module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Topology.Order | {
"line": 133,
"column": 4
} | {
"line": 133,
"column": 65
} | {
"line": 133,
"column": 66
} | [
{
"pp": "case inr\nα : Type u\ninst✝ : DecidableEq α\na₀ : α\nl : Filter α\nh : pure a₀ ≤ l\nb a : α\ns : Set α\nhs : s ∈ update pure a₀ l a\nha : a ≠ a₀\n⊢ ∀ᶠ (y : α) in update pure a₀ l a, s ∈ update pure a₀ l y",
"ppTerm": "?inr✝",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Fi... | [
"case inr\nα : Type u\ninst✝ : DecidableEq α\na₀ : α\nl : Filter α\nh : pure a₀ ≤ l\nb a : α\ns : Set α\nhs : s ∈ update pure a₀ l a\nha : a ≠ a₀\n⊢ a ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 497,
"column": 2
} | {
"line": 497,
"column": 30
} | {
"line": 497,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp a (b + p) = toIcoMod hp a b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp a (b + p) = toIcoMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 501,
"column": 2
} | {
"line": 501,
"column": 30
} | {
"line": 501,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp (a + p) b = toIcoMod hp a b + p",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp (a + p) b = toIcoMod hp a b + p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 505,
"column": 2
} | {
"line": 505,
"column": 30
} | {
"line": 505,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp a (b + p) = toIocMod hp a b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp a (b + p) = toIocMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 509,
"column": 2
} | {
"line": 509,
"column": 30
} | {
"line": 509,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp (a + p) b = toIocMod hp a b + p",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp (a + p) b = toIocMod hp a b + p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 529,
"column": 2
} | {
"line": 529,
"column": 30
} | {
"line": 529,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp a (b - p) = toIcoMod hp a b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp a (b - p) = toIcoMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 533,
"column": 2
} | {
"line": 533,
"column": 30
} | {
"line": 533,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp (a - p) b = toIcoMod hp a b - p",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp (a - p) b = toIcoMod hp a b - p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 537,
"column": 2
} | {
"line": 537,
"column": 30
} | {
"line": 537,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp a (b - p) = toIocMod hp a b",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp a (b - p) = toIocMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 541,
"column": 2
} | {
"line": 541,
"column": 30
} | {
"line": 541,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp (a - p) b = toIocMod hp a b - p",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp (a - p) b = toIocMod hp a b - p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 562,
"column": 2
} | {
"line": 562,
"column": 28
} | {
"line": 562,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp (-a) b = p - toIocMod hp a (-b)",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIcoMod hp (-a) b = p - toIocMod hp a (-b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 569,
"column": 2
} | {
"line": 569,
"column": 28
} | {
"line": 569,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp (-a) b = p - toIcoMod hp a (-b)",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"α : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b : α\n⊢ toIocMod hp (-a) b = p - toIcoMod hp a (-b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order | {
"line": 594,
"column": 4
} | {
"line": 594,
"column": 59
} | {
"line": 594,
"column": 60
} | [
{
"pp": "case mp\nα : Type u\nt : TopologicalSpace α\nh : induced ofTopology t = ⊤\n⊢ t = ⊤",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mp\nα : Type u\nt : TopologicalSpace α\nh : induced ofTopology t = ⊤\n⊢ t = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Maps.Basic | {
"line": 185,
"column": 8
} | {
"line": 185,
"column": 19
} | {
"line": 185,
"column": 20
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace X\ninst✝ : NontrivialTopology X\nf : X → Y\nhf : IsInducing f\n⊢ ¬NontrivialTopology Y → ¬NontrivialTopology X",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Indi... | [
"X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace Y\ninst✝¹ : TopologicalSpace X\ninst✝ : NontrivialTopology X\nf : X → Y\nhf : IsInducing f\n⊢ IndiscreteTopology Y → IndiscreteTopology X"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homeomorph.Defs | {
"line": 349,
"column": 14
} | {
"line": 349,
"column": 47
} | {
"line": 349,
"column": 48
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nZ : Type u_4\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : X ≃ₜ Y\nf : Y → Z\nh : IsOpenQuotientMap (f ∘ ⇑e)\n⊢ IsOpenQuotientMap f",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"X : Type u_1\nY : Type u_2\nZ : Type u_4\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : X ≃ₜ Y\nf : Y → Z\nh : IsOpenQuotientMap (f ∘ ⇑e)\n⊢ IsOpenQuotientMap f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homeomorph.Defs | {
"line": 356,
"column": 14
} | {
"line": 356,
"column": 49
} | {
"line": 356,
"column": 50
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nZ : Type u_4\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : Y ≃ₜ Z\nf : X → Y\nh : IsOpenQuotientMap (⇑e ∘ f)\n⊢ IsOpenQuotientMap f",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"X : Type u_1\nY : Type u_2\nZ : Type u_4\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : Y ≃ₜ Z\nf : X → Y\nh : IsOpenQuotientMap (⇑e ∘ f)\n⊢ IsOpenQuotientMap f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homeomorph.Defs | {
