module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 15
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝¹ : h.IsInner\ninst✝ : h.IsProper\ns : h.ι\n⊢ ⋯.index ⋯ ≠ 0",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"SSet.S",
"SSet.Subcomplex.PairingCore.equivII",
"SSe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 223,
"column": 4
} | {
"line": 223,
"column": 15
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝¹ : h.IsInner\ninst✝ : h.IsProper\ns : h.ι\n⊢ ⋯.index ⋯ ≠ Fin.last ((↑(h.equivII s)).dim + 1)",
"usedConstants": [
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"SSet.S",
"SSet.Subcomple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 244,
"column": 48
} | {
"line": 244,
"column": 78
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\ninst✝ : h.IsRegular\nthis : IsEmpty { f // ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n) }\nx✝ : { f // ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → ↑h.pairing.II\nhf : ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ h.Ancestr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 139,
"column": 8
} | {
"line": 139,
"column": 49
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.RankFunction α\ny : ↑h.pairing.II\nx : h.ι\nhxy : h.pairing.AncestralRel (h.equivII x) y\n⊢ f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm y)",
"usedConstants": [
... | obtain ⟨y, rfl⟩ := h.equivII.surjective y | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 141,
"column": 8
} | {
"line": 141,
"column": 19
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.RankFunction α\nx y : h.ι\nhxy : h.AncestralRel x y\n⊢ f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm (h.equivII y))",
"usedConstants": [
"SSet.Subcomplex.Pa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RankNat | {
"line": 41,
"column": 6
} | {
"line": 41,
"column": 17
} | [
{
"pp": "case refine_1\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\ny : ↑P.II\nT : Type (max 0 u) := { x // P.AncestralRel x y }\nU : Type := (d : Fin (↑(P.p y)).dim) × (⦋↑d⦌ ⟶ ⦋(↑(P.p y)).dim⦌)\nψ : U → X.S :=\n fun x ↦\n match x with\n | ⟨d, f⟩ => { dim := ↑d, simplex := (CategoryTheory.ConcreteCategory... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | {
"line": 256,
"column": 41
} | {
"line": 256,
"column": 71
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nh : A.PairingCore\nx✝¹ : h.pairing.IsRegular\nthis✝ : h.IsProper\nthis : IsEmpty { f // ∀ (n : ℕ), h.pairing.AncestralRel (f (n + 1)) (f n) }\nx✝ : { f // ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n) }\nf : ℕ → h.ι\nhf : ∀ (n : ℕ), h.AncestralRel (f (n + 1)) (f n)\nn : ℕ\n⊢ h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 158,
"column": 8
} | {
"line": 158,
"column": 49
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.WeakRankFunction α\ny : ↑h.pairing.II\nx : h.ι\nhxy : h.pairing.AncestralRel (h.equivII x) y\n⊢ (↑(h.equivII x)).dim = (↑y).dim → f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equ... | obtain ⟨y, rfl⟩ := h.equivII.surjective y | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | {
"line": 160,
"column": 8
} | {
"line": 160,
"column": 19
} | [
{
"pp": "X✝ : SSet\nA✝ : X✝.Subcomplex\nX : SSet\nA : X.Subcomplex\nh : A.PairingCore\nα : Type v\ninst✝ : PartialOrder α\nf : h.WeakRankFunction α\nx y : h.ι\nhxy : h.AncestralRel x y\n⊢ (↑(h.equivII x)).dim = (↑(h.equivII y)).dim →\n f.rank (h.equivII.symm (h.equivII x)) < f.rank (h.equivII.symm (h.equivII... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Set | {
"line": 41,
"column": 31
} | {
"line": 41,
"column": 42
} | [
{
"pp": "J : Type w\ninst✝¹ : Category.{w', w} J\nX : Type u\ninst✝ : IsFilteredOrEmpty J\nF : J ⥤ Set X\ni j : J\nx : X\nhx : x ∈ F.obj i\ny : X\nhy : y ∈ F.obj j\nh :\n (ConcreteCategory.hom ((functorToTypes.mapCocone (colimitCocone F).cocone).ι.app i)) ⟨x, hx⟩ =\n (ConcreteCategory.hom ((functorToTypes.m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 13
