module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 109,
"column": 59
} | {
"line": 109,
"column": 70
} | {
"line": 109,
"column": 71
} | [
{
"pp": "K : Type u_3\ninst✝ : Field K\nR : LocalSubring K\nhR : IsMax R\nx : K\nhx : x ∉ R.toSubring\nhx0 : x ≠ 0\nthis✝ : Invertible x := invertibleOfNonzero hx0\nS : Subalgebra (↥R.toSubring) K := (↥R.toSubring)[x]\nthis : R.toSubring < S.toSubring\np : Polynomial ↥R.toSubring\nhp : p.leadingCoeff - 1 ∈ maxi... | [
"K : Type u_3\ninst✝ : Field K\nR : LocalSubring K\nhR : IsMax R\nx : K\nhx : x ∉ R.toSubring\nhx0 : x ≠ 0\nthis✝ : Invertible x := invertibleOfNonzero hx0\nS : Subalgebra (↥R.toSubring) K := (↥R.toSubring)[x]\nthis : R.toSubring < S.toSubring\np : Polynomial ↥R.toSubring\nhp : p.leadingCoeff - 1 ∈ maximalIdeal ↥R.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | {
"line": 1085,
"column": 4
} | {
"line": 1085,
"column": 47
} | {
"line": 1085,
"column": 48
} | [
{
"pp": "case refine_2.refine_1\nA : Type u_2\nσ : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\nf : A\nd : ℕ\nhf : f ∈ 𝒜 d\nι' : Type u_4\ninst✝ : Fintype ι'\nv : ι' → A\nhx : Algebra.adjoin (↥(𝒜 0)) (Set.range v) = ⊤\ndv : ι' → ℕ\nhxd... | [
"case refine_2.refine_1\nA : Type u_2\nσ : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\nf : A\nd : ℕ\nhf : f ∈ 𝒜 d\nι' : Type u_4\ninst✝ : Fintype ι'\nv : ι' → A\nhx : Algebra.adjoin (↥(𝒜 0)) (Set.range v) = ⊤\ndv : ι' → ℕ\nhxd : ∀ (i : ι'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 85
} | {
"line": 135,
"column": 4
} | [
{
"pp": "case refine_1.refine_1\nK : Type u_3\ninst✝ : Field K\nA✝ : LocalSubring K\ns : Set (LocalSubring K)\nhs : s ⊆ Set.Ici A✝\nH : IsChain (fun x1 x2 ↦ x1 ≤ x2) s\ny : LocalSubring K\nhys : y ∈ s\ninst : Nonempty ↑s\nhdir : Directed LE.le (toSubring ∘ fun x ↦ ↑x)\na : K\nha : a ∈ ⨆ i, (↑i).toSubring\nb : K... | [
"case refine_1.refine_2\nK : Type u_3\ninst✝ : Field K\nA✝ : LocalSubring K\ns : Set (LocalSubring K)\nhs : s ⊆ Set.Ici A✝\nH : IsChain (fun x1 x2 ↦ x1 ≤ x2) s\ny : LocalSubring K\nhys : y ∈ s\ninst : Nonempty ↑s\nhdir : Directed LE.le (toSubring ∘ fun x ↦ ↑x)\na : K\nha : a ∈ ⨆ i, (↑i).toSubring\nb : K\nhb : b ∈ ⨆... | · exact fun h ↦ h.map (Subring.inclusion (le_iSup (fun i : s ↦ i.1.toSubring) C)) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | {
"line": 476,
"column": 12
} | {
"line": 476,
"column": 44
} | {
"line": 476,
"column": 45
} | [
{
"pp": "case e'_4\nA : Type u_1\nσ : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\nf : A\nm : ℕ\nf_deg : f ∈ 𝒜 m\nhm : 0 < m\nq : ↑↑(Spec A⁰_ f).toPresheafedSpace\nx y : A\nx✝¹ : IsHomogeneousElem 𝒜 x\nx✝ : IsHomogeneousElem 𝒜 y\nhxy :... | [
"case e'_4\nA : Type u_1\nσ : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\nf : A\nm : ℕ\nf_deg : f ∈ 𝒜 m\nhm : 0 < m\nq : ↑↑(Spec A⁰_ f).toPresheafedSpace\nx y : A\nx✝¹ : IsHomogeneousElem 𝒜 x\nx✝ : IsHomogeneousElem 𝒜 y\nhxy : x * y ∈ asI... | decompose_of_mem_ne 𝒜 _ hn.symm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 135,
"column": 4
} | {
"line": 135,
"column": 85
} | {
"line": 136,
"column": 2
} | [
{
"pp": "case refine_1.refine_2\nK : Type u_3\ninst✝ : Field K\nA✝ : LocalSubring K\ns : Set (LocalSubring K)\nhs : s ⊆ Set.Ici A✝\nH : IsChain (fun x1 x2 ↦ x1 ≤ x2) s\ny : LocalSubring K\nhys : y ∈ s\ninst : Nonempty ↑s\nhdir : Directed LE.le (toSubring ∘ fun x ↦ ↑x)\na : K\nha : a ∈ ⨆ i, (↑i).toSubring\nb : K... | [] | · exact fun h ↦ h.map (Subring.inclusion (le_iSup (fun i : s ↦ i.1.toSubring) C)) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | {
"line": 476,
"column": 12
} | {
"line": 476,
"column": 44
} | {
"line": 476,
"column": 45
} | [
{
"pp": "case e'_4\nA : Type u_1\nσ : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\nf : A\nm : ℕ\nf_deg : f ∈ 𝒜 m\nhm : 0 < m\nq : ↑↑(Spec A⁰_ f).toPresheafedSpace\nx y : A\nx✝¹ : IsHomogeneousElem 𝒜 x\nx✝ : IsHomogeneousElem 𝒜 y\nhxy :... | [
"case e'_4\nA : Type u_1\nσ : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\nf : A\nm : ℕ\nf_deg : f ∈ 𝒜 m\nhm : 0 < m\nq : ↑↑(Spec A⁰_ f).toPresheafedSpace\nx y : A\nx✝¹ : IsHomogeneousElem 𝒜 x\nx✝ : IsHomogeneousElem 𝒜 y\nhxy : x * y ∈ asI... | decompose_of_mem_ne 𝒜 _ hn.symm, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 169,
"column": 53
} | {
"line": 169,
"column": 85
} | {
"line": 169,
"column": 86
} | [
{
"pp": "K : Type u_3\ninst✝¹ : Field K\nx : K\nR : Subring K\nhxR : x ∉ R\ninst✝ : IsIntegrallyClosedIn (↥R) K\nhx0 : x ≠ 0\nthis : Invertible x := invertibleOfNonzero hx0\nB : Subalgebra (↥R) K := (↥R)[x⁻¹]\nxinv : ↥B.toSubring := ⟨x⁻¹, ⋯⟩\neq : Ideal.span {xinv} = ⊤\np : (↥R)[X]\nhp : p.leadingCoeff - 1 ∈ ⊥\... | [
"K : Type u_3\ninst✝¹ : Field K\nx : K\nR : Subring K\nhxR : x ∉ R\ninst✝ : IsIntegrallyClosedIn (↥R) K\nhx0 : x ≠ 0\nthis : Invertible x := invertibleOfNonzero hx0\nB : Subalgebra (↥R) K := (↥R)[x⁻¹]\nxinv : ↥B.toSubring := ⟨x⁻¹, ⋯⟩\neq : Ideal.span {xinv} = ⊤\np : (↥R)[X]\nhp : p.leadingCoeff - 1 ∈ ⊥\nhpx : (aeva... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 186,
"column": 60
} | {
"line": 186,
"column": 71
} | {
"line": 186,
"column": 72
} | [
{
"pp": "K : Type u_3\ninst✝¹ : Field K\nx : K\nR : LocalSubring K\nhxR : x ∉ R.toSubring\ninst✝ : IsIntegrallyClosedIn (↥R.toSubring) K\nhx0 : x ≠ 0\nthis : Invertible x := invertibleOfNonzero hx0\nB : Subalgebra (↥R.toSubring) K := (↥R.toSubring)[x⁻¹]\nxinv : ↥B.toSubring := ⟨x⁻¹, ⋯⟩\neq : Ideal.map (algebraM... | [
"K : Type u_3\ninst✝¹ : Field K\nx : K\nR : LocalSubring K\nhxR : x ∉ R.toSubring\ninst✝ : IsIntegrallyClosedIn (↥R.toSubring) K\nhx0 : x ≠ 0\nthis : Invertible x := invertibleOfNonzero hx0\nB : Subalgebra (↥R.toSubring) K := (↥R.toSubring)[x⁻¹]\nxinv : ↥B.toSubring := ⟨x⁻¹, ⋯⟩\neq : Ideal.map (algebraMap ↥R.toSubr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 188,
"column": 57
} | {
"line": 188,
"column": 68
} | {
"line": 188,
"column": 69
} | [
{
"pp": "K : Type u_3\ninst✝¹ : Field K\nx : K\nR : LocalSubring K\nhxR : x ∉ R.toSubring\ninst✝ : IsIntegrallyClosedIn (↥R.toSubring) K\nhx0 : x ≠ 0\nthis : Invertible x := invertibleOfNonzero hx0\nB : Subalgebra (↥R.toSubring) K := (↥R.toSubring)[x⁻¹]\nxinv : ↥B.toSubring := ⟨x⁻¹, ⋯⟩\neq : Ideal.map (algebraM... | [
"K : Type u_3\ninst✝¹ : Field K\nx : K\nR : LocalSubring K\nhxR : x ∉ R.toSubring\ninst✝ : IsIntegrallyClosedIn (↥R.toSubring) K\nhx0 : x ≠ 0\nthis : Invertible x := invertibleOfNonzero hx0\nB : Subalgebra (↥R.toSubring) K := (↥R.toSubring)[x⁻¹]\nxinv : ↥B.toSubring := ⟨x⁻¹, ⋯⟩\neq : Ideal.map (algebraMap ↥R.toSubr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | {
"line": 1104,
"column": 40
} | {
"line": 1104,
"column": 61
} | {
"line": 1104,
"column": 62
} | [
{
"pp": "A : Type u_2\nσ : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nf : A\nd : ℕ\nhf : f ∈ 𝒜 d\ns : Finset A\nhs : Algebra.adjoin ↥(𝒜 0) ↑s = ⊤\nhs' : ∀ i ∈ s, ∃ n, n ≠ 0 ∧ i ∈ 𝒜 n\ndx : ↥s ... | [
"A : Type u_2\nσ : Type u_3\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nf : A\nd : ℕ\nhf : f ∈ 𝒜 d\ns : Finset A\nhs : Algebra.adjoin ↥(𝒜 0) ↑s = ⊤\nhs' : ∀ i ∈ s, ∃ n, n ≠ 0 ∧ i ∈ 𝒜 n\ndx : ↥s → ℕ\nhdx : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.RingTheory.Valuation.LocalSubring | {
"line": 237,
"column": 32
} | {
"line": 237,
"column": 49
} | {
"line": 237,
"column": 50
} | [
{
"pp": "R : Type u_1\nS : Type u_2\nK : Type u_3\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\ninst✝⁶ : Field K\ninst✝⁵ : IsDomain R\ninst✝⁴ : ValuationRing R\ninst✝³ : IsLocalRing S\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nf : R →+* S\ng : S →+* K\nh : g.comp f = algebraMap R K\ninst✝ : IsLocalHom f\n... | [
