module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 160,
"column": 6
} | {
"line": 160,
"column": 17
} | {
"line": 160,
"column": 18
} | [
{
"pp": "case inr.refine_2.inr\nα : Type v\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nf : α → α\nhα : cof α ≠ ℵ₀\nhf : IsNormal f\nh✝¹ : Nonempty α\na : α\nh✝ : NoMaxOrder α\nh : IsCofinal (range fun n ↦ f^[n] a)\n⊢ #↑(range fun n ↦ f^[n] a) ≤ ℵ₀",
"ppTerm": "?inr.refine_2.inr",
"assigned": true,... | [
"case inr.refine_2.inr\nα : Type v\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nf : α → α\nhα : cof α ≠ ℵ₀\nhf : IsNormal f\nh✝¹ : Nonempty α\na : α\nh✝ : NoMaxOrder α\nh : IsCofinal (range fun n ↦ f^[n] a)\n⊢ {x | ∃ y, f^[y] a = x}.Countable"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 126,
"column": 64
} | {
"line": 126,
"column": 75
} | {
"line": 126,
"column": 76
} | [
{
"pp": "A : Type u_1\nT : ↥(tree A)\nx y : List A\nh : y <+: x ∧ [] ∈ subAt T x\nh' : y.length ≤ x.length\n⊢ x ∈ T",
"ppTerm": "?m.53",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\nT : ↥(tree A)\nx y : List A\nh : y <+: x ∧ [] ∈ subAt T x\nh' : y.length ≤ x.length\n⊢ x ∈ T"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 13
} | {
"line": 189,
"column": 14
} | [
{
"pp": "α : Type v\ns : Set α\ninst✝ : LinearOrder α\nhs : IsStationary s\n⊢ s.Nonempty",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ns : Set α\ninst✝ : LinearOrder α\nhs : IsStationary s\n⊢ s.Nonempty"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 202,
"column": 2
} | {
"line": 202,
"column": 13
} | {
"line": 202,
"column": 14
} | [
{
"pp": "α : Type v\ninst✝ : LinearOrder α\nh : IsStationary ∅\n⊢ False",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ninst✝ : LinearOrder α\nh : IsStationary ∅\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 148,
"column": 31
} | {
"line": 148,
"column": 59
} | {
"line": 148,
"column": 60
} | [
{
"pp": "A : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : x.length ≤ z.length\nhp : ¬x <+: z\nh : List.take (x ++ y).length z <+: x ++ y\nright✝ : List.drop (x ++ y).length z ∈ T\n⊢ ?m.103",
"ppTerm": "?m.104",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : x.length ≤ z.length\nhp : ¬x <+: z\nh : List.take (x ++ y).length z <+: x ++ y\nright✝ : List.drop (x ++ y).length z ∈ T\n⊢ ?m.103"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Descriptive.Tree | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 15
} | {
"line": 151,
"column": 16
} | [
{
"pp": "case inr\nA : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : z.length ≤ x.length\n⊢ z <+: x ∧ [] <+: y ∧ [] ∈ T ↔ z <+: x ++ y ∧ [] ∈ T",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Membership.mem",
"id",
"Subtype",
"List.... | [
"case inr\nA : Type u_1\nT : ↥(tree A)\nx y z : List A\nhl : z.length ≤ x.length\n⊢ [] ∈ T → (z <+: x ↔ z <+: x ++ y)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Cardinal.Cofinality.Club | {
"line": 282,
"column": 2
} | {
"line": 282,
"column": 13
} | {
"line": 282,
"column": 14
} | [
{
"pp": "α : Type v\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nhα : cof α ≠ ℵ₀\n⊢ IsStationary (s ∪ t) ↔ IsStationary s ∨ IsStationary t",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type v\ns t : Set α\ninst✝¹ : LinearOrder α\ninst✝ : WellFoundedLT α\nhα : cof α ≠ ℵ₀\n⊢ IsStationary (s ∪ t) ↔ IsStationary s ∨ IsStationary t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Commute | {
"line": 36,
"column": 39
} | {
"line": 36,
"column": 67
} | {
"line": 36,
"column": 68
} | [
{
