module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 371
values | kind stringclasses 375
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.RingTheory.Jacobson.Radical | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 22
} | {
"line": 159,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Ring R\nI : Ideal R\ninst✝ : I.IsTwoSided\nf : R ⧸ I →ₛₗ[Ideal.Quotient.mk I] R ⧸ I := { toAddHom := AddHom.id (R ⧸ I), map_smul' := ⋯ }\n⊢ ↑(Submodule.map f (Module.jacobson R (R ⧸ I))) = ↑(Module.jacobson R (R ⧸ I))",
"ppTerm": "?m.75",
"assigned": true,
"usedConsta... | [] | apply Set.image_id | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Jacobson.Radical | {
"line": 158,
"column": 4
} | {
"line": 158,
"column": 22
} | {
"line": 159,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝¹ : Ring R\nI : Ideal R\ninst✝ : I.IsTwoSided\nf : R ⧸ I →ₛₗ[Ideal.Quotient.mk I] R ⧸ I := { toAddHom := AddHom.id (R ⧸ I), map_smul' := ⋯ }\n⊢ ↑(Submodule.map f (Module.jacobson R (R ⧸ I))) = ↑(Module.jacobson R (R ⧸ I))",
"ppTerm": "?m.75",
"assigned": true,
"usedConsta... | [] | apply Set.image_id | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Jacobson.Ideal | {
"line": 125,
"column": 6
} | {
"line": 125,
"column": 14
} | {
"line": 125,
"column": 15
} | [
{
"pp": "case h\nR : Type u\ninst✝ : Ring R\nI : Ideal R\nr : R\nh : r ∈ I.jacobson\ns : R\nhs : s * 1 * r + s - 1 ∈ I\n⊢ s * (r + 1) - 1 ∈ I",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"Semiring.toModule",
"HMul.hMul",
"... | [
"case h\nR : Type u\ninst✝ : Ring R\nI : Ideal R\nr : R\nh : r ∈ I.jacobson\ns : R\nhs : s * 1 * r + s - 1 ∈ I\n⊢ s * r + s * 1 - 1 ∈ I"
] | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.Localization.Away.Basic | {
"line": 444,
"column": 2
} | {
"line": 446,
"column": 86
} | {
"line": 448,
"column": 0
} | [
{
"pp": "case refine_2\nS : Type u_4\nT : Type u_5\ninst✝⁶ : CommRing S\ninst✝⁵ : CommRing T\ninst✝⁴ : Algebra S T\nR : Type u_6\ninst✝³ : CommRing R\ninst✝² : Algebra R S\ninst✝¹ : Algebra R T\ninst✝ : IsScalarTower R S T\nh₁ : Function.Surjective ⇑(algebraMap S T)\nh₂ : Function.Surjective ⇑(algebraMap R S)\n... | [] | · rw [← (RingHom.ker (algebraMap S T)).map_comap_of_surjective _ h₂, ← map_pow,
← Ideal.map_pointwise_smul, RingHom.comap_ker, ← IsScalarTower.algebraMap_eq]
rwa [RingHom.ker_eq_comap_bot (algebraMap R S), ← Ideal.map_le_iff_le_comap] at hn | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.RingTheory.Coalgebra.CoassocSimps | {
"line": 92,
"column": 30
} | {
"line": 92,
"column": 52
} | {
"line": 92,
"column": 52
} | [
{
"pp": "R : Type u_1\nM : Type u_3\nN : Type u_4\nP : Type u_5\nM' : Type u_6\nN' : Type u_7\nP' : Type u_8\nM₁ : Type u_11\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : Module R N\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\ninst✝⁷ : AddCom... | [
"R : Type u_1\nM : Type u_3\nN : Type u_4\nP : Type u_5\nM' : Type u_6\nN' : Type u_7\nP' : Type u_8\nM₁ : Type u_11\ninst✝¹⁴ : CommSemiring R\ninst✝¹³ : AddCommMonoid M\ninst✝¹² : Module R M\ninst✝¹¹ : AddCommMonoid N\ninst✝¹⁰ : Module R N\ninst✝⁹ : AddCommMonoid P\ninst✝⁸ : Module R P\ninst✝⁷ : AddCommMonoid M'\n... | TensorProduct.map_comp | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Shapes.StrictInitial | {
"line": 253,
"column": 63
} | {
"line": 253,
"column": 91
} | {
"line": 253,
"column": 91
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nI : C\nh : ∀ (A : C) (f : I ⟶ A), IsIso f\nI' A : C\nf : I' ⟶ A\nhI' : IsTerminal I'\nthis : IsIso (hI'.from I ≫ f)\n⊢ (inv (hI'.from I ≫ f) ≫ hI'.from I) ≫ f = 𝟙 A",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Categ... | [] | rw [assoc, IsIso.inv_hom_id] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Limits.Shapes.StrictInitial | {
"line": 253,
"column": 63
} | {
"line": 253,
"column": 91
} | {
"line": 253,
"column": 91
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nI : C\nh : ∀ (A : C) (f : I ⟶ A), IsIso f\nI' A : C\nf : I' ⟶ A\nhI' : IsTerminal I'\nthis : IsIso (hI'.from I ≫ f)\n⊢ (inv (hI'.from I ≫ f) ≫ hI'.from I) ≫ f = 𝟙 A",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Categ... | [] | rw [assoc, IsIso.inv_hom_id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Shapes.StrictInitial | {
"line": 253,
"column": 63
} | {
"line": 253,
"column": 91
} | {
"line": 253,
"column": 91
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\nI : C\nh : ∀ (A : C) (f : I ⟶ A), IsIso f\nI' A : C\nf : I' ⟶ A\nhI' : IsTerminal I'\nthis : IsIso (hI'.from I ≫ f)\n⊢ (inv (hI'.from I ≫ f) ≫ hI'.from I) ≫ f = 𝟙 A",
"ppTerm": "?m.61",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Categ... | [] | rw [assoc, IsIso.inv_hom_id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.RingTheory.Localization.Integer | {
"line": 83,
"column": 2
} | {
"line": 84,
"column": 32
} | {
"line": 86,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : IsLocalization M S\na : S\n⊢ ∃ b, IsInteger R (↑b • a)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"IsLocalization.IsInteger",
"Eq.mpr",
... | [] | simp_rw [Algebra.smul_def, mul_comm _ a]
apply exists_integer_multiple' | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Localization.Integer | {
"line": 83,
"column": 2
} | {
"line": 84,
"column": 32
} | {
"line": 86,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝³ : CommSemiring R\nM : Submonoid R\nS : Type u_2\ninst✝² : CommSemiring S\ninst✝¹ : Algebra R S\ninst✝ : IsLocalization M S\na : S\n⊢ ∃ b, IsInteger R (↑b • a)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"IsLocalization.IsInteger",
"Eq.mpr",
... | [] | simp_rw [Algebra.smul_def, mul_comm _ a]
apply exists_integer_multiple' | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 118,
"column": 16
} | {
"line": 120,
"column": 94
} | {
"line": 122,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝ : Category.{v₂, u₂} J\nF : J ⥤ Cᵒᵖ\nc : Cocone F.leftOp\nhc : IsColimit c\ns : Cone F\nm : s.pt ⟶ (coneOfCoconeLeftOp c).pt\nw : ∀ (j : J), m ≫ (coneOfCoconeLeftOp c).π.app j = s.π.app j\n⊢ m = (hc.desc (coconeLeftOpOfCone s)).op",
"ppTe... | [] | by
refine Quiver.Hom.unop_inj (hc.hom_ext fun j => Quiver.Hom.op_inj ?_)
simpa only [Quiver.Hom.unop_op, IsColimit.fac, coneOfCoconeLeftOp_π_app] using! w (unop j) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 573,
"column": 2
} | {
"line": 573,
"column": 9
} | {
"line": 574,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePullbacks C\n⊢ HasWidePushouts Cᵒᵖ",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [
{
"new": true,
"index": 0,
... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePullbacks C\nι : Type w\n⊢ HasColimitsOfShape (WidePushoutShape ι) Cᵒᵖ"
