module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 88
} | {
"line": 40,
"column": 2
} | [
{
"pp": "X₁ X₂ : SSet\nm : SimplexCategoryᵒᵖ\nx₁ : X₁.obj m\nx₂ : X₂.obj m\nhx₁ : x₁ ∈ ⊤.obj m\nhx₂ : x₂ ∈ ⊤.obj m\n⊢ ∃ i i_1, (x₁, x₂) ∈ ((Subcomplex.ofSimplex i.simplex).obj m).prod ((Subcomplex.ofSimplex i_1.simplex).obj m)",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"SSet.S.s... | [
"X₁ X₂ : SSet\nm : SimplexCategoryᵒᵖ\nx₁ : X₁.obj m\nx₂ : X₂.obj m\nhx₁ : ∃ i, x₁ ∈ i.subcomplex.obj m\nhx₂ : ∃ i, x₂ ∈ i.subcomplex.obj m\n⊢ ∃ i i_1, (x₁, x₂) ∈ ((Subcomplex.ofSimplex i.simplex).obj m).prod ((Subcomplex.ofSimplex i_1.simplex).obj m)"
] | simp only [← N.iSup_subcomplex_eq_top, Subfunctor.iSup_obj, Set.mem_iUnion] at hx₁ hx₂ | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd | {
"line": 86,
"column": 32
} | {
"line": 86,
"column": 43
} | {
"line": 86,
"column": 44
} | [
{
"pp": "X₁ X₂ X₃ X₄ : SSet\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\ninst✝¹ : X₂.Finite\ninst✝ : X₃.Finite\nZ✝ : SSet\nx✝¹ x✝ : Z✝ ⟶ X₁\nh : x✝¹ ≫ lift t l = x✝ ≫ lift t l\n⊢ x✝¹ ≫ t = x✝ ≫ t",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
"usedF... | [
"X₁ X₂ X₃ X₄ : SSet\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\ninst✝¹ : X₂.Finite\ninst✝ : X₃.Finite\nZ✝ : SSet\nx✝¹ x✝ : Z✝ ⟶ X₁\nh : x✝¹ ≫ lift t l = x✝ ≫ lift t l\n⊢ x✝¹ ≫ t = x✝ ≫ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd | {
"line": 86,
"column": 62
} | {
"line": 86,
"column": 73
} | {
"line": 86,
"column": 74
} | [
{
"pp": "X₁ X₂ X₃ X₄ : SSet\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\ninst✝¹ : X₂.Finite\ninst✝ : X₃.Finite\nZ✝ : SSet\nx✝¹ x✝ : Z✝ ⟶ X₁\nh : x✝¹ ≫ lift t l = x✝ ≫ lift t l\n⊢ x✝¹ ≫ l = x✝ ≫ l",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedF... | [
"X₁ X₂ X₃ X₄ : SSet\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\ninst✝¹ : X₂.Finite\ninst✝ : X₃.Finite\nZ✝ : SSet\nx✝¹ x✝ : Z✝ ⟶ X₁\nh : x✝¹ ≫ lift t l = x✝ ≫ lift t l\n⊢ x✝¹ ≫ l = x✝ ≫ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 33
} | {
"line": 137,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝ : LinearOrder ι\nf : P.RankFunction ι\nj : ι\nc : f.Cell j\ni : ι\nh : j < i\n⊢ (↑(P.p c.s)).subcomplex ≤ f.filtration i",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"SSet.S.subcomplex",
"Preorder.toLT",
... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝ : LinearOrder ι\nf : P.RankFunction ι\nj : ι\nc : f.Cell j\ni : ι\nh : j < i\n⊢ (↑(P.p c.s)).subcomplex ≤ ⨆ j, ⨆ (_ : j < i), ⨆ c, (↑(P.p c.s)).subcomplex"
] | refine le_trans ?_ le_sup_right | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Presentable.Retracts | {
"line": 41,
"column": 22
} | {
"line": 41,
"column": 52
} | {
"line": 41,
"column": 53
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nX Y : C\nh : Retract Y X\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalPresentable X κ\nJ : Type w\nx✝¹ : SmallCategory J\nx✝ : IsCardinalFiltered J κ\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nthis✝ : EssentiallySmall.{w, w, w} J\nthis : IsFil... | [
"C : Type u\ninst✝² : Category.{v, u} C\nX Y : C\nh : Retract Y X\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\ninst✝ : IsCardinalPresentable X κ\nJ : Type w\nx✝¹ : SmallCategory J\nx✝ : IsCardinalFiltered J κ\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nthis✝ : EssentiallySmall.{w, w, w} J\nthis : IsFiltered J\nj :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 100,
"column": 60
} | {
"line": 100,
"column": 75
} | {
"line": 100,
"column": 76
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 235,
"column": 28
} | {
"line": 235,
"column": 39
} | {
"line": 235,
"column": 40
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝³ : LinearOrder ι\nf : P.RankFunction ι\ninst✝² : P.IsProper\nj : ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\nc : f.Cell j\n⊢ range c.map ≤ f.filtration (Order.succ j)",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝³ : LinearOrder ι\nf : P.RankFunction ι\ninst✝² : P.IsProper\nj : ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\nc : f.Cell j\n⊢ (↑(P.p c.s)).simplex ∈ (f.filtration (Order.succ j)).obj (op ⦋(↑(P.p c.s)).dim⦌)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 107,
"column": 60
} | {
"line": 107,
"column": 75
} | {
"line": 107,
"column": 76
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\nα : Fin (n + 1) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (↑x.1 + ↑x.2) • X.δ x.2 ≫ H.h x.1\nβ : Fin (n + 3) × Fin (n + 2) → (X _⦋n + 1⦌ ⟶ Y _⦋n + 1⦌) := fun x ↦ (-1) ^ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 318,
"column": 2
} | {
"line": 318,
"column": 41
} | {
"line": 318,
"column": 42
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : P.IsProper\nj : ι\nc : f.Cell j\nd : ℕ\nx y : Δ[c.dim + 1] _⦋d⦌\nh :\n (ConcreteCategory.hom (c.ιSigmaStdSimplex.app (op ⦋d⦌))) x =\n (ConcreteCategory.hom (c.ιSigmaStdSimplex.app (op ⦋d⦌)))... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : P.IsProper\nj : ι\nc : f.Cell j\nd : ℕ\nx y : Δ[c.dim + 1] _⦋d⦌\nh :\n (ConcreteCategory.hom (c.ιSigmaStdSimplex.app (op ⦋d⦌))) x =\n (ConcreteCategory.hom (c.ιSigmaStdSimplex.app (op ⦋d⦌))) y\n⊢ x = y"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 337,
"column": 4
} | {
"line": 338,
"column": 40
} | {
"line": 338,
"column": 41
} | [
{
"pp": "case a\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : P.IsProper\nj : ι\nc : f.Cell j\n⊢ (f.filtration j).preimage c.map ≤ c.horn",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"SSet.S.subcomplex",
"Eq.mpr",... | [
"case a\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : P.IsProper\nj : ι\nc : f.Cell j\n⊢ ¬(↑c.s).subcomplex ≤ f.filtration j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.StrongGenerator | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 78
} | {
"line": 111,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nP : ObjectProperty C\nhS : ∀ (X : C), ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, ExtremalEpi p\n⊢ P.IsSeparating ∧ ∀ ⦃X Y : C⦄ (i : X ⟶ Y) [Mono i], (∀ (G : C), P G → Function.Surjective fun f ↦ f ≫ i) → IsIso i",
"ppTerm": "?m.34",
"assigned": true,
... | [
"case refine_1\nC : Type u\ninst✝ : Category.{v, u} C\nP : ObjectProperty C\nhS : ∀ (X : C), ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, ExtremalEpi p\nX : C\n⊢ ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, Epi p",
"case refine_2\nC : Type u\ninst✝ : Category.{v, u} C\nP : ObjectProperty C\nhS : ∀ (X : C), ∃ ι s, ∃... | refine ⟨IsSeparating.mk_of_exists_epi.{w} (fun X ↦ ?_), fun X Y i _ hi ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.CategoryTheory.Generator.StrongGenerator | {
"line": 133,
"column": 2
} | {
"line": 140,
"column": 87
} | {
