X _⦋n + 1⦌\nv : HigherFacesVanish q φ\nhnbq : n + 1 = b + q\n⊢ b < n + 1 + 1",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopo... | [] | simp only [hnbq, Nat.lt_add_one_iff, le_add_iff_nonneg_right, zero_le] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.DoldKan.Degeneracies | {
"line": 48,
"column": 10
} | {
"line": 48,
"column": 80
} | {
"line": 48,
"column": 80
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nY : C\nX : SimplicialObject C\nn b q : ℕ\nφ : Y ⟶ X _⦋n + 1⦌\nv : HigherFacesVanish q φ\nhnbq : n + 1 = b + q\n⊢ b < n + 1 + 1",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"_private.Mathlib.AlgebraicTopo... | [] | simp only [hnbq, Nat.lt_add_one_iff, le_add_iff_nonneg_right, zero_le] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.DoldKan.Degeneracies | {
"line": 79,
"column": 8
} | {
"line": 80,
"column": 46
} | {
"line": 81,
"column": 8
} | [
{
"pp": "case neg.zero.«_@».Mathlib.AlgebraicTopology.DoldKan.Degeneracies.1127126258._hygCtx._hyg.66.«0»\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\nhq : ∀ (i : Fin (0 + 1)), 0 + 1 ≤ ↑i + q → X.σ i ≫ (P q).f (0 + 1) = 0\nh : ¬1 ≤ 0 + q\nhi : 0 = 0 + q\n⊢... | [
"case neg.zero.«_@».Mathlib.AlgebraicTopology.DoldKan.Degeneracies.1127126258._hygCtx._hyg.66.«0»\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nq : ℕ\nhq : ∀ (i : Fin (0 + 1)), 0 + 1 ≤ ↑i + q → X.σ i ≫ (P q).f (0 + 1) = 0\nh : ¬1 ≤ 0 + q\nhi : 0 = 0 + q\n⊢ X.σ 0 +\n ... | rw [comp_id, Fin.sum_univ_two,
Fin.sum_univ_succ, Fin.sum_univ_two] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.AlgebraicTopology.DoldKan.Degeneracies | {
"line": 67,
"column": 4
} | {
"line": 118,
"column": 11
} | {
"line": 120,
"column": 0
} | [
{
"pp": "case neg\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Preadditive C\nX : SimplicialObject C\nn q : ℕ\nhq : ∀ (i : Fin (n + 1)), n + 1 ≤ ↑i + q → X.σ i ≫ (P q).f (n + 1) = 0\ni : Fin (n + 1)\nhi : n + 1 ≤ ↑i + (q + 1)\nh : ¬n + 1 ≤ ↑i + q\n⊢ X.σ i ≫ (P (q + 1)).f (n + 1) = 0",
"ppTerm": "?... | [] | · replace hi : n = i + q := by lia
rcases n with _ | n
· fin_cases i
dsimp at h hi
rw [show q = 0 by lia]
change X.σ 0 ≫ (P 1).f 1 = 0
simp only [P_succ, HomologicalComplex.add_f_apply, comp_add,
AlternatingFaceMapComplex.obj_d_eq, Hσ,
HomologicalComplex.c... | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.DoldKan.Normalized | {
"line": 139,
"column": 4
} | {
"line": 145,
"column": 16
} | {
"line": 147,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝¹ : Category.{v_1, u_1} A\ninst✝ : Abelian A\nX : SimplicialObject A\n⊢ { app := fun X ↦ { f := inclusionOfMooreComplexMap X, comm := ⋯ }, naturality := ⋯ } ≫\n { app := fun X ↦ { f := PInftyToNormalizedMooreComplex X, comm := ⋯ }, naturality := ⋯ } =\n 𝟙 (normalizedMooreCom... | [] | ext X : 3
rw [← cancel_mono (inclusionOfMooreComplexMap X)]
simp only [NatTrans.comp_app, Karoubi.comp_f, assoc, NatTrans.id_app, Karoubi.id_f,
PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap,
inclusionOfMooreComplexMap_comp_PInfty]
dsimp only [Functor.comp_obj, toKaroubi]
rw ... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.DoldKan.Normalized | {
"line": 139,
"column": 4
} | {
"line": 145,
"column": 16
} | {
