module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Topology.Algebra.Group.Basic | {
"line": 829,
"column": 4
} | {
"line": 830,
"column": 29
} | {
"line": 830,
"column": 30
} | [
{
"pp": "G : Type w\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\nM : Type u_1\nhom : Type u_2\ninst✝⁴ : MulOneClass M\ninst✝³ : TopologicalSpace M\ninst✝² : ContinuousMul M\ninst✝¹ : FunLike hom G M\ninst✝ : MonoidHomClass hom G M\nf : hom\nhf : Tendsto (⇑f) (𝓝 1) (𝓝 1)\nx : ... | [
"G : Type w\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\nM : Type u_1\nhom : Type u_2\ninst✝⁴ : MulOneClass M\ninst✝³ : TopologicalSpace M\ninst✝² : ContinuousMul M\ninst✝¹ : FunLike hom G M\ninst✝ : MonoidHomClass hom G M\nf : hom\nhf : Tendsto (⇑f) (𝓝 1) (𝓝 1)\nx : G\n⊢ Tendsto... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 41,
"column": 2
} | {
"line": 41,
"column": 29
} | {
"line": 41,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Semifield α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ f x * r) l atTop ↔ Tendsto f l atTop",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"HMul.... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Semifield α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ r * f x) l atTop ↔ Tendsto f l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 844,
"column": 41
} | {
"line": 844,
"column": 52
} | {
"line": 844,
"column": 53
} | [
{
"pp": "G : Type w\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\nM : Type u_1\nhom : Type u_2\ninst✝⁴ : MulOneClass M\ninst✝³ : TopologicalSpace M\ninst✝² : ContinuousMul M\ninst✝¹ : FunLike hom G M\ninst✝ : MonoidHomClass hom G M\nf : hom\nhf : ContinuousAt (⇑f) 1\n⊢ Tendsto (... | [
"G : Type w\ninst✝⁷ : TopologicalSpace G\ninst✝⁶ : Group G\ninst✝⁵ : IsTopologicalGroup G\nM : Type u_1\nhom : Type u_2\ninst✝⁴ : MulOneClass M\ninst✝³ : TopologicalSpace M\ninst✝² : ContinuousMul M\ninst✝¹ : FunLike hom G M\ninst✝ : MonoidHomClass hom G M\nf : hom\nhf : ContinuousAt (⇑f) 1\n⊢ Tendsto (⇑f) (𝓝 1) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 47,
"column": 2
} | {
"line": 47,
"column": 35
} | {
"line": 47,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Semifield α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ f x / r) l atTop ↔ Tendsto f l atTop",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivIn... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Semifield α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ f x * r⁻¹) l atTop ↔ Tendsto f l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 87,
"column": 2
} | {
"line": 87,
"column": 35
} | {
"line": 87,
"column": 36
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Semifield α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\nhf : Tendsto f l atTop\n⊢ Tendsto (fun x ↦ f x / r) l atTop",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"D... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Semifield α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\nhf : Tendsto f l atTop\n⊢ Tendsto (fun x ↦ f x * r⁻¹) l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 121,
"column": 2
} | {
"line": 121,
"column": 55
} | {
"line": 121,
"column": 56
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ r * f x) l atBot ↔ Tendsto f l atBot",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NegZeroCl... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ r * -f x) l atTop ↔ Tendsto (fun x ↦ -f x) l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 127,
"column": 2
} | {
"line": 127,
"column": 29
} | {
"line": 127,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ f x * r) l atBot ↔ Tendsto f l atBot",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : 0 < r\n⊢ Tendsto (fun x ↦ r * f x) l atBot ↔ Tendsto f l atBot"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 139,
"column": 2
} | {
"line": 139,
"column": 51
} | {
"line": 139,
"column": 52
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ r * f x) l atTop ↔ Tendsto f l atBot",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ r * f x) l atTop ↔ Tendsto f l atBot"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 29
} | {
"line": 145,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ f x * r) l atTop ↔ Tendsto f l atBot",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ r * f x) l atTop ↔ Tendsto f l atBot"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 51
} | {
"line": 157,
"column": 52
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ r * f x) l atBot ↔ Tendsto f l atTop",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ r * f x) l atBot ↔ Tendsto f l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Filter.AtTopBot.Field | {
"line": 163,
"column": 2
} | {
"line": 163,
"column": 29
} | {
"line": 163,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ f x * r) l atBot ↔ Tendsto f l atTop",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"NonUnitalNonAssocCommRing... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Field α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nl : Filter β\nf : β → α\nr : α\nhr : r < 0\n⊢ Tendsto (fun x ↦ r * f x) l atBot ↔ Tendsto f l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 945,
"column": 2
} | {
"line": 946,
"column": 43
} | {
"line": 946,
"column": 44
} | [
{
"pp": "G : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nhinv : Tendsto (fun x ↦ x⁻¹) (𝓝 1) (𝓝 1)\nhleft : ∀ (x₀ : G), 𝓝 x₀ = map (fun x ↦ x₀ * x) (𝓝 1)\nhconj : ∀ (x₀ : G), Tendsto (fun x ↦ x₀ * x * x₀⁻¹) (𝓝 1) (𝓝 1)\nx₀ : G\nthis : Tendsto (fun x ↦ x₀⁻¹ * (x₀ * x⁻¹ * x₀⁻¹)) (𝓝 1) (map (fun ... | [
"G : Type u_1\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nhinv : Tendsto (fun x ↦ x⁻¹) (𝓝 1) (𝓝 1)\nhleft : ∀ (x₀ : G), 𝓝 x₀ = map (fun x ↦ x₀ * x) (𝓝 1)\nhconj : ∀ (x₀ : G), Tendsto (fun x ↦ x₀ * x * x₀⁻¹) (𝓝 1) (𝓝 1)\nx₀ : G\nthis : Tendsto (fun x ↦ x₀⁻¹ * (x₀ * x⁻¹ * x₀⁻¹)) (𝓝 1) (map (fun x ↦ x₀⁻¹ * x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 973,
"column": 2
} | {
"line": 973,
"column": 33
} | {
"line": 973,
"column": 34
} | [
{
"pp": "G : Type u\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nhmul : Tendsto (uncurry fun x1 x2 ↦ x1 * x2) (𝓝 1 ×ˢ 𝓝 1) (𝓝 1)\nhinv : Tendsto (fun x ↦ x⁻¹) (𝓝 1) (𝓝 1)\nhleft : ∀ (x₀ : G), 𝓝 x₀ = map (fun x ↦ x₀ * x) (𝓝 1)\nx₀ : G\nhconj : ∀ (x₀ : G), map (fun x ↦ x₀ * x * x₀⁻¹) (𝓝 1) = 𝓝 1\n⊢ 𝓝 ... | [
"G : Type u\ninst✝¹ : Group G\ninst✝ : TopologicalSpace G\nhmul : Tendsto (uncurry fun x1 x2 ↦ x1 * x2) (𝓝 1 ×ˢ 𝓝 1) (𝓝 1)\nhinv : Tendsto (fun x ↦ x⁻¹) (𝓝 1) (𝓝 1)\nhleft : ∀ (x₀ : G), 𝓝 x₀ = map (fun x ↦ x₀ * x) (𝓝 1)\nx₀ : G\nhconj : ∀ (x₀ : G), map (fun x ↦ x₀ * x * x₀⁻¹) (𝓝 1) = 𝓝 1\n⊢ 𝓝 x₀ = map (fu... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 996,
"column": 10
} | {
"line": 996,
"column": 36
} | {
"line": 996,
"column": 37
} | [
{
"pp": "G : Type w\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : IsTopologicalGroup G\ninst✝ : FirstCountableTopology G\nu : ℕ → Set G\nhu : (𝓝 1).HasBasis (fun x ↦ True) u\nu_anti : Antitone u\n⊢ Tendsto ?m.78 (𝓝 (1, 1)) (𝓝 1)",
"ppTerm": "?m.81",
"assigned": false,
"usedConstants": ... | [