"R : Type u_1\nS : Type u_2\nK : Type u_3\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing S\ninst✝⁶ : Field K\ninst✝⁵ : IsDomain R\ninst✝⁴ : ValuationRing R\ninst✝³ : IsLocalRing S\ninst✝² : Algebra R K\ninst✝¹ : IsFractionRing R K\nf : R →+* S\ng : S →+* K\nh : g.comp f = algebraMap R K\ninst✝ : IsLocalHom f\nV : Valuatio... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | {
"line": 696,
"column": 35
} | {
"line": 698,
"column": 48
} | {
"line": 700,
"column": 0
} | [
{
"pp": "A : Type u_1\nσ : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\nf : A\nt : NumDenSameDeg 𝒜 (Submonoid.powers f)\n⊢ ⇑(ConcreteCategory.hom (toSpec 𝒜 f).base) ⁻¹' ↑(sbo HomogeneousLocalization.mk t) =\n ↑((Opens.comap { toFun :... | [] | by
convert! (ProjIsoSpecTopComponent.ToSpec.preimage_basicOpen f t)
exact funext fun _ => toSpec_base_apply_eq _ _ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 20
} | {
"line": 53,
"column": 2
} | [
{
"pp": "case hx\nσ : Type u_1\nA : Type u_2\ninst✝³ : CommRing A\ninst✝² : SetLike σ A\ninst✝¹ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝ : GradedRing 𝒜\nd e : ℕ\nf : A\nhf : f ∈ 𝒜 d\ng : A\nhg : g ∈ 𝒜 e\nx : A\nhx : x = f * g\nhd : 0 < d\nn : ℕ\na : A\nha : a ∈ 𝒜 n\nj : ℕ\nhb' : (fun x_1 ↦ x ^ x_1) j ∈ 𝒜 ... | [] | · exact hx ▸ hfg | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.AlgebraicGeometry.Modules.Tilde | {
"line": 816,
"column": 4
} | {
"line": 816,
"column": 92
} | {
"line": 816,
"column": 93
} | [
{
"pp": "case h\nR : CommRingCat\nM : (Spec R).Modules\ng : ↑R\na : R ⟶ CommRingCat.of (Localization.Away g) := CommRingCat.ofHom (algebraMap (↑R) (Localization.Away g))\nψ : Spec (CommRingCat.of (Localization.Away g)) ⟶ Spec (CommRingCat.of ↑R) := Spec.map a\nM' : (Spec (CommRingCat.of (Localization.Away g))).... | [
"case h\nR : CommRingCat\nM : (Spec R).Modules\ng : ↑R\na : R ⟶ CommRingCat.of (Localization.Away g) := CommRingCat.ofHom (algebraMap (↑R) (Localization.Away g))\nψ : Spec (CommRingCat.of (Localization.Away g)) ⟶ Spec (CommRingCat.of ↑R) := Spec.map a\nM' : (Spec (CommRingCat.of (Localization.Away g))).Modules := M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Sites.Small | {
"line": 67,
"column": 4
} | {
"line": 67,
"column": 96
} | {
"line": 68,
"column": 4
} | [
{
"pp": "case mpr\nP : MorphismProperty Scheme\nS : Scheme\ninst✝¹ : P.IsStableUnderBaseChange\nX : Over S\n𝒰 : Cover (precoverage P) X.left\ninst✝ : Cover.Over S 𝒰\nV : Scheme\nf : V ⟶ X.left\nY : Scheme\nk : 𝒰.I₀\nh : V ⟶ 𝒰.X k\nhcomp : h ≫ 𝒰.f k = f\nthis : 𝒰.f k ≫ X.hom = 𝒰.X k ↘ S\n⊢ ∃ Y h g, 𝒰.toP... | [
"case mpr\nP : MorphismProperty Scheme\nS : Scheme\ninst✝¹ : P.IsStableUnderBaseChange\nX : Over S\n𝒰 : Cover (precoverage P) X.left\ninst✝ : Cover.Over S 𝒰\nV : Scheme\nf : V ⟶ X.left\nY : Scheme\nk : 𝒰.I₀\nh : V ⟶ 𝒰.X k\nhcomp : h ≫ 𝒰.f k = f\nthis : 𝒰.f k ≫ X.hom = 𝒰.X k ↘ S\n⊢ Over.homMk h ⋯ ≫ Hom.asOver... | refine ⟨(𝒰.X k).asOver S, Over.homMk h (by simp [← hcomp, this]), (𝒰.f k).asOver S, ⟨k⟩, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.AlgebraicGeometry.Modules.Tilde | {
"line": 818,
"column": 6
} | {
"line": 818,
"column": 84
} | {
"line": 819,
"column": 8
} | [
{
"pp": "R : CommRingCat\nM : (Spec R).Modules\ng : ↑R\na : R ⟶ CommRingCat.of (Localization.Away g) := CommRingCat.ofHom (algebraMap (↑R) (Localization.Away g))\nψ : Spec (CommRingCat.of (Localization.Away g)) ⟶ Spec (CommRingCat.of ↑R) := Spec.map a\nM' : (Spec (CommRingCat.of (Localization.Away g))).Modules ... | [
"R : CommRingCat\nM : (Spec R).Modules\ng : ↑R\na : R ⟶ CommRingCat.of (Localization.Away g) := CommRingCat.ofHom (algebraMap (↑R) (Localization.Away g))\nψ : Spec (CommRingCat.of (Localization.Away g)) ⟶ Spec (CommRingCat.of ↑R) := Spec.map a\nM' : (Spec (CommRingCat.of (Localization.Away g))).Modules := M.restric... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ValuativeCriterion | {
"line": 200,
"column": 45
} | {
"line": 200,
"column": 51
} | {
"line": 201,
"column": 2
} | [
{
"pp": "X✝ Y✝ : Scheme\nf✝ : X✝ ⟶ Y✝\nY' X X' Y : Scheme\nY'_to_Y : Y' ⟶ Y\nf : X ⟶ Y\nX'_to_X : X' ⟶ X\nf' : X' ⟶ Y'\nhP : IsPullback X'_to_X f' f Y'_to_Y\nhf : Existence f\n⊢ Existence f'",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"AlgebraicGeometry.ValuativeCommSq"
],
... | [
"X✝ Y✝ : Scheme\nf✝ : X✝ ⟶ Y✝\nY' X X' Y : Scheme\nY'_to_Y : Y' ⟶ Y\nf : X ⟶ Y\nX'_to_X : X' ⟶ X\nf' : X' ⟶ Y'\nhP : IsPullback X'_to_X f' f Y'_to_Y\nhf : Existence f\ncommSq : ValuativeCommSq f'\n⊢ ⋯.HasLift"
] | commSq | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.AlgebraicGeometry.Modules.Tilde | {
"line": 825,
"column": 4
} | {
"line": 825,
"column": 15
} | {
"line": 825,
"column": 16
} | [
{
"pp": "case h\nR : CommRingCat\nM : (Spec R).Modules\ng : ↑R\na : R ⟶ CommRingCat.of (Localization.Away g) := CommRingCat.ofHom (algebraMap (↑R) (Localization.Away g))\nψ : Spec (CommRingCat.of (Localization.Away g)) ⟶ Spec (CommRingCat.of ↑R) := Spec.map a\nM' : (Spec (CommRingCat.of (Localization.Away g))).... | [
"case h\nR : CommRingCat\nM : (Spec R).Modules\ng : ↑R\na : R ⟶ CommRingCat.of (Localization.Away g) := CommRingCat.ofHom (algebraMap (↑R) (Localization.Away g))\nψ : Spec (CommRingCat.of (Localization.Away g)) ⟶ Spec (CommRingCat.of ↑R) := Spec.map a\nM' : (Spec (CommRingCat.of (Localization.Away g))).Modules := M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ValuativeCriterion | {
"line": 298,
"column": 10
} | {
"line": 298,
"column": 21
} | {
"line": 298,
"column": 22
} | [
{
"pp": "case h₀\nX Y : Scheme\nf : X ⟶ Y\ninst✝ : IsSeparated f\nS : ValuativeCommSq f\nl₁ : Spec (CommRingCat.of S.R) ⟶ X\nhl₁ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₁ = S.i₁\nhl₁' : l₁ ≫ f = S.i₂\nl₂ : Spec (CommRingCat.of S.R) ⟶ X\nhl₂ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₂... | [
"case h₀\nX Y : Scheme\nf : X ⟶ Y\ninst✝ : IsSeparated f\nS : ValuativeCommSq f\nl₁ : Spec (CommRingCat.of S.R) ⟶ X\nhl₁ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₁ = S.i₁\nhl₁' : l₁ ≫ f = S.i₂\nl₂ : Spec (CommRingCat.of S.R) ⟶ X\nhl₂ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₂ = S.i₁\nhl₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ValuativeCriterion | {
"line": 299,
"column": 10
} | {
"line": 299,
"column": 21
} | {
"line": 299,
"column": 22
} | [
{
"pp": "case h₁\nX Y : Scheme\nf : X ⟶ Y\ninst✝ : IsSeparated f\nS : ValuativeCommSq f\nl₁ : Spec (CommRingCat.of S.R) ⟶ X\nhl₁ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₁ = S.i₁\nhl₁' : l₁ ≫ f = S.i₂\nl₂ : Spec (CommRingCat.of S.R) ⟶ X\nhl₂ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₂... | [
"case h₁\nX Y : Scheme\nf : X ⟶ Y\ninst✝ : IsSeparated f\nS : ValuativeCommSq f\nl₁ : Spec (CommRingCat.of S.R) ⟶ X\nhl₁ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₁ = S.i₁\nhl₁' : l₁ ≫ f = S.i₂\nl₂ : Spec (CommRingCat.of S.R) ⟶ X\nhl₂ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₂ = S.i₁\nhl₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ValuativeCriterion | {
"line": 300,
"column": 4
} | {
"line": 301,
"column": 29
} | {
"line": 302,
"column": 4
} | [
{
"pp": "case left\nX Y : Scheme\nf : X ⟶ Y\ninst✝ : IsSeparated f\nS : ValuativeCommSq f\nl₁ : Spec (CommRingCat.of S.R) ⟶ X\nhl₁ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₁ = S.i₁\nhl₁' : l₁ ≫ f = S.i₂\nl₂ : Spec (CommRingCat.of S.R) ⟶ X\nhl₂ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ ... | [