} | [
{
"pp": "S X₁ X₂ : Type u\nf : S ⟶ X₁\ng : S ⟶ X₂\ninst✝ : Mono f\nx₂ y₂ : X₂\nh : (ConcreteCategory.hom (inr f g)) x₂ = (ConcreteCategory.hom (inr f g)) y₂\n⊢ x₂ = y₂",
"usedConstants": [
"id",
"Eq"
]
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.FiniteColimits | {
"line": 91,
"column": 4
} | {
"line": 91,
"column": 43
} | [
{
"pp": "case refine_2\nι : Type v\ninst✝¹ : HasColimitsOfShape (Discrete ι) (Type u)\nX : ι → SSet\nY : SSet\ninst✝ : HasCoproduct X\nf : ∐ X ⟶ Y\ni : ι\n⊢ Subcomplex.range (Sigma.ι X i ≫ f) ≤ ⨆ j, Subcomplex.range ((Cofan.mk (∐ X) (Sigma.ι X)).ι.app j ≫ f)",
"usedConstants": [
"SSet.Subcomplex.range... | exact le_trans (by rfl) (le_iSup _ ⟨i⟩) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Limits.Types.Pushouts | {
"line": 278,
"column": 29
} | {
"line": 278,
"column": 53
} | [
{
"pp": "X₁ X₂ X₃ X₄ : Type u\nt : X₁ ⟶ X₂\nr : X₂ ⟶ X₄\nl : X₁ ⟶ X₃\nb : X₃ ⟶ X₄\nh : IsPushout t l r b\nx₄ : X₄\nx₁ : X₁\nhx₃ : (ConcreteCategory.hom b) ((ConcreteCategory.hom l) x₁) = x₄\n⊢ (ConcreteCategory.hom r) ((ConcreteCategory.hom t) x₁) = x₄",
"usedConstants": [
"Eq.mpr",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | {
"line": 123,
"column": 2
} | {
"line": 123,
"column": 94
} | [
{
"pp": "p q n : ℕ\nx : ↑((Δ[p] ⊗ Δ[q]).nonDegenerate n)\nm : ℕ\nhm : p + q = m\n⊢ StrictMono ⇑(orderHomOfSimplex (↑x) hm)",
"usedConstants": [
"_private.Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex.0.SSet.prodStdSimplex.strictMono_orderHomOfSimplex._simp_1_2",
"Eq.mpr",
"Opposit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 15
} | [
{
"pp": "case succ\np q n : ℕ\nx : ↑((Δ[p] ⊗ Δ[q]).nonDegenerate n)\nm : ℕ\nhm : p + q = m\ni : Fin n\nhi : ↑i.castSucc ≤ ↑((orderHomOfSimplex (↑x) hm) i.castSucc)\n⊢ ↑i.succ ≤ ↑((orderHomOfSimplex (↑x) hm) i.succ)",
"usedConstants": [
"Opposite",
"CategoryTheory.typesCartesianMonoidalCategory",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplex | {
"line": 169,
"column": 4
} | {
"line": 170,
"column": 11
} | [
{
"pp": "case a.a.h.h.snd\np q n : ℕ\nz₁ z₂ : ↑((Δ[p] ⊗ Δ[q]).nonDegenerate n)\nh : (↑z₁).1 = (↑z₂).1\nhn : p + q = n\ni : Fin (n + 1)\nh₁ : orderHomOfSimplex ↑z₁ ⋯ = OrderHom.id\nh₂ : orderHomOfSimplex ↑z₂ ⋯ = OrderHom.id\n⊢ ((objEquiv ↑z₁) i).2 = ((objEquiv ↑z₂) i).2",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd | {
"line": 39,
"column": 2
} | {
"line": 39,
"column": 88
} | [
{
"pp": "case obj.h.h\nX₁ 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)",
"usedConstants": [
"SSet.S.subcomplex",
"_private.Mat... | 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
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.FiniteProd | {
"line": 86,
"column": 62
} | {
"line": 86,
"column": 73
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 100,
"column": 60
} | {
"line": 100,
"column": 75
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 107,
"column": 60
} | {
"line": 107,
"column": 75
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 104,
"column": 12
} | {
"line": 104,
"column": 23
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ni : ι\nc : f.Cell i\ninst✝ : P.IsProper\n⊢ c.horn.image c.map ≤ (↑(P.p c.s)).subcomplex",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 105,
"column": 47
} | {
"line": 105,
"column": 67
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ni : ι\nc : f.Cell i\ninst✝ : P.IsProper\nh : c.horn.image c.map = (↑(P.p c.s)).subcomplex\n⊢ (↑c.s).subcomplex ≤ c.horn.image c.map",
"usedConstants": [
"SSet.S.subcomplex",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 33
} | [
{
"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",
"usedConstants": [