"G : Type w\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : IsTopologicalGroup G\ninst✝ : FirstCountableTopology G\nu : ℕ → Set G\nhu : (𝓝 1).HasBasis (fun x ↦ True) u\nu_anti : Antitone u\n⊢ Tendsto ?m.78 (𝓝 (1, 1)) (𝓝 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.GroupWithZero | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 35
} | {
"line": 57,
"column": 36
} | [
{
"pp": "α : Type u_1\nG₀ : Type u_3\ninst✝² : DivInvMonoid G₀\ninst✝¹ : TopologicalSpace G₀\ninst✝ : SeparatelyContinuousMul G₀\nf : α → G₀\nl : Filter α\nx : G₀\nhf : Tendsto f l (𝓝 x)\ny : G₀\n⊢ Tendsto (fun a ↦ f a / y) l (𝓝 (x / y))",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_1\nG₀ : Type u_3\ninst✝² : DivInvMonoid G₀\ninst✝¹ : TopologicalSpace G₀\ninst✝ : SeparatelyContinuousMul G₀\nf : α → G₀\nl : Filter α\nx : G₀\nhf : Tendsto f l (𝓝 x)\ny : G₀\n⊢ Tendsto (fun a ↦ f a * y⁻¹) l (𝓝 (x * y⁻¹))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.GroupWithZero | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 35
} | {
"line": 71,
"column": 36
} | [
{
"pp": "α : Type u_1\nG₀ : Type u_3\ninst✝³ : DivInvMonoid G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : SeparatelyContinuousMul G₀\nf : α → G₀\ns : Set α\ninst✝ : TopologicalSpace α\nhf : ContinuousOn f s\ny : G₀\n⊢ ContinuousOn (fun x ↦ f x / y) s",
"ppTerm": "?m.16",
"assigned": true,
"usedConstant... | [
"α : Type u_1\nG₀ : Type u_3\ninst✝³ : DivInvMonoid G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : SeparatelyContinuousMul G₀\nf : α → G₀\ns : Set α\ninst✝ : TopologicalSpace α\nhf : ContinuousOn f s\ny : G₀\n⊢ ContinuousOn (fun x ↦ f x * y⁻¹) s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.GroupWithZero | {
"line": 75,
"column": 2
} | {
"line": 75,
"column": 35
} | {
"line": 75,
"column": 36
} | [
{
"pp": "α : Type u_1\nG₀ : Type u_3\ninst✝³ : DivInvMonoid G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : SeparatelyContinuousMul G₀\nf : α → G₀\ninst✝ : TopologicalSpace α\nhf : Continuous[inst✝, inst✝²] f\ny : G₀\n⊢ Continuous[inst✝, inst✝²] fun x ↦ f x / y",
"ppTerm": "?m.16",
"assigned": true,
"use... | [
"α : Type u_1\nG₀ : Type u_3\ninst✝³ : DivInvMonoid G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : SeparatelyContinuousMul G₀\nf : α → G₀\ninst✝ : TopologicalSpace α\nhf : Continuous[inst✝, inst✝²] f\ny : G₀\n⊢ Continuous[inst✝, inst✝²] fun x ↦ f x * y⁻¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 96,
"column": 25
} | {
"line": 96,
"column": 54
} | {
"line": 96,
"column": 55
} | [
{
"pp": "G : Type u_3\ninst✝³ : Group G\ninst✝² : UniformSpace G\ninst✝¹ : IsRightUniformGroup G\ninst✝ : WeaklyLocallyCompactSpace G\nf : Filter G\nhf : f ×ˢ f ≤ 𝓤 G\nthis : f.NeBot\nK : Set G\nK_compact : IsCompact K\nK_mem : K ∈ 𝓝 1\n⊢ ∃ x, ∀ᶠ (y : G) in f, y / x ∈ K",
"ppTerm": "?m.74",
"assigned"... | [
"G : Type u_3\ninst✝³ : Group G\ninst✝² : UniformSpace G\ninst✝¹ : IsRightUniformGroup G\ninst✝ : WeaklyLocallyCompactSpace G\nf : Filter G\nhf : f ×ˢ f ≤ comap (fun x ↦ x.2 / x.1) (𝓝 1)\nthis : f.NeBot\nK : Set G\nK_compact : IsCompact K\nK_mem : K ∈ 𝓝 1\n⊢ ∃ x, ∀ᶠ (y : G) in f, y / x ∈ K"
] | uniformity_eq_comap_nhds_one, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1091,
"column": 15
} | {
"line": 1091,
"column": 26
} | {
"line": 1091,
"column": 27
} | [
{
"pp": "G : Type w\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\nα : Type u_1\nl : Filter α\nx : G\nu : α → G\nA : Tendsto (fun x_1 ↦ x) l (𝓝 x)\nh : Tendsto (fun x_1 ↦ u x_1 / x) l (𝓝 1)\n⊢ Tendsto u l (𝓝 x)",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants"... | [
"G : Type w\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\nα : Type u_1\nl : Filter α\nx : G\nu : α → G\nA : Tendsto (fun x_1 ↦ x) l (𝓝 x)\nh : Tendsto (fun x_1 ↦ u x_1 / x) l (𝓝 1)\n⊢ Tendsto u l (𝓝 x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1091,
"column": 48
} | {
"line": 1091,
"column": 59
} | {
"line": 1091,
"column": 60
} | [
{
"pp": "G : Type w\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\nα : Type u_1\nl : Filter α\nx : G\nu : α → G\nA : Tendsto (fun x_1 ↦ x) l (𝓝 x)\nh : Tendsto u l (𝓝 x)\n⊢ Tendsto (fun x_1 ↦ u x_1 / x) l (𝓝 1)",
"ppTerm": "?m.33",
"assigned": false,
"usedConstants"... | [
"G : Type w\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\nα : Type u_1\nl : Filter α\nx : G\nu : α → G\nA : Tendsto (fun x_1 ↦ x) l (𝓝 x)\nh : Tendsto u l (𝓝 x)\n⊢ Tendsto (fun x_1 ↦ u x_1 / x) l (𝓝 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1095,
"column": 2
} | {
"line": 1095,
"column": 35
} | {
"line": 1095,
"column": 36
} | [
{
"pp": "G : Type w\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ comap (fun x_1 ↦ x_1 / x) (𝓝 1) = 𝓝 x",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"InvOneClass.toOne",
... | [
"G : Type w\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\nx : G\n⊢ comap (fun x_1 ↦ x_1 * x⁻¹) (𝓝 1) = 𝓝 x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 101,
"column": 46
} | {
"line": 101,
"column": 57
} | {
"line": 101,
"column": 58
} | [
{
"pp": "G : Type u_3\ninst✝³ : Group G\ninst✝² : UniformSpace G\ninst✝¹ : IsRightUniformGroup G\ninst✝ : WeaklyLocallyCompactSpace G\nf : Filter G\nhf : Cauchy f\nthis : f.NeBot\nK : Set G\nK_compact : IsCompact K\nK_mem : K ∈ 𝓝 1\nx : G\nhx : ∀ᶠ (y : G) in f, y ∈ MulOpposite.op x • K\nKx_complete : IsComplet... | [
"G : Type u_3\ninst✝³ : Group G\ninst✝² : UniformSpace G\ninst✝¹ : IsRightUniformGroup G\ninst✝ : WeaklyLocallyCompactSpace G\nf : Filter G\nhf : Cauchy f\nthis : f.NeBot\nK : Set G\nK_compact : IsCompact K\nK_mem : K ∈ 𝓝 1\nx : G\nhx : ∀ᶠ (y : G) in f, y ∈ MulOpposite.op x • K\nKx_complete : IsComplete (MulOpposi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1107,
"column": 15
} | {
"line": 1107,
"column": 26
} | {
"line": 1107,
"column": 27
} | [
{
"pp": "G : Type w\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : ContinuousMul G\nh : IsClosed[inst✝²] {1}\nx : G\n⊢ IsClosed[inst✝²] {x}",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"G : Type w\ninst✝² : TopologicalSpace G\ninst✝¹ : Group G\ninst✝ : ContinuousMul G\nh : IsClosed[inst✝²] {1}\nx : G\n⊢ IsClosed[inst✝²] {x}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 198,
"column": 2
} | {
"line": 198,
"column": 13
} | {
"line": 198,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : IsUniformGroup α\nι : Type u_3\nl : Filter ι\nf f' : ι → β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nhf' : UniformCauchySeqOn f' l s\nu : Set (α × α)\nhu : u ∈ 𝓤 α\n⊢ ∀ᶠ (m : ι × ι) in l ×ˢ l, ∀ x ∈ s, ((f * f') m.1 x,... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : IsUniformGroup α\nι : Type u_3\nl : Filter ι\nf f' : ι → β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nhf' : UniformCauchySeqOn f' l s\nu : Set (α × α)\nhu : u ∈ 𝓤 α\n⊢ ∀ᶠ (m : ι × ι) in l ×ˢ l, ∀ x ∈ s, (f m.1 x * f' m.1 x, f m.2 x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 203,
"column": 2
} | {
"line": 203,
"column": 13
} | {
"line": 203,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : IsUniformGroup α\nι : Type u_3\nl : Filter ι\nf f' : ι → β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nhf' : UniformCauchySeqOn f' l s\nu : Set (α × α)\nhu : u ∈ 𝓤 α\n⊢ ∀ᶠ (m : ι × ι) in l ×ˢ l, ∀ x ∈ s, ((f / f') m.1 x,... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : IsUniformGroup α\nι : Type u_3\nl : Filter ι\nf f' : ι → β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nhf' : UniformCauchySeqOn f' l s\nu : Set (α × α)\nhu : u ∈ 𝓤 α\n⊢ ∀ᶠ (m : ι × ι) in l ×ˢ l, ∀ x ∈ s, (f m.1 x / f' m.1 x, f m.2 x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 208,