] | intro ι | Lean.Elab.Tactic.evalIntro | null |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 573,
"column": 2
} | {
"line": 573,
"column": 9
} | {
"line": 574,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePullbacks C\n⊢ HasWidePushouts Cᵒᵖ",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [
{
"new": true,
"index": 0,
... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePullbacks C\nι : Type w\n⊢ HasColimitsOfShape (WidePushoutShape ι) Cᵒᵖ"
] | intro ι | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 573,
"column": 2
} | {
"line": 575,
"column": 72
} | {
"line": 577,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePullbacks C\n⊢ HasWidePushouts Cᵒᵖ",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"CategoryTheory.Limits.HasColimitsOfShape",
"congrAr... | [] | intro ι
rw [hasColimitsOfShape_opposite_iff]
exact hasLimitsOfShape_of_equivalence (widePushoutShapeOpEquiv _).symm | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 573,
"column": 2
} | {
"line": 575,
"column": 72
} | {
"line": 577,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePullbacks C\n⊢ HasWidePushouts Cᵒᵖ",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"CategoryTheory.Limits.HasColimitsOfShape",
"congrAr... | [] | intro ι
rw [hasColimitsOfShape_opposite_iff]
exact hasLimitsOfShape_of_equivalence (widePushoutShapeOpEquiv _).symm | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 9
} | {
"line": 579,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePushouts C\n⊢ HasWidePullbacks Cᵒᵖ",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [
{
"new": true,
"index": 0,
... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePushouts C\nι : Type w\n⊢ HasLimitsOfShape (WidePullbackShape ι) Cᵒᵖ"
] | intro ι | Lean.Elab.Tactic.evalIntro | null |
Mathlib.CategoryTheory.Limits.Opposites | {
"line": 578,
"column": 2
} | {
"line": 578,
"column": 9
} | {
"line": 579,
"column": 2
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePushouts C\n⊢ HasWidePullbacks Cᵒᵖ",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [
{
"new": true,
"index": 0,
... | [
"C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\ninst✝ : HasWidePushouts C\nι : Type w\n⊢ HasLimitsOfShape (WidePullbackShape ι) Cᵒᵖ"
] | intro ι | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 47
} | {
"line": 155,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g)\n⊢ (iso G f g).inv ≫ G.map (pullback.fst f g) = pullback.fst (G.map... | [] | simp [PreservesPullback.iso, Iso.inv_comp_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 47
} | {
"line": 155,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g)\n⊢ (iso G f g).inv ≫ G.map (pullback.fst f g) = pullback.fst (G.map... | [] | simp [PreservesPullback.iso, Iso.inv_comp_eq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | {
"line": 153,
"column": 2
} | {
"line": 153,
"column": 47
} | {
"line": 155,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g)\n⊢ (iso G f g).inv ≫ G.map (pullback.fst f g) = pullback.fst (G.map... | [] | simp [PreservesPullback.iso, Iso.inv_comp_eq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 47
} | {
"line": 161,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g)\n⊢ (iso G f g).inv ≫ G.map (pullback.snd f g) = pullback.snd (G.map... | [] | simp [PreservesPullback.iso, Iso.inv_comp_eq] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 47
} | {
"line": 161,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g)\n⊢ (iso G f g).inv ≫ G.map (pullback.snd f g) = pullback.snd (G.map... | [] | simp [PreservesPullback.iso, Iso.inv_comp_eq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | {
"line": 159,
"column": 2
} | {
"line": 159,
"column": 47
} | {
"line": 161,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝² : PreservesLimit (cospan f g) G\ninst✝¹ : HasPullback f g\ninst✝ : HasPullback (G.map f) (G.map g)\n⊢ (iso G f g).inv ≫ G.map (pullback.snd f g) = pullback.snd (G.map... | [] | simp [PreservesPullback.iso, Iso.inv_comp_eq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 333,
"column": 45
} | {
"line": 333,
"column": 82
} | {
"line": 333,
"column": 82
} | [
{
"pp": "case h\nR : Type u\ninst✝⁵ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nT : Type u_1\ninst✝² : CommSemiring T\ninst✝¹ : Algebra R T\ninst✝ : IsLocalization S T\nx y : T\nm : M\ns : ↥S\n⊢ (IsLocalization.mk' T (IsLocalization.sec S x).1 (IsLocalization.se... | [
"case h\nR : Type u\ninst✝⁵ : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝⁴ : AddCommMonoid M\ninst✝³ : Module R M\nT : Type u_1\ninst✝² : CommSemiring T\ninst✝¹ : Algebra R T\ninst✝ : IsLocalization S T\nx y : T\nm : M\ns : ↥S\n⊢ (IsLocalization.mk' T (IsLocalization.sec S x).1 (IsLocalization.sec S x).2 *\n... | ← IsLocalization.mk'_sec (M := S) T y | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Monad.Basic | {
"line": 338,
"column": 4
} | {
"line": 338,
"column": 20
} | {
"line": 340,
"column": 0
} | [
{
"pp": "case e_a\nC : Type u₁\ninst✝ : Category.{v₁, u₁} C\nT✝ : Monad C\nG : Comonad C\nF : C ⥤ C\nT : Monad C\ni : T.toFunctor ≅ F\nX : C\n⊢ (T.map (T.map (i.inv.app X)) ≫ T.map (T.μ.app X)) ≫ T.μ.app X =\n ((T.toFunctor ⋙ T.toFunctor).map (i.inv.app X) ≫ T.μ.app (T.obj X)) ≫ T.μ.app X",
"ppTerm": "?e... | [] | simp [T.assoc X] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 395,
"column": 19
} | {
"line": 395,
"column": 34
} | {
"line": 395,
"column": 34
} | [
{
"pp": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns s' : ↥S\nm : M\n⊢ 1 • s • s' • m = 1 • (s * s') • m",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
... | [] | simp [mul_smul] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 395,
"column": 19
} | {
"line": 395,
"column": 34
} | {
"line": 395,
"column": 34
} | [
{
"pp": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns s' : ↥S\nm : M\n⊢ 1 • s • s' • m = 1 • (s * s') • m",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
... | [] | simp [mul_smul] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 395,
"column": 19
} | {
"line": 395,
"column": 34
} | {
"line": 395,
"column": 34
} | [
{
"pp": "R : Type u\ninst✝² : CommSemiring R\nS : Submonoid R\nM : Type v\ninst✝¹ : AddCommMonoid M\ninst✝ : Module R M\ns s' : ↥S\nm : M\n⊢ 1 • s • s' • m = 1 • (s * s') • m",
"ppTerm": "?m.55",
"assigned": true,
"usedConstants": [
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
... | [] | simp [mul_smul] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monad.Algebra | {
"line": 376,
"column": 19
} | {
"line": 376,
"column": 54
} | {
"line": 376,
"column": 55
} | [
{
"pp": "C : Type u₁\ninst✝ : Category.{v₁, u₁} C\nG : Comonad C\nX : G.Coalgebra\nY : C\nf : G.forget.obj X ⟶ Y\n⊢ X.a ≫ G.map (X.a ≫ G.map f) = (X.a ≫ G.map f) ≫ (G.cofree.obj Y).a",
"ppTerm": "?m.80",
