module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 165,
"column": 6
} | {
"line": 165,
"column": 67
} | {
"line": 166,
"column": 2
} | [
{
"pp": "case a.inr\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝¹ : LinearOrder ι\nf : P.RankFunction ι\ninst✝ : SuccOrder ι\nj : ι\nc : f.Cell j\nhi : ¬IsMax j\nhj : j ≤ j\n⊢ (↑(P.p c.s)).subcomplex ≤ f.filtration j ⊔ ⨆ c, (↑(P.p c.s)).subcomplex",
"ppTerm": "?a.inr✝",
"assigned": true... | [] | exact le_trans (le_trans (by rfl) (le_iSup _ c)) le_sup_right | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 216,
"column": 2
} | {
"line": 216,
"column": 33
} | {
"line": 217,
"column": 2
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝⁴ : LinearOrder ι\nf : P.RankFunction ι\ninst✝³ : P.IsProper\ninst✝² : OrderBot ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\n⊢ ⨆ i, f.filtration i = ⊤",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Lattice.toSem... | [
"X : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝⁴ : LinearOrder ι\nf : P.RankFunction ι\ninst✝³ : P.IsProper\ninst✝² : OrderBot ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\n⊢ ⊤ ≤ ⨆ i, f.filtration i"
] | refine le_antisymm (by simp) ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 220,
"column": 16
} | {
"line": 220,
"column": 65
} | {
"line": 221,
"column": 2
} | [
{
"pp": "case mem\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝⁴ : LinearOrder ι\nf : P.RankFunction ι\ninst✝³ : P.IsProper\ninst✝² : OrderBot ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\ns : X.N\na✝ : s.subcomplex ≤ ⊤\nhs : s.subcomplex ≤ A\n⊢ s.subcomplex ≤ ⨆ i, f.filtration i",
"ppTerm"... | [] | exact hs.trans (le_trans (by simp) (le_iSup _ ⊥)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 220,
"column": 16
} | {
"line": 220,
"column": 65
} | {
"line": 221,
"column": 2
} | [
{
"pp": "case mem\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝⁴ : LinearOrder ι\nf : P.RankFunction ι\ninst✝³ : P.IsProper\ninst✝² : OrderBot ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\ns : X.N\na✝ : s.subcomplex ≤ ⊤\nhs : s.subcomplex ≤ A\n⊢ s.subcomplex ≤ ⨆ i, f.filtration i",
"ppTerm"... | [] | exact hs.trans (le_trans (by simp) (le_iSup _ ⊥)) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 220,
"column": 16
} | {
"line": 220,
"column": 65
} | {
"line": 221,
"column": 2
} | [
{
"pp": "case mem\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝⁴ : LinearOrder ι\nf : P.RankFunction ι\ninst✝³ : P.IsProper\ninst✝² : OrderBot ι\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\ns : X.N\na✝ : s.subcomplex ≤ ⊤\nhs : s.subcomplex ≤ A\n⊢ s.subcomplex ≤ ⨆ i, f.filtration i",
"ppTerm"... | [] | exact hs.trans (le_trans (by simp) (le_iSup _ ⊥)) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.Generator.StrongGenerator | {
"line": 95,
"column": 65
} | {
"line": 97,
"column": 36
} | {
"line": 99,
"column": 0
} | [
{
"pp": "C : Type u\ninst✝¹ : Category.{v, u} C\nP : ObjectProperty C\nhP : P.IsStrongGenerator\nX Y : C\ni : X ⟶ Y\ninst✝ : Mono i\nhi : ¬IsIso i\n⊢ ∃ G, ∃ (_ : P G), ∃ g, ∀ (f : G ⟶ X), f ≫ i ≠ g",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Push.not_forall_eq",
... | [] | by
by_contra!
exact hi (hP.isIso_of_mono i this) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.CategoryTheory.Presentable.StrongGenerator | {
"line": 47,
"column": 4
} | {
"line": 47,
"column": 25
} | {
"line": 48,
"column": 4
} | [
{
"pp": "C : Type u\ninst✝⁷ : Category.{v, u} C\ninst✝⁶ : LocallySmall.{w, v, u} C\nJ : Type u'\ninst✝⁵ : Category.{v', u'} J\ninst✝⁴ : EssentiallySmall.{w, v', u'} J\nF : J ⥤ C\ninst✝³ : F.IsDense\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : ∀ (j : J), IsCardinalPresentable (F.obj j) κ\ninst✝ : ∀ (X ... | [
"C : Type u\ninst✝⁷ : Category.{v, u} C\ninst✝⁶ : LocallySmall.{w, v, u} C\nJ : Type u'\ninst✝⁵ : Category.{v', u'} J\ninst✝⁴ : EssentiallySmall.{w, v', u'} J\nF : J ⥤ C\ninst✝³ : F.IsDense\nκ : Cardinal.{w}\ninst✝² : Fact κ.IsRegular\ninst✝¹ : ∀ (j : J), IsCardinalPresentable (F.obj j) κ\ninst✝ : ∀ (X : C), IsCard... | rintro X ⟨Y, hY, ⟨e⟩⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | {
"line": 557,
"column": 11
} | {
"line": 557,
"column": 16
} | {
"line": 559,
"column": 0
} | [
{
"pp": "case inr.inr\nX : SSet\nA : X.Subcomplex\nP : A.Pairing\nι : Type v\ninst✝³ : LinearOrder ι\nf : P.RankFunction ι\ninst✝² : P.IsProper\ninst✝¹ : SuccOrder ι\ninst✝ : NoMaxOrder ι\nj : ι\nc c' : f.Cell j\nh : c.s = c'.s\n⊢ c = c'",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | {
"line": 48,
"column": 27
} | {
"line": 48,
"column": 32
} | {
"line": 48,
"column": 32
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nx y : ↑P.II\n⊢ ⟨N.opEquiv.symm ↑x, ⋯⟩ = ⟨N.opEquiv.symm ↑y, ⋯⟩ ↔ x = y",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.N.opEquiv",
"Eq.mpr",
"SSet.op",
"congrArg",
"PartialOrder.toPreorder",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | {
"line": 48,
"column": 27
} | {
"line": 48,
"column": 32
} | {
"line": 48,
"column": 32
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nx y : ↑P.II\n⊢ ⟨N.opEquiv.symm ↑x, ⋯⟩ = ⟨N.opEquiv.symm ↑y, ⋯⟩ ↔ x = y",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.N.opEquiv",
"Eq.mpr",
"SSet.op",
"congrArg",
"PartialOrder.toPreorder",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Op | {
"line": 48,
"column": 27
} | {
"line": 48,
"column": 32
} | {
"line": 48,
"column": 32
} | [
{
"pp": "X : SSet\nA : X.Subcomplex\nP : A.Pairing\nx y : ↑P.II\n⊢ ⟨N.opEquiv.symm ↑x, ⋯⟩ = ⟨N.opEquiv.symm ↑y, ⋯⟩ ↔ x = y",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"SSet.Subcomplex.N.opEquiv",
"Eq.mpr",
"SSet.op",
"congrArg",
"PartialOrder.toPreorder",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 327,
"column": 56
} | {
"line": 327,
"column": 61
} | {
"line": 327,
"column": 61