"column": 16
} | {
"line": 208,
"column": 27
} | {
"line": 208,
"column": 28
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : IsUniformGroup α\nι : Type u_3\nl : Filter ι\nf : ι → β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nu : Set (α × α)\nhu : u ∈ 𝓤 α\n⊢ ∀ᶠ (m : ι × ι) in l ×ˢ l, ∀ x ∈ s, (f⁻¹ m.1 x, f⁻¹ m.2 x) ∈ u",
"ppTerm": "?m.15",
... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : UniformSpace α\ninst✝¹ : Group α\ninst✝ : IsUniformGroup α\nι : Type u_3\nl : Filter ι\nf : ι → β → α\ns : Set β\nhf : UniformCauchySeqOn f l s\nu : Set (α × α)\nhu : u ∈ 𝓤 α\n⊢ ∀ᶠ (m : ι × ι) in l ×ˢ l, ∀ x ∈ s, ((f m.1 x)⁻¹, (f m.2 x)⁻¹) ∈ u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.GroupWithZero | {
"line": 344,
"column": 4
} | {
"line": 344,
"column": 57
} | {
"line": 344,
"column": 58
} | [
{
"pp": "case ofNat\nG₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : ContinuousInv₀ G₀\ninst✝ : ContinuousMul G₀\nx : G₀\nm : ℕ\nh : x ≠ 0 ∨ 0 ≤ Int.ofNat m\n⊢ ContinuousAt (fun x ↦ x ^ Int.ofNat m) x",
"ppTerm": "?ofNat",
"assigned": true,
"usedConstants": [
"... | [
"case ofNat\nG₀ : Type u_3\ninst✝³ : GroupWithZero G₀\ninst✝² : TopologicalSpace G₀\ninst✝¹ : ContinuousInv₀ G₀\ninst✝ : ContinuousMul G₀\nx : G₀\nm : ℕ\nh : x ≠ 0 ∨ 0 ≤ Int.ofNat m\n⊢ ContinuousAt (fun x ↦ x ^ m) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 367,
"column": 2
} | {
"line": 374,
"column": 26
} | {
"line": 376,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\n⊢ UniformSpace.comap (⇑(Equiv.inv G)) (IsTopologicalGroup.leftUniformSpace G) = IsTopologicalGroup.rightUniformSpace G",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | ext : 1
change comap (fun (x : G × G) ↦ (Equiv.inv G x.1, Equiv.inv G x.2))
(comap (fun p : G × G => p.1⁻¹ * p.2) (𝓝 1)) =
comap (fun p : G × G => p.2 * p.1⁻¹) (𝓝 1)
have : 𝓝 (1 : G) = comap (Homeomorph.inv G) (𝓝 1) := by rw [Homeomorph.comap_nhds_eq]; simp
nth_rewrite 1 [this]
rw [comap_comap, co... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 367,
"column": 2
} | {
"line": 374,
"column": 26
} | {
"line": 376,
"column": 0
} | [
{
"pp": "G : Type u_1\ninst✝² : Group G\ninst✝¹ : TopologicalSpace G\ninst✝ : IsTopologicalGroup G\n⊢ UniformSpace.comap (⇑(Equiv.inv G)) (IsTopologicalGroup.leftUniformSpace G) = IsTopologicalGroup.rightUniformSpace G",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [] | ext : 1
change comap (fun (x : G × G) ↦ (Equiv.inv G x.1, Equiv.inv G x.2))
(comap (fun p : G × G => p.1⁻¹ * p.2) (𝓝 1)) =
comap (fun p : G × G => p.2 * p.1⁻¹) (𝓝 1)
have : 𝓝 (1 : G) = comap (Homeomorph.inv G) (𝓝 1) := by rw [Homeomorph.comap_nhds_eq]; simp
nth_rewrite 1 [this]
rw [comap_comap, co... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 509,
"column": 4
} | {
"line": 509,
"column": 15
} | {
"line": 509,
"column": 16
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nδ : Type u_4\nG : Type u_5\ninst✝⁸ : TopologicalSpace α\ninst✝⁷ : AddCommGroup α\ninst✝⁶ : IsTopologicalAddGroup α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : AddCommGroup β\ninst✝³ : TopologicalSpace δ\ninst✝² : AddCommGroup δ\ninst✝¹ : UniformSpace G\ninst✝ : AddCommGroup G\ne ... | [
"α : Type u_1\nβ : Type u_2\nδ : Type u_4\nG : Type u_5\ninst✝⁸ : TopologicalSpace α\ninst✝⁷ : AddCommGroup α\ninst✝⁶ : IsTopologicalAddGroup α\ninst✝⁵ : TopologicalSpace β\ninst✝⁴ : AddCommGroup β\ninst✝³ : TopologicalSpace δ\ninst✝² : AddCommGroup δ\ninst✝¹ : UniformSpace G\ninst✝ : AddCommGroup G\ne : β →+ α\nde... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 524,
"column": 4
} | {
"line": 524,
"column": 15
} | {
"line": 524,
"column": 16
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nG : Type u_5\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : AddCommGroup α\ninst✝¹⁰ : IsTopologicalAddGroup α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : AddCommGroup β\ninst✝⁷ : TopologicalSpace γ\ninst✝⁶ : AddCommGroup γ\ninst✝⁵ : IsTopologicalAddGroup γ\n... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nδ : Type u_4\nG : Type u_5\ninst✝¹² : TopologicalSpace α\ninst✝¹¹ : AddCommGroup α\ninst✝¹⁰ : IsTopologicalAddGroup α\ninst✝⁹ : TopologicalSpace β\ninst✝⁸ : AddCommGroup β\ninst✝⁷ : TopologicalSpace γ\ninst✝⁶ : AddCommGroup γ\ninst✝⁵ : IsTopologicalAddGroup γ\ninst✝⁴ : Top... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1184,
"column": 4
} | {
"line": 1184,
"column": 18
} | {
"line": 1185,
"column": 4
} | [
{
"pp": "case right\nG : Type w\ninst✝² : TopologicalSpace G\ninst✝¹ : MulOneClass G\ninst✝ : ContinuousMul G\nK U : Set G\nhK : IsCompact K\nhU : IsOpen[inst✝²] U\nhKU : K ⊆ U\ns t V : Set G\nV_in : V ∈ 𝓝 1\nhV' : s * V ⊆ U\nW : Set G\nW_in : W ∈ 𝓝 1\nhW' : t * W ⊆ U\n⊢ (s ∪ t) * (V ∩ W) ⊆ U",
"ppTerm": ... | [
"case right\nG : Type w\ninst✝² : TopologicalSpace G\ninst✝¹ : MulOneClass G\ninst✝ : ContinuousMul G\nK U : Set G\nhK : IsCompact K\nhU : IsOpen[inst✝²] U\nhKU : K ⊆ U\ns t V : Set G\nV_in : V ∈ 𝓝 1\nhV' : s * V ⊆ U\nW : Set G\nW_in : W ∈ 𝓝 1\nhW' : t * W ⊆ U\n⊢ s * (V ∩ W) ∪ t * (V ∩ W) ⊆ U"
] | rw [union_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1189,
"column": 47
} | {
"line": 1189,
"column": 58
} | {
"line": 1189,
"column": 59
} | [
{
"pp": "G : Type w\ninst✝² : TopologicalSpace G\ninst✝¹ : MulOneClass G\ninst✝ : ContinuousMul G\nK U : Set G\nhK : IsCompact K\nhU : IsOpen[inst✝²] U\nhKU : K ⊆ U\nx : G\nhx : x ∈ K\n⊢ U ∈ 𝓝 (x * 1)",
"ppTerm": "?m.189",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"E... | [
"G : Type w\ninst✝² : TopologicalSpace G\ninst✝¹ : MulOneClass G\ninst✝ : ContinuousMul G\nK U : Set G\nhK : IsCompact K\nhU : IsOpen[inst✝²] U\nhKU : K ⊆ U\nx : G\nhx : x ∈ K\n⊢ U ∈ 𝓝 x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Ring.Basic | {
"line": 89,
"column": 23
} | {
"line": 89,
"column": 34
} | {
"line": 89,
"column": 35
} | [
{
"pp": "R : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : NonAssocRing R\ninst✝ : SeparatelyContinuousMul R\n⊢ Continuous[inst✝², inst✝²] fun a ↦ -a",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"R : Type u_1\ninst✝² : TopologicalSpace R\ninst✝¹ : NonAssocRing R\ninst✝ : SeparatelyContinuousMul R\n⊢ Continuous[inst✝², inst✝²] fun a ↦ -a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1265,
"column": 29
} | {
"line": 1265,
"column": 68
} | {
"line": 1265,
"column": 69
} | [
{
"pp": "G : Type w\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : IsTopologicalGroup G\ninst✝ : NoncompactSpace G\nK L : Set G\nhK : IsCompact K\nhL : IsCompact L\nA : ¬K * L⁻¹ = univ\ng : G\nhg : g ∉ K * L⁻¹\nb : G\nbL : b ∈ L\nha : (fun x ↦ g • x) b ∈ K\n⊢ b⁻¹ ∈ L⁻¹",
"ppTerm": "?m.124",
"a... | [
"G : Type w\ninst✝³ : TopologicalSpace G\ninst✝² : Group G\ninst✝¹ : IsTopologicalGroup G\ninst✝ : NoncompactSpace G\nK L : Set G\nhK : IsCompact K\nhL : IsCompact L\nA : ¬K * L⁻¹ = univ\ng : G\nhg : g ∉ K * L⁻¹\nb : G\nbL : b ∈ L\nha : (fun x ↦ g • x) b ∈ K\n⊢ b ∈ L"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.ContinuousMonoidHom | {
"line": 597,
"column": 18
} | {
"line": 597,
"column": 38
} | {
"line": 597,
"column": 38
} | [
{