"case left\nX Y : Scheme\nf : X ⟶ Y\ninst✝ : IsSeparated f\nS : ValuativeCommSq f\nl₁ : Spec (CommRingCat.of S.R) ⟶ X\nhl₁ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₁ = S.i₁\nhl₁' : l₁ ≫ f = S.i₂\nl₂ : Spec (CommRingCat.of S.R) ⟶ X\nhl₂ : Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) ≫ l₂ = S.i₁\nh... | have hg : l ≫ g = Spec.map (CommRingCat.ofHom (algebraMap S.R S.K)) :=
pullback.lift_snd _ _ _ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 133,
"column": 24
} | {
"line": 133,
"column": 35
} | {
"line": 133,
"column": 36
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝² : Category.{v₀, u₀} C₀\ninst✝¹ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nX : C\ndata : F.PreOneHypercoverDenseData X\ni₁ i₂ : data.I₀\nW₀ : C₀\np₁ : W₀ ⟶ data.X i₁\np₂ : W₀ ⟶ data... | [
"C₀ : Type u₀\nC : Type u\ninst✝² : Category.{v₀, u₀} C₀\ninst✝¹ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nX : C\ndata : F.PreOneHypercoverDenseData X\ni₁ i₂ : data.I₀\nW₀ : C₀\np₁ : W₀ ⟶ data.X i₁\np₂ : W₀ ⟶ data.X i₂\nZ Z' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 133,
"column": 50
} | {
"line": 133,
"column": 61
} | {
"line": 133,
"column": 62
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝² : Category.{v₀, u₀} C₀\ninst✝¹ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nX : C\ndata : F.PreOneHypercoverDenseData X\ni₁ i₂ : data.I₀\nW₀ : C₀\np₁ : W₀ ⟶ data.X i₁\np₂ : W₀ ⟶ data... | [
"C₀ : Type u₀\nC : Type u\ninst✝² : Category.{v₀, u₀} C₀\ninst✝¹ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝ : Category.{v', u'} A\nX : C\ndata : F.PreOneHypercoverDenseData X\ni₁ i₂ : data.I₀\nW₀ : C₀\np₁ : W₀ ⟶ data.X i₁\np₂ : W₀ ⟶ data.X i₂\nZ Z' ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 220,
"column": 2
} | {
"line": 222,
"column": 85
} | {
"line": 223,
"column": 2
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝² : Category.{v₀, u₀} C₀\ninst✝¹ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\ninst✝ : IsDenseSubsite J₀ J F\nX : C\ndata : F.OneHypercoverDenseData J₀ J X\ni₁ i₂ : data.I₀\nW : C\np₁ : W ⟶ F.obj (data.X i₁)\np₂ : W ⟶ F.obj (da... | [
"C₀ : Type u₀\nC : Type u\ninst✝² : Category.{v₀, u₀} C₀\ninst✝¹ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\ninst✝ : IsDenseSubsite J₀ J F\nX : C\ndata : F.OneHypercoverDenseData J₀ J X\ni₁ i₂ : data.I₀\nW : C\np₁ : W ⟶ F.obj (data.X i₁)\np₂ : W ⟶ F.obj (data.X i₂)\nw ... | let S := Sieve.bind (Sieve.coverByImage F W).arrows
(fun Y f hf ↦ ((F.imageSieve (hf.some.map ≫ p₁) ⊓
F.imageSieve (hf.some.map ≫ p₂)).functorPushforward F).pullback hf.some.lift) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.CategoryTheory.Limits.Elements | {
"line": 104,
"column": 16
} | {
"line": 104,
"column": 27
} | {
"line": 104,
"column": 28
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nA : C ⥤ Type w\nI : Type u₁\ninst✝³ : Category.{v₁, u₁} I\ninst✝² : Small.{w, u₁} I\nF : I ⥤ A.Elements\ninst✝¹ : HasLimitsOfShape I C\ninst✝ : PreservesLimitsOfShape I A\ns : Cone F\nm : s.pt ⟶ (liftedCone F).pt\nh : ∀ (j : I), m ≫ (liftedCone F).π.app j = s.π.a... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nA : C ⥤ Type w\nI : Type u₁\ninst✝³ : Category.{v₁, u₁} I\ninst✝² : Small.{w, u₁} I\nF : I ⥤ A.Elements\ninst✝¹ : HasLimitsOfShape I C\ninst✝ : PreservesLimitsOfShape I A\ns : Cone F\nm : s.pt ⟶ (liftedCone F).pt\nh : ∀ (j : I), m ≫ (liftedCone F).π.app j = s.π.app j\ni : I\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 140,
"column": 77
} | {
"line": 140,
"column": 88
} | {
"line": 140,
"column": 89
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i ... | [
"σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i : A) (a : i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 159,
"column": 46
} | {
"line": 159,
"column": 57
} | {
"line": 159,
"column": 58
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i ... | [
"σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i : A) (a : i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 159,
"column": 46
} | {
"line": 159,
"column": 57
} | {
"line": 159,
"column": 58
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i ... | [
"σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nx : Finset A\nhx : Algebra.adjoin ↥(𝒜 0) ↑x = ⊤\nd : (i : A) → i ∈ x → ℕ\nhd : ∀ (i : A) (a : i ∈ x), d i a ≠ 0\nhxd : ∀ (i : A) (a : i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 213,
"column": 41
} | {
"line": 213,
"column": 52
} | {
"line": 213,
"column": 53
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : SetLike σ A\ninst✝⁸ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝⁷ : GradedRing 𝒜\nO : Type u_3\ninst✝⁶ : CommRing O\ninst✝⁵ : IsDomain O\ninst✝⁴ : ValuationRing O\nK : Type u_4\ninst✝³ : Field K\ninst✝² : Algebra O K\ninst✝¹ : IsFractionRing O K\... | [
"σ : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : SetLike σ A\ninst✝⁸ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝⁷ : GradedRing 𝒜\nO : Type u_3\ninst✝⁶ : CommRing O\ninst✝⁵ : IsDomain O\ninst✝⁴ : ValuationRing O\nK : Type u_4\ninst✝³ : Field K\ninst✝² : Algebra O K\ninst✝¹ : IsFractionRing O K\nφ₀ : ↥(𝒜 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 224,
"column": 35
} | {
"line": 224,
"column": 93
} | {
"line": 224,
"column": 94
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : SetLike σ A\ninst✝⁸ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝⁷ : GradedRing 𝒜\nO : Type u_3\ninst✝⁶ : CommRing O\ninst✝⁵ : IsDomain O\ninst✝⁴ : ValuationRing O\nK : Type u_4\ninst✝³ : Field K\ninst✝² : Algebra O K\ninst✝¹ : IsFractionRing O K\... | [
"σ : Type u_1\nA : Type u_2\ninst✝¹⁰ : CommRing A\ninst✝⁹ : SetLike σ A\ninst✝⁸ : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝⁷ : GradedRing 𝒜\nO : Type u_3\ninst✝⁶ : CommRing O\ninst✝⁵ : IsDomain O\ninst✝⁴ : ValuationRing O\nK : Type u_4\ninst✝³ : Field K\ninst✝² : Algebra O K\ninst✝¹ : IsFractionRing O K\nφ₀ : ↥(𝒜 0... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Presheaf | {
"line": 51,
"column": 4
} | {
"line": 51,
"column": 15
} | {
"line": 51,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : HasCoproducts A\nX : C\nM : A\nF : Cᵒᵖ ⥤ A\nf : freeYoneda X M ⟶ F\nY : Cᵒᵖ\nφ : (yoneda.obj X).obj Y\n⊢ Sigma.ι (fun i ↦ M) φ ≫\n ((fun g ↦ { app := fun Y ↦ Sigma.desc fun φ ↦ g ≫ F.map (Quiver.Hom.op φ), n... | [
"C : Type u\ninst✝² : Category.{v, u} C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : HasCoproducts A\nX : C\nM : A\nF : Cᵒᵖ ⥤ A\nf : freeYoneda X M ⟶ F\nY : Cᵒᵖ\nφ : (yoneda.obj X).obj Y\n⊢ Sigma.ι (fun i ↦ M) (𝟙 X) ≫ f.app (op X) ≫ F.map (Quiver.Hom.op φ) = Sigma.ι (fun i ↦ M) φ ≫ f.app Y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Presheaf | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 49
} | {
"line": 78,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : HasCoproducts A\nι : Type w\nS : ι → A\nhS : (ObjectProperty.ofObj S).IsSeparating\nF G : Cᵒᵖ ⥤ A\nf g : F ⟶ G\nh :\n ∀ (G_1 : Cᵒᵖ ⥤ A),\n ObjectProperty.ofObj\n (fun x ↦\n match x with\n ... | [
"C : Type u\ninst✝² : Category.{v, u} C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : HasCoproducts A\nι : Type w\nS : ι → A\nhS : (ObjectProperty.ofObj S).IsSeparating\nF G : Cᵒᵖ ⥤ A\nf g : F ⟶ G\nh :\n ∀ (G_1 : Cᵒᵖ ⥤ A),\n ObjectProperty.ofObj\n (fun x ↦\n match x with\n | (X, i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Generator.Sheaf | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 64