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd✝ : ℕ\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\ni : Fin (d + 2)\nhi : (min x hd).castSucc < i\n⊢ i ≠ 0",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.in... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 327,
"column": 56
} | {
"line": 327,
"column": 61
} | {
"line": 327,
"column": 61
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd✝ : ℕ\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\ni : Fin (d + 2)\nhi : (min x hd).castSucc < i\n⊢ i ≠ 0",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.in... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 327,
"column": 56
} | {
"line": 327,
"column": 61
} | {
"line": 327,
"column": 61
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd✝ : ℕ\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\ni : Fin (d + 2)\nhi : (min x hd).castSucc < i\n⊢ i ≠ 0",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.in... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 353,
"column": 34
} | {
"line": 353,
"column": 55
} | {
"line": 353,
"column": 55
} | [
{
"pp": "case inl\nm : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\nhx' : StrictMono ⇑(objEquiv (x.cast hd).simplex)\ni : Fin d\nhi : i.castSucc < min x hd\n⊢ (objEquiv (x.cast hd).simplex) (i.castSucc.castSucc.castPred ⋯) < φ x hd i.castSucc.su... | [
"case inl\nm : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\nhx' : StrictMono ⇑(objEquiv (x.cast hd).simplex)\ni : Fin d\nhi : i.castSucc < min x hd\n⊢ (objEquiv (x.cast hd).simplex) i.castSucc < φ x hd i.castSucc.succ"
] | Fin.castPred_castSucc | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 371,
"column": 27
} | {
"line": 371,
"column": 32
} | {
"line": 371,
"column": 32
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\nhx' : StrictMono ⇑(objEquiv (x.cast hd).simplex)\ni : Fin d\nhi✝ : i.succ ≤ min x hd\nhi : i.succ = min x hd\nh₁ : (x.cast hd).simplex.1 i.castSucc = k.castSucc\nh₂ : (x.cast hd).simplex.... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 371,
"column": 27
} | {
"line": 371,
"column": 32
} | {
"line": 371,
"column": 32
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\nhx' : StrictMono ⇑(objEquiv (x.cast hd).simplex)\ni : Fin d\nhi✝ : i.succ ≤ min x hd\nhi : i.succ = min x hd\nh₁ : (x.cast hd).simplex.1 i.castSucc = k.castSucc\nh₂ : (x.cast hd).simplex.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 371,
"column": 27
} | {
"line": 371,
"column": 32
} | {
"line": 371,
"column": 32
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nhx : IsType₂ x\nd : ℕ\nhd : x.dim = d\nhx' : StrictMono ⇑(objEquiv (x.cast hd).simplex)\ni : Fin d\nhi✝ : i.succ ≤ min x hd\nhi : i.succ = min x hd\nh₁ : (x.cast hd).simplex.1 i.castSucc = k.castSucc\nh₂ : (x.cast hd).simplex.... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 160,
"column": 19
} | {
"line": 160,
"column": 24
} | {
"line": 161,
"column": 2
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 160,
"column": 19
} | {
"line": 160,
"column": 24
} | {
"line": 161,
"column": 2
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 160,
"column": 19
} | {
"line": 160,
"column": 24
} | {
"line": 161,
"column": 2
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 161,
"column": 20
} | {
"line": 161,
"column": 25
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 161,
"column": 20
} | {
"line": 161,
"column": 25
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 161,
"column": 20
} | {
"line": 161,
"column": 25
} | {
"line": 163,
"column": 0
} | [
{
"pp": "C₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.CategoryTheory.LiftingProperties.ParametrizedAdjunction | {
"line": 168,
"column": 4
} | {
"line": 168,
"column": 13
} | {
"line": 169,
"column": 4
} | [
{
"pp": "case mp\nC₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\... | [
"case mp\nC₁ : Type u₁\nC₂ : Type u₂\nC₃ : Type u₃\ninst✝² : Category.{v₁, u₁} C₁\ninst✝¹ : Category.{v₂, u₂} C₂\ninst✝ : Category.{v₃, u₃} C₃\nF : C₁ ⥤ C₂ ⥤ C₃\nG : C₁ᵒᵖ ⥤ C₃ ⥤ C₂\nadj₂ : F ⊣₂ G\nX₁ Y₁ : C₁\nf₁ : X₁ ⟶ Y₁\nX₂ Y₂ : C₂\nf₂ : X₂ ⟶ Y₂\nX₃ Y₃ : C₃\nf₃ : X₃ ⟶ Y₃\nsq₁₂ : F.PushoutObjObj f₁ f₂\nsq₁₃ : G.Pu... | intro h β | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.UnionProd | {
"line": 455,
"column": 2
} | {
"line": 455,
"column": 7
} | {
"line": 457,
"column": 0
} | [
{
"pp": "m : ℕ\nk : Fin (m + 1)\nn : ℕ\nx : (Λ[m + 1, k.castSucc].unionProd ∂Δ[n]).N\nd : ℕ\nhd : x.dim = d + 1\nt : Fin d\nhl✝ : IsIndex x hd t.succ.succ\nhl :\n (x.cast hd).simplex.1 t.castSucc.succ = k.castSucc ∧\n (x.cast hd).simplex.1 t.succ.succ = k.succ ∧\n (x.cast hd).simplex.2 t.succ.succ = (x... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.HomologyZero | {
"line": 135,
"column": 24
} | {
"line": 135,
"column": 39
} | {
"line": 136,
"column": 2
} | [
{
"pp": "C : Type u\ninst✝⁴ : Category.{v, u} C\ninst✝³ : HasCoproducts C\ninst✝² : Preadditive C\nX : SSet\nR : C\ninst✝¹ : CategoryWithHomology C\ninst✝ : X.IsConnected\nx : X.π₀ := Classical.arbitrary X.π₀\ny : X.π₀\n⊢ x = y",
"ppTerm": "?m.50",
"assigned": true,
"usedConstants": [
"SSet.π₀... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | {
"line": 77,
"column": 2
} | {
"line": 77,
"column": 7
} | {
"line": 79,
"column": 0
} | [
{
"pp": "X Y : SSet\nA : X.Subcomplex\nB : Y.Subcomplex\nφ : A.toSSet ⟶ B.toSSet\nf : RelativeMorphism A B φ\nn : SimplexCategoryᵒᵖ\na : X.obj n\nha : a ∈ A.obj n\nthis : (ConcreteCategory.hom (f.map.app n)) ↑⟨a, ha⟩ = ↑((ConcreteCategory.hom (φ.app n)) ⟨a, ha⟩)\n⊢ (ConcreteCategory.hom (f.map.app n)) a ∈ B.obj... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 126,
"column": 22
} | {
"line": 126,
"column": 77
} | {
"line": 126,
"column": 77
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX : SSet\nR : C\nn : ℕ\nx : X _⦋n⦌\n⊢ X.ιChainComplex x ≫ (X.toNormalizedChainComplex R).f n ≫ (X.fromNormalizedChainComplex R).f n =\n X.ιChainComplex x ≫ PInfty.f n",
"ppTerm": "?m.68",
"assigned": tru... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX : SSet\nR : C\nn : ℕ\nx : X _⦋n⦌\n⊢ X.ιChainComplex x ≫ PInfty.f n = X.ιChainComplex x ≫ PInfty.f n"