"pp": "G : Type u\ninst✝³ : TopologicalSpace G\nH : Type v\ninst✝² : TopologicalSpace H\ninst✝¹ : Mul G\ninst✝ : Mul H\ne : G ≃* H\nhe : ∀ (s : Set H), IsOpen (⇑e ⁻¹' s) ↔ IsOpen s\ns : Set G\n⊢ IsOpen (⇑e.symm ⁻¹' s) ↔ IsOpen s",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.m... | [
"case e'_2\nG : Type u\ninst✝³ : TopologicalSpace G\nH : Type v\ninst✝² : TopologicalSpace H\ninst✝¹ : Mul G\ninst✝ : Mul H\ne : G ≃* H\nhe : ∀ (s : Set H), IsOpen (⇑e ⁻¹' s) ↔ IsOpen s\ns : Set G\n⊢ s = ⇑e ⁻¹' ⇑e.symm ⁻¹' s"
] | convert! (he _).symm | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Topology.Algebra.Field | {
"line": 193,
"column": 4
} | {
"line": 193,
"column": 71
} | {
"line": 193,
"column": 72
} | [
{
"pp": "α : Type u_2\n𝕜 : Type u_3\nf g : α → 𝕜\nS : Set α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : T1Space 𝕜\ninst✝² : Field 𝕜\ninst✝¹ : ContinuousInv₀ 𝕜\ninst✝ : ContinuousMul 𝕜\nhS : IsPreconnected S\nhf : ContinuousOn f S\nhg : ContinuousOn g S\nhsq : EqOn (f ^ 2) (g ^ 2) ... | [
"α : Type u_2\n𝕜 : Type u_3\nf g : α → 𝕜\nS : Set α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : T1Space 𝕜\ninst✝² : Field 𝕜\ninst✝¹ : ContinuousInv₀ 𝕜\ninst✝ : ContinuousMul 𝕜\nhS : IsPreconnected S\nhf : ContinuousOn f S\nhg : ContinuousOn g S\nhsq : EqOn (f ^ 2) (g ^ 2) S\nhg_ne : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Field | {
"line": 194,
"column": 2
} | {
"line": 195,
"column": 9
} | {
"line": 195,
"column": 10
} | [
{
"pp": "α : Type u_2\n𝕜 : Type u_3\nf g : α → 𝕜\nS : Set α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : T1Space 𝕜\ninst✝² : Field 𝕜\ninst✝¹ : ContinuousInv₀ 𝕜\ninst✝ : ContinuousMul 𝕜\nhS : IsPreconnected S\nhf : ContinuousOn f S\nhg : ContinuousOn g S\nhsq✝ : EqOn (f ^ 2) (g ^ 2)... | [
"α : Type u_2\n𝕜 : Type u_3\nf g : α → 𝕜\nS : Set α\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : TopologicalSpace 𝕜\ninst✝³ : T1Space 𝕜\ninst✝² : Field 𝕜\ninst✝¹ : ContinuousInv₀ 𝕜\ninst✝ : ContinuousMul 𝕜\nhS : IsPreconnected S\nhf : ContinuousOn f S\nhg : ContinuousOn g S\nhsq✝ : EqOn (f ^ 2) (g ^ 2) S\nhg_ne : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1348,
"column": 2
} | {
"line": 1350,
"column": 88
} | {
"line": 1352,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝⁵ : Monoid α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : Monoid β\ninst✝² : TopologicalSpace β\ninst✝¹ : ContinuousMul α\ninst✝ : T1Space α\nf : α →* β\nhf : IsClosedEmbedding ⇑f\n⊢ IsClosedEmbedding ⇑(map f)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
... | [] | refine .of_comp isEmbedding_embedProduct ?_
exact (hf.prodMap (opHomeomorph.isClosedEmbedding.comp
<| hf.comp opHomeomorph.symm.isClosedEmbedding)).comp isClosedEmbedding_embedProduct | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Algebra.Group.Basic | {
"line": 1348,
"column": 2
} | {
"line": 1350,
"column": 88
} | {
"line": 1352,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝⁵ : Monoid α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : Monoid β\ninst✝² : TopologicalSpace β\ninst✝¹ : ContinuousMul α\ninst✝ : T1Space α\nf : α →* β\nhf : IsClosedEmbedding ⇑f\n⊢ IsClosedEmbedding ⇑(map f)",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
... | [] | refine .of_comp isEmbedding_embedProduct ?_
exact (hf.prodMap (opHomeomorph.isClosedEmbedding.comp
<| hf.comp opHomeomorph.symm.isClosedEmbedding)).comp isClosedEmbedding_embedProduct | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Filter.Interval | {
"line": 114,
"column": 6
} | {
"line": 114,
"column": 53
} | {
"line": 114,
"column": 54
} | [
{
"pp": "α : Type u_1\nl₁ l₁' l₂ l₂' : Filter α\nIxx : α → α → Set α\nh : TendstoIxxClass Ixx l₁ l₂\nh' : TendstoIxxClass Ixx l₁' l₂'\n⊢ Tendsto (fun p ↦ Ixx p.1 p.2) ((l₁ ⊓ l₁') ×ˢ (l₁ ⊓ l₁')) (l₂ ⊓ l₂').smallSets",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Filt... | [
"α : Type u_1\nl₁ l₁' l₂ l₂' : Filter α\nIxx : α → α → Set α\nh : TendstoIxxClass Ixx l₁ l₂\nh' : TendstoIxxClass Ixx l₁' l₂'\n⊢ Tendsto (fun p ↦ Ixx p.1 p.2) ((l₁ ⊓ l₁') ×ˢ (l₁ ⊓ l₁')) (l₂.smallSets ⊓ l₂'.smallSets)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 41
} | {
"line": 102,
"column": 42
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Preorder (α i)\ninst✝ : DecidableEq ι\nx y : (i : ι) → α i\ni₀ : ι\nm : α i₀\nz : (i : ι) → α i\nh₁ : z ∈ univ.pi fun i ↦ Ioc (x i) (update y i₀ m i)\nh₂ : z ∈ univ.pi fun i ↦ Ioc (update x i₀ m i) (y i)\n⊢ update y i₀ m i₀ < z i₀",
"ppTerm": "?m.4... | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Preorder (α i)\ninst✝ : DecidableEq ι\nx y : (i : ι) → α i\ni₀ : ι\nm : α i₀\nz : (i : ι) → α i\nh₁ : z ∈ univ.pi fun i ↦ Ioc (x i) (update y i₀ m i)\nh₂ : z ∈ univ.pi fun i ↦ Ioc (update x i₀ m i) (y i)\n⊢ m < z i₀"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 140,
"column": 59
} | {
"line": 140,
"column": 70
} | {
"line": 140,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Icc a (f i) = Icc (update f i a) f",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Icc a (f i) = Icc (update f i a) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 143,
"column": 59
} | {
"line": 143,
"column": 70
} | {
"line": 143,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ico a (f i) = Ico (update f i a) f",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ico a (f i) = Ico (update f i a) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 146,
"column": 59
} | {
"line": 146,
"column": 70
} | {
"line": 146,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ioc a (f i) = Ioc (update f i a) f",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ioc a (f i) = Ioc (update f i a) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 149,
"column": 59
} | {
"line": 149,
"column": 70
} | {
"line": 149,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ioo a (f i) = Ioo (update f i a) f",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' Ioo a (f i) = Ioo (update f i a) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 152,
"column": 59
} | {
"line": 152,
"column": 70
} | {
"line": 152,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Icc (f i) b = Icc f (update f i b)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Icc (f i) b = Icc f (update f i b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 155,
"column": 59
} | {
"line": 155,
"column": 70
} | {
"line": 155,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Ico (f i) b = Ico f (update f i b)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Ico (f i) b = Ico f (update f i b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 158,
"column": 59
} | {
"line": 158,
"column": 70
} | {
"line": 158,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Ioc (f i) b = Ioc f (update f i b)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Ioc (f i) b = Ioc f (update f i b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 161,
"column": 59
} | {
"line": 161,
"column": 70
} | {
"line": 161,
"column": 71
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Ioo (f i) b = Ioo f (update f i b)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → PartialOrder (α i)\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' Ioo (f i) b = Ioo f (update f i b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 13
} | {