} | {
"line": 54,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : HasCoproducts A\ninst✝ : HasWeakSheafify J A\nι : Type w\nS : ι → A\nhS : (ObjectProperty.ofObj S).IsSeparating\nF G : Sheaf J A\nf g : F ⟶ G\nhfg :\n ∀ (G_1 : Sheaf J A),\n Objec... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : HasCoproducts A\ninst✝ : HasWeakSheafify J A\nι : Type w\nS : ι → A\nhS : (ObjectProperty.ofObj S).IsSeparating\nF G : Sheaf J A\nf g : F ⟶ G\nhfg :\n ∀ (G_1 : Sheaf J A),\n ObjectProperty.of... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.Basic | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 13
} | {
"line": 171,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nΦ : J.Point\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nf : X ⟶ Y\nx : Φ.fiber.obj X\n⊢ (ConcreteCategory.hom ((shrinkYoneda.{w, v, u}.map f).app (op X))) (shrinkYonedaObjObjEquiv.symm (𝟙 X)) =\n shrinkYonedaObjObjEquiv.symm f",
... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nΦ : J.Point\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nf : X ⟶ Y\nx : Φ.fiber.obj X\n⊢ (ConcreteCategory.hom ((shrinkYoneda.{w, v, u}.map f).app (op X))) (shrinkYonedaObjObjEquiv.symm (𝟙 X)) =\n shrinkYonedaObjObjEquiv.symm f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Point.Basic | {
"line": 171,
"column": 2
} | {
"line": 171,
"column": 75
} | {
"line": 173,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : GrothendieckTopology C\nΦ : J.Point\ninst✝ : LocallySmall.{w, v, u} C\nX Y : C\nf : X ⟶ Y\nx : Φ.fiber.obj X\n⊢ (ConcreteCategory.hom ((shrinkYoneda.{w, v, u}.map f).app (op X))) (shrinkYonedaObjObjEquiv.symm (𝟙 X)) =\n shrinkYonedaObjObjEquiv.symm f",
... | [] | simpa using shrinkYoneda_map_app_shrinkYonedaObjObjEquiv_symm.{w} (𝟙 _) f | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.CategoryTheory.Sites.Point.Basic | {
"line": 253,
"column": 4
} | {
"line": 253,
"column": 15
} | {
"line": 253,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝⁷ : Category.{v, u} C\nJ : GrothendieckTopology C\nΦ : J.Point\nA : Type u'\ninst✝⁶ : Category.{v', u'} A\ninst✝⁵ : HasColimitsOfSize.{w, w, v', u'} A\nFC : A → A → Type u_1\nCC : A → Type w'\ninst✝⁴ : (X Y : A) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝³ : ConcreteCategory A FC\nP Q : Cᵒ... | [
"C : Type u\ninst✝⁷ : Category.{v, u} C\nJ : GrothendieckTopology C\nΦ : J.Point\nA : Type u'\ninst✝⁶ : Category.{v', u'} A\ninst✝⁵ : HasColimitsOfSize.{w, w, v', u'} A\nFC : A → A → Type u_1\nCC : A → Type w'\ninst✝⁴ : (X Y : A) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝³ : ConcreteCategory A FC\nP Q : Cᵒᵖ ⥤ A\ninst✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 355,
"column": 67
} | {
"line": 355,
"column": 78
} | {
"line": 355,
"column": 79
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝³ : Category.{v₀, u₀} C₀\ninst✝² : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\nG : Cᵒᵖ ⥤ A\nhG₀ : Presh... | [
"C₀ : Type u₀\nC : Type u\ninst✝³ : Category.{v₀, u₀} C₀\ninst✝² : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\nG : Cᵒᵖ ⥤ A\nhG₀ : Presheaf.IsSheaf ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.Hypercover.ZeroFamily | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 63
} | {
"line": 94,
"column": 63
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nP : PreZeroHypercoverFamily C\nh : ∀ ⦃X Y : C⦄ (f : X ⟶ Y) [IsIso f], P.property (PreZeroHypercover.singleton f)\nS T : C\nf : S ⟶ T\nhf : IsIso f\n⊢ Presieve.singleton f ∈ P.precoverage.coverings T",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants... | [
"C : Type u\ninst✝ : Category.{v, u} C\nP : PreZeroHypercoverFamily C\nh : ∀ ⦃X Y : C⦄ (f : X ⟶ Y) [IsIso f], P.property (PreZeroHypercover.singleton f)\nS T : C\nf : S ⟶ T\nhf : IsIso f\n⊢ (PreZeroHypercover.singleton f).presieve₀ ∈ P.precoverage.coverings T"
] | ← PreZeroHypercover.presieve₀_singleton.{_, _, max u v} | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 384,
"column": 10
} | {
"line": 384,
"column": 34
} | {
"line": 384,
"column": 35
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝³ : Category.{v₀, u₀} C₀\ninst✝² : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\nG : Cᵒᵖ ⥤ A\nhG₀ : Presh... | [
"C₀ : Type u₀\nC : Type u\ninst✝³ : Category.{v₀, u₀} C₀\ninst✝² : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\nG : Cᵒᵖ ⥤ A\nhG₀ : Presheaf.IsSheaf ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 388,
"column": 8
} | {
"line": 388,
"column": 19
} | {
"line": 388,
"column": 20
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝³ : Category.{v₀, u₀} C₀\ninst✝² : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\nG : Cᵒᵖ ⥤ A\nhG₀ : Presh... | [
"C₀ : Type u₀\nC : Type u\ninst✝³ : Category.{v₀, u₀} C₀\ninst✝² : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝¹ : Category.{v', u'} A\ninst✝ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\nG : Cᵒᵖ ⥤ A\nhG₀ : Presheaf.IsSheaf ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 488,
"column": 2
} | {
"line": 488,
"column": 26
} | {
"line": 488,
"column": 27
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [
"C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize.{w, w, v', ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Sites.QuasiCompact | {
"line": 183,
"column": 67
} | {
"line": 188,
"column": 16
} | {
"line": 190,
"column": 0
} | [
{
"pp": "P : MorphismProperty Scheme\nS : Scheme\nR : Presieve S\n⊢ R ∈ (propQCPrecoverage P).coverings S ↔ ∃ 𝒰, QuasiCompactCover 𝒰.toPreZeroHypercover ∧ R = 𝒰.presieve₀",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AlgebraicGeometry.QuasiCompactCover",
"... | [] | by
rw [Precoverage.mem_iff_exists_zeroHypercover]
refine ⟨fun ⟨𝒰, h⟩ ↦ ⟨𝒰.weaken propQCPrecoverage_le_precoverage, ?_, h⟩,
fun ⟨𝒰, _, h⟩ ↦ ⟨⟨𝒰.1, ⟨by simpa, 𝒰.mem₀⟩⟩, h⟩⟩
rw [← Scheme.presieve₀_mem_qcPrecoverage_iff]
exact 𝒰.mem₀.1 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 572,
"column": 2
} | {
"line": 572,
"column": 13
} | {
"line": 572,
"column": 14
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [
"C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize.{w, w, v', ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 572,
"column": 52
} | {
"line": 572,
"column": 63
} | {
"line": 572,
"column": 64
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [
"C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize.{w, w, v', ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | {
"line": 624,
"column": 60
} | {
"line": 624,
"column": 71
} | {
"line": 624,
"column": 72
} | [
{
"pp": "C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize... | [
"C₀ : Type u₀\nC : Type u\ninst✝⁴ : Category.{v₀, u₀} C₀\ninst✝³ : Category.{v, u} C\nF : C₀ ⥤ C\nJ₀ : GrothendieckTopology C₀\nJ : GrothendieckTopology C\nA : Type u'\ninst✝² : Category.{v', u'} A\ninst✝¹ : IsDenseSubsite J₀ J F\ndata : (X : C) → F.OneHypercoverDenseData J₀ J X\ninst✝ : HasLimitsOfSize.{w, w, v', ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.Sites.SheafQuasiCompact | {
"line": 89,
"column": 6
} | {
"line": 89,
"column": 30
} | {
"line": 89,
"column": 31
} | [
{
"pp": "case refine_1\nP : MorphismProperty Scheme\ninst✝² : P.IsStableUnderBaseChange\ninst✝¹ : P.IsMultiplicative\nF : Schemeᵒᵖ ⥤ Type u_1\ninst✝ : IsZariskiLocalAtSource P\nx✝ :\n Presieve.IsSheaf zariskiTopology F ∧\n ∀ {R S : CommRingCat} (f : R ⟶ S),\n P (Spec.map f) → Surjective (Spec.map f) → ... | [