] | toNormalizedChainComplex_f_fromNormalizedChainComplex_f | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate | {
"line": 157,
"column": 4
} | {
"line": 157,
"column": 59
} | {
"line": 157,
"column": 59
} | [
{
"pp": "C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX : SSet\nR : C\nn : ℕ\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ Sigma.ι (fun x ↦ R) x ≫ (X.toNormalizedChainComplex R).f n ≫ (X.fromNormalizedChainComplex R).f n =\n Sigma.ι (fun x ↦ R) ⟨x, hx⟩ ≫ (X.fromNormal... | [
"C : Type u\ninst✝² : Category.{v, u} C\ninst✝¹ : HasCoproducts C\ninst✝ : Preadditive C\nX : SSet\nR : C\nn : ℕ\nx : X _⦋n⦌\nhx : x ∈ X.nonDegenerate n\n⊢ Sigma.ι (fun x ↦ R) x ≫ PInfty.f n = Sigma.ι (fun x ↦ R) ⟨x, hx⟩ ≫ (X.fromNormalizedChainComplex R).f n"
] | toNormalizedChainComplex_f_fromNormalizedChainComplex_f | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 82,
"column": 48
} | {
"line": 82,
"column": 53
} | {
"line": 82,
"column": 53
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf : X.PtSimplex n x\ni : Fin (n + 1)\nj : Fin (n + 2)\nhj : j < i.castSucc\n⊢ i ≠ 0",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZe... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 82,
"column": 48
} | {
"line": 82,
"column": 53
} | {
"line": 82,
"column": 53
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf : X.PtSimplex n x\ni : Fin (n + 1)\nj : Fin (n + 2)\nhj : j < i.castSucc\n⊢ i ≠ 0",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 82,
"column": 48
} | {
"line": 82,
"column": 53
} | {
"line": 82,
"column": 53
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf : X.PtSimplex n x\ni : Fin (n + 1)\nj : Fin (n + 2)\nhj : j < i.castSucc\n⊢ i ≠ 0",
"ppTerm": "?m.68",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 89,
"column": 48
} | {
"line": 89,
"column": 53
} | {
"line": 89,
"column": 53
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf : X.PtSimplex n x\nj : Fin (n + 2)\ni : Fin n\nhj : i.castSucc.succ < j\n⊢ j ≠ 0",
"ppTerm": "?m.203",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZe... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 89,
"column": 48
} | {
"line": 89,
"column": 53
} | {
"line": 89,
"column": 53
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf : X.PtSimplex n x\nj : Fin (n + 2)\ni : Fin n\nhj : i.castSucc.succ < j\n⊢ j ≠ 0",
"ppTerm": "?m.203",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.KanComplex.MulStruct | {
"line": 89,
"column": 48
} | {
"line": 89,
"column": 53
} | {
"line": 89,
"column": 53
} | [
{
"pp": "X : SSet\nn : ℕ\nx : X _⦋0⦌\nf : X.PtSimplex n x\nj : Fin (n + 2)\ni : Fin n\nhj : i.castSucc.succ < j\n⊢ j ≠ 0",
"ppTerm": "?m.203",
"assigned": true,
"usedConstants": [
"not_lt_zero._simp_1",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZe... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.NonemptyFiniteChains | {
"line": 44,
"column": 43
} | {
"line": 44,
"column": 48
} | {
"line": 44,
"column": 48
} | [
{
"pp": "X : Type u\ninst✝ : PartialOrder X\nx✝² x✝¹ : NonemptyFiniteChains X\nx✝ : x✝².finset = x✝¹.finset\n⊢ x✝² = x✝¹",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"PartialOrder.NonemptyFiniteChains.ext",
"congrArg",
"Finset",
"Finset.ext",
"Membership.me... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Order.NonemptyFiniteChains | {
"line": 44,
"column": 43
} | {
"line": 44,
"column": 48
} | {
"line": 44,
"column": 48
} | [
{
"pp": "X : Type u\ninst✝ : PartialOrder X\nx✝² x✝¹ : NonemptyFiniteChains X\nx✝ : x✝².finset = x✝¹.finset\n⊢ x✝² = x✝¹",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"PartialOrder.NonemptyFiniteChains.ext",
"congrArg",
"Finset",
"Finset.ext",
"Membership.me... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.NonemptyFiniteChains | {
"line": 44,
"column": 43
} | {
"line": 44,
"column": 48
} | {
"line": 44,
"column": 48
} | [
{
"pp": "X : Type u\ninst✝ : PartialOrder X\nx✝² x✝¹ : NonemptyFiniteChains X\nx✝ : x✝².finset = x✝¹.finset\n⊢ x✝² = x✝¹",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"PartialOrder.NonemptyFiniteChains.ext",
"congrArg",
"Finset",
"Finset.ext",
"Membership.me... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.NonemptyFiniteChains | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 29
} | {
"line": 82,
"column": 4
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : PartialOrder X\ninst✝ : PartialOrder Y\nf : X →o Y\na b : NonemptyFiniteChains X\nh : a ≤ b\nx : Y\nhx : ∃ x_1 ∈ a.finset, f x_1 = x\n⊢ ∃ x_1 ∈ b.finset, f x_1 = x",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Finset",
"PartialOr... | [
"X : Type u_1\nY : Type u_2\ninst✝¹ : PartialOrder X\ninst✝ : PartialOrder Y\nf : X →o Y\na b : NonemptyFiniteChains X\nh : a ≤ b\nx : X\nhx : x ∈ a.finset\n⊢ ∃ x_1 ∈ b.finset, f x_1 = f x"
] | obtain ⟨x, hx, rfl⟩ := hx | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | {
"line": 76,
"column": 19
} | {
"line": 76,
"column": 24
} | {
"line": 77,
"column": 2
} | [
{
"pp": "X : TopCat\nx y : ↑X\nx✝ : SSet.Edge (toSSetObj₀Equiv.symm x) (toSSetObj₀Equiv.symm y)\n⊢ (fun p ↦ SSet.Edge.mk (toSSetObj₁Equiv.symm p.hom) ⋯ ⋯)\n ((fun e ↦ { hom := toSSetObj₁Equiv e.edge, hom₀ := ⋯, hom₁ := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | {
"line": 76,
"column": 19
} | {
"line": 76,
"column": 24
} | {
"line": 77,
"column": 2
} | [
{
"pp": "X : TopCat\nx y : ↑X\nx✝ : SSet.Edge (toSSetObj₀Equiv.symm x) (toSSetObj₀Equiv.symm y)\n⊢ (fun p ↦ SSet.Edge.mk (toSSetObj₁Equiv.symm p.hom) ⋯ ⋯)\n ((fun e ↦ { hom := toSSetObj₁Equiv e.edge, hom₀ := ⋯, hom₁ := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | {
"line": 76,
"column": 19
} | {
"line": 76,
"column": 24
} | {
"line": 77,
"column": 2
} | [
{
"pp": "X : TopCat\nx y : ↑X\nx✝ : SSet.Edge (toSSetObj₀Equiv.symm x) (toSSetObj₀Equiv.symm y)\n⊢ (fun p ↦ SSet.Edge.mk (toSSetObj₁Equiv.symm p.hom) ⋯ ⋯)\n ((fun e ↦ { hom := toSSetObj₁Equiv e.edge, hom₀ := ⋯, hom₁ := ⋯ }) x✝) =\n x✝",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | {
"line": 77,
"column": 20
} | {
"line": 77,
"column": 25
} | {
"line": 79,
"column": 0
} | [
{
"pp": "X : TopCat\nx y : ↑X\nx✝ : X.Path x y\n⊢ (fun e ↦ { hom := toSSetObj₁Equiv e.edge, hom₀ := ⋯, hom₁ := ⋯ })\n ((fun p ↦ SSet.Edge.mk (toSSetObj₁Equiv.symm p.hom) ⋯ ⋯) x✝) =\n x✝",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"TopCat.toSSetObjEdgeEquiv._proof_2",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | {
"line": 77,
"column": 20
} | {
"line": 77,
"column": 25
} | {
"line": 79,
"column": 0
} | [
{
"pp": "X : TopCat\nx y : ↑X\nx✝ : X.Path x y\n⊢ (fun e ↦ { hom := toSSetObj₁Equiv e.edge, hom₀ := ⋯, hom₁ := ⋯ })\n ((fun p ↦ SSet.Edge.mk (toSSetObj₁Equiv.symm p.hom) ⋯ ⋯) x✝) =\n x✝",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"TopCat.toSSetObjEdgeEquiv._proof_2",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Homotopy.TopCat.ZerothHomotopy | {
"line": 77,
"column": 20
} | {
"line": 77,
"column": 25
} | {
"line": 79,
"column": 0
} | [
{
"pp": "X : TopCat\nx y : ↑X\nx✝ : X.Path x y\n⊢ (fun e ↦ { hom := toSSetObj₁Equiv e.edge, hom₀ := ⋯, hom₁ := ⋯ })\n ((fun p ↦ SSet.Edge.mk (toSSetObj₁Equiv.symm p.hom) ⋯ ⋯) x✝) =\n x✝",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"TopCat.toSSetObjEdgeEquiv._proof_2",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.TopAdj | {
"line": 134,
"column": 66
} | {
"line": 134,
"column": 81
} | {
"line": 134,
"column": 81
} | [
{
"pp": "X : TopCat\nf : SSet.toTop.obj Δ[0] ⟶ X\n⊢ TopCat.toSSetObj₀Equiv (SSet.yonedaEquiv (sSetTopAdj.unit.app Δ[0])) =\n TopCat.toSSetObj₀Equiv (SSet.yonedaEquiv (SSet.const (TopCat.toSSetObj₀Equiv.symm default)))",
"ppTerm": "?m.75",
"assigned": true,
"usedConstants": [
"SSet.yonedaEqu... | [] | by subsingleton | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Cardinal.CountableCover | {
"line": 98,
"column": 2
} | {
"line": 100,
"column": 25
} | {
"line": 102,
"column": 0
} | [
{
"pp": "case a\nα : Type u\nι : Type v\na : Cardinal.{u}\ninst✝¹ : Countable ι\nf : ι → Set α\nl : Filter ι\ninst✝ : l.NeBot\nht : ∀ (x : α), ∀ᶠ (i : ι) in l, x ∈ f i\nh'f : ∀ (i : ι), #↑(f i) = a\n⊢ a ≤ #α",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
... | [] | · obtain ⟨i⟩ : Nonempty ι := nonempty_of_neBot l
rw [← (h'f i)]
exact mk_set_le (f i) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 182,
"column": 22
} | {
"line": 182,
"column": 67
} | {
"line": 183,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | OrderTopology.topology_eq_generate_intervals, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 217,
"column": 22
} | {
"line": 217,
"column": 67
} | {
"line": 218,
"column": 4
} | [
{
"pp": "R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1... | [
"R : Type u_1\nS : Type u_2\ninst✝⁷ : Field R\ninst✝⁶ : Field S\ninst✝⁵ : LinearOrder S\ninst✝⁴ : TopologicalSpace S\ninst✝³ : IsStrictOrderedRing S\ninst✝² : Archimedean S\ninst✝¹ : OrderTopology S\nι : Type u_3\ninst✝ : Finite ι\nv : ι → AbsoluteValue R S\nw : AbsoluteValue R S\na b : R\ni : ι\nha : 1 < (v i) a\n... | OrderTopology.topology_eq_generate_intervals, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Analysis.AbsoluteValue.Equivalence | {
"line": 421,
"column": 16
} | {
"line": 421,
"column": 33
} | {
"line": 421,
"column": 33
} | [
{
"pp": "case pos\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι),... | [
"case pos\nF : Type u_1\ninst✝¹ : Field F\nι : Type u_2\ninst✝ : Finite ι\nv : ι → AbsoluteValue F ℝ\nh : ∀ (i : ι), (v i).IsNontrivial\nhv : Pairwise fun i j ↦ ¬(v i).IsEquiv (v j)\nthis : Fintype ι\nz : (i : ι) → WithAbs (v i)\nr : ℝ\nhr : r > 0\na : ι → F\nhx : ∀ (i : ι), 1 < (v i) (a i) ∧ ∀ (j : ι), j ≠ i → (v ... | Pi.single_eq_same | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 135,
"column": 49
} | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhf : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteMulSupport F\n⊢ ∀ σ ∈ Finite.toFinset h₂f, MeromorphicAt (F σ) x... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 135,
"column": 49
} | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhf : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteMulSupport F\n⊢ ∀ σ ∈ Finite.toFinset h₂f, MeromorphicAt (F σ) x... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 135,
"column": 49
} | {
"line": 135,
"column": 54
} | {
"line": 135,
"column": 54
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhf : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteMulSupport F\n⊢ ∀ σ ∈ Finite.toFinset h₂f, MeromorphicAt (F σ) x... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 164,
"column": 46
} | {
"line": 164,
"column": 51
} | {
"line": 164,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhF : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteSupport F\n⊢ ∀ σ ∈ Finite.toFinset h₂f, MeromorphicAt (F σ) x",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 164,
"column": 46
} | {
"line": 164,
"column": 51
} | {
"line": 164,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhF : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteSupport F\n⊢ ∀ σ ∈ Finite.toFinset h₂f, MeromorphicAt (F σ) x",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 164,
"column": 46
} | {
"line": 164,
"column": 51
} | {
"line": 164,
"column": 51
} | [
{
"pp": "𝕜 : Type u_1\n𝕜' : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NontriviallyNormedField 𝕜'\ninst✝ : NormedAlgebra 𝕜 𝕜'\nι : Type u_5\nF : ι → 𝕜 → 𝕜'\nx : 𝕜\nhF : ∀ (i : ι), MeromorphicAt (F i) x\nh₂f : Function.HasFiniteSupport F\n⊢ ∀ σ ∈ Finite.toFinset h₂f, MeromorphicAt (F σ) x",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 256,
"column": 88
} | {
"line": 256,
"column": 93
} | {
"line": 256,
"column": 93
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nx : X.obj (op { obj := ⦋0⦌, property := _proof_11 })\n⊢ F.mapArrow.obj (Arrow.mk (homMk (Edge.id x))) =\n ComposableArrows.arrowEquiv\n ((ConcreteCategory.hom (((truncation 2).obj (nerv... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 256,