"line": 142,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nP : ObjectProperty C\ninst✝² : HasCoproducts C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : ObjectProperty.Small.{w, v, u} P\n⊢ P.IsStrongGenerator ↔ ∀ (X : C), ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, ExtremalEpi p",
"ppTerm": "?m.34",
"assigned": true... | [] | refine ⟨fun hP X ↦ ?_, fun hP ↦ .mk_of_exists_extremalEpi hP⟩
have := hasCoproductsOfShape_of_small.{w} C (CostructuredArrow P.ι X)
have := (coproductIsCoproduct (P.coproductFromFamily X)).whiskerEquivalence
(Discrete.equivalence (equivShrink.{w} _)).symm
refine ⟨_, fun j ↦ ((equivShrink.{w} (CostructuredArro... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Generator.StrongGenerator | {
"line": 133,
"column": 2
} | {
"line": 140,
"column": 87
} | {
"line": 142,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nP : ObjectProperty C\ninst✝² : HasCoproducts C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : ObjectProperty.Small.{w, v, u} P\n⊢ P.IsStrongGenerator ↔ ∀ (X : C), ∃ ι s, ∃ (_ : ∀ (i : ι), P (s i)), ∃ c x p, ExtremalEpi p",
"ppTerm": "?m.34",
"assigned": true... | [] | refine ⟨fun hP X ↦ ?_, fun hP ↦ .mk_of_exists_extremalEpi hP⟩
have := hasCoproductsOfShape_of_small.{w} C (CostructuredArrow P.ι X)
have := (coproductIsCoproduct (P.coproductFromFamily X)).whiskerEquivalence
(Discrete.equivalence (equivShrink.{w} _)).symm
refine ⟨_, fun j ↦ ((equivShrink.{w} (CostructuredArro... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 427,
"column": 4
} | {
"line": 427,
"column": 15
} | {
"line": 427,
"column": 16
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : P.IsProper\nj : ι\nx' : f.Cell j\nhy' : stdSimplex.objEquiv.symm (SimplexCategory.δ x'.index) ∈ x'.horn.obj (op ⦋x'.dim⦌)\n⊢ False",
"ppTerm": "?m.219",
"assigned": false,
"usedConst... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : P.IsProper\nj : ι\nx' : f.Cell j\nhy' : stdSimplex.objEquiv.symm (SimplexCategory.δ x'.index) ∈ x'.horn.obj (op ⦋x'.dim⦌)\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 96,
"column": 6
} | {
"line": 96,
"column": 51
} | {
"line": 96,
"column": 52
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\nP' : ObjectProperty C\nh₁ : P ≤ P'.isoClosure\nh₂ : P' ≤ isCardinalPresentable C κ\nX : C\nJ : Type w\nw✝¹ : SmallCategory J\nw✝ : IsCardinalFiltered J κ\nhX : ... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\nP' : ObjectProperty C\nh₁ : P ≤ P'.isoClosure\nh₂ : P' ≤ isCardinalPresentable C κ\nX : C\nJ : Type w\nw✝¹ : SmallCategory J\nw✝ : IsCardinalFiltered J κ\nhX : P.colimitsOf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 59
} | {
"line": 101,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\n⊢ P.isoClosure ≤ isCardinalPresentable C κ",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.instIsClo... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\n⊢ P ≤ isCardinalPresentable C κ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 65
} | {
"line": 117,
"column": 66
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\ninst✝ : LocallySmall.{w, v, u} C\nX : C\nJ : Type w\nw✝¹ : SmallCategory J\nw✝ : IsCardinalFiltered J κ\nhX : P.ColimitOfShape J X\nκ' : Cardinal.{w}\nh₁ : κ'.... | [
"C : Type u\ninst✝² : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝¹ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\ninst✝ : LocallySmall.{w, v, u} C\nX : C\nJ : Type w\nw✝¹ : SmallCategory J\nw✝ : IsCardinalFiltered J κ\nhX : P.ColimitOfShape J X\nκ' : Cardinal.{w}\nh₁ : κ'.IsRegular\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 59
} | {
"line": 137,
"column": 60
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\n⊢ P.retractClosure ≤ isCardinalPresentable C κ",
"ppTerm": "?refine_2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_... | [
"case refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nκ : Cardinal.{w}\ninst✝ : Fact κ.IsRegular\nh : P.IsCardinalFilteredGenerator κ\n⊢ P ≤ isCardinalPresentable C κ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 158,
"column": 27
} | {
"line": 158,
"column": 38
} | {
"line": 158,
"column": 39
} | [
{
"pp": "Ω : Type w\nC : Type u\ninst✝ : Category.{v, u} C\nh₁ : Cardinal.lift.{w, u} (Cardinal.mk C) ≤ Cardinal.lift.{u, w} (Cardinal.mk Ω)\nh₂ : ∀ (X Y : C), Cardinal.lift.{w, v} (Cardinal.mk (X ⟶ Y)) ≤ Cardinal.lift.{v, w} (Cardinal.mk Ω)\nf₁ : C ↪ Ω := ⋯.some\nf₂ : (X Y : C) → (X ⟶ Y) ↪ Ω := fun X Y ↦ ⋯.som... | [
"Ω : Type w\nC : Type u\ninst✝ : Category.{v, u} C\nh₁ : Cardinal.lift.{w, u} (Cardinal.mk C) ≤ Cardinal.lift.{u, w} (Cardinal.mk Ω)\nh₂ : ∀ (X Y : C), Cardinal.lift.{w, v} (Cardinal.mk (X ⟶ Y)) ≤ Cardinal.lift.{v, w} (Cardinal.mk Ω)\nf₁ : C ↪ Ω := ⋯.some\nf₂ : (X Y : C) → (X ⟶ Y) ↪ Ω := fun X Y ↦ ⋯.some\ne : C ≃ ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 19
} | {
"line": 185,
"column": 20
} | [
{
"pp": "κ : Cardinal.{w}\nC : Type u\ninst✝ : Category.{v, u} C\nhC : HasCardinalLT (Arrow C) κ\nΩ : Type w := κ.ord.ToType\n⊢ Cardinal.lift.{w, max u v} (Cardinal.mk (Arrow C)) ≤ Cardinal.lift.{max u v, w} (Cardinal.mk Ω)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"κ : Cardinal.{w}\nC : Type u\ninst✝ : Category.{v, u} C\nhC : HasCardinalLT (Arrow C) κ\nΩ : Type w := κ.ord.ToType\n⊢ Cardinal.lift.{w, max u v} (Cardinal.mk (Arrow C)) ≤ Cardinal.lift.{max u v, w} κ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 197,
"column": 4
} | {
"line": 197,
"column": 36
} | {
"line": 197,
"column": 37
} | [
{
"pp": "κ : Cardinal.{w}\nC : Type u\ninst✝ : Category.{v, u} C\nhC : HasCardinalLT (Arrow C) κ\nΩ : Type w := κ.ord.ToType\nι : Arrow C ↪ Ω\nh₁ : Cardinal.lift.{w, u} (Cardinal.mk C) ≤ Cardinal.lift.{u, w} (Cardinal.mk Ω)\nX Y : C\nf g : X ⟶ Y\nh : (fun f ↦ Arrow.mk f) f = (fun f ↦ Arrow.mk f) g\n⊢ f = g",
... | [
"κ : Cardinal.{w}\nC : Type u\ninst✝ : Category.{v, u} C\nhC : HasCardinalLT (Arrow C) κ\nΩ : Type w := κ.ord.ToType\nι : Arrow C ↪ Ω\nh₁ : Cardinal.lift.{w, u} (Cardinal.mk C) ≤ Cardinal.lift.{u, w} (Cardinal.mk Ω)\nX Y : C\nf g : X ⟶ Y\nh : (fun f ↦ Arrow.mk f) f = (fun f ↦ Arrow.mk f) g\n⊢ f = g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 205,
"column": 27
} | {
"line": 205,
"column": 38
} | {
"line": 205,
"column": 39
} | [
{
"pp": "κ : Cardinal.{w}\nC : Type u\ninst✝ : Category.{v, u} C\nhC : HasCardinalLT (Arrow C) κ\nΩ : Type w := κ.ord.ToType\nι : Arrow C ↪ Ω\nh₁ : Cardinal.lift.{w, u} (Cardinal.mk C) ≤ Cardinal.lift.{u, w} (Cardinal.mk Ω)\nh₂ : ∀ (X Y : C), Cardinal.lift.{w, v} (Cardinal.mk (X ⟶ Y)) ≤ Cardinal.lift.{v, w} (Ca... | [
"κ : Cardinal.{w}\nC : Type u\ninst✝ : Category.{v, u} C\nhC : HasCardinalLT (Arrow C) κ\nΩ : Type w := κ.ord.ToType\nι : Arrow C ↪ Ω\nh₁ : Cardinal.lift.{w, u} (Cardinal.mk C) ≤ Cardinal.lift.{u, w} (Cardinal.mk Ω)\nh₂ : ∀ (X Y : C), Cardinal.lift.{w, v} (Cardinal.mk (X ⟶ Y)) ≤ Cardinal.lift.{v, w} (Cardinal.mk Ω)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.KanExtension.Dense | {