"line": 394,
"column": 51
} | {
"line": 394,
"column": 62
} | {
"line": 394,
"column": 63
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nW : Type u_3\nZ✝ : Type u_4\nZ : Type u_5\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : X ≃ Y\nhe : ∀ (s : Set Y), IsOpen[inst✝²] (⇑e ⁻¹' s) ↔ IsOpen[inst✝¹] s\ns : Set X\n⊢ IsOpen[inst✝²] s → IsOpen[inst✝¹] (e.invFun ⁻¹' s)",
... | [
"X : Type u_1\nY : Type u_2\nW : Type u_3\nZ✝ : Type u_4\nZ : Type u_5\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : X ≃ Y\nhe : ∀ (s : Set Y), IsOpen[inst✝²] (⇑e ⁻¹' s) ↔ IsOpen[inst✝¹] s\ns : Set X\n⊢ IsOpen[inst✝²] s → IsOpen[inst✝¹] (⇑e.symm ⁻¹' s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Homeomorph.Defs | {
"line": 403,
"column": 62
} | {
"line": 403,
"column": 82
} | {
"line": 403,
"column": 82
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nW : Type u_3\nZ✝ : Type u_4\nZ : Type u_5\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : X ≃ Y\nhe : ∀ (s : Set Y), IsOpen[inst✝²] (⇑e ⁻¹' s) ↔ IsOpen[inst✝¹] s\ns : Set X\n⊢ IsOpen[inst✝¹] (⇑e.symm ⁻¹' s) ↔ IsOpen[inst✝²] s",
... | [
"case e'_2\nX : Type u_1\nY : Type u_2\nW : Type u_3\nZ✝ : Type u_4\nZ : Type u_5\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\ne : X ≃ Y\nhe : ∀ (s : Set Y), IsOpen[inst✝²] (⇑e ⁻¹' s) ↔ IsOpen[inst✝¹] s\ns : Set X\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.Homeomorph.Defs | {
"line": 414,
"column": 51
} | {
"line": 414,
"column": 62
} | {
"line": 414,
"column": 63
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nW : Type u_3\nZ✝ : Type u_4\nZ : Type u_5\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X ≃ Y\nhf : IsInducing ⇑f\n⊢ Continuous[inst✝¹, inst✝¹] (⇑f ∘ f.invFun)",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
... | [
"X : Type u_1\nY : Type u_2\nW : Type u_3\nZ✝ : Type u_4\nZ : Type u_5\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X ≃ Y\nhf : IsInducing ⇑f\n⊢ Continuous[inst✝¹, inst✝¹] id"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order | {
"line": 748,
"column": 2
} | {
"line": 748,
"column": 13
} | {
"line": 748,
"column": 14
} | [
{
"pp": "α : Type u\nt : TopologicalSpace α\n⊢ NontrivialTopology α ↔ ∃ x y, ¬Inseparable x y",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nt : TopologicalSpace α\n⊢ NontrivialTopology α ↔ ∃ x y, ¬Inseparable x y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Maps.Basic | {
"line": 503,
"column": 2
} | {
"line": 503,
"column": 14
} | {
"line": 504,
"column": 2
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nf : X → Y\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nh : ∀ (x : X) (l : Filter Y), ClusterPt (f x) l → ClusterPt x (comap f l)\n⊢ ∀ (x : X), ∀ s ∈ 𝓝 x, f '' s ∈ 𝓝 (f x)",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Filter.instM... | [
"X : Type u_1\nY : Type u_2\nf : X → Y\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nh : ∀ (x : X) (l : Filter Y), ClusterPt (f x) l → ClusterPt x (comap f l)\nx : X\ns : Set X\nhs : s ∈ 𝓝 x\n⊢ f '' s ∈ 𝓝 (f x)"
] | intro x s hs | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Topology.Maps.Basic | {
"line": 510,
"column": 40
} | {
"line": 510,
"column": 73
} | {
"line": 510,
"column": 74
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nf : X → Y\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nhs : ∀ (s : Set X), f '' interior s ⊆ interior (f '' s)\nu : Set X\nhu : IsOpen[inst✝¹] u\n⊢ f '' u ⊆ interior (f '' u)",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"X : Type u_1\nY : Type u_2\nf : X → Y\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nhs : ∀ (s : Set X), f '' interior s ⊆ interior (f '' s)\nu : Set X\nhu : IsOpen[inst✝¹] u\n⊢ f '' u ⊆ interior (f '' u)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.SeparatedNhds | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 81
} | {
"line": 158,
"column": 82
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\ns t u : Set X\n⊢ SeparatedNhds s u → SeparatedNhds t u → SeparatedNhds (s ∪ t) u",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"nhdsSet_union",
"congrArg",
"Filter.instCompleteLatticeFilter",
"Parti... | [
"X : Type u_1\ninst✝ : TopologicalSpace X\ns t u : Set X\n⊢ Disjoint (𝓝ˢ s) (𝓝ˢ u) → Disjoint (𝓝ˢ t) (𝓝ˢ u) → Disjoint (𝓝ˢ s) (𝓝ˢ u) ∧ Disjoint (𝓝ˢ t) (𝓝ˢ u)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 267,
"column": 6
} | {
"line": 267,
"column": 25
} | {
"line": 267,
"column": 26
} | [
{
"pp": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx : X\ny : Y\ns : Set (X × Y)\ntx : Set X\nty : Set Y\n⊢ s ∈ 𝓝[tx ×ˢ ty] (x, y) ↔ ∃ u ∈ 𝓝[tx] x, ∃ v ∈ 𝓝[ty] y, u ×ˢ v ⊆ s",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Filter.instMembersh... | [
"X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nx : X\ny : Y\ns : Set (X × Y)\ntx : Set X\nty : Set Y\n⊢ s ∈ 𝓝[tx] x ×ˢ 𝓝[ty] y ↔ ∃ u ∈ 𝓝[tx] x, ∃ v ∈ 𝓝[ty] y, u ×ˢ v ⊆ s"
] | nhdsWithin_prod_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 936,
"column": 6
} | {
"line": 936,
"column": 35
} | {
"line": 936,
"column": 36
} | [
{
"pp": "case H.H.H\nα : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\nhp' : Fact (0 < p)\nz✝² z✝¹ z✝ : α\nh₁₂₃ : toIcoMod ⋯ z✝² z✝¹ ≤ toIocMod ⋯ z✝² z✝\nh₃₂₁ : toIcoMod ⋯ z✝² z✝ ≤ toIocMod ⋯ z✝² z✝¹\n⊢ z✝² ≡ z✝¹... | [
"case H.H.H\nα : Type u_1\ninst✝² : AddCommGroup α\ninst✝¹ : LinearOrder α\ninst✝ : IsOrderedAddMonoid α\nhα : Archimedean α\np : α\nhp : 0 < p\na b c : α\nn : ℤ\nhp' : Fact (0 < p)\nz✝² z✝¹ z✝ : α\nh₁₂₃ : toIcoMod ⋯ z✝² z✝¹ ≤ toIocMod ⋯ z✝² z✝\nh₃₂₁ : toIcoMod ⋯ z✝² z✝ ≤ toIocMod ⋯ z✝² z✝¹\n⊢ z✝² ≡ z✝¹ [PMOD p] ∨ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 965,
"column": 2
} | {
"line": 965,
"column": 13
} | {