"column": 88
} | {
"line": 256,
"column": 93
} | {
"line": 256,
"column": 93
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nx : X.obj (op { obj := ⦋0⦌, property := _proof_11 })\n⊢ F.mapArrow.obj (Arrow.mk (homMk (Edge.id x))) =\n ComposableArrows.arrowEquiv\n ((ConcreteCategory.hom (((truncation 2).obj (nerv... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 256,
"column": 88
} | {
"line": 256,
"column": 93
} | {
"line": 256,
"column": 93
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nx : X.obj (op { obj := ⦋0⦌, property := _proof_11 })\n⊢ F.mapArrow.obj (Arrow.mk (homMk (Edge.id x))) =\n ComposableArrows.arrowEquiv\n ((ConcreteCategory.hom (((truncation 2).obj (nerv... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 291,
"column": 6
} | {
"line": 291,
"column": 67
} | {
"line": 291,
"column": 67
} | [
{
"pp": "X : Truncated 2\nC D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nx y : X.obj (op { obj := ⦋0⦌, property := OneTruncation₂._proof_1 })\nf : Edge x y\n⊢ nerve.homEquiv (f.map (homToNerveMk F)) = F.map (homMk f)",
"ppTerm": "?m.54",
"assigned": true,
... | [] | exact nerve.homEquiv.symm.injective (Edge.ext (by cat_disch)) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 315,
"column": 44
} | {
"line": 315,
"column": 49
} | {
"line": 315,
"column": 49
} | [
{
"pp": "X : Truncated 2\nC : Type u\ninst✝¹ : SmallCategory C\nD : Type u\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nG : C ⥤ D\nx₀ x₁ : X.obj (op { obj := ⦋0⦌, property := Edge._proof_1 })\nf : Edge x₀ x₁\n⊢ (ComposableArrows.mk₁ (G.map (F.map (homMk f)))).hom =\n eqToHom ⋯ ≫\n ComposableArr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 315,
"column": 44
} | {
"line": 315,
"column": 49
} | {
"line": 315,
"column": 49
} | [
{
"pp": "X : Truncated 2\nC : Type u\ninst✝¹ : SmallCategory C\nD : Type u\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nG : C ⥤ D\nx₀ x₁ : X.obj (op { obj := ⦋0⦌, property := Edge._proof_1 })\nf : Edge x₀ x₁\n⊢ (ComposableArrows.mk₁ (G.map (F.map (homMk f)))).hom =\n eqToHom ⋯ ≫\n ComposableArr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 315,
"column": 44
} | {
"line": 315,
"column": 49
} | {
"line": 315,
"column": 49
} | [
{
"pp": "X : Truncated 2\nC : Type u\ninst✝¹ : SmallCategory C\nD : Type u\ninst✝ : SmallCategory D\nF : X.HomotopyCategory ⥤ C\nG : C ⥤ D\nx₀ x₁ : X.obj (op { obj := ⦋0⦌, property := Edge._proof_1 })\nf : Edge x₀ x₁\n⊢ (ComposableArrows.mk₁ (G.map (F.map (homMk f)))).hom =\n eqToHom ⋯ ≫\n ComposableArr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.AlgebraicTopology.SimplicialSet.NerveAdjunction | {
"line": 347,
"column": 18
} | {
"line": 349,
"column": 58
} | {
"line": 351,
"column": 0
} | [
{
"pp": "C D : Type u\ninst✝¹ : SmallCategory C\ninst✝ : SmallCategory D\nφ : nerveFunctor₂.obj (Cat.of C) ⟶ nerveFunctor₂.obj (Cat.of D)\nX✝ Y✝ Z✝ : C\nf : X✝ ⟶ Y✝\ng : Y✝ ⟶ Z✝\n⊢ homEquiv ((edgeMk (f ≫ g)).toTruncated.map φ) =\n homEquiv ((edgeMk f).toTruncated.map φ) ≫ homEquiv ((edgeMk g).toTruncated.map... | [] | by
obtain ⟨h⟩ := (nerve.nonempty_compStruct_iff f g (f ≫ g)).2 rfl
exact (nerve.homEquiv_comp (h.toTruncated.map φ)).symm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 147,
"column": 2
} | {
"line": 147,
"column": 95
} | {
"line": 148,
"column": 2
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\nb c : 𝕂\nk : ℕ\n⊢ (ordinaryHypergeometricSeries 𝔸 (-↑k) b c).radius = ⊤",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"IsTopological... | [
"𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\nb c : 𝕂\nk n : ℕ\n⊢ ordinaryHypergeometricSeries 𝔸 (-↑k) b c (n + (1 + k)) = 0"
] | refine FormalMultilinearSeries.radius_eq_top_of_forall_image_add_eq_zero _ (1 + k) fun n ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 148,
"column": 75
} | {
"line": 148,
"column": 80
} | {
"line": 148,
"column": 80
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\nb c : 𝕂\nk n : ℕ\n⊢ ↑?m.51 = - -↑k ∨ ↑?m.51 = -b ∨ ↑?m.51 = -c",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnit... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 148,
"column": 75
} | {
"line": 148,
"column": 80
} | {
"line": 148,
"column": 80
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\nb c : 𝕂\nk n : ℕ\n⊢ ↑?m.51 = - -↑k ∨ ↑?m.51 = -b ∨ ↑?m.51 = -c",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnit... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 148,
"column": 75
} | {
"line": 148,
"column": 80
} | {
"line": 148,
"column": 80
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\nb c : 𝕂\nk n : ℕ\n⊢ ↑?m.51 = - -↑k ∨ ↑?m.51 = -b ∨ ↑?m.51 = -c",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnit... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 95
} | {
"line": 158,
"column": 2
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b : 𝕂\nk : ℕ\n⊢ (ordinaryHypergeometricSeries 𝔸 a b (-↑k)).radius = ⊤",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"NegZeroClass.toNeg",
"IsTopological... | [
"𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b : 𝕂\nk n : ℕ\n⊢ ordinaryHypergeometricSeries 𝔸 a b (-↑k) (n + (1 + k)) = 0"
] | refine FormalMultilinearSeries.radius_eq_top_of_forall_image_add_eq_zero _ (1 + k) fun n ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 158,
"column": 75
} | {
"line": 158,
"column": 80
} | {
"line": 158,
"column": 80
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b : 𝕂\nk n : ℕ\n⊢ ↑?m.51 = -a ∨ ↑?m.51 = -b ∨ ↑?m.51 = - -↑k",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnit... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 158,
"column": 75
} | {
"line": 158,
"column": 80
} | {
"line": 158,
"column": 80
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b : 𝕂\nk n : ℕ\n⊢ ↑?m.51 = -a ∨ ↑?m.51 = -b ∨ ↑?m.51 = - -↑k",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnit... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | {
"line": 158,
"column": 75
} | {
"line": 158,
"column": 80
} | {
"line": 158,
"column": 80
} | [
{
"pp": "𝕂 : Type u_1\n𝔸 : Type u_2\ninst✝² : RCLike 𝕂\ninst✝¹ : NormedDivisionRing 𝔸\ninst✝ : NormedAlgebra 𝕂 𝔸\na b : 𝕂\nk n : ℕ\n⊢ ↑?m.51 = -a ∨ ↑?m.51 = -b ∨ ↑?m.51 = - -↑k",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnit... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Meromorphic.Basic | {
"line": 384,
"column": 4
} | {
"line": 384,
"column": 9
} | {
"line": 385,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_3\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : CompleteSpace E\nf : 𝕜 → E\nx : 𝕜\nn : ℤ\ng : 𝕜 → E\nh₁g : AnalyticAt 𝕜 g x\nh₂g : ∀ᶠ (z : 𝕜) in 𝓝[≠] x, f z = (z - x) ^ n • g z\nz₀ : 𝕜\nh₁ : AnalyticAt 𝕜 g z₀\nh... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Analytic.Order | {
"line": 555,
"column": 57
} | {
"line": 555,
"column": 62
} | {
"line": 555,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\ng : 𝕜 → 𝕜\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f (g z₀)\nhg : AnalyticAt 𝕜 g z₀\nhg_nc : ¬analyticOrderAt (fun x ↦ g x - g z₀) z₀ = ⊤\nhf' : ¬analyticOrderAt f (g z₀) = ⊤\nr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Analytic.Order | {
"line": 555,
"column": 57
} | {
"line": 555,
"column": 62
} | {
"line": 555,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\ng : 𝕜 → 𝕜\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f (g z₀)\nhg : AnalyticAt 𝕜 g z₀\nhg_nc : ¬analyticOrderAt (fun x ↦ g x - g z₀) z₀ = ⊤\nhf' : ¬analyticOrderAt f (g z₀) = ⊤\nr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.Analytic.Order | {
"line": 555,
"column": 57
} | {
"line": 555,
"column": 62
} | {
"line": 555,
"column": 62
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nf : 𝕜 → E\ng : 𝕜 → 𝕜\nz₀ : 𝕜\nhf : AnalyticAt 𝕜 f (g z₀)\nhg : AnalyticAt 𝕜 g z₀\nhg_nc : ¬analyticOrderAt (fun x ↦ g x - g z₀) z₀ = ⊤\nhf' : ¬analyticOrderAt f (g z₀) = ⊤\nr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.Analytic.Order | {
"line": 590,
"column": 6
} | {
"line": 590,
"column": 92
} | {
"line": 591,
"column": 6
} | [
{
"pp": "case left.inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nhf : AnalyticOnNhd 𝕜 f U\nz : ↑U\nhz : z ∈ {u | analyticOrderAt f ↑u = ⊤}ᶜ\nh : ∀ᶠ (z : 𝕜) in 𝓝[≠] ↑z, f z ≠ 0\n⊢ ∃ t ⊆ {u | analyticOrder... | [
"case left.inr\n𝕜 : Type u_1\nE : Type u_2\ninst✝² : NontriviallyNormedField 𝕜\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace 𝕜 E\nU : Set 𝕜\nf : 𝕜 → E\nhf : AnalyticOnNhd 𝕜 f U\nz : ↑U\nhz : z ∈ {u | analyticOrderAt f ↑u = ⊤}ᶜ\nh : ∀ᶠ (z : 𝕜) in 𝓝[≠] ↑z, f z ≠ 0\nt' : Set 𝕜\nh₁t' : ∀ y ∈ t', y ∈ {↑z}... | obtain ⟨t', h₁t', h₂t', h₃t'⟩ := eventually_nhds_iff.1 (eventually_nhdsWithin_iff.1 h) | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.RingTheory.Binomial | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 50
} | {
"line": 204,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nr : R\nn : ℕ\n⊢ (ascPochhammer ℕ n).smeval r = eval r (ascPochhammer R n)",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"MonoidWithZero.toMulActionWithZero",
"Semiring.toModule",
"congrA... | [] | rw [eval_eq_smeval, ascPochhammer_smeval_cast R] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.RingTheory.Binomial | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 50
} | {
"line": 204,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nr : R\nn : ℕ\n⊢ (ascPochhammer ℕ n).smeval r = eval r (ascPochhammer R n)",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"MonoidWithZero.toMulActionWithZero",
"Semiring.toModule",
"congrA... | [] | rw [eval_eq_smeval, ascPochhammer_smeval_cast R] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.RingTheory.Binomial | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 50
} | {
"line": 204,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : Semiring R\nr : R\nn : ℕ\n⊢ (ascPochhammer ℕ n).smeval r = eval r (ascPochhammer R n)",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Polynomial.eval",
"MonoidWithZero.toMulActionWithZero",
"Semiring.toModule",
"congrA... | [] | rw [eval_eq_smeval, ascPochhammer_smeval_cast R] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 259,
"column": 2
} | {
"line": 294,
"column": 15
} | {
"line": 296,
"column": 0
} | [
{
"pp": "x : ℝ\nhx : x ≠ 0\nr : ℂ\nhr : r ≠ -1\n⊢ HasDerivAt (fun y ↦ ↑y ^ (r + 1) / (r + 1)) (↑x ^ r) x",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"NonUnit... | [] | rw [Ne, ← add_eq_zero_iff_eq_neg, ← Ne] at hr
rcases lt_or_gt_of_ne hx.symm with (hx | hx)
· -- easy case : `0 < x`
apply HasDerivAt.comp_ofReal (e := fun y => (y : ℂ) ^ (r + 1) / (r + 1))
convert! HasDerivAt.div_const (𝕜 := ℂ) ?_ (r + 1) using 1
· exact (mul_div_cancel_right₀ _ hr).symm
· convert!... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 259,
"column": 2
} | {
"line": 294,
"column": 15
} | {
"line": 296,
"column": 0
} | [
{
"pp": "x : ℝ\nhx : x ≠ 0\nr : ℂ\nhr : r ≠ -1\n⊢ HasDerivAt (fun y ↦ ↑y ^ (r + 1) / (r + 1)) (↑x ^ r) x",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"NonUnit... | [] | rw [Ne, ← add_eq_zero_iff_eq_neg, ← Ne] at hr
rcases lt_or_gt_of_ne hx.symm with (hx | hx)
· -- easy case : `0 < x`
apply HasDerivAt.comp_ofReal (e := fun y => (y : ℂ) ^ (r + 1) / (r + 1))
convert! HasDerivAt.div_const (𝕜 := ℂ) ?_ (r + 1) using 1
· exact (mul_div_cancel_right₀ _ hr).symm
· convert!... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Analysis.SpecialFunctions.Pow.Deriv | {
"line": 547,
"column": 65
} | {
"line": 549,
"column": 72
} | {
"line": 551,
"column": 0
} | [
{
"pp": "E : Type u_1\ninst✝¹ : NormedAddCommGroup E\ninst✝ : NormedSpace ℝ E\nf g : E → ℝ\nx : E\nhf : DifferentiableAt ℝ f x\nhg : DifferentiableAt ℝ g x\nh : f x ≠ 0\n⊢ DifferentiableAt ℝ (fun x ↦ f x ^ g x) x",
"ppTerm": "?m.48",
"assigned": true,
"usedConstants": [
"Real.instPow",
"... | [] | by
-- `by exact` to deal with tricky unification.