"line": 119,
"column": 14
} | {
"line": 120,
"column": 62
} | {
"line": 121,
"column": 16
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\nC' : Type u₃\ninst✝¹ : Category.{v₃, u₃} C'\nF : C ⥤ D\ninst✝ : F.IsDense\nY Z : D\nf : (restrictedULiftYoneda F).obj Y ⟶ (restrictedULiftYoneda F).obj Z\ng₁ g₂ : CostructuredArrow F Y\nφ : g₁ ⟶ g₂\n⊢ (CostructuredArr... | [
"C : Type u₁\nD : Type u₂\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\nC' : Type u₃\ninst✝¹ : Category.{v₃, u₃} C'\nF : C ⥤ D\ninst✝ : F.IsDense\nY Z : D\nf : (restrictedULiftYoneda F).obj Y ⟶ (restrictedULiftYoneda F).obj Z\ng₁ g₂ : CostructuredArrow F Y\nφ : g₁ ⟶ g₂\n⊢ F.map φ.left ≫ ((ConcreteCat... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.KanExtension.Dense | {
"line": 126,
"column": 4
} | {
"line": 126,
"column": 15
} | {
"line": 126,
"column": 16
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\nC' : Type u₃\ninst✝¹ : Category.{v₃, u₃} C'\nF : C ⥤ D\ninst✝ : F.IsDense\nY Z : D\nf : (restrictedULiftYoneda F).obj Y ⟶ (restrictedULiftYoneda F).obj Z\nc : Cocone (CostructuredArrow.proj F Y ⋙ F) :=\n { pt := Z,\n... | [
"C : Type u₁\nD : Type u₂\ninst✝³ : Category.{v₁, u₁} C\ninst✝² : Category.{v₂, u₂} D\nC' : Type u₃\ninst✝¹ : Category.{v₃, u₃} C'\nF : C ⥤ D\ninst✝ : F.IsDense\nY Z : D\nf : (restrictedULiftYoneda F).obj Y ⟶ (restrictedULiftYoneda F).obj Z\nc : Cocone (CostructuredArrow.proj F Y ⋙ F) :=\n { pt := Z,\n ι := { a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.StrongGenerator | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 13
} | {
"line": 69,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁴ : ObjectProperty.EssentiallySmall.{w, v, u} P\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\ninst✝² : P.ι.IsDense\ninst✝¹ : LocallySmall.{w, v, u} C\nhP : P ≤ isCardinalPresentable C κ\ninst✝ : ∀ (X : C), IsCardinalFiltered (Costructur... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nP : ObjectProperty C\ninst✝⁴ : ObjectProperty.EssentiallySmall.{w, v, u} P\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\ninst✝² : P.ι.IsDense\ninst✝¹ : LocallySmall.{w, v, u} C\nhP : P ≤ isCardinalPresentable C κ\ninst✝ : ∀ (X : C), IsCardinalFiltered (CostructuredArrow P.ι ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.KanExtension.Dense | {
"line": 151,
"column": 6
} | {
"line": 151,
"column": 17
} | {
"line": 151,
"column": 18
} | [
{
"pp": "C : Type u₁\nD : Type u₂\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝ : F.Full\nh : (restrictedULiftYoneda F).FullyFaithful\nY : D\nφ : (s : Cocone (CostructuredArrow.proj F Y ⋙ F)) →\n (restrictedULiftYoneda F).obj Y ⟶ (restrictedULiftYoneda F).obj s.pt := ⋯\ns : Coco... | [
"C : Type u₁\nD : Type u₂\ninst✝² : Category.{v₁, u₁} C\ninst✝¹ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝ : F.Full\nh : (restrictedULiftYoneda F).FullyFaithful\nY : D\nφ : (s : Cocone (CostructuredArrow.proj F Y ⋙ F)) →\n (restrictedULiftYoneda F).obj Y ⟶ (restrictedULiftYoneda F).obj s.pt :=\n fun s ↦\n {\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Presheaf | {
"line": 66,
"column": 8
} | {
"line": 66,
"column": 19
} | {
"line": 66,
"column": 20
} | [
{
"pp": "A : Type u'\ninst✝³ : Category.{v', u'} A\nP : ObjectProperty A\ninst✝² : HasCoproducts A\ninst✝¹ : HasPullbacks A\nC : Type w\ninst✝ : SmallCategory C\nhP₁ : P.IsSeparating\nhP₂ : ∀ ⦃X Y : A⦄ (i : X ⟶ Y) [Mono i], (∀ (G : A), P G → Function.Surjective fun f ↦ f ≫ i) → IsIso i\n⊢ (ObjectProperty.ofObj ... | [
"A : Type u'\ninst✝³ : Category.{v', u'} A\nP : ObjectProperty A\ninst✝² : HasCoproducts A\ninst✝¹ : HasPullbacks A\nC : Type w\ninst✝ : SmallCategory C\nhP₁ : P.IsSeparating\nhP₂ : ∀ ⦃X Y : A⦄ (i : X ⟶ Y) [Mono i], (∀ (G : A), P G → Function.Surjective fun f ↦ f ≫ i) → IsIso i\n⊢ P.IsSeparating"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 544,
"column": 4
} | {
"line": 545,
"column": 31
} | {
"line": 547,
"column": 0
} | [
{
"pp": "case inr\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝³ : LinearOrder ι\nf : P.RankFunction ι\ninst✝² : P.IsProper\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\nj : ι\nc : f.Cell j\n⊢ (f.mapN (Cell.type₂ f c)).simplex ∈ X.nonDegenerate (f.mapN (Cell.type₂ f c)).dim",
"ppTerm": "?inr"... | [] | rw [f.mapN_type₂]
exact c.s.val.nonDegenerate | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 544,
"column": 4
} | {
"line": 545,
"column": 31
} | {
"line": 547,
"column": 0
} | [
{
"pp": "case inr\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝³ : LinearOrder ι\nf : P.RankFunction ι\ninst✝² : P.IsProper\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\nj : ι\nc : f.Cell j\n⊢ (f.mapN (Cell.type₂ f c)).simplex ∈ X.nonDegenerate (f.mapN (Cell.type₂ f c)).dim",
"ppTerm": "?inr"... | [] | rw [f.mapN_type₂]
exact c.s.val.nonDegenerate | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Presentable.StrongGenerator | {
"line": 127,
"column": 54
} | {
"line": 127,
"column": 65
} | {
"line": 127,
"column": 66
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\ninst✝² : HasColimitsOfSize.{w, w, v, u} C\ninst✝¹ : LocallySmall.{w, v, u} C\nP : ObjectProperty C\ninst✝ : ObjectProperty.Small.{w, v, u} P\nhS₁ : P.IsStrongGenerator\nhS₂ : P ≤ isCardinalPresentable C κ\nX : C\nE : (... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nκ : Cardinal.{w}\ninst✝³ : Fact κ.IsRegular\ninst✝² : HasColimitsOfSize.{w, w, v, u} C\ninst✝¹ : LocallySmall.{w, v, u} C\nP : ObjectProperty C\ninst✝ : ObjectProperty.Small.{w, v, u} P\nhS₁ : P.IsStrongGenerator\nhS₂ : P ≤ isCardinalPresentable C κ\nX : C\nE : (P.colimitsCa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Basic | {
"line": 139,
"column": 29
} | {
"line": 139,
"column": 40
} | {
"line": 139,
"column": 41
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsRegular\nB : X.Subcomplex\nh : range A.ι = B\n⊢ B = A",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsRegular\nB : X.Subcomplex\nh : range A.ι = B\n⊢ B = A"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | {
"line": 60,
"column": 4
} | {
"line": 60,
"column": 41
} | {
"line": 60,
"column": 42
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsRegular\nhP : IsEmpty { f // ∀ (n : ℕ), P.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑P.op.II\nhf : ∀ (n : ℕ), P.op.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ P.AncestralRel ((fun n ↦ ⟨N.opEquiv ↑(f n), ⋯⟩) (n + 1)) ((fun n ↦ ⟨N.opEquiv ↑(f n), ⋯⟩) n)... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsRegular\nhP : IsEmpty { f // ∀ (n : ℕ), P.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑P.op.II\nhf : ∀ (n : ℕ), P.op.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ P.op.AncestralRel (f (n + 1)) (f n)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 567,