"line": 965,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ b - ↑(toIcoDiv hp a b) * p = toIcoMod hp a b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ b - ↑(toIcoDiv hp a b) * p = toIcoMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 969,
"column": 2
} | {
"line": 969,
"column": 13
} | {
"line": 969,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ b - ↑(toIocDiv hp a b) * p = toIocMod hp a b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ b - ↑(toIocDiv hp a b) * p = toIocMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 973,
"column": 2
} | {
"line": 973,
"column": 13
} | {
"line": 973,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ ↑(toIcoDiv hp a b) * p - b = -toIcoMod hp a b",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ ↑(toIcoDiv hp a b) * p - b = -toIcoMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 977,
"column": 2
} | {
"line": 977,
"column": 13
} | {
"line": 977,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ ↑(toIocDiv hp a b) * p - b = -toIocMod hp a b",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ ↑(toIocDiv hp a b) * p - b = -toIocMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 993,
"column": 2
} | {
"line": 993,
"column": 13
} | {
"line": 993,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ toIcoMod hp a b + ↑(toIcoDiv hp a b) * p = b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ toIcoMod hp a b + ↑(toIcoDiv hp a b) * p = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 997,
"column": 2
} | {
"line": 997,
"column": 13
} | {
"line": 997,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ toIocMod hp a b + ↑(toIocDiv hp a b) * p = b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": ... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\n⊢ toIocMod hp a b + ↑(toIocDiv hp a b) * p = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1010,
"column": 2
} | {
"line": 1010,
"column": 13
} | {
"line": 1010,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp a (b + ↑m * p) = toIcoDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp a (b + ↑m * p) = toIcoDiv hp a b + m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1025,
"column": 2
} | {
"line": 1025,
"column": 13
} | {
"line": 1025,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp (a + ↑m * p) b = toIcoDiv hp a b - m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp (a + ↑m * p) b = toIcoDiv hp a b - m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1040,
"column": 2
} | {
"line": 1040,
"column": 13
} | {
"line": 1040,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp a (b + ↑m * p) = toIocDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp a (b + ↑m * p) = toIocDiv hp a b + m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1055,
"column": 2
} | {
"line": 1055,
"column": 13
} | {
"line": 1055,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp (a + ↑m * p) b = toIocDiv hp a b - m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp (a + ↑m * p) b = toIocDiv hp a b - m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1070,
"column": 2
} | {
"line": 1070,
"column": 13
} | {
"line": 1070,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp a (↑m * p + b) = m + toIcoDiv hp a b",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp a (↑m * p + b) = m + toIcoDiv hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1087,
"column": 2
} | {
"line": 1087,
"column": 13
} | {
"line": 1087,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp a (↑m * p + b) = m + toIocDiv hp a b",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp a (↑m * p + b) = m + toIocDiv hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1104,
"column": 2
} | {
"line": 1104,
"column": 13
} | {
"line": 1104,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp a (b - ↑m * p) = toIcoDiv hp a b - m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp a (b - ↑m * p) = toIcoDiv hp a b - m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1119,
"column": 2
} | {
"line": 1119,
"column": 13
} | {
"line": 1119,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp (a - ↑m * p) b = toIcoDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoDiv hp (a - ↑m * p) b = toIcoDiv hp a b + m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1134,
"column": 2
} | {
"line": 1134,
"column": 13
} | {
"line": 1134,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp a (b - ↑m * p) = toIocDiv hp a b - m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp a (b - ↑m * p) = toIocDiv hp a b - m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1149,
"column": 2
} | {
"line": 1149,
"column": 13
} | {
"line": 1149,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp (a - ↑m * p) b = toIocDiv hp a b + m",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocDiv hp (a - ↑m * p) b = toIocDiv hp a b + m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1164,
"column": 2
} | {
"line": 1164,
"column": 13
} | {
"line": 1164,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp a (b + ↑m * p) = toIcoMod hp a b",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ ↑m * p ≡ 0 [PMOD p]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1179,
"column": 2
} | {
"line": 1179,
"column": 13
} | {
"line": 1179,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp (a + ↑m * p) b = toIcoMod hp a b + ↑m * p",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp (a + ↑m * p) b = toIcoMod hp a b + ↑m * p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1194,
"column": 2
} | {
"line": 1194,
"column": 13
} | {
"line": 1194,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp a (b + ↑m * p) = toIocMod hp a b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp a (b + ↑m * p) = toIocMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1209,