"assigned": true,
"usedConstants": [
"CategoryTheory.Category.assoc",
"CategoryTheor... | [] | by simp [← Coalgebra.coassoc_assoc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Category.Ring.Constructions | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 66
} | {
"line": 360,
"column": 0
} | [
{
"pp": "case property.right\nA B : CommRingCat\nf g : A ⟶ B\ns : Fork f g\nm : s.pt ⟶ (equalizerFork f g).pt\nhm : m ≫ (equalizerFork f g).ι = s.ι\nx : ↑s.pt\n⊢ (Hom.hom m) x = (Hom.hom (ofHom ((Hom.hom s.ι).codRestrict ((Hom.hom f).eqLocus (Hom.hom g)) ⋯))) x",
"ppTerm": "?property.right",
"assigned":... | [] | exact Subtype.ext <| RingHom.congr_fun (congrArg Hom.hom hm) x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Algebra.Category.Ring.Under.Basic | {
"line": 105,
"column": 16
} | {
"line": 107,
"column": 8
} | {
"line": 109,
"column": 0
} | [
{
"pp": "R S : CommRingCat\nA B : Type u\ninst✝³ : CommRing A\ninst✝² : CommRing B\ninst✝¹ : Algebra (↑R) A\ninst✝ : Algebra (↑R) B\nf : A ≃ₐ[↑R] B\n⊢ (↑f.symm).toUnder ≫ (↑f).toUnder = 𝟙 (R.mkUnder B)",
"ppTerm": "?m.78",
"assigned": true,
"usedConstants": [
"CategoryTheory.instCategoryUnder... | [] | by
ext a
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 932,
"column": 2
} | {
"line": 932,
"column": 37
} | {
"line": 933,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S f\ng : M →ₗ... | [
"R : Type u_1\ninst✝⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S f\ng : M →ₗ[R] M''\nh :... | dsimp only [IsLocalizedModule.lift] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Algebra.Module.LocalizedModule.Basic | {
"line": 952,
"column": 2
} | {
"line": 952,
"column": 37
} | {
"line": 953,
"column": 2
} | [
{
"pp": "R : Type u_1\ninst✝⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S f\ng : M →ₗ... | [
"R : Type u_1\ninst✝⁷ : CommSemiring R\nS : Submonoid R\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝⁶ : AddCommMonoid M\ninst✝⁵ : AddCommMonoid M'\ninst✝⁴ : AddCommMonoid M''\ninst✝³ : Module R M\ninst✝² : Module R M'\ninst✝¹ : Module R M''\nf : M →ₗ[R] M'\ninst✝ : IsLocalizedModule S f\ng : M →ₗ[R] M''\nh :... | dsimp only [IsLocalizedModule.lift] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.RingTheory.FinitePresentation | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 35
} | {
"line": 178,
"column": 0
} | [
{
"pp": "case intro.refine_2\nR : Type w₁\nA : Type w₂\ninst✝⁴ : CommRing R\ninst✝³ : CommRing A\ninst✝² : Algebra R A\ninst✝¹ : FinitePresentation R A\nι : Type v\ninst✝ : Finite ι\nι' : Type v\nw✝ : Fintype ι'\nf : MvPolynomial ι' R →ₐ[R] A\nhf_surj : Surjective ⇑f\nhf_ker : (RingHom.ker f.toRingHom).FG\ng : ... | [] | exact hf_ker.map MvPolynomial.C | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.RingTheory.FinitePresentation | {
"line": 239,
"column": 4
} | {
"line": 239,
"column": 28
} | {
"line": 240,
"column": 4
} | [
{
"pp": "case refine_2\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : Algebra A B\ninst✝² : IsScalarTower R A B\ninst✝¹ : FinitePresentation R B\ninst✝ : FiniteType R A\nn : ℕ\nf : MvPolynomial (Fin n) R... | [
"case refine_2\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : Algebra A B\ninst✝² : IsScalarTower R A B\ninst✝¹ : FinitePresentation R B\ninst✝ : FiniteType R A\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] B\nhf... | change Ideal.span s₀ = I | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 289,
"column": 2
} | {
"line": 290,
"column": 43
} | {
"line": 292,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝⁵ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁴ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝³ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝² : Q.IsMultiplicative\ninst✝¹ : W.IsMultiplicative\nX Y : Morphis... | [] | apply IsIso.eq_inv_of_hom_inv_id
rw [← comp_hom, IsIso.hom_inv_id, id_hom] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 289,
"column": 2
} | {
"line": 290,
"column": 43
} | {
"line": 292,
"column": 0
} | [
{
"pp": "A : Type u_1\ninst✝⁵ : Category.{v_1, u_1} A\nB : Type u_2\ninst✝⁴ : Category.{v_2, u_2} B\nT : Type u_3\ninst✝³ : Category.{v_3, u_3} T\nL : A ⥤ T\nR : B ⥤ T\nP : MorphismProperty T\nQ : MorphismProperty A\nW : MorphismProperty B\ninst✝² : Q.IsMultiplicative\ninst✝¹ : W.IsMultiplicative\nX Y : Morphis... | [] | apply IsIso.eq_inv_of_hom_inv_id
rw [← comp_hom, IsIso.hom_inv_id, id_hom] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 742,
"column": 2
} | {
"line": 744,
"column": 11
} | {
"line": 746,
"column": 0
} | [
{
"pp": "T : Type u_1\ninst✝¹ : Category.{v_1, u_1} T\nP Q : MorphismProperty T\nX : T\ninst✝ : Q.IsMultiplicative\nA B : P.Under Q X\nf g : A ⟶ B\nh : f.right = g.right\n⊢ f = g",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismProperty",
"CategoryTheory.... | [] | ext
· simp
· exact h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 742,
"column": 2
} | {
"line": 744,
"column": 11
} | {
"line": 746,
"column": 0
} | [
{
"pp": "T : Type u_1\ninst✝¹ : Category.{v_1, u_1} T\nP Q : MorphismProperty T\nX : T\ninst✝ : Q.IsMultiplicative\nA B : P.Under Q X\nf g : A ⟶ B\nh : f.right = g.right\n⊢ f = g",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismProperty",
"CategoryTheory.... | [] | ext
· simp
· exact h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.MorphismProperty.Comma | {
"line": 741,
"column": 89
} | {
"line": 744,
"column": 11
} | {
"line": 746,
"column": 0
} | [
{
"pp": "T : Type u_1\ninst✝¹ : Category.{v_1, u_1} T\nP Q : MorphismProperty T\nX : T\ninst✝ : Q.IsMultiplicative\nA B : P.Under Q X\nf g : A ⟶ B\nh : f.right = g.right\n⊢ f = g",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"CategoryTheory.MorphismProperty",
"CategoryTheory.... | [] | by
ext
· simp
· exact h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FinitePresentation | {
"line": 278,
"column": 21
} | {
"line": 278,
"column": 29
} | {
"line": 278,
"column": 30
} | [
{
"pp": "case refine_4\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : Algebra A B\ninst✝² : IsScalarTower R A B\ninst✝¹ : FinitePresentation R B\ninst✝ : FiniteType R A\nn : ℕ\nf : MvPolynomial (Fin n) R... | [
"case refine_4\nR : Type w₁\nA : Type w₂\nB : Type w₃\ninst✝⁸ : CommRing R\ninst✝⁷ : CommRing A\ninst✝⁶ : Algebra R A\ninst✝⁵ : CommRing B\ninst✝⁴ : Algebra R B\ninst✝³ : Algebra A B\ninst✝² : IsScalarTower R A B\ninst✝¹ : FinitePresentation R B\ninst✝ : FiniteType R A\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] B\nhf... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Grothendieck | {
"line": 209,
"column": 4
} | {
"line": 210,
"column": 12
} | {