"column": 66
} | {
"line": 588,
"column": 19
} | {
"line": 588,
"column": 19
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝³ : LinearOrder ι\nf : P.RankFunction ι\ninst✝² : P.IsProper\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\nj : ι\nx✝ : SimplexCategoryᵒᵖ\nd : ℕ\n⊢ IsColimit\n (CategoryTheory.evaluation SimplexCategoryᵒᵖ (Type u) _⦋d⦌.mapCocone (PushoutCocon... | [] | by
refine (isColimitMapCoconePushoutCoconeEquiv _ _).symm
(IsPushout.isColimit ?_)
refine Types.isPushout_of_isPullback_of_mono'
((f.isPullback j).map ((CategoryTheory.evaluation _ _).obj _))
(f.range_homOfLE_app_union_range_b_app _ _) (fun x₁ x₂ hx₁ hx₂ h ↦ ?_)
obtain ⟨s₁, g₁, _, hg₁⟩ := ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 134,
"column": 15
} | {
"line": 134,
"column": 26
} | {
"line": 134,
"column": 27
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\ni : Fin ((x.cast hd).dim + 1)\nhi : (x.cast hd).simplex.1 i = k.succ\n⊢ i ∈ finset x hd",
"ppTerm": "?m.44",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"Eq.mpr",
... | [
"m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\ni : Fin ((x.cast hd).dim + 1)\nhi : (x.cast hd).simplex.1 i = k.succ\n⊢ (x.cast hd).simplex.1 i = k.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 157,
"column": 35
} | {
"line": 157,
"column": 46
} | {
"line": 157,
"column": 47
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\ni : Fin (d + 1)\nh✝ : k.succ ≤ (x.cast hd).simplex.1 i\nh : k.succ = (x.cast hd).simplex.1 i\n⊢ i ∈ finset x hd",
"ppTerm": "?m.132",
"assigned": true,
"usedConstants": [
"SSet.S.simple... | [
"m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\ni : Fin (d + 1)\nh✝ : k.succ ≤ (x.cast hd).simplex.1 i\nh : k.succ = (x.cast hd).simplex.1 i\n⊢ (x.cast hd).simplex.1 i = k.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 197,
"column": 38
} | {
"line": 197,
"column": 49
} | {
"line": 197,
"column": 50
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\nl : Fin d\nhl : IsIndex x hd l.succ\n⊢ l.succ ∈ finset x hd",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"SSet.S.simplex",
"Eq.mpr",
"Opposite",
"Category... | [
"m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d\nl : Fin d\nhl : IsIndex x hd l.succ\n⊢ (x.cast hd).simplex.1 l.succ = k.succ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 527,
"column": 2
} | {
"line": 527,
"column": 44
} | {
"line": 529,
"column": 0
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d + 1\nl : Fin (d + 1)\nhl : IsIndex x hd l.succ\ny : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd' : ℕ\nhd' : y.dim = d' + 1\nl' : Fin (d' + 1)\nhl' : IsIndex y hd' l'.succ\nh : hl.δ = hl'.δ\nh₁ : ⋯.type₁ ⋯... | [] | exact congr_arg Type₁.x (h₂.symm.trans h₁) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 553,
"column": 31
} | {
"line": 553,
"column": 52
} | {
"line": 553,
"column": 53
} | [
{
"pp": "m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd m : ℕ\nk : Fin (m + 1)\nn : ℕ\ns t : Type₁ k n\nh : s.δ = t.δ\nu : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhs : s.δ = u\n⊢ IsType₂ u",
"ppTerm": "?m.188",
"assigned": false,
"usedConstants": [],
"use... | [
"m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd m : ℕ\nk : Fin (m + 1)\nn : ℕ\ns t : Type₁ k n\nh : s.δ = t.δ\nu : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhs : s.δ = u\n⊢ IsType₂ u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 625,
"column": 14
} | {
"line": 625,
"column": 25
} | {
"line": 625,
"column": 26
} | [
{
"pp": "m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd✝ m : ℕ\nk : Fin (m + 1)\nn d : ℕ\nis it : Fin (d + 1)\ns : (Δ[m + 1] ⊗ Δ[n]) _⦋d + 1⦌\nhs₁ : s ∈ (Δ[m + 1] ⊗ Δ[n]).nonDegenerate (d + 1)\nhs₂ : s ∉ (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).obj (Opposite.op ⦋d + 1⦌)\nhs ... | [
"m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd✝ m : ℕ\nk : Fin (m + 1)\nn d : ℕ\nis it : Fin (d + 1)\ns : (Δ[m + 1] ⊗ Δ[n]) _⦋d + 1⦌\nhs₁ : s ∈ (Δ[m + 1] ⊗ Δ[n]).nonDegenerate (d + 1)\nhs₂ : s ∉ (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).obj (Opposite.op ⦋d + 1⦌)\nhs : IsIndex (S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 636,
"column": 12
} | {
"line": 636,
"column": 44
} | {
"line": 636,
"column": 45
} | [
{
"pp": "m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd✝ m : ℕ\nk : Fin (m + 1)\nn d : ℕ\nis it : Fin (d + 1)\ns : (Δ[m + 1] ⊗ Δ[n]) _⦋d + 1⦌\nhs₁ : s ∈ (Δ[m + 1] ⊗ Δ[n]).nonDegenerate (d + 1)\nhs₂ : s ∉ (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).obj (Opposite.op ⦋d + 1⦌)\nhs ... | [
"m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd✝ m : ℕ\nk : Fin (m + 1)\nn d : ℕ\nis it : Fin (d + 1)\ns : (Δ[m + 1] ⊗ Δ[n]) _⦋d + 1⦌\nhs₁ : s ∈ (Δ[m + 1] ⊗ Δ[n]).nonDegenerate (d + 1)\nhs₂ : s ∉ (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).obj (Opposite.op ⦋d + 1⦌)\nhs : IsIndex (S... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 635,
"column": 10
} | {
"line": 636,
"column": 64
} | {
"line": 637,
"column": 10
} | [
{
"pp": "case inr.right.inl\nm✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd✝ m : ℕ\nk : Fin (m + 1)\nn d : ℕ\nis it : Fin (d + 1)\ns : (Δ[m + 1] ⊗ Δ[n]) _⦋d + 1⦌\nhs₁ : s ∈ (Δ[m + 1] ⊗ Δ[n]).nonDegenerate (d + 1)\nhs₂ : s ∉ (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).obj (Oppos... | [
"case inr.right.inl\nm✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd✝ m : ℕ\nk : Fin (m + 1)\nn d : ℕ\nis it : Fin (d + 1)\ns : (Δ[m + 1] ⊗ Δ[n]) _⦋d + 1⦌\nhs₁ : s ∈ (Δ[m + 1] ⊗ Δ[n]).nonDegenerate (d + 1)\nhs₂ : s ∉ (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).obj (Opposite.op ⦋d + ... | have : it.succ ∈ St := by
simpa [St, mem_finset_iff] using ht.simplex_fst_succ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplexOne | {
"line": 57,
"column": 6
} | {
"line": 57,
"column": 17
} | {
"line": 57,
"column": 18
} | [
{
"pp": "case refine_1\np : ℕ\nx✝¹ x✝ : Fin (p + 1)\nh :\n (fun i ↦ ⟨(stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc), ⋯⟩) x✝¹ =\n (fun i ↦ ⟨(stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc), ⋯⟩) x✝\n⊢ x✝¹ = x✝",
"ppTerm": "?refine_1",
"assigned": false... | [
"case refine_1\np : ℕ\nx✝¹ x✝ : Fin (p + 1)\nh :\n (fun i ↦ ⟨(stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc), ⋯⟩) x✝¹ =\n (fun i ↦ ⟨(stdSimplex.objEquiv.symm (SimplexCategory.σ i), objMk₁ i.succ.castSucc), ⋯⟩) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 648,
"column": 50
} | {
"line": 648,
"column": 68
} | {
"line": 648,
"column": 69
} | [
{