"column": 2
} | {
"line": 1209,
"column": 13
} | {
"line": 1209,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp (a + ↑m * p) b = toIocMod hp a b + ↑m * p",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp (a + ↑m * p) b = toIocMod hp a b + ↑m * p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1224,
"column": 2
} | {
"line": 1224,
"column": 13
} | {
"line": 1224,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp a (↑m * p + b) = toIcoMod hp a b",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ ↑m * p ≡ 0 [PMOD p]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1284,
"column": 2
} | {
"line": 1284,
"column": 13
} | {
"line": 1284,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp a (b - ↑m * p) = toIcoMod hp a b",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ b - ↑m * p ≡ b [PMOD p]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1299,
"column": 2
} | {
"line": 1299,
"column": 13
} | {
"line": 1299,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp (a - ↑m * p) b = toIcoMod hp a b - ↑m * p",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIcoMod hp (a - ↑m * p) b = toIcoMod hp a b - ↑m * p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1314,
"column": 2
} | {
"line": 1314,
"column": 13
} | {
"line": 1314,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp a (b - ↑m * p) = toIocMod hp a b",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedG... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp a (b - ↑m * p) = toIocMod hp a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1329,
"column": 2
} | {
"line": 1329,
"column": 13
} | {
"line": 1329,
"column": 14
} | [
{
"pp": "R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp (a - ↑m * p) b = toIocMod hp a b - ↑m * p",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"R : Type u_1\ninst✝³ : NonAssocRing R\ninst✝² : LinearOrder R\ninst✝¹ : IsOrderedAddMonoid R\ninst✝ : Archimedean R\np : R\nhp : 0 < p\na b : R\nm : ℤ\n⊢ toIocMod hp (a - ↑m * p) b = toIocMod hp a b - ↑m * p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 453,
"column": 2
} | {
"line": 453,
"column": 94
} | {
"line": 453,
"column": 95
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set (X × X)\nx : X\nhx : s ∈ 𝓝 (x, x)\n⊢ ∃ U, IsOpen[inst✝] U ∧ x ∈ U ∧ U ×ˢ U ⊆ s",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns : Set (X × X)\nx : X\nhx : s ∈ 𝓝 (x, x)\n⊢ ∃ U, IsOpen[inst✝] U ∧ x ∈ U ∧ U ×ˢ U ⊆ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.NhdsWithin | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 45
} | {
"line": 90,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\nt : Set α\na : α\ns : Set α\n⊢ t ∈ 𝓝[s] a ↔ ∃ u, IsOpen[inst✝] u ∧ a ∈ u ∧ u ∩ s ⊆ t",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : TopologicalSpace α\nt : Set α\na : α\ns : Set α\n⊢ t ∈ 𝓝[s] a ↔ ∃ u, IsOpen[inst✝] u ∧ a ∈ u ∧ u ∩ s ⊆ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 501,
"column": 8
} | {
"line": 501,
"column": 48
} | {
"line": 501,
"column": 49
} | [
{
"pp": "case inr.mp.refine_1\nX : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ns : Set X\nt : Set Y\nh : (s ×ˢ t).Nonempty\nst : s.Nonempty ∧ t.Nonempty\nH : IsOpen[instTopologicalSpaceProd] (s ×ˢ t)\n⊢ IsOpen[inst✝¹] s",
"ppTerm": "?inr.mp.refine_1",
"assigned": false,
... | [
"case inr.mp.refine_1\nX : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ns : Set X\nt : Set Y\nh : (s ×ˢ t).Nonempty\nst : s.Nonempty ∧ t.Nonempty\nH : IsOpen[instTopologicalSpaceProd] (s ×ˢ t)\n⊢ IsOpen[inst✝¹] s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 502,
"column": 8
} | {
"line": 502,
"column": 48
} | {
"line": 502,
"column": 49
} | [
{
"pp": "case inr.mp.refine_2\nX : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ns : Set X\nt : Set Y\nh : (s ×ˢ t).Nonempty\nst : s.Nonempty ∧ t.Nonempty\nH : IsOpen[instTopologicalSpaceProd] (s ×ˢ t)\n⊢ IsOpen[inst✝] t",
"ppTerm": "?inr.mp.refine_2",
"assigned": false,
... | [
"case inr.mp.refine_2\nX : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ns : Set X\nt : Set Y\nh : (s ×ˢ t).Nonempty\nst : s.Nonempty ∧ t.Nonempty\nH : IsOpen[instTopologicalSpaceProd] (s ×ˢ t)\n⊢ IsOpen[inst✝] t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1419,
"column": 2
} | {
"line": 1419,
"column": 63
} | {
"line": 1420,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\na : α\n⊢ ⋃ n, Icc (a + n • p) (a + (n + 1) • p) = univ",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [... | [
"α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\na : α\n⊢ ⋃ n, Icc (a + n • p) (a + (n + 1) • p) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1423,
"column": 2
} | {
"line": 1423,
"column": 29
} | {
"line": 1423,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\n⊢ ⋃ n, Ioc (n • p) ((n + 1) • p) = univ",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\n⊢ ⋃ n, Ioc (n • p) ((n + 1) • p) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 521,
"column": 57
} | {
"line": 521,
"column": 76
} | {
"line": 521,
"column": 77
} | [
{
"pp": "X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ns : Set X\nt : Set Y\nx✝ : X × Y\na : X\nb : Y\n⊢ (𝓝[s ×ˢ t] (a, b)).NeBot ↔ (𝓝[s] a).NeBot ∧ (𝓝[t] b).NeBot",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
... | [
"X : Type u\nY : Type v\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\ns : Set X\nt : Set Y\nx✝ : X × Y\na : X\nb : Y\n⊢ (𝓝[s] a ×ˢ 𝓝[t] b).NeBot ↔ (𝓝[s] a).NeBot ∧ (𝓝[t] b).NeBot"
] | nhdsWithin_prod_eq, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1426,
"column": 2
} | {
"line": 1426,
"column": 29
} | {
"line": 1426,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\n⊢ ⋃ n, Ico (n • p) ((n + 1) • p) = univ",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\n⊢ ⋃ n, Ico (n • p) ((n + 1) • p) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1429,