"line": 210,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u₁\ninst✝ : Category.{v₁, u₁} D\nF : C ⥤ Cat\nX Y : Grothendieck F\ne₁ : X.base ≅ Y.base\ne₂ : (F.map e₁.hom).toFunctor.obj X.fiber ≅ Y.fiber\n⊢ eqToHom ⋯ ≫\n ({ base := e₁.inv, fiber := (F.map e₁.inv).toFunctor.map e₂.inv ≫ eqToHom ⋯ } ≫\n ... | [] | have := Functor.congr_hom congr($((F.mapIso e₁).inv_hom_id).toFunctor) e₂.inv
simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Grothendieck | {
"line": 209,
"column": 4
} | {
"line": 210,
"column": 12
} | {
"line": 210,
"column": 12
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u₁\ninst✝ : Category.{v₁, u₁} D\nF : C ⥤ Cat\nX Y : Grothendieck F\ne₁ : X.base ≅ Y.base\ne₂ : (F.map e₁.hom).toFunctor.obj X.fiber ≅ Y.fiber\n⊢ eqToHom ⋯ ≫\n ({ base := e₁.inv, fiber := (F.map e₁.inv).toFunctor.map e₂.inv ≫ eqToHom ⋯ } ≫\n ... | [] | have := Functor.congr_hom congr($((F.mapIso e₁).inv_hom_id).toFunctor) e₂.inv
simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 304,
"column": 6
} | {
"line": 306,
"column": 12
} | {
"line": 306,
"column": 12
} | [
{
"pp": "case star.star\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nZ : D\nF : C ⥤ D\nM : (x : C) → F.obj x ⟶ Z\nhM : ∀ (x y : C) (f : x ⟶ y), F.map f ≫ M y = M x\nG : WithTerminal C ⥤ D\nh : incl ⋙ G ≅ F\nhG : G.obj star ≅ Z\nhh : ∀ (x : C), G.map (starTerminal.from (i... | [] | · cases f
change G.map (𝟙 _) ≫ hG.hom = hG.hom ≫ 𝟙 _
simp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Limits.Final | {
"line": 338,
"column": 2
} | {
"line": 340,
"column": 16
} | {
"line": 342,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝² : F.Final\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nG : D ⥤ E\ninst✝ : HasColimit G\n⊢ IsIso (colimit.pre G F)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"CategoryT... | [] | simp only [colimit.pre_eq (colimitCoconeComp F (getColimitCocone G)) (getColimitCocone G),
colimitCoconeComp_cocone, IsColimit.desc_self]
infer_instance | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Final | {
"line": 338,
"column": 2
} | {
"line": 340,
"column": 16
} | {
"line": 342,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝⁴ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝³ : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝² : F.Final\nE : Type u₃\ninst✝¹ : Category.{v₃, u₃} E\nG : D ⥤ E\ninst✝ : HasColimit G\n⊢ IsIso (colimit.pre G F)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"CategoryT... | [] | simp only [colimit.pre_eq (colimitCoconeComp F (getColimitCocone G)) (getColimitCocone G),
colimitCoconeComp_cocone, IsColimit.desc_self]
infer_instance | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.WithTerminal.Basic | {
"line": 718,
"column": 6
} | {
"line": 720,
"column": 12
} | {
"line": 720,
"column": 12
} | [
{
"pp": "case star.star\nC : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u_1\ninst✝ : Category.{v_1, u_1} D\nZ : D\nF : C ⥤ D\nM : (x : C) → Z ⟶ F.obj x\nhM : ∀ (x y : C) (f : x ⟶ y), M x ≫ F.map f = M y\nG : WithInitial C ⥤ D\nh : incl ⋙ G ≅ F\nhG : G.obj star ≅ Z\nhh : ∀ (x : C), hG.symm.hom ≫ G.map (starIni... | [] | · cases f
change G.map (𝟙 _) ≫ hG.hom = hG.hom ≫ 𝟙 _
simp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.EffectiveEpi.Basic | {
"line": 272,
"column": 15
} | {
"line": 274,
"column": 15
} | {
"line": 275,
"column": 2
} | [
{
"pp": "C : Type u_1\ninst✝ : Category.{v_1, u_1} C\nB : C\nα : Type u_2\nα' : Type u_3\nX : α → C\nπ : (a : α) → X a ⟶ B\ne : α' ≃ α\nP : EffectiveEpiFamilyStruct (fun a ↦ X (e a)) fun a ↦ π (e a)\nW✝ : C\nx✝¹ : (a : α) → X a ⟶ W✝\nx✝ : ∀ {Z : C} (a₁ a₂ : α) (g₁ : Z ⟶ X a₁) (g₂ : Z ⟶ X a₂), g₁ ≫ π a₁ = g₂ ≫ π... | [] | by
obtain ⟨a, rfl⟩ := e.surjective a
apply P.fac | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FinitePresentation | {
"line": 354,
"column": 12
} | {
"line": 354,
"column": 20
} | {
"line": 354,
"column": 21
} | [
{
"pp": "case refine_4\nR : Type w₁\nA : Type w₂\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] A\nhf : Surjective ⇑f\ninst✝ : FinitePresentation R A\nm : ℕ\nf' : MvPolynomial (Fin m) R →ₐ[R] A\nhf' : Surjective ⇑f'\ns : Finset (MvPolynomial (Fin m) R)\n... | [
"case refine_4\nR : Type w₁\nA : Type w₂\ninst✝³ : CommRing R\ninst✝² : CommRing A\ninst✝¹ : Algebra R A\nn : ℕ\nf : MvPolynomial (Fin n) R →ₐ[R] A\nhf : Surjective ⇑f\ninst✝ : FinitePresentation R A\nm : ℕ\nf' : MvPolynomial (Fin m) R →ₐ[R] A\nhf' : Surjective ⇑f'\ns : Finset (MvPolynomial (Fin m) R)\nhs : Ideal.s... | mul_add, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Final | {
"line": 600,
"column": 14
} | {
"line": 601,
"column": 39
} | {
"line": 602,
"column": 12
} | [
{
"pp": "case h₂\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\nc : Cone (F ⋙ G)\nX Y : D\nf : X ⟶ Y\nZ₁ Z₂ : C\nk₁ : F.obj Z₁ ⟶ Y\nk₂ : F.obj Z₂ ⟶ Y\ng : Z₁ ⟶ Z₂\na : F.map g ≫ k₂ = k₁\nz... | [] | rw [← a, Functor.map_comp, ← Functor.comp_map, ← Category.assoc, ← Category.assoc,
c.w, z, Category.assoc] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.CategoryTheory.Limits.Final | {
"line": 624,
"column": 2
} | {
"line": 627,
"column": 17
} | {
"line": 628,
"column": 2
} | [
{
"pp": "case h₁\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\ns : Cone (F ⋙ G)\nj : C\n⊢ ∀ (X₁ X₂ : C) (k₁ : F.obj X₁ ⟶ F.obj j) (k₂ : F.obj X₂ ⟶ F.obj j) (f : X₁ ⟶ X₂),\n F.map f ≫ k... | [
"case h₂\nC : Type u₁\ninst✝³ : Category.{v₁, u₁} C\nD : Type u₂\ninst✝² : Category.{v₂, u₂} D\nF : C ⥤ D\ninst✝¹ : F.Initial\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nG : D ⥤ E\ns : Cone (F ⋙ G)\nj : C\n⊢ ∀ (X₁ X₂ : C) (k₁ : F.obj X₁ ⟶ F.obj j) (k₂ : F.obj X₂ ⟶ F.obj j) (f : X₁ ⟶ X₂),\n F.map f ≫ k₂ = k₁ → s.π... | · intro j₁ j₂ k₁ k₂ f w h
rw [← s.w f]
rw [← w] at h
simpa using h | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | {
"line": 227,
"column": 25
} | {
"line": 227,
"column": 44
} | {
"line": 227,
"column": 44
} | [
{
"pp": "C : Type u₁\ninst✝¹ : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝ : Category.{v₂, u₂} J\nX Y : C\nf g : X ⟶ Y\nc : Fork f g\n⊢ (Iso.refl c.op.unop.pt).hom ≫ c.ι = c.op.unop.ι",
"ppTerm": "?m.35",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.Cofork.unop",
"CategoryTheo... | [] | by simp [op_unop_ι] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | {
"line": 366,
"column": 9
} | {
"line": 366,
"column": 30
} | {
"line": 366,
"column": 30
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\nX Y : Cᵒᵖ\nf : X ⟶ Y\ninst✝ : HasPullback f f\nh : IsColimit (ofπ f ⋯)\n⊢ (Iso.refl (Opposite.unop X)).hom ≫ pushout.inl f.unop f.unop =\n (pullback.fst f f).unop ≫ (pullbackIsoOpPushout f f).unop.symm.hom",
"p... | [] | by simp [← unop_comp] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Final | {
"line": 876,
"column": 78
} | {
"line": 892,
"column": 80
} | {
"line": 894,
"column": 0