"pp": "m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd m : ℕ\nk : Fin m\nn : ℕ\ns : Type₁ k.succ n\nh : (pairingCore k.succ n).index s = 0\nthis : s.index = 0\n⊢ IsIndex s.x ⋯ (Fin.succ 0)",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"instNe... | [
"m✝ : ℕ\nk✝ : Fin (m✝ + 1)\nn✝ : ℕ\nx : (Λ[m✝ + 1, k✝.castSucc].unionProd ∂Δ[n✝]).N\nd m : ℕ\nk : Fin m\nn : ℕ\ns : Type₁ k.succ n\nh : (pairingCore k.succ n).index s = 0\nthis : s.index = 0\n⊢ IsIndex s.x ⋯ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 46
} | {
"line": 80,
"column": 47
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf : RelativeMorphism A B φ\n⊢ A ≤ B.preimage f.map",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"PartialOrder.toPreorder",
"_private.Mathlib.AlgebraicTopology.... | [
"X Y : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf : RelativeMorphism A B φ\n⊢ A.image f.map ≤ B"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 48
} | {
"line": 156,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX : SSet\nR : C\nn : ℕ\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ X.ιNormalizedChainComplex x = Sigma.ι (fun x ↦ R) ⟨x, hx⟩",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"CategoryTheor... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX : SSet\nR : C\nn : ℕ\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ Sigma.ι (fun x ↦ R) x ≫ (X.toNormalizedChainComplex R).f n = Sigma.ι (fun x ↦ R) ⟨x, hx⟩"
] | dsimp [ιNormalizedChainComplex, ιChainComplex] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 169,
"column": 6
} | {
"line": 169,
"column": 17
} | {
"line": 169,
"column": 18
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX Y : SSet\nf : X ⟶ Y\nR : C\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ (Cofan.mk (∐ fun x ↦ R) (Sigma.ι fun x ↦ R)).inj ⟨x, hx⟩ ≫\n (Iso.refl (Cofan.mk (∐ fun x ↦ R) (Sigma.ι... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX Y : SSet\nf : X ⟶ Y\nR : C\nn : ℕ\nx✝ : ↑(X.nonDegenerate n)\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ Sigma.ι (fun x ↦ R) ⟨x, hx⟩ = X.ιNormalizedChainComplex x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 214,
"column": 2
} | {
"line": 215,
"column": 84
} | {
"line": 216,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX Y : SSet\nf : X ⟶ Y\nR : C\nn : ℕ\nx : X _⦋n⦌\n⊢ X.ιNormalizedChainComplex x ≫ (normalizedChainComplexMap f R).f n =\n Y.ιNormalizedChainComplex ((ConcreteCategory.hom (f.app (Opposite.op ⦋n⦌))) x)",
"ppTe... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX Y : SSet\nf : X ⟶ Y\nR : C\nn : ℕ\nx : X _⦋n⦌\n⊢ (X.ιChainComplex x ≫ (X.toNormalizedChainComplex R).f n) ≫ (normalizedChainComplexMap f R).f n =\n Y.ιChainComplex ((ConcreteCategory.hom (f.app (Opposite.op ⦋n⦌))) x) ≫ (Y... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 167,
"column": 8
} | {
"line": 167,
"column": 64
} | {
"line": 168,
"column": 8
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf g : X.PtSimplex n x\ni : Fin n\nh : g.MulStruct RelativeMorphism.const f i\nj : Fin (n + 2)\nhj : j < i.castSucc.succ\n⊢ stdSimplex.δ j ≫ h.map = const x",
"ppTerm": "?m.112",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"SSet.Subcomplex.toSSet"... | [
"case inl\nX : SSet\nn : ℕ\nx : X _⦋0⦌\nf g : X.PtSimplex n x\ni : Fin n\nh : g.MulStruct RelativeMorphism.const f i\nhj : i.castSucc.castSucc < i.castSucc.succ\n⊢ stdSimplex.δ i.castSucc.castSucc ≫ h.map = const x",
"case inr\nX : SSet\nn : ℕ\nx : X _⦋0⦌\nf g : X.PtSimplex n x\ni : Fin n\nh : g.MulStruct Relativ... | obtain rfl | hj := (Fin.le_castSucc_iff.mpr hj).eq_or_lt | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.SetTheory.Cardinal.CountableCover | {
"line": 51,
"column": 36
} | {
"line": 51,
"column": 74
} | {
"line": 51,
"column": 75
} | [
{
"pp": "α ι : Type u\ninst✝¹ : Countable ι\nf : ι → Set α\nl : Filter ι\ninst✝ : l.NeBot\nt : Set α\nht : ∀ x ∈ t, ∀ᶠ (i : ι) in l, x ∈ f i\nn : ℕ\nh'f : ∀ (i : ι), #↑(f i) ≤ ↑n\nha : ↑n < ℵ₀\ns : Finset α\nhs : ↑s ⊆ t\nA : ∀ x ∈ s, ∀ᶠ (i : ι) in l, x ∈ f i\nB : ∀ᶠ (i : ι) in l, ∀ x ∈ s, x ∈ f i\ni : ι\nhi : ∀... | [
"α ι : Type u\ninst✝¹ : Countable ι\nf : ι → Set α\nl : Filter ι\ninst✝ : l.NeBot\nt : Set α\nht : ∀ x ∈ t, ∀ᶠ (i : ι) in l, x ∈ f i\nn : ℕ\nh'f : ∀ (i : ι), #↑(f i) ≤ ↑n\nha : ↑n < ℵ₀\ns : Finset α\nhs : ↑s ⊆ t\nA : ∀ x ∈ s, ∀ᶠ (i : ι) in l, x ∈ f i\nB : ∀ᶠ (i : ι) in l, ∀ x ∈ s, x ∈ f i\ni : ι\nhi : ∀ x ∈ s, x ∈ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | {
"line": 37,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nf : (ℕ → Bool) → 𝕜\nf_inj : Injective f\n⊢ 𝔠 ≤ #𝕜",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.mk",
"id",
"LE.le",
"Cardinal.inst... | [
"𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nf : (ℕ → Bool) → 𝕜\nf_inj : Injective f\n⊢ 𝔠 ≤ #𝕜"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 46,
"column": 22
} | {
"line": 46,
"column": 33
} | {
"line": 46,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nx : 𝕜\nx✝ : x ∈ Set.univ\nU : Set 𝕜\nhU : U ∈ 𝓝 x\nc : 𝕜\nc_pos : 0 < ‖c‖\nhc : ‖c‖ < 1\nA : Tendsto (fun n ↦ x + c ^ n) atTop (𝓝 x)\nB : ∀ᶠ (n : ℕ) in atTop, x + c ^ n ∈ U\nn : ℕ\nhn : x + c ^ n ∈ U\n⊢ x + c ^ n ∈ U ∩ S... | [
"𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nx : 𝕜\nx✝ : x ∈ Set.univ\nU : Set 𝕜\nhU : U ∈ 𝓝 x\nc : 𝕜\nc_pos : 0 < ‖c‖\nhc : ‖c‖ < 1\nA : Tendsto (fun n ↦ x + c ^ n) atTop (𝓝 x)\nB : ∀ᶠ (n : ℕ) in atTop, x + c ^ n ∈ U\nn : ℕ\nhn : x + c ^ n ∈ U\n⊢ x + c ^ n ∈ U"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 13
} | {
"line": 49,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nx : 𝕜\nx✝ : x ∈ Set.univ\nU : Set 𝕜\nhU : U ∈ 𝓝 x\nc : 𝕜\nc_pos : 0 < ‖c‖\nhc : ‖c‖ < 1\nA : Tendsto (fun n ↦ x + c ^ n) atTop (𝓝 x)\nB : ∀ᶠ (n : ℕ) in atTop, x + c ^ n ∈ U\nn : ℕ\nhn : x + c ^ n ∈ U\n⊢ c ≠ 0",
"ppTe... | [
"𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nx : 𝕜\nx✝ : x ∈ Set.univ\nU : Set 𝕜\nhU : U ∈ 𝓝 x\nc : 𝕜\nc_pos : 0 < ‖c‖\nhc : ‖c‖ < 1\nA : Tendsto (fun n ↦ x + c ^ n) atTop (𝓝 x)\nB : ∀ᶠ (n : ℕ) in atTop, x + c ^ n ∈ U\nn : ℕ\nhn : x + c ^ n ∈ U\n⊢ ¬c = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 15
} | {
"line": 57,
"column": 16
} | [
{
"pp": "𝕜 : Type u\nE : Type v\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CompleteSpace 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : Nontrivial E\n⊢ lift.{v, u} 𝔠 ≤ lift.{v, u} #𝕜",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"... | [
"𝕜 : Type u\nE : Type v\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CompleteSpace 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : Nontrivial E\n⊢ 𝔠 ≤ #𝕜"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 13
} | {
"line": 58,
"column": 14
} | [
{
"pp": "𝕜 : Type u\nE : Type v\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CompleteSpace 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : Nontrivial E\nA : lift.{v, u} 𝔠 ≤ lift.{v, u} #𝕜\n⊢ 𝔠 ≤ #E",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Card... | [