"line": 147,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝¹ : Category.{v_1, u_1} A\ninst✝ : Abelian A\nX : SimplicialObject A\n⊢ { app := fun X ↦ { f := inclusionOfMooreComplexMap X, comm := ⋯ }, naturality := ⋯ } ≫\n { app := fun X ↦ { f := PInftyToNormalizedMooreComplex X, comm := ⋯ }, naturality := ⋯ } =\n 𝟙 (normalizedMooreCom... | [] | ext X : 3
rw [← cancel_mono (inclusionOfMooreComplexMap X)]
simp only [NatTrans.comp_app, Karoubi.comp_f, assoc, NatTrans.id_app, Karoubi.id_f,
PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap,
inclusionOfMooreComplexMap_comp_PInfty]
dsimp only [Functor.comp_obj, toKaroubi]
rw ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.DoldKan.NReflectsIso | {
"line": 60,
"column": 6
} | {
"line": 60,
"column": 32
} | {
"line": 61,
"column": 6
} | [
{
"pp": "case zero\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX Y : SimplicialObject C\nf : X ⟶ Y\ninst✝ : IsIso (N₁.map f)\nh₂ : ∀ (i : ℕ), (inv (N₁.map f)).f.f i ≫ PInfty.f i ≫ f.app (op ⦋i⦌) = PInfty.f i\nh₃ :\n ∀ (n : ℕ), PInfty.f n ≫ (inv (N₁.map f)).f.f n ≫ f.app (op ⦋n⦌) = (i... | [
"case h\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\ninst✝¹ : Preadditive C\nX Y : SimplicialObject C\nf : X ⟶ Y\ninst✝ : IsIso (N₁.map f)\nh₂ : ∀ (i : ℕ), (inv (N₁.map f)).f.f i ≫ PInfty.f i ≫ f.app (op ⦋i⦌) = PInfty.f i\nh₃ :\n ∀ (n : ℕ), PInfty.f n ≫ (inv (N₁.map f)).f.f n ≫ f.app (op ⦋n⦌) = (inv (N₁.map f)).... | use (inv (N₁.map f)).f.f 0 | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Topology.ContinuousMap.Ordered | {
"line": 30,
"column": 56
} | {
"line": 30,
"column": 61
} | {
"line": 30,
"column": 61
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : PartialOrder β\nf g : C(α, β)\nx✝ : (fun f ↦ f.toFun) f = (fun f ↦ f.toFun) g\n⊢ f = g",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"ContinuousMap",
"Eq.m... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Topology.ContinuousMap.Ordered | {
"line": 30,
"column": 56
} | {
"line": 30,
"column": 61
} | {
"line": 30,
"column": 61
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : PartialOrder β\nf g : C(α, β)\nx✝ : (fun f ↦ f.toFun) f = (fun f ↦ f.toFun) g\n⊢ f = g",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"ContinuousMap",
"Eq.m... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ContinuousMap.Ordered | {
"line": 30,
"column": 56
} | {
"line": 30,
"column": 61
} | {
"line": 30,
"column": 61
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : TopologicalSpace α\ninst✝¹ : TopologicalSpace β\ninst✝ : PartialOrder β\nf g : C(α, β)\nx✝ : (fun f ↦ f.toFun) f = (fun f ↦ f.toFun) g\n⊢ f = g",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"congrArg",
"ContinuousMap",
"Eq.m... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.TopCat.Monoidal | {
"line": 146,
"column": 44
} | {
"line": 146,
"column": 49
} | {
"line": 147,
"column": 0
} | [
{
"pp": "⊢ (ConcreteCategory.hom symm) 1 = 0",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Topology.Category.TopCat.Monoidal | {
"line": 146,
"column": 44
} | {
"line": 146,
"column": 49
} | {
"line": 147,
"column": 0
} | [
{
"pp": "⊢ (ConcreteCategory.hom symm) 1 = 0",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.TopCat.Monoidal | {
"line": 146,
"column": 44
} | {
"line": 146,