"column": 2
} | {
"line": 1429,
"column": 29
} | {
"line": 1429,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\n⊢ ⋃ n, Icc (n • p) ((n + 1) • p) = univ",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : AddCommGroup α\ninst✝² : LinearOrder α\ninst✝¹ : IsOrderedAddMonoid α\ninst✝ : Archimedean α\np : α\nhp : 0 < p\n⊢ ⋃ n, Icc (n • p) ((n + 1) • p) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1438,
"column": 2
} | {
"line": 1438,
"column": 71
} | {
"line": 1439,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ ⋃ n, Ioc (a + ↑n) (a + ↑n + 1) = univ",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ ⋃ n, Ioc (a + ↑n) (a + ↑n + 1) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1442,
"column": 2
} | {
"line": 1442,
"column": 71
} | {
"line": 1443,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ ⋃ n, Ico (a + ↑n) (a + ↑n + 1) = univ",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ ⋃ n, Ico (a + ↑n) (a + ↑n + 1) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1446,
"column": 2
} | {
"line": 1446,
"column": 71
} | {
"line": 1447,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ ⋃ n, Icc (a + ↑n) (a + ↑n + 1) = univ",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\na : α\n⊢ ⋃ n, Icc (a + ↑n) (a + ↑n + 1) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1452,
"column": 2
} | {
"line": 1452,
"column": 29
} | {
"line": 1452,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\n⊢ ⋃ n, Ioc (↑n) (↑n + 1) = univ",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\n⊢ ⋃ n, Ioc (↑n) (↑n + 1) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1455,
"column": 2
} | {
"line": 1455,
"column": 29
} | {
"line": 1455,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\n⊢ ⋃ n, Ico (↑n) (↑n + 1) = univ",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\n⊢ ⋃ n, Ico (↑n) (↑n + 1) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.ToIntervalMod | {
"line": 1458,
"column": 2
} | {
"line": 1458,
"column": 29
} | {
"line": 1458,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\n⊢ ⋃ n, Icc (↑n) (↑n + 1) = univ",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝³ : Ring α\ninst✝² : LinearOrder α\ninst✝¹ : IsStrictOrderedRing α\ninst✝ : Archimedean α\n⊢ ⋃ n, Icc (↑n) (↑n + 1) = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 554,
"column": 44
} | {
"line": 554,
"column": 78
} | {
"line": 554,
"column": 79
} | [
{
"pp": "X : Type u\nY : Type v\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X → Y → Z\nx : X\ny : Y\ns : Set X\nt : Set Y\nu : Set Z\nhf : Continuous[instTopologicalSpaceProd, inst✝] (uncurry f)\nhx : x ∈ closure[inst✝²] s\nhy : y ∈ closure[inst✝¹] t\... | [
"X : Type u\nY : Type v\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X → Y → Z\nx : X\ny : Y\ns : Set X\nt : Set Y\nu : Set Z\nhf : Continuous[instTopologicalSpaceProd, inst✝] (uncurry f)\nhx : x ∈ closure[inst✝²] s\nhy : y ∈ closure[inst✝¹] t\nh : ∀ a ∈ s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.NhdsWithin | {
"line": 312,
"column": 2
} | {
"line": 312,
"column": 68
} | {
"line": 312,
"column": 69
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\nx : α\ns t : Set α\nhst : 𝓝[s] x = 𝓝[t] x\nh : x ∈ interior s\n⊢ x ∈ interior t",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"_private.Mathlib.Topology.NhdsWithin.0.Filter.Eventuall... | [
"α : Type u_1\ninst✝ : TopologicalSpace α\nx : α\ns t : Set α\nhst : 𝓝[s] x = 𝓝[t] x\nh : x ∈ interior s\n⊢ 𝓝[t] x = 𝓝 x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.NhdsWithin | {
"line": 338,
"column": 2
} | {
"line": 338,
"column": 26
} | {
"line": 338,
"column": 27
} | [
{
"pp": "ι : Type u_5\nX : ι → Type u_6\ninst✝¹ : (i : ι) → TopologicalSpace (X i)\ninst✝ : Finite ι\ns : (i : ι) → Set (X i)\nx : (i : ι) → X i\n⊢ 𝓝[univ.pi s] x = ⨅ i, comap (fun x ↦ x i) (𝓝[s i] x i)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"iInf",
"... | [
"ι : Type u_5\nX : ι → Type u_6\ninst✝¹ : (i : ι) → TopologicalSpace (X i)\ninst✝ : Finite ι\ns : (i : ι) → Set (X i)\nx : (i : ι) → X i\n⊢ 𝓝 x ⊓ 𝓟 (univ.pi s) = ⨅ i, comap (fun x ↦ x i) (𝓝 (x i)) ⊓ 𝓟 ((fun x ↦ x i) ⁻¹' s i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions.SumProd | {
"line": 843,
"column": 2
} | {
"line": 850,
"column": 62
} | {
"line": 852,
"column": 0
} | [
{
"pp": "X : Type u\nY : Type v\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X ⊕ Y → Z\n⊢ IsClosedMap f ↔ (IsClosedMap fun a ↦ f (inl a)) ∧ IsClosedMap fun b ↦ f (inr b)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.e... | [] | constructor
· intro h
exact ⟨h.comp IsClosedEmbedding.inl.isClosedMap, h.comp IsClosedEmbedding.inr.isClosedMap⟩
· rintro h Z hZ
rw [isClosed_sum_iff] at hZ
convert! (h.1 _ hZ.1).union (h.2 _ hZ.2)
ext
simp only [mem_image, Sum.exists, mem_union, mem_preimage] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Constructions.SumProd | {
"line": 843,
"column": 2
} | {
"line": 850,
"column": 62
} | {
"line": 852,
"column": 0
} | [
{
"pp": "X : Type u\nY : Type v\nZ : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ninst✝ : TopologicalSpace Z\nf : X ⊕ Y → Z\n⊢ IsClosedMap f ↔ (IsClosedMap fun a ↦ f (inl a)) ∧ IsClosedMap fun b ↦ f (inr b)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Set.e... | [] | constructor
· intro h
exact ⟨h.comp IsClosedEmbedding.inl.isClosedMap, h.comp IsClosedEmbedding.inr.isClosedMap⟩
· rintro h Z hZ
rw [isClosed_sum_iff] at hZ
convert! (h.1 _ hZ.1).union (h.2 _ hZ.2)
ext
simp only [mem_image, Sum.exists, mem_union, mem_preimage] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.ContinuousOn | {
"line": 105,
"column": 4
} | {
"line": 106,
"column": 73
} | {