"SSet.S.subcomplex",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Oppos... | refine le_trans ?_ le_sup_right | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 232,
"column": 28
} | {
"line": 232,
"column": 39
} | [
{
"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)",
"usedConstants": [
"SSet.S.subcomplex",
"SSet.S.simple... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 315,
"column": 2
} | {
"line": 315,
"column": 41
} | [
{
"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⦌)))... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 334,
"column": 4
} | {
"line": 335,
"column": 40
} | [
{
"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",
"usedConstants": [
"SSet.S.subcomplex",
"Eq.mpr",
"SSet.Subcomplex.Pairing.RankFunctio... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Limits | {
"line": 76,
"column": 10
} | {
"line": 76,
"column": 62
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nK : Type u'\ninst✝³ : Category.{v', u'} K\nF : K ⥤ C ⥤ Type w'\nc : Cone F\nhc : (Y : C) → IsLimit (((evaluation C (Type w')).obj Y).mapCone c)\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\nhK : HasCardinalLT (Arrow K) κ\nJ : Type w\ninst✝¹ : SmallCategory J\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Retracts | {
"line": 40,
"column": 22
} | {
"line": 40,
"column": 52
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Limits | {
"line": 91,
"column": 6
} | {
"line": 91,
"column": 21
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nK : Type u'\ninst✝³ : Category.{v', u'} K\nF : K ⥤ C ⥤ Type w'\nc : Cone F\nhc : (Y : C) → IsLimit (((evaluation C (Type w')).obj Y).mapCone c)\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\nhK : HasCardinalLT (Arrow K) κ\nJ : Type w\ninst✝¹ : SmallCategory J\nins... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.StrongGenerator | {
"line": 110,
"column": 2
} | {
"line": 110,
"column": 78
} | [
{
"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",
"usedConstants": [
"CategoryTheory.IsIs... | refine ⟨IsSeparating.mk_of_exists_epi.{w} (fun X ↦ ?_), fun X Y i _ hi ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 424,
"column": 4
} | {
"line": 424,
"column": 15
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.StrongGenerator | {
"line": 133,
"column": 2
} | {
"line": 140,
"column": 87
} | [
{
"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",
"usedConstants": [
"CategoryTheor... | 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
} | [
{
"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",
"usedConstants": [
"CategoryTheor... | 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.CategoryTheory.Presentable.Limits | {
"line": 71,
"column": 43
} | {
"line": 92,
"column": 50
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nK : Type u'\ninst✝³ : Category.{v', u'} K\nF : K ⥤ C ⥤ Type w'\nc : Cone F\nhc : (Y : C) → IsLimit (((evaluation C (Type w')).obj Y).mapCone c)\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\nhK : HasCardinalLT (Arrow K) κ\nJ : Type w\ninst✝¹ : SmallCategory J\nins... | by
have H {k k' : K} (φ : k ⟶ k') :=
(Types.FilteredColimit.isColimit_eq_iff' (ht := hF k')
(x := (F.map φ).app _ (z k)) (y := z k')).1 (by
dsimp at hz ⊢
simpa only [← NatTrans.naturality_apply, ← hz] using y.2 φ)
let j {k k' : K} (φ : k ⟶ k') : J := (H φ).choose
let g {k k... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 96,
"column": 6
} | {
"line": 96,
"column": 51
} | [
{
"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 : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 101,
"column": 8
} | {
"line": 101,
"column": 59
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"CategoryTheory.instIsClosedUnderIsomorphismsIsCardinalPresentable",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 117,