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nD : Type u₂\ninst✝¹ : Category.{v₂, u₂} D\nE : Type u₃\ninst✝ : Category.{v₃, u₃} E\nF : C ⥤ D\nG : D ⥤ E\nhF : F.Final\nhFG : (F ⋙ G).Final\n⊢ G.Final",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CategoryTheory.... | [] | by
let s₁ : C ≌ AsSmall.{max u₁ v₁ u₂ v₂ u₃ v₃} C := AsSmall.equiv
let s₂ : D ≌ AsSmall.{max u₁ v₁ u₂ v₂ u₃ v₃} D := AsSmall.equiv
let s₃ : E ≌ AsSmall.{max u₁ v₁ u₂ v₂ u₃ v₃} E := AsSmall.equiv
let _i : s₁.inverse ⋙ (F ⋙ G) ⋙ s₃.functor ≅
(s₁.inverse ⋙ F ⋙ s₂.functor) ⋙ (s₂.inverse ⋙ G ⋙ s₃.functor) :=
... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.Opposites.Equalizers | {
"line": 366,
"column": 33
} | {
"line": 366,
"column": 54
} | {
"line": 366,
"column": 54
} | [
{
"pp": "C : Type u₁\ninst✝² : Category.{v₁, u₁} C\nJ : Type u₂\ninst✝¹ : Category.{v₂, u₂} J\nX Y : Cᵒᵖ\nf : X ⟶ Y\ninst✝ : HasPullback f f\nh : IsColimit (ofπ f ⋯)\n⊢ (Iso.refl (Opposite.unop X)).hom ≫ pushout.inr f.unop f.unop =\n (pullback.snd f f).unop ≫ (pullbackIsoOpPushout f f).unop.symm.hom",
"p... | [] | by simp [← unop_comp] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.RingTheory.FinitePresentation | {
"line": 498,
"column": 10
} | {
"line": 498,
"column": 29
} | {
"line": 498,
"column": 29
} | [
{
"pp": "P : (R : Type u) → [inst : CommRing R] → (S : Type u) → [inst_1 : CommRing S] → (R →+* S) → Prop\nQ : (R : Type u) → [inst : CommRing R] → (S : Type v) → [inst_1 : CommRing S] → (R →+* S) → Prop\npolynomial : ∀ (R : Type u) [inst : CommRing R], P R R[X] C\nfg_ker :\n ∀ (R : Type u) [inst : CommRing R]... | [
"P : (R : Type u) → [inst : CommRing R] → (S : Type u) → [inst_1 : CommRing S] → (R →+* S) → Prop\nQ : (R : Type u) → [inst : CommRing R] → (S : Type v) → [inst_1 : CommRing S] → (R →+* S) → Prop\npolynomial : ∀ (R : Type u) [inst : CommRing R], P R R[X] C\nfg_ker :\n ∀ (R : Type u) [inst : CommRing R] (S : Type v... | ← RingHom.comap_ker | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.RingTheory.RingHomProperties | {
"line": 118,
"column": 4
} | {
"line": 120,
"column": 21
} | {
"line": 122,
"column": 0
} | [
{
"pp": "case right\nP : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nhP : StableUnderComposition P\nhP' : ∀ {R S : Type u} [inst : CommRing R] [inst_1 : CommRing S] (e : R ≃+* S), P e.toRingHom\n⊢ ∀ {R S T : Type u} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRin... | [] | introv H
apply hP
exacts [hP' e, H] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.RingHomProperties | {
"line": 118,
"column": 4
} | {
"line": 120,
"column": 21
} | {
"line": 122,
"column": 0
} | [
{
"pp": "case right\nP : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop\nhP : StableUnderComposition P\nhP' : ∀ {R S : Type u} [inst : CommRing R] [inst_1 : CommRing S] (e : R ≃+* S), P e.toRingHom\n⊢ ∀ {R S T : Type u} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRin... | [] | introv H
apply hP
exacts [hP' e, H] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 135,
"column": 4
} | {
"line": 136,
"column": 56
} | {
"line": 138,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nD : Type u'\ninst✝¹ : Category.{v', u'} D\nP : ObjectProperty C\ninst✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\n⊢ ∃ Q, ∃ (_ : ObjectProperty.Small.{w, v, u} Q), P.isoClosure ≤ Q.isoClosure",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": ... | [] | obtain ⟨Q, _, _, _⟩ := EssentiallySmall.exists_small_le.{w} P
exact ⟨Q, inferInstance, by rwa [isoClosure_le_iff]⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 135,
"column": 4
} | {
"line": 136,
"column": 56
} | {
"line": 138,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\nD : Type u'\ninst✝¹ : Category.{v', u'} D\nP : ObjectProperty C\ninst✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\n⊢ ∃ Q, ∃ (_ : ObjectProperty.Small.{w, v, u} Q), P.isoClosure ≤ Q.isoClosure",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": ... | [] | obtain ⟨Q, _, _, _⟩ := EssentiallySmall.exists_small_le.{w} P
exact ⟨Q, inferInstance, by rwa [isoClosure_le_iff]⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.MorphismProperty.Limits | {
"line": 376,
"column": 2
} | {
"line": 385,
"column": 57
} | {
"line": 387,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nP : MorphismProperty C\ninst✝³ : P.IsStableUnderCobaseChange\ninst✝² : P.IsStableUnderComposition\nS X X' Y Y' : C\nf : S ⟶ X\ng : S ⟶ Y\nf' : S ⟶ X'\ng' : S ⟶ Y'\ni₁ : X ⟶ X'\ninst✝¹ : HasPushoutsAlong f\ninst✝ : HasPushoutsAlong g'\ni₂ : Y ⟶ Y'\nh₁ : P i₁\nh₂ :... | [] | have : HasPushoutsAlong (Under.mk g').hom := by cat_disch
have : pushout.map f g f' g' i₁ i₂ (𝟙 _) (by simp [e₁]) (by simp [e₂]) =
((pushoutSymmetry _ _).hom ≫
((Under.pushout f).map (Under.homMk _ e₂.symm : Under.mk g ⟶ Under.mk g')).right) ≫
(pushoutSymmetry _ _).hom ≫
((Under.pushout... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.MorphismProperty.Limits | {
"line": 376,
"column": 2
} | {
"line": 385,
"column": 57
} | {
"line": 387,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\nP : MorphismProperty C\ninst✝³ : P.IsStableUnderCobaseChange\ninst✝² : P.IsStableUnderComposition\nS X X' Y Y' : C\nf : S ⟶ X\ng : S ⟶ Y\nf' : S ⟶ X'\ng' : S ⟶ Y'\ni₁ : X ⟶ X'\ninst✝¹ : HasPushoutsAlong f\ninst✝ : HasPushoutsAlong g'\ni₂ : Y ⟶ Y'\nh₁ : P i₁\nh₂ :... | [] | have : HasPushoutsAlong (Under.mk g').hom := by cat_disch
have : pushout.map f g f' g' i₁ i₂ (𝟙 _) (by simp [e₁]) (by simp [e₂]) =
((pushoutSymmetry _ _).hom ≫
((Under.pushout f).map (Under.homMk _ e₂.symm : Under.mk g ⟶ Under.mk g')).right) ≫
(pushoutSymmetry _ _).hom ≫
((Under.pushout... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 199,
"column": 2
} | {
"line": 202,
"column": 51
} | {
"line": 204,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nP : ObjectProperty C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\n⊢ EssentiallySmall.{w, v, u} P.FullSubcategory",
"ppTerm": "?m.8",
"assigned": true,
"usedConstant... | [] | obtain ⟨Q, _, h₁, h₂⟩ := EssentiallySmall.exists_small_le P
have := (isEquivalence_ιOfLE_iff h₁).2 h₂
rw [← essentiallySmall_congr (ιOfLE h₁).asEquivalence]
exact essentiallySmall_of_small_of_locallySmall _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 199,
"column": 2
} | {
"line": 202,
"column": 51
} | {
"line": 204,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nP : ObjectProperty C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\n⊢ EssentiallySmall.{w, v, u} P.FullSubcategory",
"ppTerm": "?m.8",
"assigned": true,
"usedConstant... | [] | obtain ⟨Q, _, h₁, h₂⟩ := EssentiallySmall.exists_small_le P
have := (isEquivalence_ιOfLE_iff h₁).2 h₂
rw [← essentiallySmall_congr (ιOfLE h₁).asEquivalence]