"line": 107,
"column": 2
} | [
{
"pp": "case mp\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\n⊢ (∀ x ∈ s, ContinuousWithinAt f s x) → ∀ (x : ↑s), ContinuousAt (s.restrict f) x",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"ContinuousWithinAt",
"Co... | [] | rintro h ⟨x, xs⟩
exact (continuousWithinAt_iff_continuousAt_restrict f xs).mp (h x xs) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ContinuousOn | {
"line": 105,
"column": 4
} | {
"line": 106,
"column": 73
} | {
"line": 107,
"column": 2
} | [
{
"pp": "case mp\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\n⊢ (∀ x ∈ s, ContinuousWithinAt f s x) → ∀ (x : ↑s), ContinuousAt (s.restrict f) x",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
"ContinuousWithinAt",
"Co... | [] | rintro h ⟨x, xs⟩
exact (continuousWithinAt_iff_continuousAt_restrict f xs).mp (h x xs) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.NhdsWithin | {
"line": 555,
"column": 2
} | {
"line": 555,
"column": 25
} | {
"line": 555,
"column": 26
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\ns t u : Set α\n⊢ u ∈ 𝓝ˢ[t] s ↔ ∃ v, IsOpen[inst✝] v ∧ s ⊆ v ∧ v ∩ t ⊆ u",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : TopologicalSpace α\ns t u : Set α\n⊢ u ∈ 𝓝ˢ[t] s ↔ ∃ v, IsOpen[inst✝] v ∧ s ⊆ v ∧ v ∩ t ⊆ u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 124,
"column": 25
} | {
"line": 124,
"column": 67
} | {
"line": 124,
"column": 68
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nt : Set β\nu : Set α\nou : IsOpen[inst✝¹] u\nuseq : s ∩ u = s ∩ f ⁻¹' t\n⊢ f ⁻¹' t ∩ s = u ∩ s",
"ppTerm": "?m.87",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nt : Set β\nu : Set α\nou : IsOpen[inst✝¹] u\nuseq : s ∩ u = s ∩ f ⁻¹' t\n⊢ s ∩ u = s ∩ f ⁻¹' t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 124,
"column": 25
} | {
"line": 124,
"column": 67
} | {
"line": 124,
"column": 68
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nt : Set β\nu : Set α\nou : IsOpen[inst✝¹] u\nuseq : f ⁻¹' t ∩ s = u ∩ s\n⊢ s ∩ u = s ∩ f ⁻¹' t",
"ppTerm": "?m.114",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nt : Set β\nu : Set α\nou : IsOpen[inst✝¹] u\nuseq : f ⁻¹' t ∩ s = u ∩ s\n⊢ s ∩ u = s ∩ f ⁻¹' t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.NhdsWithin | {
"line": 588,
"column": 2
} | {
"line": 588,
"column": 29
} | {
"line": 588,
"column": 30
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\ns t : Set α\n⊢ 𝓟 (s ∩ t) ≤ 𝓝ˢ[t] s",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"and_true",
"Set.inter_subset_right._simp_1",
"congrArg",
"Filter.instCompleteLattic... | [
"α : Type u_1\ninst✝ : TopologicalSpace α\ns t : Set α\n⊢ 𝓟 (s ∩ t) ≤ 𝓝ˢ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.NhdsWithin | {
"line": 592,
"column": 2
} | {
"line": 592,
"column": 46
} | {
"line": 592,
"column": 47
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns s' : Set α\nt t' : Set β\n⊢ 𝓝ˢ[s' ×ˢ t'] (s ×ˢ t) ≤ 𝓝ˢ[s'] s ×ˢ 𝓝ˢ[t'] t",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Eq.mpr",
"and_true",
"_priva... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\ns s' : Set α\nt t' : Set β\n⊢ 𝓝ˢ (s ×ˢ t) ⊓ 𝓟 (s' ×ˢ t') ≤ 𝓝ˢ s ×ˢ 𝓝ˢ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 161,
"column": 4
} | {
"line": 161,
"column": 82
} | {
"line": 161,
"column": 83
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\na : α\n⊢ ContinuousWithinAt f {a} a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Filter.instMembership",
"nhdsWithin_singleton",
"Eq.mpr",
... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\na : α\n⊢ ∀ s ∈ 𝓝 (f a), f a ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.NhdsWithin | {
"line": 600,
"column": 38
} | {
"line": 600,
"column": 48
} | {
"line": 600,
"column": 48
} | [
{
"pp": "α : Type u_5\nβ : Type u_6\nt : TopologicalSpace β\nf : α → β\ns u : Set α\nthis : TopologicalSpace α := TopologicalSpace.induced f t\nx✝ : ∃ U, (∃ t_1, IsOpen[t] t_1 ∧ f ⁻¹' t_1 = U) ∧ s ⊆ U ∧ U ⊆ u\nv : Set α\nv' : Set β\nhv' : IsOpen[t] v' ∧ f ⁻¹' v' = v\nhv : s ⊆ v ∧ v ⊆ u\n⊢ f '' v ⊆ v'",
"ppT... | [] | simp [hv'] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.NhdsWithin | {
"line": 600,
"column": 38
} | {
"line": 600,
"column": 48
} | {
"line": 600,
"column": 48
} | [
{
"pp": "α : Type u_5\nβ : Type u_6\nt : TopologicalSpace β\nf : α → β\ns u : Set α\nthis : TopologicalSpace α := TopologicalSpace.induced f t\nx✝ : ∃ U, (∃ t_1, IsOpen[t] t_1 ∧ f ⁻¹' t_1 = U) ∧ s ⊆ U ∧ U ⊆ u\nv : Set α\nv' : Set β\nhv' : IsOpen[t] v' ∧ f ⁻¹' v' = v\nhv : s ⊆ v ∧ v ⊆ u\n⊢ f '' v ⊆ v'",
"ppT... | [] | simp [hv'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.NhdsWithin | {
"line": 600,
"column": 38
} | {
"line": 600,
"column": 48
} | {
"line": 600,
"column": 48
} | [
{
"pp": "α : Type u_5\nβ : Type u_6\nt : TopologicalSpace β\nf : α → β\ns u : Set α\nthis : TopologicalSpace α := TopologicalSpace.induced f t\nx✝ : ∃ U, (∃ t_1, IsOpen[t] t_1 ∧ f ⁻¹' t_1 = U) ∧ s ⊆ U ∧ U ⊆ u\nv : Set α\nv' : Set β\nhv' : IsOpen[t] v' ∧ f ⁻¹' v' = v\nhv : s ⊆ v ∧ v ⊆ u\n⊢ f '' v ⊆ v'",
"ppT... | [] | simp [hv'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.SetAccumulate | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 23
} | {
"line": 61,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : α → Set β\ninst✝ : Preorder α\nx : α\n⊢ ⋃ y, ⋃ (_ : y ≤ x), accumulate s y = ⋃ y, ⋃ (_ : y ≤ x), s y",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Set.Subset.antisymm",
"Preorder.toLE",
"LE.le",
"Set.accumulate",
"Se... | [
"case h₁\nα : Type u_1\nβ : Type u_2\ns : α → Set β\ninst✝ : Preorder α\nx : α\n⊢ ⋃ y, ⋃ (_ : y ≤ x), accumulate s y ⊆ ⋃ y, ⋃ (_ : y ≤ x), s y",
"case h₂\nα : Type u_1\nβ : Type u_2\ns : α → Set β\ninst✝ : Preorder α\nx : α\n⊢ ⋃ y, ⋃ (_ : y ≤ x), s y ⊆ ⋃ y, ⋃ (_ : y ≤ x), accumulate s y"
] | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Order.SetAccumulate | {
"line": 66,
"column": 2
} | {
"line": 66,
"column": 23
} | {
"line": 67,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : α → Set β\ninst✝ : Preorder α\n⊢ ⋃ x, accumulate s x = ⋃ x, s x",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Set.Subset.antisymm",
"Preorder.toLE",
"Set.accumulate",
"Set.iUnion"
],
"usedFVars": [
"β",
... | [
"case h₁\nα : Type u_1\nβ : Type u_2\ns : α → Set β\ninst✝ : Preorder α\n⊢ ⋃ x, accumulate s x ⊆ ⋃ x, s x",
"case h₂\nα : Type u_1\nβ : Type u_2\ns : α → Set β\ninst✝ : Preorder α\n⊢ ⋃ x, s x ⊆ ⋃ x, accumulate s x"
] | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Topology.Bornology.Basic | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 57
} | {
"line": 206,
"column": 0
} | [
{
"pp": "α : Type u_2\ns : Set α\nB : Set (Set α)\nempty_mem : ∅ ∈ B\nsubset_mem : ∀ s₁ ∈ B, ∀ s₂ ⊆ s₁, s₂ ∈ B\nunion_mem : ∀ s₁ ∈ B, ∀ s₂ ∈ B, s₁ ∪ s₂ ∈ B\nsUnion_univ : ∀ (x : α), {x} ∈ B\n⊢ IsBounded s ↔ s ∈ B",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Filter.instMembership"... | [] | rw [isBounded_def, ofBounded_cobounded, compl_mem_comk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Bornology.Basic | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 57
} | {
"line": 206,
"column": 0
} | [
{
"pp": "α : Type u_2\ns : Set α\nB : Set (Set α)\nempty_mem : ∅ ∈ B\nsubset_mem : ∀ s₁ ∈ B, ∀ s₂ ⊆ s₁, s₂ ∈ B\nunion_mem : ∀ s₁ ∈ B, ∀ s₂ ∈ B, s₁ ∪ s₂ ∈ B\nsUnion_univ : ∀ (x : α), {x} ∈ B\n⊢ IsBounded s ↔ s ∈ B",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Filter.instMembership"... | [] | rw [isBounded_def, ofBounded_cobounded, compl_mem_comk] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Bornology.Basic | {
"line": 204,
"column": 2
} | {
"line": 204,
"column": 57
} | {
"line": 206,
"column": 0
} | [
{
"pp": "α : Type u_2\ns : Set α\nB : Set (Set α)\nempty_mem : ∅ ∈ B\nsubset_mem : ∀ s₁ ∈ B, ∀ s₂ ⊆ s₁, s₂ ∈ B\nunion_mem : ∀ s₁ ∈ B, ∀ s₂ ∈ B, s₁ ∪ s₂ ∈ B\nsUnion_univ : ∀ (x : α), {x} ∈ B\n⊢ IsBounded s ↔ s ∈ B",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Filter.instMembership"... | [] | rw [isBounded_def, ofBounded_cobounded, compl_mem_comk] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Constructions | {
"line": 663,
"column": 2
} | {
"line": 663,
"column": 13
} | {
"line": 663,
"column": 14
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nt : Set ↑s\nht : IsOpen[instTopologicalSpaceSubtype] t\n⊢ ∃ c, IsOpen[inst✝] c ∧ Subtype.val '' t = c ∩ s",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nt : Set ↑s\nht : IsOpen[instTopologicalSpaceSubtype] t\n⊢ ∃ c, IsOpen[inst✝] c ∧ Subtype.val '' t = c ∩ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 678,
"column": 4
} | {
"line": 678,
"column": 15
} | {
"line": 678,
"column": 16
} | [
{
"pp": "case refine_2\nX : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nhs : ∀ (U : Set X), IsOpen[inst✝] U → U.Nonempty → (U ∩ s).Nonempty\nv : Set X\nhv1 : IsOpen[inst✝] v\nt : Set X\nht : IsOpen[inst✝] t\nht' : t.Nonempty\nhud : ∀ (U : Set ↑s), IsOpen[instTopologicalSpaceSubtype] U → U.Nonempty → (U ∩ Sub... | [
"case refine_2\nX : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nhs : ∀ (U : Set X), IsOpen[inst✝] U → U.Nonempty → (U ∩ s).Nonempty\nv : Set X\nhv1 : IsOpen[inst✝] v\nt : Set X\nht : IsOpen[inst✝] t\nht' : t.Nonempty\nhud : ∀ (U : Set ↑s), IsOpen[instTopologicalSpaceSubtype] U → U.Nonempty → (U ∩ Subtype.val ⁻¹'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 685,
"column": 2
} | {
"line": 685,
"column": 13
} | {
"line": 685,
"column": 14
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nt : Set ↑s\nht : IsClosed[instTopologicalSpaceSubtype] t\n⊢ ∃ c, IsClosed[inst✝] c ∧ Subtype.val '' t = c ∩ s",
"ppTerm": "?m.16",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns : Set X\nt : Set ↑s\nht : IsClosed[instTopologicalSpaceSubtype] t\n⊢ ∃ c, IsClosed[inst✝] c ∧ Subtype.val '' t = c ∩ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 689,
"column": 14
} | {
"line": 689,
"column": 25
} | {
"line": 689,
"column": 26
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nhs : IsOpen[inst✝] s\nh : IsOpen[instTopologicalSpaceSubtype] (s ↓∩ t)\n⊢ IsOpen[inst✝] (s ∩ t)",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nhs : IsOpen[inst✝] s\nh : IsOpen[instTopologicalSpaceSubtype] (s ↓∩ t)\n⊢ IsOpen[inst✝] (s ∩ t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 694,
"column": 14
} | {
"line": 694,
"column": 25
} | {
"line": 694,
"column": 26
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nhs : IsClosed[inst✝] s\nh : IsClosed[instTopologicalSpaceSubtype] (s ↓∩ t)\n⊢ IsClosed[inst✝] (s ∩ t)",
"ppTerm": "?m.17",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"X : Type u\ninst✝ : TopologicalSpace X\ns t : Set X\nhs : IsClosed[inst✝] s\nh : IsClosed[instTopologicalSpaceSubtype] (s ↓∩ t)\n⊢ IsClosed[inst✝] (s ∩ t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 943,
"column": 54
} | {
"line": 943,
"column": 65
} | {
"line": 943,
"column": 66
} | [
{
"pp": "Y : Type v\nn : ℕ\nA : Fin (n + 1) → Type u_9\ninst✝ : (i : Fin (n + 1)) → TopologicalSpace (A i)\nf : Y → A 0\ng : Y → (j : Fin n) → A j.succ\nl : Filter Y\nx : A 0\ny : (j : Fin n) → A j.succ\nhf : Tendsto f l (𝓝 x)\nhg : Tendsto g l (𝓝 y)\nj : Fin (n + 1)\n⊢ ∀ (i : Fin n), Tendsto (fun i_1 ↦ Fin.c... | [
"Y : Type v\nn : ℕ\nA : Fin (n + 1) → Type u_9\ninst✝ : (i : Fin (n + 1)) → TopologicalSpace (A i)\nf : Y → A 0\ng : Y → (j : Fin n) → A j.succ\nl : Filter Y\nx : A 0\ny : (j : Fin n) → A j.succ\nhf : Tendsto f l (𝓝 x)\nhg : Tendsto g l (𝓝 y)\nj : Fin (n + 1)\n⊢ ∀ (i : Fin n), Tendsto (fun i_1 ↦ g i_1 i) l (𝓝 (y... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 979,