"pp": "o₁ o₂ : Ordinal.{u_1}\nhcomm : AddCommute o₁ o₂\nih : ∀ y < o₁ + o₂, ∀ {o₁ o₂ : Ordinal.{u_1}}, AddCommute o₁ o₂ → o₁ + o₂ = y → ∃ o n₁ n₂, o * ↑n₁ = o₁ ∧ o * ↑n₂ = o₂\nhle : o₁ ≤ o₂\nh₁ : o₁ ≠ 0\no₃ : Ordinal.{u_1} := o₂ - o₁\nhsub : o₁ + o₃ = o₂\nhcomm' : AddCommute o₁ o₃\n⊢ o₁ + o₃ < o₁ + o₂",
"... | [
"o₁ o₂ : Ordinal.{u_1}\nhcomm : AddCommute o₁ o₂\nih : ∀ y < o₁ + o₂, ∀ {o₁ o₂ : Ordinal.{u_1}}, AddCommute o₁ o₂ → o₁ + o₂ = y → ∃ o n₁ n₂, o * ↑n₁ = o₁ ∧ o * ↑n₂ = o₂\nhle : o₁ ≤ o₂\nh₁ : o₁ ≠ 0\no₃ : Ordinal.{u_1} := o₂ - o₁\nhsub : o₁ + o₃ = o₂\nhcomm' : AddCommute o₁ o₃\n⊢ 0 < o₁"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 57,
"column": 4
} | {
"line": 57,
"column": 56
} | {
"line": 57,
"column": 57
} | [
{
"pp": "α : Type u\ng : Ordinal.{u} → α\nh_inj : InjOn g (Iio (succ #α).ord)\nh : lift.{u, u + 1} #↑(Iio (succ #α).ord) ≤ lift.{u + 1, u} #α\n⊢ #↑(Iio (succ #α).ord) = lift.{u + 1, u} (succ #α)",
"ppTerm": "?m.32",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"α : Type u\ng : Ordinal.{u} → α\nh_inj : InjOn g (Iio (succ #α).ord)\nh : lift.{u, u + 1} #↑(Iio (succ #α).ord) ≤ lift.{u + 1, u} #α\n⊢ #↑(Iio (succ #α).ord) = lift.{u + 1, u} (succ #α)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 105,
"column": 2
} | {
"line": 105,
"column": 13
} | {
"line": 105,
"column": 14
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\na : Ordinal.{u}\n⊢ ⨆ b, ⨆ (_ : b < a + 1), f (lfpApprox f x b) ≤ f (lfpApprox f x a)",
"ppTerm": "?m.62",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\na : Ordinal.{u}\n⊢ ∀ i ≤ a, f (lfpApprox f x i) ≤ f (lfpApprox f x a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 15
} | {
"line": 114,
"column": 16
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\na : Ordinal.{u}\nha : IsSuccLimit a\nb : Ordinal.{u}\nhab : b < a\n⊢ f (lfpApprox f x b) ≤ lfpApprox f x ↑⟨b + 1, ⋯⟩",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"ChainCompletePartialOrder.instOfCompleteLattice",
... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\na : Ordinal.{u}\nha : IsSuccLimit a\nb : Ordinal.{u}\nhab : b < a\n⊢ f (lfpApprox f x b) ≤ lfpApprox f x (b + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Lists | {
"line": 109,
"column": 24
} | {
"line": 109,
"column": 42
} | {
"line": 109,
"column": 43
} | [
{
"pp": "case cons'\nα : Type u_1\nb✝¹ b✝ : Bool\nb : Lists' α b✝\na : Lists' α true\na_ih✝ :\n ∀ (h : true = b✝),\n let l' := ⋯ ▸ b;\n ofList l'.toList = l'\nIH :\n ∀ (h : true = true),\n let l' := ⋯ ▸ a;\n ofList l'.toList = l'\nh : true = true\n⊢ let l' := ⋯ ▸ b.cons' a;\n ofList l'.toList = l... | [
"case cons'\nα : Type u_1\nb✝¹ b✝ : Bool\nb : Lists' α b✝\na : Lists' α true\na_ih✝ :\n ∀ (h : true = b✝),\n let l' := ⋯ ▸ b;\n ofList l'.toList = l'\nIH :\n ∀ (h : true = true),\n let l' := ⋯ ▸ a;\n ofList l'.toList = l'\nh : true = true\n⊢ ofList a.toList = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 149,
"column": 4
} | {
"line": 149,
"column": 32
} | {
"line": 150,
"column": 6
} | [
{
"pp": "case refine_2\nα : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\nh : f x = x\no : Ordinal.{u}\nthis : lfpApprox f x 0 ∈ fixedPoints ⇑f\n⊢ lfpApprox f x o = x",
"ppTerm": "?refine_2",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case refine_2\nα : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\nh : f x = x\no : Ordinal.{u}\nthis : lfpApprox f x 0 ∈ fixedPoints ⇑f\n⊢ lfpApprox f x o = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 173,
"column": 36
} | {
"line": 173,
"column": 64
} | {
"line": 173,
"column": 65
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\no : Ordinal.{u}\nh : lfpApprox f x o = x\nho : o ≠ 0\nhpos : 0 < o\nhmem : lfpApprox f x 0 ∈ fixedPoints ⇑f\n⊢ x ∈ fixedPoints ⇑f",