exact essentiallySmall_of_small_of_locallySmall _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 223,
"column": 2
} | {
"line": 226,
"column": 51
} | {
"line": 228,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nP : ObjectProperty C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\n⊢ EssentiallySmall.{w, v, u} P.FullSubcategory",
"ppTerm": "?m.8",
"assigned": true,
"usedConstant... | [] | obtain ⟨Q, _, h₁, h₂⟩ := EssentiallySmall.exists_small_le P
have := (isEquivalence_ιOfLE_iff h₁).2 h₂
rw [← essentiallySmall_congr (ιOfLE h₁).asEquivalence]
exact essentiallySmall_of_small_of_locallySmall _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.Small | {
"line": 223,
"column": 2
} | {
"line": 226,
"column": 51
} | {
"line": 228,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nP : ObjectProperty C\ninst✝¹ : LocallySmall.{w, v, u} C\ninst✝ : ObjectProperty.EssentiallySmall.{w, v, u} P\n⊢ EssentiallySmall.{w, v, u} P.FullSubcategory",
"ppTerm": "?m.8",
"assigned": true,
"usedConstant... | [] | obtain ⟨Q, _, h₁, h₂⟩ := EssentiallySmall.exists_small_le P
have := (isEquivalence_ιOfLE_iff h₁).2 h₂
rw [← essentiallySmall_congr (ιOfLE h₁).asEquivalence]
exact essentiallySmall_of_small_of_locallySmall _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Shapes.Diagonal | {
"line": 402,
"column": 64
} | {
"line": 402,
"column": 72
} | {
"line": 402,
"column": 72
} | [
{
"pp": "case h₀\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\ninst✝ : HasPullbacks C\nS : C\ng : Y ⟶ X\nf : X ⟶ S\ni : pullback (g ≫ f) f ≅ pullback (g ≫ f) (𝟙 X ≫ f) := ⋯\n⊢ (map (g ≫ f) (𝟙 X ≫ f) f f g (𝟙 X) (𝟙 S) ⋯ ⋯ ≫ 𝟙 (diagonalObj f)) ≫ fst f f =\n (i.inv ≫ map (g ≫ f) f f f g (𝟙 X) (�... | [] | simp [i] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.Limits.Shapes.Diagonal | {
"line": 402,
"column": 64
} | {
"line": 402,
"column": 72
} | {
"line": 402,
"column": 72
} | [
{
"pp": "case h₁\nC : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\nX Y : C\ninst✝ : HasPullbacks C\nS : C\ng : Y ⟶ X\nf : X ⟶ S\ni : pullback (g ≫ f) f ≅ pullback (g ≫ f) (𝟙 X ≫ f) := ⋯\n⊢ (map (g ≫ f) (𝟙 X ≫ f) f f g (𝟙 X) (𝟙 S) ⋯ ⋯ ≫ 𝟙 (diagonalObj f)) ≫ snd f f =\n (i.inv ≫ map (g ≫ f) f f f g (𝟙 X) (�... | [] | simp [i] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.CategoryTheory.MorphismProperty.Limits | {
"line": 720,
"column": 4
} | {
"line": 721,
"column": 69
} | {
"line": 722,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type u_1\ninst✝ : W.RespectsIso\nhW :\n ∀ (X₁ X₂ : J → C) [inst : HasProduct X₁] [inst_1 : HasProduct X₂] (f : (j : J) → X₁ j ⟶ X₂ j),\n (∀ (j : J), W (f j)) → W (Limits.Pi.map f)\nX₁ X₂ : Discrete J ⥤ C\nc₁ : Cone X₁\nc₂ : Cone X₂... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nW : MorphismProperty C\nJ : Type u_1\ninst✝ : W.RespectsIso\nhW :\n ∀ (X₁ X₂ : J → C) [inst : HasProduct X₁] [inst_1 : HasProduct X₂] (f : (j : J) → X₁ j ⟶ X₂ j),\n (∀ (j : J), W (f j)) → W (Limits.Pi.map f)\nX₁ X₂ : Discrete J ⥤ C\nc₁ : Cone X₁\nc₂ : Cone X₂\nhc₁ : IsLi... | have : HasProduct fun j ↦ X₂.obj (Discrete.mk j) :=
hasLimit_of_iso (Discrete.natIso (fun j ↦ Iso.refl (X₂.obj j))) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 48
} | {
"line": 349,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nP : ObjectProperty C\nJ : Type u'\ninst✝² : Category.{v', u'} J\nJ' : Type u''\ninst✝¹ : Category.{v'', u''} J'\ninst✝ : P.IsClosedUnderColimitsOfShape Jᵒᵖ\n⊢ P.op.IsClosedUnderLimitsOfShape J",
"ppTerm": "?... | [] | rwa [← isClosedUnderColimitsOfShape_op_iff_op] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticRwa___1 | Lean.Parser.Tactic.tacticRwa__ |
Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 48
} | {
"line": 349,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nP : ObjectProperty C\nJ : Type u'\ninst✝² : Category.{v', u'} J\nJ' : Type u''\ninst✝¹ : Category.{v'', u''} J'\ninst✝ : P.IsClosedUnderColimitsOfShape Jᵒᵖ\n⊢ P.op.IsClosedUnderLimitsOfShape J",
"ppTerm": "?... | [] | rwa [← isClosedUnderColimitsOfShape_op_iff_op] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape | {
"line": 347,
"column": 2
} | {
"line": 347,
"column": 48
} | {
"line": 349,
"column": 0
} | [
{
"pp": "C : Type u_1\nD : Type u_2\ninst✝⁴ : Category.{v_1, u_1} C\ninst✝³ : Category.{v_2, u_2} D\nP : ObjectProperty C\nJ : Type u'\ninst✝² : Category.{v', u'} J\nJ' : Type u''\ninst✝¹ : Category.{v'', u''} J'\ninst✝ : P.IsClosedUnderColimitsOfShape Jᵒᵖ\n⊢ P.op.IsClosedUnderLimitsOfShape J",
"ppTerm": "?... | [] | rwa [← isClosedUnderColimitsOfShape_op_iff_op] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 218,
"column": 52
} | {
"line": 218,
"column": 66
} | {
"line": 218,
"column": 66
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX₁ X₂ X₃ Y₁ Y₂ Y₃ Z₁ Z₂ : C\nthis : MonoidalCategoryStruct C :=\n { tensorObj := ofChosenFiniteProducts.tensorObj ℬ,\n whiskerLeft := fun X {x x_1} g ↦ ofChosenFiniteProducts.tensorHom ℬ (... | [] | simpa using hf | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 218,
"column": 52
} | {
"line": 218,
"column": 66
} | {
"line": 218,
"column": 66
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX₁ X₂ X₃ Y₁ Y₂ Y₃ Z₁ Z₂ : C\nthis : MonoidalCategoryStruct C :=\n { tensorObj := ofChosenFiniteProducts.tensorObj ℬ,\n whiskerLeft := fun X {x x_1} g ↦ ofChosenFiniteProducts.tensorHom ℬ (... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 218,
"column": 52
} | {
"line": 218,
"column": 66
} | {
"line": 218,
"column": 66
} | [
{
"pp": "C : Type u\ninst✝ : Category.{v, u} C\n𝒯 : LimitCone (Functor.empty C)\nℬ : (X Y : C) → LimitCone (pair X Y)\nX₁ X₂ X₃ Y₁ Y₂ Y₃ Z₁ Z₂ : C\nthis : MonoidalCategoryStruct C :=\n { tensorObj := ofChosenFiniteProducts.tensorObj ℬ,\n whiskerLeft := fun X {x x_1} g ↦ ofChosenFiniteProducts.tensorHom ℬ (... | [] | simpa using hf | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 725,
"column": 87
} | {
"line": 727,
"column": 16
} | {
"line": 729,
"column": 0
} | [
{
"pp": "C✝ : Type u\ninst✝⁹ : Category.{v, u} C✝\nC : Type u\ninst✝⁸ : Category.{v, u} C\ninst✝⁷ : CartesianMonoidalCategory C\nD : Type u₁\ninst✝⁶ : Category.{v₁, u₁} D\ninst✝⁵ : CartesianMonoidalCategory D\nF : C ⥤ D\nE✝ : Type u₂\ninst✝⁴ : Category.{v₂, u₂} E✝\ninst✝³ : CartesianMonoidalCategory E✝\nG✝ : D ... | [] | by
rw [← prodComparisonIso_hom]
infer_instance | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic | {
"line": 824,
"column": 17
} | {
"line": 824,
"column": 46
} | {
"line": 825,
"column": 2
} | [
{
"pp": "C✝ : Type u\ninst✝⁴ : Category.{v, u} C✝\nC : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : CartesianMonoidalCategory C\nP : ObjectProperty C\ninst✝¹ : P.IsClosedUnderLimitsOfShape (Discrete PEmpty.{1})\ninst✝ : P.IsClosedUnderLimitsOfShape (Discrete WalkingPair)\nX Y : P.FullSubcategory\n⊢ ObjectProper... | [] | by ext; exact fst_def X.1 Y.1 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Limits.Shapes.SplitEqualizer | {