"column": 58
} | {
"line": 979,
"column": 69
} | {
"line": 979,
"column": 70
} | [
{
"pp": "Y : Type v\nn : ℕ\nA : Fin (n + 1) → Type u_9\ninst✝ : (i : Fin (n + 1)) → TopologicalSpace (A i)\nf : Y → (j : Fin n) → A j.castSucc\ng : Y → A (Fin.last n)\nl : Filter Y\nx : (j : Fin n) → A j.castSucc\ny : A (Fin.last n)\nhf : Tendsto f l (𝓝 x)\nhg : Tendsto g l (𝓝 y)\nj : Fin (n + 1)\n⊢ ∀ (i : Fi... | [
"Y : Type v\nn : ℕ\nA : Fin (n + 1) → Type u_9\ninst✝ : (i : Fin (n + 1)) → TopologicalSpace (A i)\nf : Y → (j : Fin n) → A j.castSucc\ng : Y → A (Fin.last n)\nl : Filter Y\nx : (j : Fin n) → A j.castSucc\ny : A (Fin.last n)\nhf : Tendsto f l (𝓝 x)\nhg : Tendsto g l (𝓝 y)\nj : Fin (n + 1)\n⊢ ∀ (i : Fin n), Tendst... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Constructions | {
"line": 996,
"column": 65
} | {
"line": 996,
"column": 76
} | {
"line": 996,
"column": 77
} | [
{
"pp": "Y : Type v\nn : ℕ\nA : Fin (n + 1) → Type u_9\ninst✝ : (i : Fin (n + 1)) → TopologicalSpace (A i)\ni : Fin (n + 1)\nf : Y → A i\ng : Y → (j : Fin n) → A (i.succAbove j)\nl : Filter Y\nx : A i\ny : (j : Fin n) → A (i.succAbove j)\nhf : Tendsto f l (𝓝 x)\nhg : Tendsto g l (𝓝 y)\nj : Fin (n + 1)\n⊢ ∀ (j... | [
"Y : Type v\nn : ℕ\nA : Fin (n + 1) → Type u_9\ninst✝ : (i : Fin (n + 1)) → TopologicalSpace (A i)\ni : Fin (n + 1)\nf : Y → A i\ng : Y → (j : Fin n) → A (i.succAbove j)\nl : Filter Y\nx : A i\ny : (j : Fin n) → A (i.succAbove j)\nhf : Tendsto f l (𝓝 x)\nhg : Tendsto g l (𝓝 y)\nj : Fin (n + 1)\n⊢ ∀ (j : Fin n), T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 805,
"column": 4
} | {
"line": 805,
"column": 25
} | {
"line": 805,
"column": 26
} | [
{
"pp": "case a\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ng : β → α\nx : β\ns : Set β\nh : LeftInvOn f g s\nhx : f (g x) = x\nhf : ContinuousWithinAt f (g '' s) (g x)\nhg : ContinuousWithinAt g s x\nA : g ∘ f =ᶠ[𝓝[g '' s] g x] id\n⊢ Tendsto f (𝓝[g '' s] g... | [
"case a\nα : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ng : β → α\nx : β\ns : Set β\nh : LeftInvOn f g s\nhx : f (g x) = x\nhf : ContinuousWithinAt f (g '' s) (g x)\nhg : ContinuousWithinAt g s x\nA : g ∘ f =ᶠ[𝓝[g '' s] g x] id\n⊢ Tendsto f (𝓝[g '' s] g x) (𝓝[s] x... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 810,
"column": 2
} | {
"line": 810,
"column": 48
} | {
"line": 811,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ng : β → α\nx : β\nh : LeftInverse f g\nhf : ContinuousWithinAt f (range g) (g x)\nhg : ContinuousAt g x\n⊢ map g (𝓝 x) = 𝓝[range g] g x",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": ... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ng : β → α\nx : β\nh : LeftInverse f g\nhf : ContinuousWithinAt f (range g) (g x)\nhg : ContinuousAt g x\n⊢ map g (𝓝 x) = 𝓝[range g] g x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Bases | {
"line": 99,
"column": 42
} | {
"line": 99,
"column": 53
} | {
"line": 99,
"column": 54
} | [
{
"pp": "α : Type u\nt✝ : TopologicalSpace α\ns : Set (Set α)\nhsg : t✝ = generateFrom s\nhsi : FiniteInter s\nt : Set α\nht : t ∈ s\n⊢ {t} ∈ {f | f.Finite ∧ f ⊆ s} ∧ (fun f ↦ ⋂₀ f) {t} = t",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"and_true",
"congrArg",
... | [
"α : Type u\nt✝ : TopologicalSpace α\ns : Set (Set α)\nhsg : t✝ = generateFrom s\nhsi : FiniteInter s\nt : Set α\nht : t ∈ s\n⊢ t ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Bases | {
"line": 106,
"column": 52
} | {
"line": 106,
"column": 63
} | {
"line": 106,
"column": 64
} | [
{
"pp": "α : Type u\nt : TopologicalSpace α\nr : Set (Set α)\nhsg : t = generateFrom r\nhsi : ∀ ⦃s : Set α⦄, s ∈ r → ∀ ⦃t : Set α⦄, t ∈ r → s ∩ t ∈ r\n⊢ t = generateFrom (insert univ r)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.univ",
... | [
"α : Type u\nt : TopologicalSpace α\nr : Set (Set α)\nhsg : t = generateFrom r\nhsi : ∀ ⦃s : Set α⦄, s ∈ r → ∀ ⦃t : Set α⦄, t ∈ r → s ∩ t ∈ r\n⊢ t = generateFrom r"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Bases | {
"line": 123,
"column": 42
} | {
"line": 123,
"column": 65
} | {
"line": 123,
"column": 66
} | [
{
"pp": "α : Type u\nt : TopologicalSpace α\ns : Set (Set α)\nh_open : ∀ u ∈ s, IsOpen[t] u\nh_nhds : ∀ (a : α) (u : Set α), a ∈ u → IsOpen[t] u → ∃ v ∈ s, a ∈ v ∧ v ⊆ u\na : α\n⊢ ∀ (i : Set α), a ∈ i ∧ IsOpen[t] i → ∃ i', (i' ∈ s ∧ a ∈ i') ∧ id i' ⊆ i",
"ppTerm": "?m.38",
"assigned": true,
"usedCon... | [
"α : Type u\nt : TopologicalSpace α\ns : Set (Set α)\nh_open : ∀ u ∈ s, IsOpen[t] u\nh_nhds : ∀ (a : α) (u : Set α), a ∈ u → IsOpen[t] u → ∃ v ∈ s, a ∈ v ∧ v ⊆ u\na : α\n⊢ ∀ (i : Set α), a ∈ i → IsOpen[t] i → ∃ i' ∈ s, a ∈ i' ∧ i' ⊆ i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 964,
"column": 2
} | {
"line": 964,
"column": 17
} | {
"line": 964,
"column": 18
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nhf : ContinuousOn f s\nt u : Set β\nh : u ∈ 𝓝ˢ t\n⊢ f ⁻¹' u ∈ 𝓝ˢ[s] (s ∩ f ⁻¹' t)",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": [... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\ns : Set α\nhf : ContinuousOn f s\nt u : Set β\nh : u ∈ 𝓝ˢ t\n⊢ f ⁻¹' u ∈ 𝓝ˢ[s] (s ∩ f ⁻¹' t)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ContinuousOn | {
"line": 968,
"column": 2
} | {
"line": 968,
"column": 13
} | {
"line": 968,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\nhf : Continuous[inst✝¹, inst✝] f\ns u s' : Set β\nh : u ∈ 𝓝ˢ[s'] s\n⊢ f ⁻¹' u ∈ 𝓝ˢ[f ⁻¹' s'] (f ⁻¹' s)",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : TopologicalSpace α\ninst✝ : TopologicalSpace β\nf : α → β\nhf : Continuous[inst✝¹, inst✝] f\ns u s' : Set β\nh : u ∈ 𝓝ˢ[s'] s\n⊢ f ⁻¹' u ∈ 𝓝ˢ[f ⁻¹' s'] (f ⁻¹' s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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