"ppTerm": "?m.115",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ChainCo... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\nx : α\nhx : x ≤ f x\no : Ordinal.{u}\nh : lfpApprox f x o = x\nho : o ≠ 0\nhpos : 0 < o\nhmem : lfpApprox f x 0 ∈ fixedPoints ⇑f\n⊢ IsFixedPt (⇑f) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 154,
"column": 8
} | {
"line": 155,
"column": 36
} | {
"line": 156,
"column": 6
} | [
{
"pp": "case refine_2.inr.inl\nb o✝ o : Ordinal.{u_1}\nho : o ≠ 0\nIH : List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b (o % b ^ log b o)))\nhb : 1 < b\nhob : o < b\n⊢ List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b o))",
"ppTerm": "?refine_2.inr.inl",
"assigned": true,
"usedConst... | [] | rw [CNF.of_lt ho hob]
exact pairwise_singleton _ _ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 154,
"column": 8
} | {
"line": 155,
"column": 36
} | {
"line": 156,
"column": 6
} | [
{
"pp": "case refine_2.inr.inl\nb o✝ o : Ordinal.{u_1}\nho : o ≠ 0\nIH : List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b (o % b ^ log b o)))\nhb : 1 < b\nhob : o < b\n⊢ List.Pairwise (fun x1 x2 ↦ x1 > x2) (map Prod.fst (CNF b o))",
"ppTerm": "?refine_2.inr.inl",
"assigned": true,
"usedConst... | [] | rw [CNF.of_lt ho hob]
exact pairwise_singleton _ _ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Lists | {
"line": 311,
"column": 4
} | {
"line": 311,
"column": 15
} | {
"line": 311,
"column": 16
} | [
{
"pp": "case D1\nα : Type u_1\ntrans : Lists α → Prop := fun l₁ ↦ ∀ ⦃l₂ l₃ : Lists α⦄, l₁ ~ l₂ → l₂ ~ l₃ → l₁ ~ l₃\na : Lists α\nl : Lists' α true\nIH₁ : trans a\nIH₂ : ∀ (l' : Lists α), l' ∈ l.toList → trans l'\n⊢ ∀ (l' : Lists α), l' ∈ (Lists'.cons a l).toList → trans l'",
"ppTerm": "?D1",
"assigned"... | [
"case D1\nα : Type u_1\ntrans : Lists α → Prop := fun l₁ ↦ ∀ ⦃l₂ l₃ : Lists α⦄, l₁ ~ l₂ → l₂ ~ l₃ → l₁ ~ l₃\na : Lists α\nl : Lists' α true\nIH₁ : trans a\nIH₂ : ∀ (l' : Lists α), l' ∈ l.toList → trans l'\n⊢ trans a ∧ ∀ (a : Lists α), a ∈ l.toList → trans a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 15
} | {
"line": 186,
"column": 16
} | [
{
"pp": "b o : Ordinal.{u_1}\na : Ordinal.{u_1} × Ordinal.{u_1}\nha : a ∈ CNF b o\n⊢ decide (a.toSigma.snd ≠ 0) = true",
"ppTerm": "?m.54",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableNot",
"Ordinal.instLinearOrder",
"Bool.not",
"Prod.toSigma",
"L... | [
"b o : Ordinal.{u_1}\na : Ordinal.{u_1} × Ordinal.{u_1}\nha : a ∈ CNF b o\n⊢ ¬a.2 = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.FixedPointApproximants | {
"line": 219,
"column": 6
} | {
"line": 219,
"column": 87
} | {
"line": 220,
"column": 8
} | [
{
"pp": "α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\n⊢ ∃ y, lfpApprox f ⊥ (succ #α).ord = ↑y",
"ppTerm": "?m.83",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Order.succ",
"ChainCompletePartialOrder.instOfCompleteLattice",
"Cardinal... | [
"α : Type u\ninst✝ : CompleteLattice α\nf : α →o α\n⊢ IsFixedPt (⇑f) (lfpApprox f ⊥ (succ #α).ord)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 229,
"column": 6
} | {
"line": 229,
"column": 17
} | {
"line": 229,
"column": 18
} | [
{
"pp": "case inr.inr\nb : Ordinal.{u_1}\nhb : b ≤ 1\no a : Ordinal.{u_1}\nho : o ≠ 0\nha : a ≠ 0\n⊢ a ∉ map Prod.fst [(0, o)]",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"List.map_cons",
"congrArg",
"List.map",
"Membership.mem"... | [
"case inr.inr\nb : Ordinal.{u_1}\nhb : b ≤ 1\no a : Ordinal.{u_1}\nho : o ≠ 0\nha : a ≠ 0\n⊢ ¬a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 243,