"column": 19
} | {
"line": 117,
"column": 65
} | [
{
"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'.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.CardinalFilteredPresentation | {
"line": 137,
"column": 4
} | {
"line": 137,
"column": 59
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.CategoryTheory.Presentable.Cardin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 492,
"column": 6
} | {
"line": 493,
"column": 47
} | [
{
"pp": "case refine_1\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\nx✝ : SimplexCategoryᵒᵖ\nd : ℕ\ny : ↑((f.filtration j).obj (op ⦋d⦌))\nx : f.Cell j\nb : Δ[x.dim + 1] _⦋d⦌\nh : ⟨↑y, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 542,
"column": 4
} | {
"line": 543,
"column": 31
} | [
{
"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",
"usedConstants":... | rw [f.mapN_type₂]
exact c.s.val.nonDegenerate | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 542,
"column": 4
} | {
"line": 543,
"column": 31
} | [
{
"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",
"usedConstants":... | rw [f.mapN_type₂]
exact c.s.val.nonDegenerate | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 131,
"column": 32
} | {
"line": 131,
"column": 43
} | [
{
"pp": "Ω : Type w\nC : Type u\ninst✝ : Category.{v, u} C\nh : CoreSmallCategoryOfSet Ω C\nx y : ↑h.smallCategoryOfSet.obj\nf : (𝟭 ↑h.smallCategoryOfSet.obj).obj x ⟶ (𝟭 ↑h.smallCategoryOfSet.obj).obj y\nx' y' : ↑h.smallCategoryOfSet.obj\ng : (𝟭 ↑h.smallCategoryOfSet.obj).obj x' ⟶ (𝟭 ↑h.smallCategoryOfSet.o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 132,
"column": 32
} | {
"line": 132,
"column": 43
} | [
{
"pp": "Ω : Type w\nC : Type u\ninst✝ : Category.{v, u} C\nh : CoreSmallCategoryOfSet Ω C\nx y : ↑h.smallCategoryOfSet.obj\nf : (𝟭 ↑h.smallCategoryOfSet.obj).obj x ⟶ (𝟭 ↑h.smallCategoryOfSet.obj).obj y\ny' : ↑h.smallCategoryOfSet.obj\ng : (𝟭 ↑h.smallCategoryOfSet.obj).obj x ⟶ (𝟭 ↑h.smallCategoryOfSet.obj).... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 133,
"column": 31
} | {
"line": 133,
"column": 63
} | [
{
"pp": "Ω : Type w\nC : Type u\ninst✝ : Category.{v, u} C\nh : CoreSmallCategoryOfSet Ω C\nx y : ↑h.smallCategoryOfSet.obj\nf g : (𝟭 ↑h.smallCategoryOfSet.obj).obj x ⟶ (𝟭 ↑h.smallCategoryOfSet.obj).obj y\nhfg :\n h.functor.mapArrow.obj { left := x, right := y, hom := f } =\n h.functor.mapArrow.obj { left... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 157,
"column": 27
} | {
"line": 157,
"column": 38
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 184,
"column": 4
} | {
"line": 184,
"column": 19
} | [
{
"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)",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"Card... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 196,
"column": 4
} | {
"line": 196,
"column": 36
} | [
{
"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",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallRepresentatives | {
"line": 204,
"column": 27
} | {
"line": 204,
"column": 38
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialObject.ChainHomotopy | {
"line": 174,
"column": 2
} | {
"line": 174,
"column": 13
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : Preadditive C\nX Y : SimplicialObject C\nf g : X ⟶ Y\ninst✝ : CategoryWithHomology C\nH : Homotopy f g\nn : ℕ\n⊢ (HomologicalComplex.homologyFunctor C (ComplexShape.down ℕ) n).map ((alternatingFaceMapComplex C).map f) =\n (HomologicalComplex.homologyF... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 565,
"column": 66
} | {
"line": 586,
"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.CategoryTheory.Functor.KanExtension.Dense | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 17
} | [
{