"𝕜 : Type u\nE : Type v\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : CompleteSpace 𝕜\ninst✝² : AddCommGroup E\ninst✝¹ : Module 𝕜 E\ninst✝ : Nontrivial E\nA : lift.{v, u} 𝔠 ≤ lift.{v, u} #𝕜\n⊢ 𝔠 ≤ #E"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 70,
"column": 31
} | {
"line": 70,
"column": 46
} | {
"line": 70,
"column": 47
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nh : 1 < Module.rank ℝ E\ns : Set E\nhs : s.Countable\nthis : Nontrivial E\na : E\nha : a ∈ sᶜ\nb : E\nhb : b ∈ sᶜ\nhab : a ≠ b\nc : E := 2⁻¹ • (a + b)\nx : E :=... | [
"E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nh : 1 < Module.rank ℝ E\ns : Set E\nhs : s.Countable\nthis : Nontrivial E\na : E\nha : a ∈ sᶜ\nb : E\nhb : b ∈ sᶜ\nhab : a ≠ b\nc : E := 2⁻¹ • (a + b)\nx : E := 2⁻¹ • (b - ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 107,
"column": 68
} | {
"line": 107,
"column": 83
} | {
"line": 107,
"column": 84
} | [
{
"pp": "E : Type u_1\n𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddGroup E\ninst✝³ : MulActionWithZero 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\ns : Set E\nx : E\nhs : s ∈ 𝓝 x\ng : E ≃ₜ E := Homeomorph.addLeft x\nt : Set E := ⇑g ⁻¹' s\n⊢ s ∈ �... | [
"E : Type u_1\n𝕜 : Type u_2\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : AddGroup E\ninst✝³ : MulActionWithZero 𝕜 E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\ns : Set E\nx : E\nhs : s ∈ 𝓝 x\ng : E ≃ₜ E := Homeomorph.addLeft x\nt : Set E := ⇑g ⁻¹' s\n⊢ s ∈ 𝓝 x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 78,
"column": 6
} | {
"line": 78,
"column": 68
} | {
"line": 78,
"column": 69
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nh : 1 < Module.rank ℝ E\ns : Set E\nhs : s.Countable\nthis : Nontrivial E\na : E\nha : a ∈ sᶜ\nb : E\nhb : b ∈ sᶜ\nhab : a ≠ b\nc : E := 2⁻¹ • (a + b)\nx : E :=... | [
"E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nh : 1 < Module.rank ℝ E\ns : Set E\nhs : s.Countable\nthis : Nontrivial E\na : E\nha : a ∈ sᶜ\nb : E\nhb : b ∈ sᶜ\nhab : a ≠ b\nc : E := 2⁻¹ • (a + b)\nx : E := 2⁻¹ • (b - ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 46
} | {
"line": 127,
"column": 47
} | [
{
"pp": "E : Type u_1\n𝕜 : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : CompleteSpace 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : Nontrivial E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\ns : Set E\nhs : IsOpen[inst✝²] s\nh's : s.Nonempty\n⊢ 𝔠... | [
"E : Type u_1\n𝕜 : Type u_2\ninst✝⁷ : NontriviallyNormedField 𝕜\ninst✝⁶ : CompleteSpace 𝕜\ninst✝⁵ : AddCommGroup E\ninst✝⁴ : Module 𝕜 E\ninst✝³ : Nontrivial E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul 𝕜 E\ns : Set E\nhs : IsOpen[inst✝²] s\nh's : s.Nonempty\n⊢ 𝔠 ≤ #E"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 28
} | {
"line": 66,
"column": 29
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x < 1 ↔ w x < 1",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x < 1 ↔ w x < 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 28
} | {
"line": 70,
"column": 29
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ 1 < v x ↔ 1 < w x",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ 1 < v x ↔ 1 < w x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 28
} | {
"line": 74,
"column": 29
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x ≤ 1 ↔ w x ≤ 1",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x ≤ 1 ↔ w x ≤ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 28
} | {
"line": 78,
"column": 29
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ 1 ≤ v x ↔ 1 ≤ w x",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ 1 ≤ v x ↔ 1 ≤ w x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 81,
"column": 2
} | {
"line": 81,
"column": 28
} | {
"line": 81,
"column": 29
} | [
{
"pp": "R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x = 1 ↔ w x = 1",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝⁴ : Semiring R\nS : Type u_2\ninst✝³ : Semiring S\ninst✝² : PartialOrder S\nv w : AbsoluteValue R S\ninst✝¹ : IsDomain S\ninst✝ : Nontrivial R\nh : v.IsEquiv w\nx : R\n⊢ v x = 1 ↔ w x = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 88,
"column": 6
} | {
"line": 88,
"column": 68
} | {
"line": 88,
"column": 69
} | [
{
"pp": "E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nh : 1 < Module.rank ℝ E\ns : Set E\nhs : s.Countable\nthis : Nontrivial E\na : E\nha : a ∈ sᶜ\nb : E\nhb : b ∈ sᶜ\nhab : a ≠ b\nc : E := 2⁻¹ • (a + b)\nx : E :=... | [
"E : Type u_1\ninst✝⁴ : AddCommGroup E\ninst✝³ : Module ℝ E\ninst✝² : TopologicalSpace E\ninst✝¹ : ContinuousAdd E\ninst✝ : ContinuousSMul ℝ E\nh : 1 < Module.rank ℝ E\ns : Set E\nhs : s.Countable\nthis : Nontrivial E\na : E\nha : a ∈ sᶜ\nb : E\nhb : b ∈ sᶜ\nhab : a ≠ b\nc : E := 2⁻¹ • (a + b)\nx : E := 2⁻¹ • (b - ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 215,
"column": 4
} | {
"line": 215,
"column": 15
} | {
"line": 215,
"column": 16
} | [
{
"pp": "case inl\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nhr : 0 ≤ 0\n⊢ IsPathConnected (sphere x 0)",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"IsPathConnected",
"Eq.mpr",
"Real",
"Metric.sphere_zer... | [
"case inl\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nhr : 0 ≤ 0\n⊢ IsPathConnected {x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 179,
"column": 4
} | {
"line": 179,
"column": 19
} | {
"line": 179,
"column": 20
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 15
} | {
"line": 221,
"column": 16
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : 0 ≤ r\nrpos : 0 < r\nf : E → E := fun y ↦ x + (r * ‖y‖⁻¹) • y\ny : E\nhy : y ∈ {0}ᶜ\n⊢ ‖id y‖ ≠ 0",
"ppTerm": "?m.146",
"assigned": true,
"usedConstants": [
"AddGroup.toSu... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : 0 ≤ r\nrpos : 0 < r\nf : E → E := fun y ↦ x + (r * ‖y‖⁻¹) • y\ny : E\nhy : y ∈ {0}ᶜ\n⊢ ¬y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 25
} | {
"line": 226,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : 0 ≤ r\nrpos : 0 < r\nf : E → E := fun y ↦ x + (r * ‖y‖⁻¹) • y\nA : ContinuousOn f {0}ᶜ\nB : IsPathConnected {0}ᶜ\nC : IsPathConnected (f '' {0}ᶜ)\n⊢ f '' {0}ᶜ = sphere x r",
"ppTerm": "... | [
"case h₁\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : 0 ≤ r\nrpos : 0 < r\nf : E → E := ⋯\nA : ContinuousOn f {0}ᶜ\nB : IsPathConnected {0}ᶜ\nC : IsPathConnected (f '' {0}ᶜ)\n⊢ f '' {0}ᶜ ⊆ sphere x r",
"case h₂\nE : Type u_1\ninst✝¹ : NormedAdd... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 227,
"column": 27
} | {
"line": 227,
"column": 38
} | {
"line": 227,
"column": 39