"case refine_1\nP : MorphismProperty Scheme\ninst✝² : P.IsStableUnderBaseChange\ninst✝¹ : P.IsMultiplicative\nF : Schemeᵒᵖ ⥤ Type u_1\ninst✝ : IsZariskiLocalAtSource P\nx✝ :\n Presieve.IsSheaf zariskiTopology F ∧\n ∀ {R S : CommRingCat} (f : R ⟶ S),\n P (Spec.map f) → Surjective (Spec.map f) → Presieve.IsS... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 319,
"column": 80
} | {
"line": 319,
"column": 91
} | {
"line": 319,
"column": 92
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nO : Type u_2\ncommRing✝ : CommRing O\ndomain✝ : IsDomain O\nvaluationRing✝ : ValuationRing O\nK : Type u_2\nfield✝ : Field K\... | [
"σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nO : Type u_2\ncommRing✝ : CommRing O\ndomain✝ : IsDomain O\nvaluationRing✝ : ValuationRing O\nK : Type u_2\nfield✝ : Field K\nalgebra✝ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | {
"line": 335,
"column": 72
} | {
"line": 335,
"column": 83
} | {
"line": 335,
"column": 84
} | [
{
"pp": "σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nO : Type u_2\ncommRing✝ : CommRing O\ndomain✝ : IsDomain O\nvaluationRing✝ : ValuationRing O\nK : Type u_2\nfield✝ : Field K\... | [
"σ : Type u_1\nA : Type u_2\ninst✝⁴ : CommRing A\ninst✝³ : SetLike σ A\ninst✝² : AddSubgroupClass σ A\n𝒜 : ℕ → σ\ninst✝¹ : GradedRing 𝒜\ninst✝ : Algebra.FiniteType (↥(𝒜 0)) A\nO : Type u_2\ncommRing✝ : CommRing O\ndomain✝ : IsDomain O\nvaluationRing✝ : ValuationRing O\nK : Type u_2\nfield✝ : Field K\nalgebra✝ : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.CommSq | {
"line": 146,
"column": 4
} | {
"line": 146,
"column": 20
} | {
"line": 146,
"column": 21
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\nA₀ : C\nz : A₀ ⟶ cokernel t\nhz : z ≫ cokernel.map t b l r ⋯ = 0\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₂ : A₁ ⟶ X₂\nhx₂ : π₁ ≫ z = x₂ ≫ cokernel.π t\nt... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPullback t l r b\nA₀ : C\nz : A₀ ⟶ cokernel t\nhz : z ≫ cokernel.map t b l r ⋯ = 0\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₂ : A₁ ⟶ X₂\nhx₂ : π₁ ≫ z = x₂ ≫ cokernel.π t\nthis : { X₁ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.CommSq | {
"line": 160,
"column": 4
} | {
"line": 160,
"column": 15
} | {
"line": 160,
"column": 16
} | [
{
"pp": "case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPushout t l r b\nA₀ : C\nz : A₀ ⟶ kernel b\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₁ :\n A₁ ⟶\n { X₁ := X₁, X₂ := X₂ ⊞ X₃, X₃ := ⋯.cokernelCofork.pt, f ... | [
"case refine_1\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPushout t l r b\nA₀ : C\nz : A₀ ⟶ kernel b\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₁ :\n A₁ ⟶\n { X₁ := X₁, X₂ := X₂ ⊞ X₃, X₃ := ⋯.cokernelCofork.pt, f := biprod.li... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.CommSq | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 15
} | {
"line": 162,
"column": 16
} | [
{
"pp": "case refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPushout t l r b\nA₀ : C\nz : A₀ ⟶ kernel b\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₁ :\n A₁ ⟶\n { X₁ := X₁, X₂ := X₂ ⊞ X₃, X₃ := ⋯.cokernelCofork.pt, f ... | [
"case refine_2\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : Abelian C\nX₁ X₂ X₃ X₄ : C\nt : X₁ ⟶ X₂\nl : X₁ ⟶ X₃\nr : X₂ ⟶ X₄\nb : X₃ ⟶ X₄\nsq : IsPushout t l r b\nA₀ : C\nz : A₀ ⟶ kernel b\nA₁ : C\nπ₁ : A₁ ⟶ A₀\nw✝ : Epi π₁\nx₁ :\n A₁ ⟶\n { X₁ := X₁, X₂ := X₂ ⊞ X₃, X₃ := ⋯.cokernelCofork.pt, f := biprod.li... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject | {
"line": 57,
"column": 62
} | {
"line": 57,
"column": 73
} | {
"line": 57,
"column": 74
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nF : J ⥤ MonoOver X\ninst✝ : IsFiltered J\nc : Cocone (F ⋙ MonoOver.forget X ⋙ Over.forget X)\nhc : IsColimit c\nf : c.pt ⟶ X\nhf : ∀ (j : J), c.ι.app j ≫ ... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nF : J ⥤ MonoOver X\ninst✝ : IsFiltered J\nc : Cocone (F ⋙ MonoOver.forget X ⋙ Over.forget X)\nhc : IsColimit c\nf : c.pt ⟶ X\nhf : ∀ (j : J), c.ι.app j ≫ f = (F.obj j... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject | {
"line": 77,
"column": 10
} | {
"line": 78,
"column": 35
} | {
"line": 78,
"column": 36
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\ninst✝³ : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝² : SmallCategory J\nF : J ⥤ MonoOver X\ninst✝¹ : IsFiltered J\nc : Cocone (F ⋙ MonoOver.forget X ⋙ Over.forget X)\nhc : IsColimit c\nf✝ : c.pt ⟶ X\nhf : ∀ (j : J), c.ι.app j ... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Abelian C\ninst✝³ : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝² : SmallCategory J\nF : J ⥤ MonoOver X\ninst✝¹ : IsFiltered J\nc : Cocone (F ⋙ MonoOver.forget X ⋙ Over.forget X)\nhc : IsColimit c\nf✝ : c.pt ⟶ X\nhf : ∀ (j : J), c.ι.app j ≫ f✝ = (F.ob... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ColimCoyoneda | {
"line": 138,
"column": 18
} | {
"line": 138,
"column": 70
} | {
"line": 138,
"column": 71
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nκ : Cardinal.{w}\nhκ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhXκ : HasCardinalLT (Subobject X) κ\nj... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : Abelian C\ninst✝² : IsGrothendieckAbelian.{w, v, u} C\nX : C\nJ : Type w\ninst✝¹ : SmallCategory J\nY : J ⥤ C\nc : Cocone Y\nhc : IsColimit c\nκ : Cardinal.{w}\nhκ : Fact κ.IsRegular\ninst✝ : IsCardinalFiltered J κ\nhXκ : HasCardinalLT (Subobject X) κ\nj₀ : J\ny₁ y₂... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.InitialSeg | {
"line": 29,
"column": 32
} | {
"line": 29,
"column": 43
} | {
"line": 29,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx : ↑(Iic j)\nk : α\nh : k < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ } x\n⊢ k ∈ range ⇑{ toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ }",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Rel... | [
"α : Type u_1\ninst✝ : Preorder α\ni j✝ j : α\nx : ↑(Iic j)\nk : α\nh : k < { toFun := fun j_1 ↦ ↑j_1, inj' := ⋯, map_rel_iff' := ⋯ } x\n⊢ k ≤ j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Limit | {
"line": 42,
"column": 27
} | {
"line": 42,
"column": 38
} | {
"line": 42,
"column": 39
} | [
{
"pp": "J : Type u\ninst✝ : LinearOrder J\nj : J\nm : ↑(Ici j)\nhm : Order.IsSuccLimit m\nb : J\nhb : b < ↑m\nhb' : b < j\nthis : ↑m ≤ j\nk : J\nhk : k ∈ Ici j\na✝ : ⟨k, hk⟩ ≤ m\n⊢ j ≤ ↑⟨k, hk⟩",
"ppTerm": "?m.123",
"assigned": true,
"usedConstants": [
"Set.Ici",
"PartialOrder.toPreorde... | [
"J : Type u\ninst✝ : LinearOrder J\nj : J\nm : ↑(Ici j)\nhm : Order.IsSuccLimit m\nb : J\nhb : b < ↑m\nhb' : b < j\nthis : ↑m ≤ j\nk : J\nhk : k ∈ Ici j\na✝ : ⟨k, hk⟩ ≤ m\n⊢ j ≤ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.SuccOrder | {
"line": 31,
"column": 51
} | {
"line": 31,
"column": 62
} | {
"line": 31,
"column": 63
} | [
{
"pp": "J : Type u_1\ninst✝¹ : PartialOrder J\ninst✝ : SuccOrder J\nj : J\ni : ↑(Iic j)\nhi : ¬IsMax i\n⊢ i ≠ ⊤",
"ppTerm": "?m.42",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.Elem",
"id",
"Ne",
"... | [
"J : Type u_1\ninst✝¹ : PartialOrder J\ninst✝ : SuccOrder J\nj : J\ni : ↑(Iic j)\nhi : ¬IsMax i\n⊢ ¬i = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.SuccOrder | {
"line": 46,
"column": 60
} | {
"line": 46,
"column": 71
} | {
"line": 46,
"column": 72
} | [
{
"pp": "J : Type u_1\ninst✝¹ : PartialOrder J\ninst✝ : PredOrder J\nj : J\ni : ↑(Ici j)\nhi : ¬IsMin i\n⊢ i ≠ ⊥",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"Set.Ici",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"S... | [