"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\nX✝ Y✝ : D\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : (restrictedULiftYoneda F).map a₁✝ = (restrictedULiftYoneda F).map a₂✝\nX : C\np : F.obj X ⟶ X✝\n⊢ (Structure... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.KanExtension.Dense | {
"line": 117,
"column": 14
} | {
"line": 118,
"column": 62
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.KanExtension.Dense | {
"line": 124,
"column": 4
} | {
"line": 124,
"column": 15
} | [
{
"pp": "case w.h.h.toFun.h\nC : 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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.Presheaf | {
"line": 65,
"column": 8
} | {
"line": 65,
"column": 19
} | [
{
"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 ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Functor.KanExtension.Dense | {
"line": 148,
"column": 6
} | {
"line": 148,
"column": 17
} | [
{
"pp": "case w.h.h.toFun.h.a\nC : 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).o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Basic | {
"line": 139,
"column": 29
} | {
"line": 139,
"column": 40
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\ninst✝ : P.IsRegular\nB : X.Subcomplex\nh : range A.ι = B\n⊢ B = A",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.StrongGenerator | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | {
"line": 58,
"column": 4
} | {
"line": 58,
"column": 41
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Presentable.StrongGenerator | {
"line": 126,
"column": 54
} | {
"line": 126,
"column": 65
} | [
{
"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 : (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.PiZero | {
"line": 131,
"column": 6
} | {
"line": 131,
"column": 47
} | [
{
"pp": "X Y Z : SSet\ns : Cofork (SimplicialObject.δ X 1) (SimplicialObject.δ X 0)\nx₀ x₁ : X _⦋0⦌\ne : Edge x₀ x₁\n⊢ (ConcreteCategory.hom s.π) x₀ = (ConcreteCategory.hom s.π) x₁",
"usedConstants": [
"Eq.mpr",
"SSet.Edge.tgt_eq",
"Opposite",
"CategoryTheory.Limits.WalkingParallelPa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.ProdStdSimplexOne | {
"line": 56,
"column": 6
} | {
"line": 56,
"column": 17
} | [
{
"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✝",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 46
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Opposite",
"PartialOrder.toPreorder",
"_private.Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism.0.SSet.Relativ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homotopy | {
"line": 98,
"column": 6
} | {
"line": 99,
"column": 58
} | [
{
"pp": "case h.toFun.h.h.fst\nX Y : SSet\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nhij : i ≤ j.castSucc\nx : X _⦋n + 1⦌\n⊢ ((ConcreteCategory.hom\n (X.map\n (stdSimplex.objEquiv\n ((ConcreteCategory.hom (δ Δ[n + 1] i.castSucc))\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homotopy | {
"line": 125,
"column": 44
} | {
"line": 125,
"column": 55
} | [
{
"pp": "X Y : SSet\nf g : X ⟶ Y\nH : Homotopy f g\nn : ℕ\ni : Fin (n + 2)\nj : Fin (n + 1)\nhij : j.castSucc < i\nx : X _⦋n + 1⦌\nk : Fin (n + 1 + 1)\n⊢ j.castSucc.castSucc.succ ≤ i.succ.castSucc",
"usedConstants": [
"Eq.mpr",
"Fin.succ",
"Fin.castSucc_le_castSucc_iff._simp_1",
"Fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 155,
"column": 2
} | {
"line": 155,
"column": 48
} | [
{
"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⟩",
"usedConstants": [
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
... | dsimp [ιNormalizedChainComplex, ιChainComplex] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 169,
"column": 6
} | {
"line": 169,
"column": 17
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 214,
"column": 2
} | {
"line": 215,
"column": 84
} | [
{
"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)",
"used... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 167,