"column": 49
} | {
"line": 147,
"column": 0
} | [
{
"pp": "⊢ (ConcreteCategory.hom symm) 1 = 0",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.TopCat.Monoidal | {
"line": 147,
"column": 45
} | {
"line": 147,
"column": 50
} | {
"line": 149,
"column": 0
} | [
{
"pp": "⊢ (ConcreteCategory.hom symm) 0 = 1",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"CategoryTheory.ConcreteCa... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Topology.Category.TopCat.Monoidal | {
"line": 147,
"column": 45
} | {
"line": 147,
"column": 50
} | {
"line": 149,
"column": 0
} | [
{
"pp": "⊢ (ConcreteCategory.hom symm) 0 = 1",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"CategoryTheory.ConcreteCa... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.TopCat.Monoidal | {
"line": 147,
"column": 45
} | {
"line": 147,
"column": 50
} | {
"line": 149,
"column": 0
} | [
{
"pp": "⊢ (ConcreteCategory.hom symm) 0 = 1",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"congrArg",
"CategoryTheory.ConcreteCa... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Homotopy.TopCat.Basic | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 24
} | {
"line": 55,
"column": 0
} | [
{
"pp": "X Y : TopCat\nf₀ f₁ : X ⟶ Y\nF : Homotopy f₀ f₁\nx : ↑X\n⊢ (ConcreteCategory.hom (ι₁ ≫ F.h)) x = (ConcreteCategory.hom f₁) x",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"TopCat.str",
"TopCat.carrier",
"TopCat.Hom.hom",
"ContinuousMap.Homotopy.map_one_le... | [] | exact F.map_one_left x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Homotopy.Equiv | {
"line": 137,
"column": 4
} | {
"line": 138,
"column": 57
} | {
"line": 140,
"column": 0
} | [
{
"pp": "X : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\nh₁ : X ≃ₕ Y\nh₂ : Y ≃ₕ Z\n⊢ ((h₂.toFun.comp h₁.toFun).comp (h₁.invFun.comp h₂.invFun)).Homotopic (ContinuousMap.id Z)",
"ppTerm": "?m.... | [] | refine Homotopic.trans ?_ h₂.right_inv
exact .comp (.refl _) <| .comp h₁.right_inv (.refl _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Homotopy.Equiv | {
"line": 137,
"column": 4
} | {
"line": 138,
"column": 57
} | {
"line": 140,
"column": 0
} | [
{
"pp": "X : Type u\nY : Type v\nZ : Type w\nZ' : Type x\ninst✝³ : TopologicalSpace X\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace Z\ninst✝ : TopologicalSpace Z'\nh₁ : X ≃ₕ Y\nh₂ : Y ≃ₕ Z\n⊢ ((h₂.toFun.comp h₁.toFun).comp (h₁.invFun.comp h₂.invFun)).Homotopic (ContinuousMap.id Z)",
"ppTerm": "?m.... | [] | refine Homotopic.trans ?_ h₂.right_inv
exact .comp (.refl _) <| .comp h₁.right_inv (.refl _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Homotopy.Product | {
"line": 206,
"column": 56
} | {
"line": 209,
"column": 7
} | {
"line": 211,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\na₁ a₂ : α\nb₁ b₂ : β\nq₁ : Homotopic.Quotient a₁ a₂\nq₂ : Homotopic.Quotient b₁ b₂\n⊢ projRight (prod q₁ q₂) = q₂",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"ContinuousMap.continuous",
... | [] | by
induction q₁, q₂ using Path.Homotopic.Quotient.ind₂
rw [projRight, prod_lift, ← Path.Homotopic.Quotient.mk_map]
congr | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps | {
"line": 270,
"column": 2
} | {
"line": 272,
"column": 7
} | {
"line": 273,
"column": 2
} | [
{