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : 0 ≤ r\nrpos : 0 < r\nf : E → E := fun y ↦ x + (r * ‖y‖⁻¹) • y\nA : ContinuousOn f {0}ᶜ\nB : IsPathConnected {0}ᶜ\nC : IsPathConnected (f '' {0}ᶜ)\ny : E\nhy : y ∈ {0}ᶜ\n⊢ ‖y‖ ≠ 0",
"ppT... | [
"E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : 0 ≤ r\nrpos : 0 < r\nf : E → E := fun y ↦ x + (r * ‖y‖⁻¹) • y\nA : ContinuousOn f {0}ᶜ\nB : IsPathConnected {0}ᶜ\nC : IsPathConnected (f '' {0}ᶜ)\ny : E\nhy : y ∈ {0}ᶜ\n⊢ ¬y = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 19
} | {
"line": 181,
"column": 20
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall | {
"line": 35,
"column": 4
} | {
"line": 35,
"column": 15
} | {
"line": 35,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : RCLike 𝕜\nf : 𝕜 → 𝕜\nx : 𝕜\nr : ENNReal\nhr_pos : 0 < r\nh : AnalyticOnNhd 𝕜 f (Metric.eball x r)\np : FormalMultilinearSeries 𝕜 𝕜 𝕜 := FormalMultilinearSeries.ofScalars 𝕜 fun n ↦ iteratedDeriv n f x / ↑n.factorial\nhr : r ≤ p.radius\ng : 𝕜 → 𝕜 := fun t ↦ p.sum (t - x)... | [
"𝕜 : Type u_1\ninst✝ : RCLike 𝕜\nf : 𝕜 → 𝕜\nx : 𝕜\nr : ENNReal\nhr_pos : 0 < r\nh : AnalyticOnNhd 𝕜 f (Metric.eball x r)\np : FormalMultilinearSeries 𝕜 𝕜 𝕜 := FormalMultilinearSeries.ofScalars 𝕜 fun n ↦ iteratedDeriv n f x / ↑n.factorial\nhr : r ≤ p.radius\ng : 𝕜 → 𝕜 := fun t ↦ p.sum (t - x)\n⊢ HasFPowe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | {
"line": 37,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\ninst✝ : RCLike 𝕜\nf : 𝕜 → 𝕜\nx : 𝕜\nr : ENNReal\nhr_pos : 0 < r\nh : AnalyticOnNhd 𝕜 f (Metric.eball x r)\np : FormalMultilinearSeries 𝕜 𝕜 𝕜 := FormalMultilinearSeries.ofScalars 𝕜 fun n ↦ iteratedDeriv n f x / ↑n.factorial\nhr : r ≤ p.radius\ng : 𝕜 → 𝕜 := fun t ↦ p.sum (t - x)... | [
"𝕜 : Type u_1\ninst✝ : RCLike 𝕜\nf : 𝕜 → 𝕜\nx : 𝕜\nr : ENNReal\nhr_pos : 0 < r\nh : AnalyticOnNhd 𝕜 f (Metric.eball x r)\np : FormalMultilinearSeries 𝕜 𝕜 𝕜 := FormalMultilinearSeries.ofScalars 𝕜 fun n ↦ iteratedDeriv n f x / ↑n.factorial\nhr : r ≤ p.radius\ng : 𝕜 → 𝕜 := fun t ↦ p.sum (t - x)\nhg : HasFP... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 185,
"column": 55
} | {
"line": 185,
"column": 66
} | {
"line": 185,
"column": 67
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 248,
"column": 4
} | {
"line": 248,
"column": 20
} | {
"line": 248,
"column": 21
} | [
{
"pp": "case inr\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : r < 0\n⊢ IsPreconnected (sphere x r)",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Metric.sphere_eq_empty_of_neg",
... | [
"case inr\nE : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nh : 1 < Module.rank ℝ E\nx : E\nr : ℝ\nhr : r < 0\n⊢ IsPreconnected ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 15
} | {
"line": 190,
"column": 16
} | [
{
"pp": "case refine_2\nR : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R... | [
"case refine_2\nR : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 209,
"column": 4
} | {
"line": 209,
"column": 19
} | {
"line": 209,
"column": 20
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 213,
"column": 4
} | {
"line": 213,
"column": 19
} | {
"line": 213,
"column": 20
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 216,
"column": 4
} | {
"line": 216,
"column": 19
} | {
"line": 216,
"column": 20
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 220,
"column": 55
} | {
"line": 220,
"column": 66
} | {
"line": 220,
"column": 67
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv | {
"line": 188,
"column": 4
} | {
"line": 188,
"column": 36
} | {
"line": 188,
"column": 37
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\nf' : E ≃L[𝕜] F\na : E\ninst✝ : CompleteSpace E\nhf : HasStrictFDerivAt f (↑f') a\n⊢ HasStrictFD... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\nf' : E ≃L[𝕜] F\na : E\ninst✝ : CompleteSpace E\nhf : HasStrictFDerivAt f (↑f') a\n⊢ HasStrictFDerivAt f (↑f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 15
} | {
"line": 292,
"column": 16
} | [
{
"pp": "case inl\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : w a ≠ 1\nhwa : w a < 1\n⊢ 0 < log (w a) / log (v a)",
"ppTerm": "?inl",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inl\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : w a ≠ 1\nhwa : w a < 1\n⊢ 0 < log (w a) / log (v a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 307,
"column": 4
} | {
"line": 307,
"column": 15
} | {
"line": 307,
"column": 16
} | [
{
"pp": "case inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nthis :\n ∀ {a : F},\n a ≠ 0 → v a ≠ 1 → ∀ {b : F}, b ≠ 0 → v b ≠ 1 → log (v b) / log (w b) ≠... | [
"case inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nthis :\n ∀ {a : F},\n a ≠ 0 → v a ≠ 1 → ∀ {b : F}, b ≠ 0 → v b ≠ 1 → log (v b) / log (w b) ≠ log (v a) /... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 310,
"column": 4
} | {
"line": 310,
"column": 15
} | {
"line": 310,
"column": 16
} | [
{
"pp": "case inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nha : 1 < v a\nthis :\n ∀ {a : F},\n a ≠ 0 →\n v a ≠ 1 → ∀ {b : F}, b ≠ 0 → v b ≠ 1 → lo... | [
"case inr\nF : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nh : v.IsEquiv w\na : F\nha₀ : a ≠ 0\nha₁ : v a ≠ 1\nb : F\nhb₀ : b ≠ 0\nhb₁ : v b ≠ 1\nh_ne : log (v b) / log (w b) ≠ log (v a) / log (w a)\nha : 1 < v a\nthis :\n ∀ {a : F},\n a ≠ 0 →\n v a ≠ 1 → ∀ {b : F}, b ≠ 0 → v b ≠ 1 → log (v b) / lo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.InverseFunctionTheorem.ApproximatesLinearOn | {
"line": 190,
"column": 8
} | {
"line": 190,
"column": 35
} | {
"line": 190,
"column": 36
} | [
{
"pp": "case hbc\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\ninst✝ : CompleteSpace E\ns : Set E\nc : ℝ≥0\nf' : E →L[𝕜] F\nhf : ApproximatesLinearO... | [
"case hbc\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nF : Type u_3\ninst✝² : NormedAddCommGroup F\ninst✝¹ : NormedSpace 𝕜 F\nf : E → F\ninst✝ : CompleteSpace E\ns : Set E\nc : ℝ≥0\nf' : E →L[𝕜] F\nhf : ApproximatesLinearOn f f' s c\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 386,
"column": 20
} | {
"line": 386,
"column": 51
} | {
"line": 386,
"column": 52
} | [
{
"pp": "F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nx✝ : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F)) ∧ Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nhi : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F))\nright✝ : Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\... | [
"F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nx✝ : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F)) ∧ Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nhi : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F))\nright✝ : Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nx : F\nh : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 387,
"column": 4
} | {
"line": 387,
"column": 35
} | {