"J : Type u_1\ninst✝¹ : PartialOrder J\ninst✝ : PredOrder J\nj : J\ni : ↑(Ici j)\nhi : ¬IsMin i\n⊢ ¬i = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | {
"line": 85,
"column": 8
} | {
"line": 85,
"column": 32
} | {
"line": 85,
"column": 33
} | [
{
"pp": "J : Type w\ninst✝⁶ : LinearOrder J\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : HasIterationOfShape J C\ninst✝³ : SuccOrder J\ninst✝² : WellFoundedLT J\nα : Type u_1\ninst✝¹ : PartialOrder α\nf : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSeg hf\ni : J\nhi... | [
"J : Type w\ninst✝⁶ : LinearOrder J\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : HasIterationOfShape J C\ninst✝³ : SuccOrder J\ninst✝² : WellFoundedLT J\nα : Type u_1\ninst✝¹ : PartialOrder α\nf : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSeg hf\ni : J\nhi : ¬IsMax i\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Limits.Shapes.Preorder.HasIterationOfShape | {
"line": 90,
"column": 42
} | {
"line": 90,
"column": 64
} | {
"line": 90,
"column": 65
} | [
{
"pp": "J : Type w\ninst✝⁶ : LinearOrder J\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : HasIterationOfShape J C\ninst✝³ : SuccOrder J\ninst✝² : WellFoundedLT J\nα : Type u_1\ninst✝¹ : PartialOrder α\nf : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSeg hf\na : α\nhi... | [
"J : Type w\ninst✝⁶ : LinearOrder J\nC : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : HasIterationOfShape J C\ninst✝³ : SuccOrder J\ninst✝² : WellFoundedLT J\nα : Type u_1\ninst✝¹ : PartialOrder α\nf : α ≤i J\ninst✝ : Nonempty α\nhf : ¬Function.Surjective ⇑f\ns : α <i J := f.toPrincipalSeg hf\na : α\nhi : ¬IsMax (s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.AttachCells | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 24
} | {
"line": 97,
"column": 25
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nα : Type t\nA B : α → C\ng : (a : α) → A a ⟶ B a\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nc : AttachCells g f\nZ : C\nφ φ' : X₂ ⟶ Z\nh₀ : f ≫ φ = f ≫ φ'\nh : ∀ (i : c.ι), c.cell i ≫ φ = c.cell i ≫ φ'\n⊢ ∀ (i : c.ι), c.cofan₂.inj i ≫ c.g₂ ≫ φ = c.cofan₂.inj i ≫ c.g₂ ≫ φ'",
"pp... | [
"C : Type u\ninst✝ : Category.{v, u} C\nα : Type t\nA B : α → C\ng : (a : α) → A a ⟶ B a\nX₁ X₂ : C\nf : X₁ ⟶ X₂\nc : AttachCells g f\nZ : C\nφ φ' : X₂ ⟶ Z\nh₀ : f ≫ φ = f ≫ φ'\nh : ∀ (i : c.ι), c.cell i ≫ φ = c.cell i ≫ φ'\n⊢ ∀ (i : c.ι), c.cofan₂.inj i ≫ c.g₂ ≫ φ = c.cofan₂.inj i ≫ c.g₂ ≫ φ'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 56,
"column": 14
} | {
"line": 56,
"column": 56
} | {
"line": 56,
"column": 57
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\n⊢ ¬↑⟨Order.succ j, ⋯⟩ ≤ j",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"congrArg",... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\n⊢ ¬IsMax j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 92,
"column": 18
} | {
"line": 92,
"column": 60
} | {
"line": 92,
"column": 61
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\n⊢ ¬Order.succ j ≤ j",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\n⊢ ¬IsMax j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition | {
"line": 255,
"column": 4
} | {
"line": 255,
"column": 15
} | {
"line": 255,
"column": 16
} | [
{
"pp": "case isMin\nC : Type u\ninst✝⁵ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : WellFoundedLT J\nX Y : C\nf : X ⟶ Y\nhf : W.TransfiniteCompositionOfShape J f\ninst✝ : W.IsMultiplicative\nhJ :\n ∀ (J : Type w) [inst : L... | [
"case isMin\nC : Type u\ninst✝⁵ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : WellFoundedLT J\nX Y : C\nf : X ⟶ Y\nhf : W.TransfiniteCompositionOfShape J f\ninst✝ : W.IsMultiplicative\nhJ :\n ∀ (J : Type w) [inst : LinearOrder J... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 102,
"column": 20
} | {
"line": 102,
"column": 62
} | {
"line": 102,
"column": 63
} | [
{
"pp": "C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\nhi : Order.succ j ≤ Order.succ j\nh₁ : ¬Order.succ j ≤ j\n⊢ ¬Order.succ j ≤ j",
"ppTerm": "?m.110",
"assigned": true,
... | [
"C : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\nhi : Order.succ j ≤ Order.succ j\nh₁ : ¬Order.succ j ≤ j\n⊢ ¬IsMax j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | {
"line": 109,
"column": 2
} | {
"line": 111,
"column": 19
} | {
"line": 112,
"column": 2
} | [
{
"pp": "case pos\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\ni₁ i₂ i₃ : J\nh₁₂ : i₁ ≤ i₂\nh₂₃ : i₂ ≤ i₃\nh : i₃ ≤ Order.succ j\nh₁ : i₃ ≤ j\n⊢ map hj F τ i₁ i₃ ⋯ h = map hj F τ i... | [
"case neg\nC : Type u_1\ninst✝² : Category.{v_1, u_1} C\nJ : Type u\ninst✝¹ : LinearOrder J\ninst✝ : SuccOrder J\nj : J\nhj : ¬IsMax j\nF : ↑(Set.Iic j) ⥤ C\nX : C\nτ : F.obj ⟨j, ⋯⟩ ⟶ X\ni₁ i₂ i₃ : J\nh₁₂ : i₁ ≤ i₂\nh₂₃ : i₂ ≤ i₃\nh : i₃ ≤ Order.succ j\nh₁ : ¬i₃ ≤ j\n⊢ map hj F τ i₁ i₃ ⋯ h = map hj F τ i₁ i₂ h₁₂ ⋯ ... | · rw [map_eq hj F τ i₁ i₂ _ (h₂₃.trans h₁), map_eq hj F τ i₂ i₃ _ h₁,
map_eq hj F τ i₁ i₃ _ h₁, assoc, assoc, Iso.inv_hom_id_assoc, ← Functor.map_comp_assoc,
homOfLE_comp] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition | {
"line": 386,
"column": 2
} | {
"line": 387,
"column": 85
} | {
"line": 389,
"column": 0
} | [
{
"pp": "case mpr\nC : Type u\ninst✝¹ : Category.{v, u} C\nP Q : MorphismProperty C\ninst✝ : Q.IsStableUnderTransfiniteComposition\n⊢ P ≤ Q → transfiniteCompositions.{w, v, u} P ≤ Q",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismProperty",
"CategoryTheor... | [] | · intro h
exact (transfiniteCompositions_monotone.{w} h).trans Q.transfiniteCompositions_le | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone | {
"line": 59,
"column": 45
} | {
"line": 59,
"column": 56
} | {
"line": 59,
"column": 57
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : Type u\ninst✝ : LinearOrder J\nj : J\nF : ↑(Set.Iio j) ⥤ C\nc : Cocone F\ni₁ i₂ : J\nhi : i₁ ≤ i₂\nhi₂ : i₂ ≤ j\nh₂ : ¬i₂ < j\n⊢ j ≤ i₂",
"ppTerm": "?m.174",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : Type u\ninst✝ : LinearOrder J\nj : J\nF : ↑(Set.Iio j) ⥤ C\nc : Cocone F\ni₁ i₂ : J\nhi : i₁ ≤ i₂\nhi₂ : i₂ ≤ j\nh₂ : ¬i₂ < j\n⊢ j ≤ i₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.FunctorOfCocone | {
"line": 63,
"column": 58
} | {
"line": 63,
"column": 69
} | {
"line": 63,
"column": 70
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : Type u\ninst✝ : LinearOrder J\nj : J\nF : ↑(Set.Iio j) ⥤ C\nc : Cocone F\ni₁ i₂ : J\nhi : i₁ ≤ i₂\nhi₂ : i₂ ≤ j\nh₂ : ¬i₂ < j\nh₂' : i₂ = j\nh₁ : ¬i₁ < j\n⊢ j ≤ i₁",
"ppTerm": "?m.194",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nJ : Type u\ninst✝ : LinearOrder J\nj : J\nF : ↑(Set.Iio j) ⥤ C\nc : Cocone F\ni₁ i₂ : J\nhi : i₁ ≤ i₂\nhi₂ : i₂ ≤ j\nh₂ : ¬i₂ < j\nh₂' : i₂ = j\nh₁ : ¬i₁ < j\n⊢ j ≤ i₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 97,
"column": 52
} | {
"line": 97,
"column": 63
} | {
"line": 97,
"column": 64
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : PartialOrder J\nj : J\nF : ↑(Set.Iic j) ⥤ C\ni : J\nhi : i ≤ j\nk₁ k₂ : ↑(Set.Iio i)\nφ : k₁ ⟶ k₂\n⊢ ⋯.functor.obj k₁ ≤ ⋯.functor.obj k₂",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : PartialOrder J\nj : J\nF : ↑(Set.Iic j) ⥤ C\ni : J\nhi : i ≤ j\nk₁ k₂ : ↑(Set.Iio i)\nφ : k₁ ⟶ k₂\n⊢ k₁ ≤ k₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 116,
"column": 52
} | {
"line": 116,
"column": 63
} | {
"line": 116,
"column": 64