"pp": "case left\nX Y : TopCat\nf g : C(↑X, ↑Y)\nH : f.Homotopy g\nx₀ x₁ : ↑X\np : fromTop x₀ ⟶ fromTop x₁\n⊢ (hcast ⋯ ≫\n (π.map (TopCat.ofHom H.uliftMap)).map\n ((prodToProdTop (TopCat.of (ULift.{u, 0} ↑I)) X).map (𝟙 (fromTop { down := 0 }), p)) ≫\n hcast ⋯) ≫\n hcast ⋯ ≫\n ... | [
"case right\nX Y : TopCat\nf g : C(↑X, ↑Y)\nH : f.Homotopy g\nx₀ x₁ : ↑X\np : fromTop x₀ ⟶ fromTop x₁\n⊢ (hcast ⋯ ≫\n (π.map (TopCat.ofHom H.uliftMap)).map\n ((prodToProdTop (TopCat.of (ULift.{u, 0} ↑I)) X).map (uhpath01, 𝟙 (fromTop x₀))) ≫\n hcast ⋯) ≫\n hcast ⋯ ≫\n (π.map (... | · slice_lhs 2 4 => rw [eqToHom_trans, eqToHom_refl] -- Porting note: this ↓ `simp` didn't do this
slice_lhs 2 4 => simp [← CategoryTheory.Functor.map_comp]
rfl | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicTopology.FundamentalGroupoid.InducedMaps | {
"line": 273,
"column": 2
} | {
"line": 275,
"column": 7
} | {
"line": 277,
"column": 0
} | [
{
"pp": "case right\nX Y : TopCat\nf g : C(↑X, ↑Y)\nH : f.Homotopy g\nx₀ x₁ : ↑X\np : fromTop x₀ ⟶ fromTop x₁\n⊢ (hcast ⋯ ≫\n (π.map (TopCat.ofHom H.uliftMap)).map\n ((prodToProdTop (TopCat.of (ULift.{u, 0} ↑I)) X).map (uhpath01, 𝟙 (fromTop x₀))) ≫\n hcast ⋯) ≫\n hcast ⋯ ≫\n ... | [] | · slice_lhs 2 4 => rw [eqToHom_trans, eqToHom_refl] -- Porting note: this ↓ `simp` didn't do this
slice_lhs 2 4 => simp [← CategoryTheory.Functor.map_comp]
rfl | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Subfunctor.Equalizer | {
"line": 49,
"column": 58
} | {
"line": 49,
"column": 63
} | {
"line": 51,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF₁ F₂ : C ⥤ Type w\nA : Subfunctor F₁\nf : A.toFunctor ⟶ F₂\n⊢ Subfunctor.equalizer f f = A",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Set.ext",
"and_true",
"Iff.of_eq",
"congrArg",
"CategoryTheory.Concrete... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.Subfunctor.Equalizer | {
"line": 49,
"column": 58
} | {
"line": 49,
"column": 63
} | {
"line": 51,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF₁ F₂ : C ⥤ Type w\nA : Subfunctor F₁\nf : A.toFunctor ⟶ F₂\n⊢ Subfunctor.equalizer f f = A",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Set.ext",
"and_true",
"Iff.of_eq",
"congrArg",
"CategoryTheory.Concrete... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Subfunctor.Equalizer | {
"line": 49,
"column": 58
} | {
"line": 49,
"column": 63
} | {
"line": 51,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nF₁ F₂ : C ⥤ Type w\nA : Subfunctor F₁\nf : A.toFunctor ⟶ F₂\n⊢ Subfunctor.equalizer f f = A",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Set.ext",
"and_true",
"Iff.of_eq",
"congrArg",
"CategoryTheory.Concrete... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Types.Multicoequalizer | {
"line": 49,
"column": 6
} | {
"line": 49,
"column": 27
} | {
"line": 50,
"column": 2
} | [
{
"pp": "case right\nJ : MultispanShape\nd : MultispanIndex J (Type u)\nc : d.multispan.CoconeTypes\nr : J.R\nz : d.multispan.obj (WalkingMultispan.right r)\n⊢ ∃ i a, d.multispan.ιColimitType (WalkingMultispan.right i) a = d.multispan.ιColimitType (WalkingMultispan.right r) z",
"ppTerm": "?right",
"assi... | [] | exact ⟨r, z, by simp⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
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