"line": 243,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Lattice (α i)\ninst✝ : DecidableEq ι\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' uIcc a (f i) = uIcc (update f i a) f",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Lattice (α i)\ninst✝ : DecidableEq ι\nf : (i : ι) → α i\ni : ι\na : α i\n⊢ update f i '' uIcc a (f i) = uIcc (update f i a) f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 247,
"column": 2
} | {
"line": 247,
"column": 13
} | {
"line": 247,
"column": 14
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Lattice (α i)\ninst✝ : DecidableEq ι\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' uIcc (f i) b = uIcc f (update f i b)",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Lattice (α i)\ninst✝ : DecidableEq ι\nf : (i : ι) → α i\ni : ι\nb : α i\n⊢ update f i '' uIcc (f i) b = uIcc f (update f i b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.Pi | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 53
} | {
"line": 311,
"column": 54
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → LinearOrder (α i)\nx y z a : (i : ι) → α i\nhay : a ∉ univ.pi fun i ↦ Ioc (y i) (z i)\nhax : x ≤ a\nhaz : a ≤ z\n⊢ a ∈ ⋃ i, Icc x (update z i (y i))",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.... | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → LinearOrder (α i)\nx y z a : (i : ι) → α i\nhay : a ∉ univ.pi fun i ↦ Ioc (y i) (z i)\nhax : x ≤ a\nhaz : a ≤ z\n⊢ ∃ i, a i ≤ y i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 655,
"column": 8
} | {
"line": 655,
"column": 84
} | {
"line": 655,
"column": 85
} | [
{
"pp": "G : Type u\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : FirstCountableTopology G\nN : Subgroup G\ninst✝¹ : N.Normal\ninst✝ : CompleteSpace G\nthis✝¹ : UniformSpace (G ⧸ N) := IsTopologicalGroup.rightUniformSpace (G ⧸ N)\nthis✝ : UniformSpace G := IsTopological... | [
"G : Type u\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : FirstCountableTopology G\nN : Subgroup G\ninst✝¹ : N.Normal\ninst✝ : CompleteSpace G\nthis✝¹ : UniformSpace (G ⧸ N) := IsTopologicalGroup.rightUniformSpace (G ⧸ N)\nthis✝ : UniformSpace G := IsTopologicalGroup.rightU... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Group | {
"line": 113,
"column": 6
} | {
"line": 113,
"column": 87
} | {
"line": 113,
"column": 88
} | [
{
"pp": "case inr.inl\nG : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\nthis : ∀ {a : G}, Dense (range fun x ↦ a ^ x) → 1 < a → (range fun x ↦ a ^ x) = univ\nh : Dense (range fun x ↦ 1 ^ x)\nha₀ : 1 ≤ 1\n⊢ (range fun x ... | [
"case inr.inl\nG : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\nthis : ∀ {a : G}, Dense (range fun x ↦ a ^ x) → 1 < a → (range fun x ↦ a ^ x) = univ\nh : Dense (range fun x ↦ 1 ^ x)\nha₀ : 1 ≤ 1\n⊢ {1} = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Group | {
"line": 115,
"column": 8
} | {
"line": 115,
"column": 57
} | {
"line": 115,
"column": 58
} | [
{
"pp": "G : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : Dense (range fun x ↦ a ^ x)\nha₀ : a ≤ 1\nthis : ∀ {a : G}, Dense (range fun x ↦ a ^ x) → 1 < a → (range fun x ↦ a ^ x) = univ\nhlt : a < 1\n⊢ (range ... | [
"G : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : Dense (range fun x ↦ a ^ x)\nha₀ : a ≤ 1\nthis : ∀ {a : G}, Dense (range fun x ↦ a ^ x) → 1 < a → (range fun x ↦ a ^ x) = univ\nhlt : a < 1\n⊢ (range fun x ↦ a⁻¹ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Group | {
"line": 121,
"column": 4
} | {
"line": 121,
"column": 15
} | {
"line": 121,
"column": 16
} | [
{
"pp": "G : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : DenseRange fun x ↦ a ^ x\nha₀ : 1 < a\nb : G\nhne : (Ioo b (b * a * a)).Nonempty\n⊢ ∃ m, a ^ m ∈ Ioo b (b * a * a)",
"ppTerm": "?m.194",
"assi... | [
"G : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : DenseRange fun x ↦ a ^ x\nha₀ : 1 < a\nb : G\nhne : (Ioo b (b * a * a)).Nonempty\n⊢ ∃ m, b < a ^ m ∧ a ^ m < b * a * a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Group | {
"line": 125,
"column": 35
} | {
"line": 125,
"column": 75
} | {
"line": 125,
"column": 76
} | [
{
"pp": "G : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : DenseRange fun x ↦ a ^ x\nha₀ : 1 < a\nb : G\nm : ℤ\nhm : b < a ^ m\nhm' : a ^ m < b * a * a\nhne : b ≠ a ^ (m - 1)\nthis : (Ioo (a ^ m) (a ^ (m + 1))... | [
"G : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : DenseRange fun x ↦ a ^ x\nha₀ : 1 < a\nb : G\nm : ℤ\nhm : b < a ^ m\nhm' : a ^ m < b * a * a\nhne : b ≠ a ^ (m - 1)\nthis : (Ioo (a ^ m) (a ^ (m + 1))).Nonempty\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Group | {
"line": 129,
"column": 4
} | {
"line": 130,
"column": 33
} | {
"line": 130,
"column": 34
} | [
{
"pp": "case inr.inl\nG : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : DenseRange fun x ↦ a ^ x\nha₀ : 1 < a\nb : G\nm : ℤ\nhm : b < a ^ m\nhm' : a ^ m < b * a * a\nhne : b ≠ a ^ (m - 1)\nhlt : b < a ^ (m - ... | [
"case inr.inl\nG : Type u_1\ninst✝⁴ : TopologicalSpace G\ninst✝³ : CommGroup G\ninst✝² : LinearOrder G\ninst✝¹ : IsOrderedMonoid G\ninst✝ : OrderTopology G\na : G\nh : DenseRange fun x ↦ a ^ x\nha₀ : 1 < a\nb : G\nm : ℤ\nhm : b < a ^ m\nhm' : a ^ m < b * a * a\nhne : b ≠ a ^ (m - 1)\nhlt : b < a ^ (m - 1)\n⊢ b * a ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 50,
"column": 2
} | {
"line": 50,
"column": 29
} | {
"line": 50,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Semifield 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atTop\n⊢ Tendsto (fun x ↦ f x * g x) l atTop",
... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Semifield 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atTop\n⊢ Tendsto (fun x ↦ f x * g x) l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 93,
"column": 2
} | {
"line": 93,
"column": 31
} | {
"line": 93,
"column": 32
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : Semifield 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nn : ℤ\nN : ℕ\nhn : 0 < N\nh : ↑N = -n\n⊢ Tendsto (fun x ↦ x ^ n) atTop (𝓝 0)",
"ppTerm": "?m.79",
"assigned": false,
"usedConstants": [],
... | [
"𝕜 : Type u_1\ninst✝⁴ : Semifield 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nn : ℤ\nN : ℕ\nhn : 0 < N\nh : ↑N = -n\n⊢ Tendsto (fun x ↦ x ^ n) atTop (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 144,
"column": 4
} | {
"line": 144,
"column": 15
} | {
"line": 144,
"column": 16
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\n⊢ (𝓝 0).HasBasis (fun x ↦ 0 < x) fun ε ↦ {x | |x| < ε}",
"ppTerm": "?m.36",
"assigned": false,
"used... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\n⊢ (𝓝 0).HasBasis (fun x ↦ 0 < x) fun ε ↦ {x | |x| < ε}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 151,
"column": 2
} | {
"line": 151,
"column": 67
} | {
"line": 152,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l atTop\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x ↦ f x * -g x) l atTop\... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l atTop\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x ↦ f x * -g x) l atTop\n⊢ Tendsto (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 29
} | {
"line": 158,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atTop\n⊢ Tendsto (fun x ↦ f x * g x) l atBot",
... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atTop\n⊢ Tendsto (fun x ↦ f x * g x) l atBot"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 165,