exact (differentiableAt_rpow_of_ne (f x, g x) h).comp x (hf.prodMk hg) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Analysis.Analytic.Binomial | {
"line": 242,
"column": 90
} | {
"line": 242,
"column": 95
} | {
"line": 243,
"column": 2
} | [
{
"pp": "a : ℝ\n⊢ binomialSeries ℂ a = FormalMultilinearSeries.restrictScalars ℝ (binomialSeries ℂ ↑a)",
"ppTerm": "?m.79",
"assigned": true,
"usedConstants": [
"instInnerProductSpaceRealComplex",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Analysis.Asymptotics.LinearGrowth | {
"line": 208,
"column": 6
} | {
"line": 208,
"column": 19
} | {
"line": 208,
"column": 19
} | [
{
"pp": "u : ℕ → EReal\nh : 0 < linearGrowthInf u\nM a : ℝ\na_0 : 0 < ↑a\na_v : ↑a < linearGrowthInf u\n⊢ ∃ a_1, ∀ (b : ℕ), a_1 ≤ b → ↑M < ↑a * ↑b",
"ppTerm": "?m.104",
"assigned": true,
"usedConstants": [
"instAddCommMonoidWithOneEReal",
"EReal.instDivInvMonoid",
"Real",
"Pr... | [
"u : ℕ → EReal\nh : 0 < linearGrowthInf u\nM a : ℝ\na_0 : 0 < a\na_v : ↑a < linearGrowthInf u\n⊢ ∃ a_1, ∀ (b : ℕ), a_1 ≤ b → ↑M < ↑a * ↑b"
] | EReal.coe_pos | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Asymptotics.LinearGrowth | {
"line": 219,
"column": 34
} | {
"line": 219,
"column": 74
} | {
"line": 219,
"column": 74
} | [
{
"pp": "u v : ℕ → EReal\nn : ℕ\n⊢ u n / ↑n + v n / ↑n = (u n + v n) / ↑n",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"instAddCommMonoidWithOneEReal",
"Eq.mpr",
"EReal.instDivInvMonoid",
"instHDiv",
"congrArg",
"PartialOrder.toPreorder",
"EReal... | [
"u v : ℕ → EReal\nn : ℕ\n⊢ (u n + v n) / ↑n = (u n + v n) / ↑n"
] | ← add_div_of_nonneg_right n.cast_nonneg' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Analysis.Asymptotics.LinearGrowth | {
"line": 226,
"column": 34
} | {
"line": 226,
"column": 74
} | {
"line": 226,
"column": 74
} | [
{
"pp": "u v : ℕ → EReal\nh : linearGrowthSup u ≠ ⊥ ∨ linearGrowthInf v ≠ ⊤\nh' : linearGrowthSup u ≠ ⊤ ∨ linearGrowthInf v ≠ ⊥\nn : ℕ\n⊢ u n / ↑n + v n / ↑n = (u n + v n) / ↑n",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"instAddCommMonoidWithOneEReal",
"Eq.mpr",
"ERe... | [
"u v : ℕ → EReal\nh : linearGrowthSup u ≠ ⊥ ∨ linearGrowthInf v ≠ ⊤\nh' : linearGrowthSup u ≠ ⊤ ∨ linearGrowthInf v ≠ ⊥\nn : ℕ\n⊢ (u n + v n) / ↑n = (u n + v n) / ↑n"
] | ← add_div_of_nonneg_right n.cast_nonneg' | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.VitaliFamily | {
"line": 190,
"column": 14
} | {
"line": 190,
"column": 18
} | {
"line": 190,
"column": 19
} | [
{
"pp": "X : Type u_1\ninst✝ : PseudoMetricSpace X\nm0 : MeasurableSpace X\nμ : Measure X\nv : VitaliFamily μ\nδ : ℝ\nδpos : 0 < δ\ns : Set X\nf : X → Set (Set X)\n⊢ (∀ x ∈ s, f x ⊆ v.setsAt x ∪ {s | MeasurableSet s ∧ (interior s).Nonempty ∧ ¬s ⊆ closedBall x δ}) →\n (∀ x ∈ s, ∀ ε > 0, ∃ t ∈ f x, t ⊆ closedB... | [
"X : Type u_1\ninst✝ : PseudoMetricSpace X\nm0 : MeasurableSpace X\nμ : Measure X\nv : VitaliFamily μ\nδ : ℝ\nδpos : 0 < δ\ns : Set X\nf : X → Set (Set X)\nfset : ∀ x ∈ s, f x ⊆ v.setsAt x ∪ {s | MeasurableSet s ∧ (interior s).Nonempty ∧ ¬s ⊆ closedBall x δ}\n⊢ (∀ x ∈ s, ∀ ε > 0, ∃ t ∈ f x, t ⊆ closedBall x ε) →\n ... | fset | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Analysis.Asymptotics.ExpGrowth | {
"line": 357,
"column": 29
} | {
"line": 357,
"column": 51
} | {
"line": 357,
"column": 52
} | [
{
"pp": "case insert\nα : Type u_1\nu : α → ℕ → ℝ≥0∞\na : α\nt : Finset α\na_t : a ∉ t\nha : expGrowthSup (∑ x ∈ t, u x) = ⨆ x ∈ t, expGrowthSup (u x)\n⊢ expGrowthSup (∑ x ∈ insert a t, u x) = ⨆ x ∈ insert a t, expGrowthSup (u x)",
"ppTerm": "?insert",
"assigned": true,
"usedConstants": [
"Eq.... | [
"case insert\nα : Type u_1\nu : α → ℕ → ℝ≥0∞\na : α\nt : Finset α\na_t : a ∉ t\nha : expGrowthSup (∑ x ∈ t, u x) = ⨆ x ∈ t, expGrowthSup (u x)\n⊢ expGrowthSup (u a + ∑ x ∈ t, u x) = ⨆ x ∈ insert a t, expGrowthSup (u x)"
] | Finset.sum_insert a_t, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Covering.Vitali | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 53
} | {
"line": 133,
"column": 2
} | [
{
"pp": "case refine_2\nα : Type u_1\nι : Type u_2\nB : ι → Set α\nt : Set ι\nδ : ι → ℝ\nτ : ℝ\nhτ : 1 < τ\nδnonneg : ∀ a ∈ t, 0 ≤ δ a\nR : ℝ\nδle : ∀ a ∈ t, δ a ≤ R\nhne : ∀ a ∈ t, (B a).Nonempty\nT : Set (Set ι) :=\n {u |\n u ⊆ t ∧\n u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c... | [] | exact hu.prop.2.1.insert fun b bu _ => a'A.2 b bu | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Covering.Vitali | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 53
} | {
"line": 133,
"column": 2
} | [
{
"pp": "case refine_2\nα : Type u_1\nι : Type u_2\nB : ι → Set α\nt : Set ι\nδ : ι → ℝ\nτ : ℝ\nhτ : 1 < τ\nδnonneg : ∀ a ∈ t, 0 ≤ δ a\nR : ℝ\nδle : ∀ a ∈ t, δ a ≤ R\nhne : ∀ a ∈ t, (B a).Nonempty\nT : Set (Set ι) :=\n {u |\n u ⊆ t ∧\n u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c... | [] | exact hu.prop.2.1.insert fun b bu _ => a'A.2 b bu | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.MeasureTheory.Covering.Vitali | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 53