"column": 2
} | {
"line": 243,
"column": 16
} | {
"line": 244,
"column": 2
} | [
{
"pp": "b e x y : Ordinal.{u_1}\nhb : 1 < b\nhx : x ≠ 0\nhxb : x < b\nhy : y < b ^ e\ne' : Ordinal.{u_1}\n⊢ (coeff b (b ^ e * x + y)) e' = (single e x + coeff b y) e'",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"HMul.hMul",
"Mul... | [
"b e x y : Ordinal.{u_1}\nhb : 1 < b\nhx : x ≠ 0\nhxb : x < b\nhy : y < b ^ e\ne' : Ordinal.{u_1}\n⊢ (coeff b (b ^ e * x + y)) e' = (single e x) e' + (coeff b y) e'"
] | rw [add_apply] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Order.SuccPred | {
"line": 44,
"column": 65
} | {
"line": 44,
"column": 76
} | {
"line": 44,
"column": 77
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ l, l < a",
"ppTerm": "?m.34",
"assigned": false,
"usedConstants": [],
"usedF... | [
"α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ l, l < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.SuccPred | {
"line": 45,
"column": 10
} | {
"line": 45,
"column": 42
} | {
"line": 45,
"column": 43
} | [
{
"pp": "α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ u, a < u",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedF... | [
"α : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : TopologicalSpace α\ninst✝² : OrderTopology α\na : α\ninst✝¹ : SuccOrder α\ninst✝ : NoMaxOrder α\na✝ : Nontrivial α\nh : IsOpen[inst✝³] {a}\nha : IsSuccLimit a\n⊢ ∃ u, a < u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 291,
"column": 2
} | {
"line": 291,
"column": 13
} | {
"line": 291,
"column": 14
} | [
{
"pp": "b e x : Ordinal.{u_1}\n⊢ eval b (single e x) = b ^ e * x",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"b e x : Ordinal.{u_1}\n⊢ eval b (single e x) = b ^ e * x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.CantorNormalForm | {
"line": 304,
"column": 6
} | {
"line": 304,
"column": 27
} | {
"line": 304,
"column": 28
} | [
{
"pp": "b x e' y : Ordinal.{u_1}\nf : Ordinal.{u_1} →₀ Ordinal.{u_1}\nhf : ∀ c ∈ f.support, c < e'\nhy : y ≠ 0\na : Ordinal.{u_1}\nha : a ∈ (single e' y + f).support\nh : ∀ e'_1 ∈ (single e' y + f).support, e'_1 ≤ a\na✝ : single e' y + f = f → eval b (single a x + (single e' y + f)) = b ^ a * x + eval b (singl... | [
"b x e' y : Ordinal.{u_1}\nf : Ordinal.{u_1} →₀ Ordinal.{u_1}\nhf : ∀ c ∈ f.support, c < e'\nhy : y ≠ 0\na : Ordinal.{u_1}\nha : a ∈ (single e' y + f).support\nh : ∀ e'_1 ∈ (single e' y + f).support, e'_1 ≤ a\na✝ : single e' y + f = f → eval b (single a x + (single e' y + f)) = b ^ a * x + eval b (single e' y + f)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 231,
"column": 2
} | {
"line": 231,
"column": 32
} | {
"line": 231,
"column": 33
} | [
{
"pp": "e : ONote\nn : ℕ+\na : ONote\nh : (e.oadd n a).NF\ne0 : e = 0\n⊢ a = 0",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"e : ONote\nn : ℕ+\na : ONote\nh : (e.oadd n a).NF\ne0 : e = 0\n⊢ a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 40,
"column": 2
} | {
"line": 40,
"column": 35
} | {
"line": 40,
"column": 36
} | [
{
"pp": "x y : ZFSet.{u}\nh : x ⊆ y\n⊢ x.card ≤ y.card",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x y : ZFSet.{u}\nh : x ⊆ y\n⊢ x.card ≤ y.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 32
} | {
"line": 57,
"column": 33
} | [
{
"pp": "x : ZFSet.{u}\n⊢ {x}.card = 1",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : ZFSet.{u}\n⊢ {x}.card = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 37
} | {
"line": 70,
"column": 38
} | [
{
"pp": "x : ZFSet.{u}\n⊢ lift.{u + 1, u} x.powerset.card = lift.{u + 1, u} (2 ^ x.card)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"ZFSet",