"column": 2
} | {
"line": 165,
"column": 33
} | {
"line": 165,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l atBot\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x ↦ (Neg.neg ∘ f) x * g ... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l atBot\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x ↦ (Neg.neg ∘ f) x * g x) l atTop\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 172,
"column": 2
} | {
"line": 172,
"column": 33
} | {
"line": 172,
"column": 34
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l atBot\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x ↦ (Neg.neg ∘ f) x * g ... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l atBot\nhg : Tendsto g l (𝓝 C)\nthis : Tendsto (fun x ↦ (Neg.neg ∘ f) x * g x) l atBot\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 178,
"column": 2
} | {
"line": 178,
"column": 29
} | {
"line": 178,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atBot\n⊢ Tendsto (fun x ↦ f x * g x) l atBot",
... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : 0 < C\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atBot\n⊢ Tendsto (fun x ↦ f x * g x) l atBot"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.Order.Field | {
"line": 184,
"column": 2
} | {
"line": 184,
"column": 29
} | {
"line": 184,
"column": 30
} | [
{
"pp": "𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atBot\n⊢ Tendsto (fun x ↦ f x * g x) l atTop",
... | [
"𝕜 : Type u_1\nα : Type u_2\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nl : Filter α\nf g : α → 𝕜\nC : 𝕜\nhC : C < 0\nhf : Tendsto f l (𝓝 C)\nhg : Tendsto g l atBot\n⊢ Tendsto (fun x ↦ f x * g x) l atTop"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Algebra.IsUniformGroup.Basic | {
"line": 691,
"column": 14
} | {
"line": 691,
"column": 42
} | {
"line": 691,
"column": 43
} | [
{
"pp": "G : Type u\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : FirstCountableTopology G\nN : Subgroup G\ninst✝¹ : N.Normal\ninst✝ : CompleteSpace G\nthis✝¹ : UniformSpace (G ⧸ N) := IsTopologicalGroup.rightUniformSpace (G ⧸ N)\nthis✝ : UniformSpace G := IsTopological... | [
"G : Type u\ninst✝⁵ : Group G\ninst✝⁴ : TopologicalSpace G\ninst✝³ : IsTopologicalGroup G\ninst✝² : FirstCountableTopology G\nN : Subgroup G\ninst✝¹ : N.Normal\ninst✝ : CompleteSpace G\nthis✝¹ : UniformSpace (G ⧸ N) := IsTopologicalGroup.rightUniformSpace (G ⧸ N)\nthis✝ : UniformSpace G := IsTopologicalGroup.rightU... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.LeftRightNhds | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 60
} | {
"line": 160,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\ns : Set α\nt : Set α := {x | x ∈ s ∧ 𝓝[s ∩ Ioi x] x = ⊥ ∧ ¬IsTop x}\ny : α → α\nhy : ∀ x ∈ t, y x > x\nh'y : ∀ x ∈ t, s ∩ Ioo x (y x) = ∅\na : α\nha : a ∈ t\nb : α\nhb : b ∈ ... | [] | exact fun u hu v hv ↦ ((hu.2.trans_le this).trans hv.1).ne | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Algebra.Order.Field | {
"line": 295,
"column": 6
} | {
"line": 295,
"column": 53
} | {
"line": 295,
"column": 54
} | [
{
"pp": "case refine_1.ofNat\n𝕜 : Type u_1\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nc d : 𝕜\nhc : c ≠ 0\nn : ℕ\nh : Tendsto (fun x ↦ c * x ^ Int.ofNat n) atTop (𝓝 d)\n⊢ Int.ofNat n = 0 ∧ c = d",
"ppTerm": "?refin... | [
"case refine_1.ofNat\n𝕜 : Type u_1\ninst✝⁴ : Field 𝕜\ninst✝³ : LinearOrder 𝕜\ninst✝² : IsStrictOrderedRing 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nc d : 𝕜\nhc : c ≠ 0\nn : ℕ\nh : Tendsto (fun x ↦ c * x ^ Int.ofNat n) atTop (𝓝 d)\n⊢ n = 0 ∧ c = d"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.LeftRightNhds | {
"line": 447,
"column": 2
} | {
"line": 447,
"column": 13
} | {
"line": 447,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : CommGroup α\ninst✝³ : LinearOrder α\ninst✝² : IsOrderedMonoid α\ninst✝¹ : OrderTopology α\ninst✝ : NoMaxOrder α\n⊢ (𝓝 1).HasBasis (fun ε ↦ 1 < ε) fun ε ↦ {b | |b|ₘ < ε}",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"use... | [
"α : Type u_1\ninst✝⁵ : TopologicalSpace α\ninst✝⁴ : CommGroup α\ninst✝³ : LinearOrder α\ninst✝² : IsOrderedMonoid α\ninst✝¹ : OrderTopology α\ninst✝ : NoMaxOrder α\n⊢ (𝓝 1).HasBasis (fun ε ↦ 1 < ε) fun ε ↦ {b | |b|ₘ < ε}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Logic.Equiv.PartialEquiv | {
"line": 887,
"column": 76
} | {
"line": 887,
"column": 91
} | {
"line": 887,
"column": 92
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ne : PartialEquiv α β\nh : e.source = univ\n⊢ Injective ↑e",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\ne : PartialEquiv α β\nh : e.source = univ\n⊢ Injective ↑e"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Basic | {
"line": 378,
"column": 2
} | {
"line": 378,
"column": 54
} | {
"line": 378,
"column": 55
} | [
{
"pp": "α : Type u\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTop α\ninst✝¹ : OrderTopology α\ninst✝ : Nontrivial α\nthis : ∃ x, x < ⊤\n⊢ (𝓝 ⊤).HasBasis (fun a ↦ a < ⊤) fun a ↦ Ioi a",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"α : Type u\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTop α\ninst✝¹ : OrderTopology α\ninst✝ : Nontrivial α\nthis : ∃ x, x < ⊤\n⊢ (𝓝 ⊤).HasBasis (fun a ↦ a < ⊤) fun a ↦ Ioi a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Basic | {
"line": 436,
"column": 4
} | {
"line": 436,
"column": 27
} | {
"line": 436,
"column": 28
} | [
{
"pp": "case h\nα : Type u\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na : α\ns : Set α\nhs : s ∈ 𝓝[≥] a\nha : IsMax a\n⊢ a ≤ a ∧ Icc a a ∈ 𝓝[≥] a ∧ Icc a a ⊆ s",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Filter.instMembershi... | [
"case h\nα : Type u\ninst✝² : TopologicalSpace α\ninst✝¹ : LinearOrder α\ninst✝ : OrderTopology α\na : α\ns : Set α\nhs : s ∈ 𝓝[≥] a\nha : IsMax a\n⊢ a ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Basic | {
"line": 465,
"column": 4
} | {
"line": 465,
"column": 50
} | {
"line": 467,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : Nontrivial α\ns : Set α\nhs : IsOpen[inst✝³] s\nx : α\nhx : x ∈ s\ny : α\nhy : y ≠ x\nH : y < x\nl : α\nlx : l < x\nhl : Ioc l x ⊆ s\n⊢ ∃ a b, a < b ∧ Ioo a b ⊆ s",
"ppTerm": "?inr.inr",... | [] | exact ⟨l, x, lx, Ioo_subset_Ioc_self.trans hl⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Order.Basic | {
"line": 482,
"column": 2
} | {
"line": 482,
"column": 13
} | {
"line": 482,
"column": 14
} | [
{
"pp": "α : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : WellFoundedLT α\ns : Set α\nh : IsLowerSet s\n⊢ IsOpen[inst✝³] s",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : WellFoundedLT α\ns : Set α\nh : IsLowerSet s\n⊢ IsOpen[inst✝³] s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Basic | {
"line": 590,
"column": 4
} | {
"line": 590,
"column": 48
} | {
"line": 590,
"column": 49
} | [
{
"pp": "α : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\na✝ : Nontrivial α\ns : Set α := ⋯\ny : α → α\nhy : ∀ x ∈ s, x ⋖ y x\nHy : ∀ (x z : α), x ∈ s → z < y x → z ≤ x\na : Set α\nha : IsOpen[inst✝³] a\nt : Set α := ⋯\nx : α\nhx : x ∈... | [
"α : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\na✝ : Nontrivial α\ns : Set α := ⋯\ny : α → α\nhy : ∀ x ∈ s, x ⋖ y x\nHy : ∀ (x z : α), x ∈ s → z < y x → z ≤ x\na : Set α\nha : IsOpen[inst✝³] a\nt : Set α := ⋯\nx : α\nhx : x ∈ t\n⊢ ∃ l, l... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Basic | {