"column": 8
} | {
"line": 167,
"column": 64
} | [
{
"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",
"usedConstants": [
"Iff.mpr",
"LE.le.eq_or_lt",
"Fin.succ",
"instOfNatNat",
"LE.le... | 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.AlgebraicTopology.SimplicialSet.Skeleton | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 13
} | [
{
"pp": "X : SSet\ni : ℕ\nx : X _⦋i⦌\nn : ℕ\nhi : i < n\n⊢ Subcomplex.ofSimplex x ≤ X.skeleton n",
"usedConstants": [
"Eq.mpr",
"SSet.Subcomplex.ofSimplex",
"Opposite",
"PartialOrder.toPreorder",
"SSet.skeleton",
"Preorder.toLE",
"Membership.mem",
"CategoryThe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 60
} | [
{
"pp": "X Y : SSet\ni : X ⟶ Y\nd n : ℕ\nc : Cell i d\ns : Δ[d] _⦋n⦌\nhy :\n (ConcreteCategory.hom (c.ιSigmaStdSimplex.app (op ⦋n⦌))) s ∉ Set.range ⇑(ConcreteCategory.hom ((l i d).app (op ⦋n⦌)))\nhs : s ∉ ∂Δ[d].obj (op ⦋n⦌)\n⊢ Epi (stdSimplex.objEquiv s)",
"usedConstants": [
"Eq.mpr",
"Opposite... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | {
"line": 181,
"column": 2
} | {
"line": 181,
"column": 13
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\ninst✝¹ : PreservesColimitsOfShape (Discrete PEmpty.{1}) (F.flip.obj X₂)\ninst✝ : PreservesColimits... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | {
"line": 209,
"column": 2
} | {
"line": 209,
"column": 13
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\ninst✝¹ : PreservesColimitsOfShape (Discrete PEmpty.{1}) (F.obj X₁)\ninst✝ : PreservesColimitsOfSha... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | {
"line": 415,
"column": 2
} | {
"line": 415,
"column": 13
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\ninst✝¹ : PreservesLimitsOfShape (Discrete PEmpty.{1}) (G.flip.obj X₃)\ninst✝ : PreservesLimitsOf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | {
"line": 443,
"column": 2
} | {
"line": 443,
"column": 13
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝⁴ : Category.{v₁, u₁} C₁\ninst✝³ : Category.{v₂, u₂} C₂\ninst✝² : Category.{v₃, u₃} C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\ninst✝¹ : PreservesLimitsOfShape (Discrete PEmpty.{1}) (G.obj (op X₁))\ninst✝ : PreservesLimitsOf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 203,
"column": 16
} | {
"line": 203,
"column": 27
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nφ : X ⟶ (truncation 2).obj (nerve C)\nx : X.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\n⊢ (fun {x y} e ↦ nerve.homEquiv (e.map φ)) (Edge.id x) =\n 𝟙\n ((fun x ↦ nerveEquiv ((ConcreteCategory.hom... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.CountableCover | {
"line": 51,
"column": 36
} | {
"line": 51,
"column": 74
} | [
{
"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 : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.CountableCover | {
"line": 79,
"column": 4
} | {
"line": 79,
"column": 72
} | [
{
"pp": "case ht\nα : Type u\nι : Type v\na : Cardinal.{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\nh'f : ∀ (i : ι), #↑(f i) ≤ a\ng : ULift.{u, v} ι → Set (ULift.{v, u} α) := (fun x ↦ ULift.down ⁻¹' x) ∘ f ∘ ULift.down\nl' : Filter (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.CountableCover | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 19
} | [
{
"pp": "case h'f\nα : Type u\nι : Type v\na : Cardinal.{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\nh'f : ∀ (i : ι), #↑(f i) ≤ a\ng : ULift.{u, v} ι → Set (ULift.{v, u} α) := (fun x ↦ ULift.down ⁻¹' x) ∘ f ∘ ULift.down\nl' : Filter ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹ : NontriviallyNormedField 𝕜\ninst✝ : CompleteSpace 𝕜\nf : (ℕ → Bool) → 𝕜\nf_inj : Injective f\n⊢ 𝔠 ≤ #𝕜",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.mk",
"id",
"LE.le",
"Cardinal.instLE",
"Cardinal.continuum",