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : PartialOrder J\nj : J\nF : ↑(Set.Iic j) ⥤ C\ni : J\nhi : i ≤ j\nk₁ k₂ : ↑(Set.Iic i)\nφ : k₁ ⟶ k₂\n⊢ ⋯.functor.obj k₁ ≤ ⋯.functor.obj k₂",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nJ : Type w\ninst✝ : PartialOrder J\nj : J\nF : ↑(Set.Iic j) ⥤ C\ni : J\nhi : i ≤ j\nk₁ k₂ : ↑(Set.Iic i)\nφ : k₁ ⟶ k₂\n⊢ k₁ ≤ k₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 375,
"column": 32
} | {
"line": 375,
"column": 43
} | {
"line": 375,
"column": 44
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj : J\nh : IsMin ⊥\niter₁ iter₂ : Φ.Iteration ⊥\nk₁ k₂ : J\nh₁₂ : k₁ ≤ k₂\nh₂ : k₂ ≤ ⊥\n⊢ k₂ = ⊥",
"ppT... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj : J\nh : IsMin ⊥\niter₁ iter₂ : Φ.Iteration ⊥\nk₁ k₂ : J\nh₁₂ : k₁ ≤ k₂\nh₂ : k₂ ≤ ⊥\n⊢ k₂ = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Construction | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 13
} | {
"line": 129,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝¹ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝ : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\nx : FunctorObjIndex f πX\n⊢ f x.i ≫ Sigma.ι (functorObjTgtFamily... | [
"C : Type u\ninst✝² : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝¹ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝ : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\nx : FunctorObjIndex f πX\n⊢ f x.i ≫ Sigma.ι (functorObjTgtFamily f πX) x ≫ ρ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 376,
"column": 32
} | {
"line": 376,
"column": 43
} | {
"line": 376,
"column": 44
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj : J\nh : IsMin ⊥\niter₁ iter₂ : Φ.Iteration ⊥\nk₁ : J\nh₁₂ : k₁ ≤ ⊥\nh₂ : ⊥ ≤ ⊥\n⊢ k₁ = ⊥",
"ppTerm":... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj : J\nh : IsMin ⊥\niter₁ iter₂ : Φ.Iteration ⊥\nk₁ : J\nh₁₂ : k₁ ≤ ⊥\nh₂ : ⊥ ≤ ⊥\n⊢ k₁ = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | {
"line": 45,
"column": 46
} | {
"line": 45,
"column": 57
} | {
"line": 45,
"column": 58
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\nx✝ : J\nh₁ : Order.IsSuccLimit x✝\nh₂ : x✝ ≤ ⊥\n⊢ IsMin x✝",
"ppTerm": "?m.53",
"assigned": t... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\nx✝ : J\nh₁ : Order.IsSuccLimit x✝\nh₂ : x✝ ≤ ⊥\n⊢ x✝ = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | {
"line": 62,
"column": 8
} | {
"line": 62,
"column": 32
} | {
"line": 62,
"column": 33
} | [
{
"pp": "case inl\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\nj : J\nhj : ¬IsMax j\niter : Φ.Iteration j\ni : J\nhi₁✝¹ : i < Order.succ j\nhi₁✝ : i ≤ j\n... | [
"case inl\nC : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\nj : J\nhj : ¬IsMax j\niter : Φ.Iteration j\ni : J\nhi₁✝¹ : i < Order.succ j\nhi₁✝ : i ≤ j\nhi₁ : i < j\... | ← arrowSucc_def _ _ hi₁, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.SmallObject.Construction | {
"line": 179,
"column": 31
} | {
"line": 179,
"column": 46
} | {
"line": 179,
"column": 47
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝³ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝² : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\ninst✝¹ : LocallySmall.{t, v, u} C\ninst✝ : Small.{t, w} I\nφ : ... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝³ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝² : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\ninst✝¹ : LocallySmall.{t, v, u} C\ninst✝ : Small.{t, w} I\nφ : FunctorObjIn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Construction | {
"line": 180,
"column": 4
} | {
"line": 180,
"column": 31
} | {
"line": 180,
"column": 32
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝³ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝² : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\ninst✝¹ : LocallySmall.{t, v, u} C\ninst✝ : Small.{t, w} I\nφ : ... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nI : Type w\nA B : I → C\nf : (i : I) → A i ⟶ B i\nS X : C\nπX : X ⟶ S\ninst✝³ : HasColimitsOfShape (Discrete (FunctorObjIndex f πX)) C\ninst✝² : HasPushout (functorObjTop f πX) (functorObjLeft f πX)\ninst✝¹ : LocallySmall.{t, v, u} C\ninst✝ : Small.{t, w} I\nφ : FunctorObjIn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 405,
"column": 47
} | {
"line": 405,
"column": 58
} | {
"line": 405,
"column": 59
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj✝ j : J\nh₁ : Order.IsSuccLimit j\nh₂ : ∀ b < j, ∀ (iter₁ iter₂ : Φ.Iteration b), iter₁.F = iter₂.F\niter₁... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj✝ j : J\nh₁ : Order.IsSuccLimit j\nh₂ : ∀ b < j, ∀ (iter₁ iter₂ : Φ.Iteration b), iter₁.F = iter₂.F\niter₁ iter₂ : Φ.I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 411,
"column": 53
} | {
"line": 411,
"column": 64
} | {
"line": 411,
"column": 65
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj✝ j : J\nh₁ : Order.IsSuccLimit j\nh₂ : ∀ b < j, ∀ (iter₁ iter₂ : Φ.Iteration b), iter₁.F = iter₂.F\niter₁... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj✝ j : J\nh₁ : Order.IsSuccLimit j\nh₂ : ∀ b < j, ∀ (iter₁ iter₂ : Φ.Iteration b), iter₁.F = iter₂.F\niter₁ iter₂ : Φ.I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Basic | {
"line": 420,
"column": 48
} | {
"line": 420,
"column": 59
} | {
"line": 420,
"column": 60
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj₁ j₂ : J\niter₁ : Φ.Iteration j₁\niter₂ : Φ.Iteration j₂\nk : J\nh₁ : k ≤ j₁\nh₂ : k ≤ j₂\nthis :\n ∀ {j₁... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\nΦ : SuccStruct C\ninst✝⁴ : LinearOrder J\ninst✝³ : SuccOrder J\ninst✝² : OrderBot J\ninst✝¹ : HasIterationOfShape J C\ninst✝ : WellFoundedLT J\nj₁ j₂ : J\niter₁ : Φ.Iteration j₁\niter₂ : Φ.Iteration j₂\nk : J\nh₁ : k ≤ j₁\nh₂ : k ≤ j₂\nthis :\n ∀ {j₁ j₂ : J} (it... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.Iteration.Nonempty | {
"line": 156,
"column": 31
} | {
"line": 156,
"column": 42
} | {
"line": 156,
"column": 43
} | [
{
"pp": "C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\ni : J\nhi : IsMin i\n⊢ i = ⊥",
"ppTerm": "?m.39",
"assigned": false,
"usedConstants": [],... | [
"C : Type u_1\ninst✝⁵ : Category.{v_1, u_1} C\nΦ : SuccStruct C\nJ : Type u\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\ninst✝² : SuccOrder J\ninst✝¹ : WellFoundedLT J\ninst✝ : HasIterationOfShape J C\ni : J\nhi : IsMin i\n⊢ i = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.MorphismProperty.IsSmall | {
"line": 45,
"column": 2
} | {
"line": 45,
"column": 32
} | {
"line": 47,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nW : MorphismProperty C\nι : Type t\ninst✝ : Small.{w, t} ι\nA B : ι → C\nf : (i : ι) → A i ⟶ B i\nφ : ι → ↑(ofHoms f).toSet := fun i ↦ ⟨Arrow.mk (f i), ⋯⟩\nhφ : Function.Surjective φ\n⊢ IsSmall.{w, v, u} (ofHoms f)",
"ppTerm": "?m.38",
"assigned": true,
... | [] | exact ⟨small_of_surjective hφ⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 136,
"column": 29
} | {
"line": 136,
"column": 40
} | {
"line": 136,
"column": 41
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : IsMin i\n⊢ i = ⊥",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"us... | [
"J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : IsMin i\n⊢ i = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 87,
"column": 4
} | {
"line": 87,
"column": 43
} | {
"line": 87,
"column": 44
} | [
{
"pp": "case isMin\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\... | [
"case isMin\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\nZ : C\nφ₁ φ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 90,
"column": 6
} | {
"line": 90,
"column": 17
} | {
"line": 90,
"column": 18
} | [