"line": 98,
"column": 49
} | {
"line": 98,
"column": 74
} | {
"line": 98,
"column": 75
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y : C\nf g : X ⟶ Y\nW : C\nι : W ⟶ X\nq : IsSplitEqualizer f g ι\nF : C ⥤ D\n⊢ F.map (g ≫ q.rightRetraction) = 𝟙 (F.obj X)",
"ppTerm": "?m.145",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [
"C : Type u\ninst✝¹ : Category.{v, u} C\nD : Type u₂\ninst✝ : Category.{v₂, u₂} D\nG : C ⥤ D\nX Y : C\nf g : X ⟶ Y\nW : C\nι : W ⟶ X\nq : IsSplitEqualizer f g ι\nF : C ⥤ D\n⊢ F.map (𝟙 X) = 𝟙 (F.obj X)"
] | q.bottom_rightRetraction, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.CategoryTheory.Limits.Constructions.Equalizers | {
"line": 173,
"column": 4
} | {
"line": 180,
"column": 14
} | {
"line": 182,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nG : C ⥤ D\ninst✝¹ : HasBinaryCoproducts C\ninst✝ : HasPushouts C\nF : WalkingParallelPair ⥤ C\n⊢ ∀ (s : Cocone F) (m : (coequalizerCocone F).pt ⟶ s.pt),\n (∀ (j : WalkingParallelPair), (coequalizerCocone F).ι.app j ≫ ... | [] | intro c m J
have J1 : pushoutInl F ≫ m = c.ι.app WalkingParallelPair.one := by
simpa using J WalkingParallelPair.one
apply pushout.hom_ext
· rw [colimit.ι_desc]
exact J1
· rw [colimit.ι_desc, ← pushoutInl_eq_pushout_inr]
exact J1 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Limits.Constructions.Equalizers | {
"line": 173,
"column": 4
} | {
"line": 180,
"column": 14
} | {
"line": 182,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nD : Type u'\ninst✝² : Category.{v', u'} D\nG : C ⥤ D\ninst✝¹ : HasBinaryCoproducts C\ninst✝ : HasPushouts C\nF : WalkingParallelPair ⥤ C\n⊢ ∀ (s : Cocone F) (m : (coequalizerCocone F).pt ⟶ s.pt),\n (∀ (j : WalkingParallelPair), (coequalizerCocone F).ι.app j ≫ ... | [] | intro c m J
have J1 : pushoutInl F ≫ m = c.ι.app WalkingParallelPair.one := by
simpa using J WalkingParallelPair.one
apply pushout.hom_ext
· rw [colimit.ι_desc]
exact J1
· rw [colimit.ι_desc, ← pushoutInl_eq_pushout_inr]
exact J1 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Limits.Constructions.Equalizers | {
"line": 210,
"column": 10
} | {
"line": 210,
"column": 87
} | {
"line": 211,
"column": 10
} | [
{
"pp": "case refine_3\nC : Type u\ninst✝⁵ : Category.{v, u} C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nG : C ⥤ D\ninst✝³ : HasBinaryCoproducts C\ninst✝² : HasPushouts C\ninst✝¹ : PreservesColimitsOfShape (Discrete WalkingPair) G\ninst✝ : PreservesColimitsOfShape WalkingSpan G\nK : WalkingParallelPair ⥤ C\nc... | [
"case refine_3\nC : Type u\ninst✝⁵ : Category.{v, u} C\nD : Type u'\ninst✝⁴ : Category.{v', u'} D\nG : C ⥤ D\ninst✝³ : HasBinaryCoproducts C\ninst✝² : HasPushouts C\ninst✝¹ : PreservesColimitsOfShape (Discrete WalkingPair) G\ninst✝ : PreservesColimitsOfShape WalkingSpan G\nK : WalkingParallelPair ⥤ C\nc : Cocone (K... | apply (mapIsColimitOfPreservesOfIsColimit G _ _ (coprodIsCoprod _ _)).hom_ext | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Algebra.Category.Grp.Colimits | {
"line": 127,
"column": 2
} | {
"line": 128,
"column": 59
} | {
"line": 129,
"column": 2
} | [
{
"pp": "J : Type u\ninst✝¹ : Category.{v, u} J\nF : J ⥤ AddCommGrpCat\ninst✝ : DecidableEq J\nj : J\nx : ↑(F.obj j)\n⊢ (QuotientAddGroup.lift (Relations F)\n (DFinsupp.sumAddHom fun j ↦\n ((QuotientAddGroup.mk' (Relations (F ⋙ uliftFunctor))).comp\n (DFinsupp.singleAddHom (fun j ... | [
"J : Type u\ninst✝¹ : Category.{v, u} J\nF : J ⥤ AddCommGrpCat\ninst✝ : DecidableEq J\nj : J\nx : ↑(F.obj j)\n⊢ (DFinsupp.sumAddHom fun j ↦\n ((QuotientAddGroup.mk' (Relations (F ⋙ uliftFunctor))).comp\n (DFinsupp.singleAddHom (fun j ↦ ↑((F ⋙ uliftFunctor).obj j)) j)).comp\n ↑AddEquiv.u... | conv_lhs => erw [AddMonoidHom.comp_apply (QuotientAddGroup.mk' (Relations F))
(DFinsupp.singleAddHom _ j), QuotientAddGroup.lift_mk'] | Mathlib.Tactic.Conv._aux_Mathlib_Tactic_Conv___macroRules_Mathlib_Tactic_Conv_convLHS_1 | Mathlib.Tactic.Conv.convLHS |
Mathlib.Algebra.Category.Grp.Colimits | {
"line": 138,
"column": 80
} | {
"line": 144,
"column": 6
} | {
"line": 146,
"column": 0
} | [
{
"pp": "J : Type u\ninst✝¹ : Category.{v, u} J\nF : J ⥤ AddCommGrpCat\nc : Cocone F\ninst✝ : DecidableEq J\n⊢ Quot (F ⋙ uliftFunctor) →+ Quot F",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"AddEquivClass.instAddMonoidHomClass",
"Eq.mpr",
"ULift.addZeroClass",
"S... | [] | by
refine QuotientAddGroup.lift (Relations (F ⋙ uliftFunctor))
(DFinsupp.sumAddHom (fun j ↦ (Quot.ι _ j).comp AddEquiv.ulift.toAddMonoidHom)) ?_
rw [AddSubgroup.closure_le]
intro _ hx
obtain ⟨j, j', u, a, rfl⟩ := hx
simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Abelian.Basic | {
"line": 180,
"column": 2
} | {
"line": 181,
"column": 16
} | {
"line": 183,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasKernels C\ninst✝² : HasCokernels C\ninst✝¹ : HasZeroObject C\nX Y : C\nf : X ⟶ Y\ninst✝ : Epi f\n⊢ IsIso (imageMonoFactorisation f).m",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"CategoryTheory.L... | [] | dsimp
infer_instance | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.Abelian.Basic | {
"line": 180,
"column": 2
} | {
"line": 181,
"column": 16
} | {
"line": 183,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝⁵ : Category.{v, u} C\ninst✝⁴ : Preadditive C\ninst✝³ : HasKernels C\ninst✝² : HasCokernels C\ninst✝¹ : HasZeroObject C\nX Y : C\nf : X ⟶ Y\ninst✝ : Epi f\n⊢ IsIso (imageMonoFactorisation f).m",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"CategoryTheory.L... | [] | dsimp
infer_instance | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Lift | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 52
} | {
"line": 68,
"column": 2
} | [
{
"pp": "α : Type u_1\nγ : Type u_3\nι : Type u_6\np : ι → Prop\ns : ι → Set α\nf : Filter α\nhf : f.HasBasis p s\nβ : ι → Type u_5\npg : (i : ι) → β i → Prop\nsg : (i : ι) → β i → Set γ\ng : Set α → Filter γ\nhg : ∀ (i : ι), (g (s i)).HasBasis (pg i) (sg i)\ngm : Monotone g\n⊢ (f.lift g).HasBasis (fun i ↦ p i.... | [
"α : Type u_1\nγ : Type u_3\nι : Type u_6\np : ι → Prop\ns : ι → Set α\nf : Filter α\nhf : f.HasBasis p s\nβ : ι → Type u_5\npg : (i : ι) → β i → Prop\nsg : (i : ι) → β i → Set γ\ng : Set α → Filter γ\nhg : ∀ (i : ι), (g (s i)).HasBasis (pg i) (sg i)\ngm : Monotone g\nt : Set γ\n⊢ (∃ i, p i ∧ ∃ x, pg i x ∧ sg i x ⊆... | refine ⟨fun t => (hf.mem_lift_iff hg gm).trans ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Order.Filter.Lift | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 87
} | {