"ge_if... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 46,
"column": 22
} | {
"line": 46,
"column": 33
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 13
} | [
{
"pp": "case h\n𝕜 : 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
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"congrArg",
"Cardinal.lift",
"Car... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 58,
"column": 2
} | {
"line": 58,
"column": 13
} | [
{
"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",
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.mk",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 107,
"column": 68
} | {
"line": 107,
"column": 83
} | [
{
"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 ∈ �... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Module.Cardinality | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 46
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Field.WithAbs | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 13
} | [
{
"pp": "R : Type u_1\ninst✝ : Field R\nv : AbsoluteValue R ℝ\na : R\nha : v a < 1\n⊢ Filter.Tendsto (fun n ↦ (equiv v).symm (1 / (1 + a ^ n))) Filter.atTop (𝓝 1)",
"usedConstants": [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.p... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Field.WithAbs | {
"line": 71,
"column": 47
} | {
"line": 71,
"column": 58
} | [
{
"pp": "R : Type u_1\ninst✝ : Field R\nv : AbsoluteValue R ℝ\na : R\nha : v a < 1\n⊢ Filter.Tendsto (fun e ↦ ‖1⁻¹ + toAbs v a ^ e - 1‖) Filter.atTop (𝓝 0)",
"usedConstants": [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Seminorm... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 235,
"column": 6
} | {
"line": 235,
"column": 87
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nx : X.obj (op { obj := ⦋2⦌, property := _proof_14 })\ny : ((truncation 2).obj (nerve C)).obj (op { obj := ⦋2⦌, property := _proof_14 })\nh₂ :\n (fun f ↦ ComposableArrows.mk₁ (F.map (homMk (Edg... | obtain ⟨x₀, x₁, x₂, e₀₁, e₁₂, e₀₂, h, rfl⟩ := Edge.CompStruct.exists_of_simplex x | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 70,
"column": 31
} | {
"line": 70,
"column": 46
} | [
{
"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 :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 78,
"column": 6
} | {
"line": 78,
"column": 68
} | [
{
"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 :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall | {
"line": 35,
"column": 4
} | {
"line": 35,
"column": 15
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 88,
"column": 6
} | {
"line": 88,
"column": 68
} | [
{
"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 :=... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.IteratedDeriv.ConvergenceOnBall | {
"line": 37,
"column": 4
} | {
"line": 37,
"column": 15
} | [
{
"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)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 215,
"column": 4
} | {
"line": 215,
"column": 15
} | [
{
"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)",
"usedConstants": [
"IsPathConnected",
"Eq.mpr",
"Real",
"Metric.sphere_zero",
"Real.instZero",
"congrArg",... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 221,
"column": 4
} | {
"line": 221,
"column": 15
} | [
{
"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",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 25
} | [
{
"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",
"usedConsta... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Analysis.Normed.Module.Connected | {
"line": 227,
"column": 27
} | {
"line": 227,
"column": 38
} | [
{
"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",
"use... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 28
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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