"line": 612,
"column": 2
} | {
"line": 612,
"column": 39
} | {
"line": 612,
"column": 40
} | [
{
"pp": "α : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\n⊢ {x | ∃ y < x, Ioo y x = ∅}.Countable",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"CovB... | [
"α : Type u\ninst✝³ : TopologicalSpace α\ninst✝² : LinearOrder α\ninst✝¹ : OrderTopology α\ninst✝ : SecondCountableTopology α\n⊢ {x | ∃ y, y ⋖ x}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Module.CharacterModule | {
"line": 217,
"column": 68
} | {
"line": 217,
"column": 81
} | {
"line": 217,
"column": 81
} | [
{
"pp": "A : Type uA\ninst✝ : AddCommGroup A\na : A\nne_zero : a ≠ 0\nc : CharacterModule A\nhc : (dual (ℤ ∙ a).subtype) c = ofSpanSingleton a\nh : c a = 0\n⊢ (ofSpanSingleton a) ⟨a, ⋯⟩ = 0",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Rat.instOfNat",
"Eq.mpr",
"Submod... | [] | by rwa [← hc] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Algebra.Module.CharacterModule | {
"line": 240,
"column": 2
} | {
"line": 240,
"column": 62
} | {
"line": 241,
"column": 2
} | [
{
"pp": "R : Type uR\ninst✝⁴ : CommRing R\nA : Type uA\ninst✝³ : AddCommGroup A\nA' : Type u_1\ninst✝² : AddCommGroup A'\ninst✝¹ : Module R A\ninst✝ : Module R A'\nf : A →ₗ[R] A'\nhf : Function.Injective ⇑(dual f)\nc : CharacterModule (A' ⧸ f.range)\nb : A'\n⊢ c ((QuotientAddGroup.mk' f.range.toAddSubgroup) b) ... | [
"R : Type uR\ninst✝⁴ : CommRing R\nA : Type uA\ninst✝³ : AddCommGroup A\nA' : Type u_1\ninst✝² : AddCommGroup A'\ninst✝¹ : Module R A\ninst✝ : Module R A'\nf : A →ₗ[R] A'\nhf : Function.Injective ⇑(dual f)\nc : CharacterModule (A' ⧸ f.range)\nb : A'\n⊢ (dual f.range.mkQ) c = 0"
] | suffices eq : dual (Submodule.mkQ _) c = 0 from congr($eq b) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Topology.Order.Basic | {
"line": 666,
"column": 4
} | {
"line": 666,
"column": 46
} | {
"line": 666,
"column": 47
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : LinearOrder β\ninst✝ : SecondCountableTopology α\nt : Set β\nf : β → α\na✝ : Nontrivial β\nthis : Nonempty α\ns : Set β := {x | x ∈ t ∧ ∃ z, f x < z ∧ ∀ y ∈ t, x < y → z ≤ f y}\nz : β → α\nhz... | [
"α : Type u\nβ : Type v\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : LinearOrder β\ninst✝ : SecondCountableTopology α\nt : Set β\nf : β → α\na✝ : Nontrivial β\nthis : Nonempty α\ns : Set β := {x | x ∈ t ∧ ∃ z, f x < z ∧ ∀ y ∈ t, x < y → z ≤ f y}\nz : β → α\nhz : ∀ x ∈ s, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.Basic | {
"line": 676,
"column": 2
} | {
"line": 676,
"column": 13
} | {
"line": 676,
"column": 14
} | [
{
"pp": "α : Type u\nβ : Type v\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : LinearOrder β\nf : β → α\ninst✝ : SecondCountableTopology α\n⊢ {x | ∃ z, f x < z ∧ ∀ (y : β), x < y → z ≤ f y}.Countable",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [... | [
"α : Type u\nβ : Type v\ninst✝⁴ : TopologicalSpace α\ninst✝³ : LinearOrder α\ninst✝² : OrderTopology α\ninst✝¹ : LinearOrder β\nf : β → α\ninst✝ : SecondCountableTopology α\n⊢ {x | ∃ z, f x < z ∧ ∀ (y : β), x < y → z ≤ f y}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 298,
"column": 6
} | {
"line": 298,
"column": 62
} | {
"line": 298,
"column": 63
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : AddCommGroup 𝕜\np : 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsOrderedAddMonoid 𝕜\nhp : 0 < p\nn : ℤ\nhx : n ≤ 0\n⊢ n • p ≤ 0",
"ppTerm": "?m.76",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
... | [
"𝕜 : Type u_1\ninst✝² : AddCommGroup 𝕜\np : 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsOrderedAddMonoid 𝕜\nhp : 0 < p\nn : ℤ\nhx : n ≤ 0\n⊢ 0 ≤ -n • p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 391,
"column": 17
} | {
"line": 391,
"column": 44
} | {
"line": 391,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : AddCommGroup 𝕜\np : 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\na : AddCircle p\nb : ↑(Ico 0 (0 + p)) := (QuotientAddGroup.equivIcoMod ⋯ 0) a\n⊢ ↑b ∈ Ico 0 p",
"ppTerm": "?m.44",
"assigned": false,
"usedCon... | [
"𝕜 : Type u_1\ninst✝³ : AddCommGroup 𝕜\np : 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\na : AddCircle p\nb : ↑(Ico 0 (0 + p)) := (QuotientAddGroup.equivIcoMod ⋯ 0) a\n⊢ ↑b ∈ Ico 0 p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 397,
"column": 17
} | {
"line": 397,
"column": 44
} | {
"line": 397,
"column": 45
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : AddCommGroup 𝕜\np : 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\na : AddCircle p\nb : ↑(Ioc 0 (0 + p)) := (QuotientAddGroup.equivIocMod ⋯ 0) a\n⊢ ↑b ∈ Ioc 0 p",
"ppTerm": "?m.44",
"assigned": false,
"usedCon... | [
"𝕜 : Type u_1\ninst✝³ : AddCommGroup 𝕜\np : 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\na : AddCircle p\nb : ↑(Ioc 0 (0 + p)) := (QuotientAddGroup.equivIocMod ⋯ 0) a\n⊢ ↑b ∈ Ioc 0 p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 402,
"column": 36
} | {
"line": 402,
"column": 72
} | {
"line": 402,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : AddCommGroup 𝕜\np : 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝ : Archimedean 𝕜\nha : a ∈ Ico 0 p\n⊢ 0 ∈ Ico 0 (0 + p)",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",... | [
"𝕜 : Type u_1\ninst✝³ : AddCommGroup 𝕜\np : 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝ : Archimedean 𝕜\nha : a ∈ Ico 0 p\n⊢ 0 < p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 423,
"column": 2
} | {
"line": 425,
"column": 96
} | {
"line": 427,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : AddCommGroup 𝕜\np : 𝕜\ninst✝⁴ : LinearOrder 𝕜\ninst✝³ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝² : Archimedean 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nx : AddCircle p\nhx : x ≠ ↑a\n⊢ ContinuousAt (⇑(equivIco p a)) x",
"ppTerm": "?m.25",... | [] | induction x using QuotientAddGroup.induction_on
rw [ContinuousAt, Filter.Tendsto, QuotientAddGroup.nhds_eq, Filter.map_map]
exact (continuousAt_toIcoMod hp.out a <| not_modEq_iff_ne_mod_zmultiples.mpr hx).codRestrict _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 423,
"column": 2
} | {
"line": 425,
"column": 96
} | {
"line": 427,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : AddCommGroup 𝕜\np : 𝕜\ninst✝⁴ : LinearOrder 𝕜\ninst✝³ : IsOrderedAddMonoid 𝕜\nhp : Fact (0 < p)\na : 𝕜\ninst✝² : Archimedean 𝕜\ninst✝¹ : TopologicalSpace 𝕜\ninst✝ : OrderTopology 𝕜\nx : AddCircle p\nhx : x ≠ ↑a\n⊢ ContinuousAt (⇑(equivIco p a)) x",
"ppTerm": "?m.25",... | [] | induction x using QuotientAddGroup.induction_on
rw [ContinuousAt, Filter.Tendsto, QuotientAddGroup.nhds_eq, Filter.map_map]
exact (continuousAt_toIcoMod hp.out a <| not_modEq_iff_ne_mod_zmultiples.mpr hx).codRestrict _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 657,
"column": 2
} | {
"line": 657,
"column": 13
} | {
"line": 657,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : Field 𝕜\np : 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nhp : Fact (0 < p)\na : 𝕜\n⊢ IsOfFinAddOrder ↑a ↔ ∃ q, ↑q = a / p",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"𝕜 : Type u_1\ninst✝² : Field 𝕜\np : 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nhp : Fact (0 < p)\na : 𝕜\n⊢ IsOfFinAddOrder ↑a ↔ ∃ q, ↑q = a / p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.ModuleCat.Subobject | {