"line": 158,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : Filter α\ng : Set α → Filter β\nhm : Monotone g\n⊢ (f.lift g).NeBot ↔ ∀ s ∈ f, (g s).NeBot",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"congrArg",
"_private.Mathlib.Order.Filter.Lift.0.Filter.lift_neBot... | [] | simp only [neBot_iff, Ne, ← empty_mem_iff_bot, mem_lift_sets hm, not_exists, not_and] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.Filter.Lift | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 87
} | {
"line": 158,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : Filter α\ng : Set α → Filter β\nhm : Monotone g\n⊢ (f.lift g).NeBot ↔ ∀ s ∈ f, (g s).NeBot",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"congrArg",
"_private.Mathlib.Order.Filter.Lift.0.Filter.lift_neBot... | [] | simp only [neBot_iff, Ne, ← empty_mem_iff_bot, mem_lift_sets hm, not_exists, not_and] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Filter.Lift | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 87
} | {
"line": 158,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : Filter α\ng : Set α → Filter β\nhm : Monotone g\n⊢ (f.lift g).NeBot ↔ ∀ s ∈ f, (g s).NeBot",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"congrArg",
"_private.Mathlib.Order.Filter.Lift.0.Filter.lift_neBot... | [] | simp only [neBot_iff, Ne, ← empty_mem_iff_bot, mem_lift_sets hm, not_exists, not_and] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Basic | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 33
} | {
"line": 89,
"column": 0
} | [
{
"pp": "X : Type u\nα : Type u_1\ns : Set X\ninst✝ : TopologicalSpace X\nf : α → Set X\nho : ∀ (i : α), IsOpen[inst✝] (f i)\nhU : ⋃ i, f i = univ\nh : ∀ (i : α), IsOpen[inst✝] (f i ∩ s)\n⊢ IsOpen[inst✝] (⋃ i, f i ∩ s)",
"ppTerm": "?m.39",
"assigned": true,
"usedConstants": [
"Set.instInter",
... | [] | exact isOpen_iUnion fun i ↦ h i | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Closure | {
"line": 448,
"column": 4
} | {
"line": 448,
"column": 15
} | {
"line": 450,
"column": 0
} | [
{
"pp": "case mpr\nX : Type u\ninst✝ : TopologicalSpace X\nx : X\nho : ¬IsOpen {x}\nhU : IsOpen {x}\nhne : {x}.Nonempty\nhUx : {x} ⊆ {x}\n⊢ False",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [],
"usedFVars": [
"ho",
"hU"
],
"usedGoals": []
}
] | [] | exact ho hU | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.CategoryTheory.Abelian.Basic | {
"line": 720,
"column": 90
} | {
"line": 723,
"column": 87
} | {
"line": 725,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\ninst✝² : Abelian C\ninst✝¹ : HasPullbacks C\nX Y Z : C\nf : X ⟶ Z\ng : Y ⟶ Z\ninst✝ : Epi f\ns : PullbackCone f g\nhs : IsLimit s\n⊢ Epi s.snd",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"CategoryTheory.Limits.Cone.π",
"Categ... | [] | by
haveI : Epi (NatTrans.app (limit.cone (cospan f g)).π WalkingCospan.right) :=
Abelian.epi_pullback_of_epi_f f g
apply epi_of_epi_fac (IsLimit.conePointUniqueUpToIso_hom_comp (limit.isLimit _) hs _) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.ClusterPt | {
"line": 250,
"column": 2
} | {
"line": 251,
"column": 51
} | {
"line": 253,
"column": 0
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\nf : Filter X\n⊢ IsClosed[inst✝] {x | ClusterPt x f}",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"isClosed_biInter",
"congrArg",
"Set.iInter",
"setOf",
"Membershi... | [] | simp only [clusterPt_iff_forall_mem_closure, setOf_forall]
exact isClosed_biInter fun _ _ ↦ isClosed_closure | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ClusterPt | {
"line": 250,
"column": 2
} | {
"line": 251,
"column": 51
} | {
"line": 253,
"column": 0
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\nf : Filter X\n⊢ IsClosed[inst✝] {x | ClusterPt x f}",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"isClosed_biInter",
"congrArg",
"Set.iInter",
"setOf",
"Membershi... | [] | simp only [clusterPt_iff_forall_mem_closure, setOf_forall]
exact isClosed_biInter fun _ _ ↦ isClosed_closure | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Prod | {
"line": 300,
"column": 72
} | {
"line": 302,
"column": 45
} | {
"line": 304,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : Filter α\ng : Filter β\nh : Filter γ\n⊢ map (⇑(Equiv.prodAssoc α β γ).symm) (f ×ˢ g ×ˢ h) = (f ×ˢ g) ×ˢ h",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Equiv.instEquivLike",
"CompleteLattice.toLattice",
... | [] | by
simp_rw [map_equiv_symm, prod_eq_inf, comap_inf, comap_comap, inf_assoc,
Function.comp_def, Equiv.prodAssoc_apply] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Homeomorph.Defs | {
"line": 241,
"column": 4
} | {
"line": 241,
"column": 48
} | {
"line": 243,
"column": 0
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nh : X ≃ₜ Y\n⊢ IsQuotientMap (⇑h ∘ ⇑h.symm)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"Function.comp",
"id",
"_private.Mathlib.Topology.Homeomorph.Defs.0.H... | [] | simp only [self_comp_symm, IsQuotientMap.id] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.Homeomorph.Defs | {
"line": 241,
"column": 4
} | {
"line": 241,
"column": 48
} | {
"line": 243,
"column": 0
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nh : X ≃ₜ Y\n⊢ IsQuotientMap (⇑h ∘ ⇑h.symm)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"Function.comp",
"id",
"_private.Mathlib.Topology.Homeomorph.Defs.0.H... | [] | simp only [self_comp_symm, IsQuotientMap.id] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Homeomorph.Defs | {
"line": 241,
"column": 4
} | {
"line": 241,
"column": 48
} | {
"line": 243,
"column": 0
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nh : X ≃ₜ Y\n⊢ IsQuotientMap (⇑h ∘ ⇑h.symm)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"Function.comp",
"id",
"_private.Mathlib.Topology.Homeomorph.Defs.0.H... | [] | simp only [self_comp_symm, IsQuotientMap.id] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order | {
"line": 971,
"column": 2
} | {
"line": 971,
"column": 25
} | {
"line": 973,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : Filter α\np : α → Prop\nq : Prop\n⊢ Tendsto p l (𝓝 q) ↔ q → ∀ᶠ (x : α) in l, p x",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Pure.pure",
"False",
"eq_false",
"nhds_false",
"congrArg",
"Filter.Eventually",
"nhds_true"... | [] | by_cases q <;> simp [*] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Topology.Order | {
"line": 971,
"column": 2
} | {
"line": 971,
"column": 25
} | {
"line": 973,
"column": 0
} | [
{
"pp": "α : Type u_1\nl : Filter α\np : α → Prop\nq : Prop\n⊢ Tendsto p l (𝓝 q) ↔ q → ∀ᶠ (x : α) in l, p x",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Pure.pure",
"False",
"eq_false",
"nhds_false",
"congrArg",
"Filter.Eventually",
"nhds_true"... | [] | by_cases q <;> simp [*] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
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