"line": 387,
"column": 36
} | [
{
"pp": "F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nx✝ : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F)) ∧ Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nhi : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F))\nright✝ : Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\... | [
"F : Type u_1\ninst✝ : Field F\nv w : AbsoluteValue F ℝ\nx✝ : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F)) ∧ Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nhi : IsEmbedding ⇑(WithAbs.congr v w (RingEquiv.refl F))\nright✝ : Function.Surjective ⇑(WithAbs.congr v w (RingEquiv.refl F))\nx : F\nh : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 76,
"column": 11
} | {
"line": 76,
"column": 84
} | {
"line": 77,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : analyticOrderAt f z₀ = ⊤\n⊢ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"ENat.zero_ne_top._s... | [] | by unfold analyticOrderAt at hf; split_ifs at hf with h <;> simp [*] at * | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 423,
"column": 8
} | {
"line": 423,
"column": 48
} | {
"line": 423,
"column": 49
} | [
{
"pp": "F : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι), j ≠ i → (... | [
"F : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι), j ≠ i → (v j) (a i) <... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 81,
"column": 2
} | {
"line": 82,
"column": 9
} | {
"line": 82,
"column": 10
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\n⊢ EventuallyConst f (𝓝 z₀) ↔ analyticOrderAt (fun x ↦ f x - f z₀) z₀ = ⊤",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"AddGroup... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\n⊢ (∃ c, f =ᶠ[𝓝 z₀] fun x ↦ c) ↔ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = f z₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 424,
"column": 6
} | {
"line": 424,
"column": 17
} | {
"line": 424,
"column": 18
} | [
{
"pp": "case pos\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι),... | [
"case pos\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι), j ≠ i → (v ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 432,
"column": 6
} | {
"line": 432,
"column": 17
} | {
"line": 432,
"column": 18
} | [
{
"pp": "case neg\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis✝ : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι)... | [
"case neg\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis✝ : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι), j ≠ i → (v... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 15
} | {
"line": 157,
"column": 16
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh : ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\n⊢ ↑n ≤ ⊤ ↔ ∃ g, AnalyticAt 𝕜 g z₀ ∧ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g ... | [
"case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh : ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\n⊢ ∃ g, AnalyticAt 𝕜 g z₀ ∧ ∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = (z - z₀) ^ n • g z"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 167,
"column": 8
} | {
"line": 167,
"column": 45
} | {
"line": 168,
"column": 6
} | [
{
"pp": "case neg.refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh✝ : ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\nm : ℕ := ⋯.choose\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhm : ∀ᶠ (z : 𝕜... | [] | simp [m, Nat.sub_ne_zero_of_lt hg_ne] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Analysis.Analytic.Order | {
"line": 167,
"column": 8
} | {
"line": 167,
"column": 45
} | {
"line": 168,
"column": 6
} | [
{
"pp": "case neg.refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh✝ : ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\nm : ℕ := ⋯.choose\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhm : ∀ᶠ (z : 𝕜... | [] | simp [m, Nat.sub_ne_zero_of_lt hg_ne] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Order | {
"line": 167,
"column": 8
} | {
"line": 167,
"column": 45
} | {
"line": 168,
"column": 6
} | [
{
"pp": "case neg.refine_2\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\nh✝ : ¬∀ᶠ (z : 𝕜) in 𝓝 z₀, f z = 0\nm : ℕ := ⋯.choose\ng : 𝕜 → E\nhg : AnalyticAt 𝕜 g z₀\nhm : ∀ᶠ (z : 𝕜... | [] | simp [m, Nat.sub_ne_zero_of_lt hg_ne] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Order | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 54
} | {
"line": 179,
"column": 4
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : f =ᶠ[𝓝 z₀] g\nhf : AnalyticAt 𝕜 f z₀\n⊢ analyticOrderAt f z₀ = analyticOrderAt g z₀",
"ppTerm": "?pos✝",
"assigned": true,
"use... | [
"case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : f =ᶠ[𝓝 z₀] g\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\n⊢ ↑n ≤ analyticOrderAt f z₀ ↔ ↑n ≤ analyticOrderAt g z₀"
] | refine ENat.eq_of_forall_natCast_le_iff fun n ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Analytic.Order | {
"line": 190,
"column": 4
} | {
"line": 190,
"column": 54
} | {
"line": 191,
"column": 4
} | [
{
"pp": "case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\n⊢ analyticOrderAt (-f) z₀ = analyticOrderAt f z₀",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
... | [
"case pos\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f z₀\nn : ℕ\n⊢ ↑n ≤ analyticOrderAt (-f) z₀ ↔ ↑n ≤ analyticOrderAt f z₀"
] | refine ENat.eq_of_forall_natCast_le_iff fun n ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.Analytic.Order | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 30
} | {
"line": 210,
"column": 31
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\n⊢ min (analyticOrderAt f z₀) (analyticOrderAt g z₀) ≤ analyticOrderAt (f - g) z₀",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\n⊢ analyticOrderAt f z₀ ≤ analyticOrderAt (f + -g) z₀ ∨ analyticOrderAt g z₀ ≤ analyticOrderAt (f + -g) z₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 214,
"column": 18
} | {
"line": 214,
"column": 42
} | {
"line": 214,
"column": 43
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt (f + g) z₀ ≤ analyticOrderAt f z₀",
"ppTerm": "?m.34",
"assigned": false,
"u... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt (f + g) z₀ ≤ analyticOrderAt f z₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Analytic.Order | {
"line": 215,
"column": 8
} | {
"line": 215,
"column": 28
} | {
"line": 215,
"column": 29
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt f z₀ ≤ analyticOrderAt (f + g) z₀",
"ppTerm": "?m.35",
"assigned": false,
"u... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf g : 𝕜 → E\nz₀ : 𝕜\nhfg : analyticOrderAt f z₀ < analyticOrderAt g z₀\n⊢ analyticOrderAt f z₀ ≤ analyticOrderAt (f + g) z₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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