"line": 63,
"column": 10
} | {
"line": 63,
"column": 40
} | {
"line": 64,
"column": 10
} | [
{
"pp": "case e'_3\nR : Type u\ninst✝ : Ring R\nM : ModuleCat R\nS T : Submodule R ↑M\nh :\n { toFun := fun N ↦ mk (↟N.subtype), invFun := fun S ↦ (Hom.hom S.arrow).range, left_inv := ⋯, right_inv := ⋯ } S ≤\n { toFun := fun N ↦ mk (↟N.subtype), invFun := fun S ↦ (Hom.hom S.arrow).range, left_inv := ⋯, righ... | [
"case e'_3\nR : Type u\ninst✝ : Ring R\nM : ModuleCat R\nS T : Submodule R ↑M\nh :\n { toFun := fun N ↦ mk (↟N.subtype), invFun := fun S ↦ (Hom.hom S.arrow).range, left_inv := ⋯, right_inv := ⋯ } S ≤\n { toFun := fun N ↦ mk (↟N.subtype), invFun := fun S ↦ (Hom.hom S.arrow).range, left_inv := ⋯, right_inv := ⋯ }... | rw [← hom_comp, ofMkLEMk_comp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 686,
"column": 69
} | {
"line": 686,
"column": 98
} | {
"line": 686,
"column": 99
} | [
{
"pp": "𝕜 : Type u_1\ninst✝² : Field 𝕜\np : 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nhp : Fact (0 < p)\nh : ¬∃ u, ¬IsOfFinAddOrder u\n⊢ IsEmpty { u // ¬IsOfFinAddOrder u }",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Classical.not_not._simp_... | [
"𝕜 : Type u_1\ninst✝² : Field 𝕜\np : 𝕜\ninst✝¹ : LinearOrder 𝕜\ninst✝ : IsStrictOrderedRing 𝕜\nhp : Fact (0 < p)\nh : ¬∃ u, ¬IsOfFinAddOrder u\n⊢ ∀ (x : AddCircle p), IsOfFinAddOrder x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Instances.AddCircle.Defs | {
"line": 788,
"column": 28
} | {
"line": 788,
"column": 56
} | {
"line": 788,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\ninst✝³ : AddCommGroup 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\np a : 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\nf : 𝕜 → B\nhf : f a = f (a + p)\nq : 𝕋\n⊢ ?m.37",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"𝕜 : Type u_1\nB : Type u_2\ninst✝³ : AddCommGroup 𝕜\ninst✝² : LinearOrder 𝕜\ninst✝¹ : IsOrderedAddMonoid 𝕜\np a : 𝕜\nhp : Fact (0 < p)\ninst✝ : Archimedean 𝕜\nf : 𝕜 → B\nhf : f a = f (a + p)\nq : 𝕋\n⊢ ?m.37"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.ModuleCat.AB | {
"line": 46,
"column": 2
} | {
"line": 46,
"column": 13
} | {
"line": 46,
"column": 14
} | [
{
"pp": "R : Type u\ninst✝¹ : Ring R\ninst✝ : Small.{v, u} R\nX Y : ModuleCat R\nf g : X ⟶ Y\nh : ∀ (h : of R (Shrink.{v, u} R) ⟶ X) (x : Shrink.{v, u} R), (Hom.hom f) ((Hom.hom h) x) = (Hom.hom g) ((Hom.hom h) x)\nx : ↑X\n⊢ (Hom.hom f) x = (Hom.hom g) x",
"ppTerm": "?m.39",
"assigned": false,
"used... | [
"R : Type u\ninst✝¹ : Ring R\ninst✝ : Small.{v, u} R\nX Y : ModuleCat R\nf g : X ⟶ Y\nh : ∀ (h : of R (Shrink.{v, u} R) ⟶ X) (x : Shrink.{v, u} R), (Hom.hom f) ((Hom.hom h) x) = (Hom.hom g) ((Hom.hom h) x)\nx : ↑X\n⊢ (Hom.hom f) x = (Hom.hom g) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Refinements | {
"line": 104,
"column": 29
} | {
"line": 104,
"column": 79
} | {
"line": 104,
"column": 80
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS : ShortComplex C\nhS : ∀ ⦃A : C⦄ (y : A ⟶ S.cycles), ∃ A' π, ∃ (_ : Epi π), ∃ x, π ≫ y = x ≫ S.toCycles\nA : C\na : A ⟶ S.X₂\nha : a ≫ S.g = 0\nA' : C\nπ : A' ⟶ A\nhπ : Epi π\nx₁ : A' ⟶ S.X₁\nfac : π ≫ S.liftCycles a ha = x₁ ≫ S.toCycle... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS : ShortComplex C\nhS : ∀ ⦃A : C⦄ (y : A ⟶ S.cycles), ∃ A' π, ∃ (_ : Epi π), ∃ x, π ≫ y = x ≫ S.toCycles\nA : C\na : A ⟶ S.X₂\nha : a ≫ S.g = 0\nA' : C\nπ : A' ⟶ A\nhπ : Epi π\nx₁ : A' ⟶ S.X₁\nfac : π ≫ S.liftCycles a ha = x₁ ≫ S.toCycles\n⊢ π ≫ a =... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Refinements | {
"line": 199,
"column": 41
} | {
"line": 199,
"column": 52
} | {
"line": 199,
"column": 53
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex C\nφ : S₁ ⟶ S₂\nh : Mono (homologyMap φ)\nA : C\nx₂ : A ⟶ S₁.X₂\nhx₂ : x₂ ≫ S₁.g = 0\ny₁ : A ⟶ S₂.X₁\nfac : x₂ ≫ φ.τ₂ = y₁ ≫ S₂.f\n⊢ 𝟙 A ≫ x₂ ≫ φ.τ₂ = y₁ ≫ S₂.f",
"ppTerm": "?m.146",
"assigned": true,
"us... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex C\nφ : S₁ ⟶ S₂\nh : Mono (homologyMap φ)\nA : C\nx₂ : A ⟶ S₁.X₂\nhx₂ : x₂ ≫ S₁.g = 0\ny₁ : A ⟶ S₂.X₁\nfac : x₂ ≫ φ.τ₂ = y₁ ≫ S₂.f\n⊢ x₂ ≫ φ.τ₂ = y₁ ≫ S₂.f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Refinements | {
"line": 231,
"column": 13
} | {
"line": 231,
"column": 37
} | {
"line": 231,
"column": 38
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex C\nφ : S₁ ⟶ S₂\nh : ∀ ⦃A : C⦄ (y : A ⟶ S₂.homology), ∃ A' π, ∃ (_ : Epi π), ∃ x, π ≫ y = x ≫ homologyMap φ\nA : C\ny₂ : A ⟶ S₂.X₂\nhy₂ : y₂ ≫ S₂.g = 0\nA₁ : C\nπ₁ : A₁ ⟶ A\nhπ₁ : Epi π₁\nγ : A₁ ⟶ S₁.homology\nA₂ : C\n... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex C\nφ : S₁ ⟶ S₂\nh : ∀ ⦃A : C⦄ (y : A ⟶ S₂.homology), ∃ A' π, ∃ (_ : Epi π), ∃ x, π ≫ y = x ≫ homologyMap φ\nA : C\ny₂ : A ⟶ S₂.X₂\nhy₂ : y₂ ≫ S₂.g = 0\nA₁ : C\nπ₁ : A₁ ⟶ A\nhπ₁ : Epi π₁\nγ : A₁ ⟶ S₁.homology\nA₂ : C\nπ₂ : A₂ ⟶ A₁... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.CategoryTheory.Abelian.Refinements | {
"line": 238,
"column": 42
} | {
"line": 238,
"column": 68
} | {
"line": 238,
"column": 69
} | [
{
"pp": "C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex C\nφ : S₁ ⟶ S₂\nh :\n ∀ ⦃A : C⦄ (y₂ : A ⟶ S₂.X₂),\n y₂ ≫ S₂.g = 0 → ∃ A' π, ∃ (_ : Epi π), ∃ x₂, ∃ (_ : x₂ ≫ S₁.g = 0), ∃ y₁, π ≫ y₂ = x₂ ≫ φ.τ₂ + y₁ ≫ S₂.f\nA : C\nγ : A ⟶ S₂.homology\nA₁ : C\nπ₁ : A₁ ⟶ A\nhπ₁ : ... | [
"C : Type u_1\ninst✝¹ : Category.{v_1, u_1} C\ninst✝ : Abelian C\nS₁ S₂ : ShortComplex C\nφ : S₁ ⟶ S₂\nh :\n ∀ ⦃A : C⦄ (y₂ : A ⟶ S₂.X₂),\n y₂ ≫ S₂.g = 0 → ∃ A' π, ∃ (_ : Epi π), ∃ x₂, ∃ (_ : x₂ ≫ S₁.g = 0), ∃ y₁, π ≫ y₂ = x₂ ≫ φ.τ₂ + y₁ ≫ S₂.f\nA : C\nγ : A ⟶ S₂.homology\nA₁ : C\nπ₁ : A₁ ⟶ A\nhπ₁ : Epi π₁\ny₂ :... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Category.ModuleCat.Adjunctions | {
"line": 322,
"column": 6
} | {
"line": 322,
"column": 36
} | {
"line": 323,
"column": 6
} | [
{
"pp": "case add.h_add\nR : Type u_1\ninst✝⁴ : CommRing R\nC : Type u\ninst✝³ : Category.{v, u} C\nD : Type u\ninst✝² : Category.{v, u} D\ninst✝¹ : Preadditive D\ninst✝ : Linear R D\nF : C ⥤ D\nX Y Z : Free R C\ng : Y ⟶ Z\nf₁ f₂ : (X ⟶ Y) →₀ R\nw₁ : (sum (f₁ ≫ g) fun f' r ↦ r • F.map f') = (f₁.sum fun f' r ↦ r... | [
"case add.h_zero\nR : Type u_1\ninst✝⁴ : CommRing R\nC : Type u\ninst✝³ : Category.{v, u} C\nD : Type u\ninst✝² : Category.{v, u} D\ninst✝¹ : Preadditive D\ninst✝ : Linear R D\nF : C ⥤ D\nX Y Z : Free R C\ng : Y ⟶ Z\nf₁ f₂ : (X ⟶ Y) →₀ R\nw₁ : (sum (f₁ ≫ g) fun f' r ↦ r • F.map f') = (f₁.sum fun f' r ↦ r • F.map f'... | · intros; simp only [add_smul] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Algebra.Category.ModuleCat.Adjunctions | {
"line": 324,
"column": 6
} | {
"line": 324,
"column": 36
} | {
"line": 325,
"column": 4
} | [
{
"pp": "case add.h_add\nR : Type u_1\ninst✝⁴ : CommRing R\nC : Type u\ninst✝³ : Category.{v, u} C\nD : Type u\ninst✝² : Category.{v, u} D\ninst✝¹ : Preadditive D\ninst✝ : Linear R D\nF : C ⥤ D\nX Y Z : Free R C\ng : Y ⟶ Z\nf₁ f₂ : (X ⟶ Y) →₀ R\nw₁ : (sum (f₁ ≫ g) fun f' r ↦ r • F.map f') = (f₁.sum fun f' r ↦ r... | [] | · intros; simp only [add_smul] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
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