} | {
"line": 133,
"column": 2
} | [
{
"pp": "case refine_2\nα : Type u_1\nι : Type u_2\nB : ι → Set α\nt : Set ι\nδ : ι → ℝ\nτ : ℝ\nhτ : 1 < τ\nδnonneg : ∀ a ∈ t, 0 ≤ δ a\nR : ℝ\nδle : ∀ a ∈ t, δ a ≤ R\nhne : ∀ a ∈ t, (B a).Nonempty\nT : Set (Set ι) :=\n {u |\n u ⊆ t ∧\n u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c... | [] | exact hu.prop.2.1.insert fun b bu _ => a'A.2 b bu | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 263,
"column": 18
} | {
"line": 263,
"column": 51
} | {
"line": 263,
"column": 51
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\n| μ",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"congrArg",
"MeasureTheory.Measure.instHaveLebesgueDecompositionZeroRight",
"MeasureT... | [
"α : Type u_1\nm : MeasurableSpace α\nμ : Measure α\n| μ.singularPart 0 + withDensity 0 (μ.rnDeriv 0)"
] | haveLebesgueDecomposition_add μ 0 | Lean.Elab.Tactic.Conv.evalRewrite | null |
Mathlib.MeasureTheory.Integral.Average | {
"line": 791,
"column": 6
} | {
"line": 791,
"column": 44
} | {
"line": 792,
"column": 6
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : CompleteSpace E\nι : Type u_4\na : ι → Set α\nl : Filter ι\nf : α → E\nc : E\ng : ι → α → ℝ\nK : ℝ\nhf : Tendsto (fun i ↦ ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (𝓝 0)\nf_int :... | [
"α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\nμ : Measure α\ninst✝ : CompleteSpace E\nι : Type u_4\na : ι → Set α\nl : Filter ι\nf : α → E\nc : E\ng : ι → α → ℝ\nK : ℝ\nhf : Tendsto (fun i ↦ ⨍ (y : α) in a i, ‖f y - c‖ ∂μ) l (𝓝 0)\nf_int : ∀ᶠ (i : ι) ... | apply Integrable.smul_of_top_right hif | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.MeasureTheory.Covering.DensityTheorem | {
"line": 117,
"column": 6
} | {
"line": 117,
"column": 75
} | {
"line": 118,
"column": 6
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\ninst✝³ : IsUnifLocDoublingMeasure μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nK : ℝ\nx : α\nι : Type u_2\nl : Filter ι\nw : ι → α\nδ : ι → ℝ\nδlim : Tendsto δ l (𝓝... | [
"α : Type u_1\ninst✝⁵ : PseudoMetricSpace α\ninst✝⁴ : MeasurableSpace α\nμ : Measure α\ninst✝³ : IsUnifLocDoublingMeasure μ\ninst✝² : SecondCountableTopology α\ninst✝¹ : BorelSpace α\ninst✝ : IsLocallyFiniteMeasure μ\nK : ℝ\nx : α\nι : Type u_2\nl : Filter ι\nw : ι → α\nδ : ι → ℝ\nδlim : Tendsto δ l (𝓝[>] 0)\nxmem... | rcases (xmem.and (δlim self_mem_nhdsWithin)).exists with ⟨j, hj, h'j⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Order.Monotone.Extension | {
"line": 40,
"column": 10
} | {
"line": 40,
"column": 44
} | {
"line": 41,
"column": 8
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : ConditionallyCompleteLinearOrder β\nf : α → β\ns : Set α\nh : MonotoneOn f s\nhu : BddAbove (f '' s)\na : β\nha : a ∈ lowerBounds (f '' s)\nhu' : ∀ (x : α), BddAbove (f '' (Iic x ∩ s))\ng : α → β := fun x ↦ if Disjoint (Iic x) s then a else sS... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : LinearOrder α\ninst✝ : ConditionallyCompleteLinearOrder β\nf : α → β\ns : Set α\nh : MonotoneOn f s\nhu : BddAbove (f '' s)\na : β\nha : a ∈ lowerBounds (f '' s)\nhu' : ∀ (x : α), BddAbove (f '' (Iic x ∩ s))\ng : α → β := fun x ↦ if Disjoint (Iic x) s then a else sSup (f '' (Ii... | if_neg this.nonempty.not_disjoint, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | {
"line": 917,
"column": 18
} | {
"line": 917,
"column": 49
} | {
"line": 917,
"column": 49
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\ng : ℕ → ℝ≥0∞\nh✝ : Monotone g\nhg₂ : Filter.Tendsto g Filter.atTop (nhds (sSup (measurableLEEval ν μ)))\nf : ℕ → α → ℝ≥0∞\nhf₁ : ∀ (n : ℕ), f n ∈ measurableLE ν μ\nhf₂ : ∀ (n : ℕ), (fun f ↦ ∫⁻ (... | [
"α : Type u_1\nm : MeasurableSpace α\nμ ν : Measure α\ninst✝¹ : IsFiniteMeasure μ\ninst✝ : IsFiniteMeasure ν\ng : ℕ → ℝ≥0∞\nh✝ : Monotone g\nhg₂ : Filter.Tendsto g Filter.atTop (nhds (sSup (measurableLEEval ν μ)))\nf : ℕ → α → ℝ≥0∞\nhf₁ : ∀ (n : ℕ), f n ∈ measurableLE ν μ\nhf₂ : ∀ (n : ℕ), (fun f ↦ ∫⁻ (x : α), f x ... | ← measure_inter_add_sdiff A hE₁ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.EMetricSpace.VariationOnFromTo | {
"line": 53,
"column": 2
} | {
"line": 54,
"column": 67
} | {
"line": 56,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\na b : α\nh : b ≤ a\n⊢ variationOnFromTo f s a b ≤ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",... | [] | rw [variationOnFromTo.eq_neg_swap]
exact neg_nonpos_of_nonneg (variationOnFromTo.nonneg_of_le f s h) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.EMetricSpace.VariationOnFromTo | {
"line": 53,
"column": 2
} | {
"line": 54,
"column": 67
} | {
"line": 56,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nf : α → E\ns : Set α\na b : α\nh : b ≤ a\n⊢ variationOnFromTo f s a b ≤ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",... | [] | rw [variationOnFromTo.eq_neg_swap]
exact neg_nonpos_of_nonneg (variationOnFromTo.nonneg_of_le f s h) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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