{
"pp": "case succ.h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell ... | [
"case succ.h₀\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\nZ : C\nφ₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 92,
"column": 6
} | {
"line": 92,
"column": 48
} | {
"line": 92,
"column": 49
} | [
{
"pp": "case succ.h\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f... | [
"case succ.h\nC : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\nZ : C\nφ₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.AlgebraicTopology.RelativeCellComplex.Basic | {
"line": 95,
"column": 24
} | {
"line": 95,
"column": 35
} | {
"line": 95,
"column": 36
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\nZ : C\nφ₁ φ... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nJ : Type w'\ninst✝³ : LinearOrder J\ninst✝² : OrderBot J\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nα : J → Type t\nA B : (j : J) → α j → C\nbasicCell : (j : J) → (i : α j) → A j i ⟶ B j i\nX Y : C\nf : X ⟶ Y\nc : RelativeCellComplex basicCell f\nZ : C\nφ₁ φ₂ : Y ⟶ Z\nh... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 175,
"column": 29
} | {
"line": 175,
"column": 40
} | {
"line": 175,
"column": 41
} | [
{
"pp": "J : Type u\ninst✝² : LinearOrder J\ninst✝¹ : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝ : OrderBot J\nval₀ : F.obj (op ⊥)\ni : J\nhi : Order.IsSuccLimit i\nhij : i ≤ ⊥\n⊢ i = ⊥",
"ppTerm": "?m.47",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"J : Type u\ninst✝² : LinearOrder J\ninst✝¹ : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝ : OrderBot J\nval₀ : F.obj (op ⊥)\ni : J\nhi : Order.IsSuccLimit i\nhij : i ≤ ⊥\n⊢ i = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 15
} | {
"line": 176,
"column": 16
} | [
{
"pp": "J : Type u\ninst✝² : LinearOrder J\ninst✝¹ : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝ : OrderBot J\nval₀ : F.obj (op ⊥)\nhi : Order.IsSuccLimit ⊥\nhij : ⊥ ≤ ⊥\n⊢ (ConcreteCategory.hom (F.map (homOfLE hij).op)) val₀ =\n d.lift ⊥ hi\n ⟨fun x ↦\n match x with\n ... | [
"J : Type u\ninst✝² : LinearOrder J\ninst✝¹ : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝ : OrderBot J\nval₀ : F.obj (op ⊥)\nhi : Order.IsSuccLimit ⊥\nhij : ⊥ ≤ ⊥\n⊢ val₀ = d.lift ⊥ hi ⟨fun x ↦ (ConcreteCategory.hom (F.map (homOfLE ⋯).op)) val₀, ⋯⟩"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 182,
"column": 4
} | {
"line": 182,
"column": 15
} | {
"line": 182,
"column": 16
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type w\ninst✝² : LinearOrder J\ninst✝¹ : OrderBot J\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\np : X ⟶ Y\nf : F.obj ⊥ ⟶ X\ng : c.pt ⟶ Y\ninst✝ : F.IsWellOrderContinuous\nj : J\nhj : Order.IsSuccLimit j\ns : ↑(⋯.functor.op ⋙ sqFunctor c p f g).sectio... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nJ : Type w\ninst✝² : LinearOrder J\ninst✝¹ : OrderBot J\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\np : X ⟶ Y\nf : F.obj ⊥ ⟶ X\ng : c.pt ⟶ Y\ninst✝ : F.IsWellOrderContinuous\nj : J\nhj : Order.IsSuccLimit j\ns : ↑(⋯.functor.op ⋙ sqFunctor c p f g).sections\nh : ⊥ < ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 233,
"column": 30
} | {
"line": 233,
"column": 41
} | {
"line": 233,
"column": 42
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\np : X ⟶ Y\nf : F.obj ⊥ ⟶ X\ng✝ : c.pt ⟶ Y\ninst✝² : F.IsWellOrderContinuous\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nhF : ∀ (j : J), ¬IsMax j → Has... | [
"C : Type u\ninst✝⁵ : Category.{v, u} C\nJ : Type w\ninst✝⁴ : LinearOrder J\ninst✝³ : OrderBot J\nF : J ⥤ C\nc : Cocone F\nhc : IsColimit c\nX Y : C\np : X ⟶ Y\nf : F.obj ⊥ ⟶ X\ng✝ : c.pt ⟶ Y\ninst✝² : F.IsWellOrderContinuous\ninst✝¹ : SuccOrder J\ninst✝ : WellFoundedLT J\nhF : ∀ (j : J), ¬IsMax j → HasLiftingPrope... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 283,
"column": 2
} | {
"line": 283,
"column": 13
} | {
"line": 283,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\n⊢ (coproducts.{t, v, u} W).pushouts.transfiniteCompositionsOfShape J ≤ W.rlp.llp",
"ppTerm": "?m.21",
"assigned": false,
"u... | [
"C : Type u\ninst✝⁴ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type w\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\ninst✝¹ : OrderBot J\ninst✝ : WellFoundedLT J\n⊢ (coproducts.{t, v, u} W).pushouts.transfiniteCompositionsOfShape J ≤ W.rlp.llp"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 13
} | {
"line": 299,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nW : MorphismProperty C\n⊢ transfiniteCompositions.{w, v, u} (coproducts.{w, v, u} W).pushouts ≤ W.rlp.llp",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismP... | [
"C : Type u\ninst✝ : Category.{v, u} C\nW : MorphismProperty C\n⊢ W ≤ W.rlp.llp"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 221,
"column": 31
} | {
"line": 221,
"column": 62
} | {
"line": 221,
"column": 63
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ⊥ < j",
"ppTerm": "?m.112",
"assigned": true,... | [
"J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ¬j = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 222,
"column": 4
} | {
"line": 222,
"column": 15
} | {
"line": 222,
"column": 16
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ↑⟨fun x ↦\n match x with\n | op ⟨i,... | [
"J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ (e ⊥ ⋯).val = val₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 222,
"column": 25
} | {
"line": 222,
"column": 56
} | {
"line": 222,
"column": 57
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ⊥ < j",
"ppTerm": "?m.130",
"assigned": true,... | [
"J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\nj : J\nhj : Order.IsSuccLimit j\ne : (i : J) → i < j → d.Extension val₀ i\n⊢ ¬j = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | {
"line": 245,
"column": 2
} | {
"line": 245,
"column": 33
} | {
"line": 246,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nj : κ.ord.ToType\n⊢ (succStruct I κ).prop ((iterationFunctor I κ).map (homOfLE ⋯))",
"ppTerm": "?m.34",
"ass... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nj : κ.ord.ToType\nthis : HasIterationOfShape κ.ord.ToType C\n⊢ (succStruct I κ).prop ((iterationFunctor I κ).map (homOfLE ⋯))"
] | have := hasIterationOfShape I κ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | {
"line": 318,
"column": 2
} | {
"line": 318,
"column": 33
} | {
"line": 319,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nX Y : C\nf : X ⟶ Y\n⊢ RelativeCellComplex (fun x ↦ I.homFamily) (ιObj I κ f)",
"ppTerm": "?m.30",
"assigned"... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nI : MorphismProperty C\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : OrderBot κ.ord.ToType\ninst✝ : I.IsCardinalForSmallObjectArgument κ\nX Y : C\nf : X ⟶ Y\nthis : HasIterationOfShape κ.ord.ToType C\n⊢ RelativeCellComplex (fun x ↦ I.homFamily) (ιObj I κ f)"
] | have := hasIterationOfShape I κ | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | {
"line": 256,
"column": 29
} | {
"line": 256,
"column": 40
} | {
"line": 256,
"column": 41
} | [
{
"pp": "J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : IsMin i\n⊢ i = ⊥",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"us... | [
"J : Type u\ninst✝³ : LinearOrder J\ninst✝² : SuccOrder J\nF : Jᵒᵖ ⥤ Type v\nd : F.WellOrderInductionData\ninst✝¹ : OrderBot J\nval₀ : F.obj (op ⊥)\ninst✝ : WellFoundedLT J\ni : J\nhi : IsMin i\n⊢ i = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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