"PartialOrder.toPreorder",
"Nat.instAtLe... | [
"x : ZFSet.{u}\n⊢ #{ x_1 // x_1 ⊆ x } = 2 ^ #↥x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 74,
"column": 2
} | {
"line": 74,
"column": 60
} | {
"line": 74,
"column": 61
} | [
{
"pp": "x : ZFSet.{u}\nf : ZFSet.{u} → ZFSet.{u}\ninst✝ : Definable₁ f\n⊢ (image f x).card ≤ x.card",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : ZFSet.{u}\nf : ZFSet.{u} → ZFSet.{u}\ninst✝ : Definable₁ f\n⊢ (image f x).card ≤ x.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 79,
"column": 2
} | {
"line": 79,
"column": 60
} | {
"line": 79,
"column": 61
} | [
{
"pp": "α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{max u (v + 1), max u v} (lift.{u, v} (range f).card) ≤ lift.{v + 1, u} #α",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.lift_lift",
"congrArg",
"Cardinal.... | [
"α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{max u (v + 1), v} (range f).card ≤ lift.{v + 1, u} #α"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 83,
"column": 2
} | {
"line": 83,
"column": 93
} | {
"line": 84,
"column": 4
} | [
{
"pp": "α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ ⨆ i, (f i).card ≤ (⋃ (i : α), f i).card",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ ⨆ i, (f i).card ≤ (⋃ (i : α), f i).card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Cardinal | {
"line": 89,
"column": 2
} | {
"line": 89,
"column": 62
} | {
"line": 90,
"column": 4
} | [
{
"pp": "α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{v + 1, max u v} (lift.{u, v} (⋃ (i : α), f i).card) ≤ lift.{v + 1, max u v} (sum fun i ↦ (f i).card)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Cardinal",
"Cardinal.lift_lift",
"... | [
"α : Type u\ninst✝ : Small.{v, u} α\nf : α → ZFSet.{v}\n⊢ lift.{max u (v + 1), v} (⋃ (i : α), f i).card ≤ sum fun i ↦ lift.{v + 1, v} (f i).card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 131,
"column": 2
} | {
"line": 131,
"column": 13
} | {
"line": 131,
"column": 14
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f 1 = deriv f",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f 1 = deriv f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 203,
"column": 18
} | {
"line": 203,
"column": 29
} | {
"line": 203,
"column": 30
} | [
{
"pp": "case h\nf : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\nhp : 0 < f 0\no : Ordinal.{u}\nho : IsSuccLimit o\na : Ordinal.{u}\nIH : ∀ b < o, veblenWith f b 0 ≤ a\n⊢ 0 < o ∧ List.foldr (fun x ↦ veblenWith f ↑x) 0 [] ≤ veblenWith f 0 0",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
... | [
"case h\nf : Ordinal.{u} → Ordinal.{u}\nhf : IsNormal f\nhp : 0 < f 0\no : Ordinal.{u}\nho : IsSuccLimit o\na : Ordinal.{u}\nIH : ∀ b < o, veblenWith f b 0 ≤ a\n⊢ 0 < o"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 218,
"column": 87
} | {
"line": 220,
"column": 49
} | {
"line": 222,
"column": 0
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\no₁ o₂ a : Ordinal.{u}\nhf : IsNormal f\nh : o₂ ≤ o₁\n⊢ veblenWith f o₂ a < veblenWith f o₁ (veblenWith f o₂ a) ↔ a < veblenWith f o₁ a",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder"... | [] | by
simp_rw [(right_le_veblenWith hf ..).lt_iff_ne', ne_eq,
veblenWith_veblenWith_eq_veblenWith_iff hf h] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 223,
"column": 2
} | {
"line": 223,
"column": 13
} | {
"line": 223,
"column": 14
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f o (f a) = f a ↔ veblenWith f o a = a",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ veblenWith f o (f a) = f a ↔ veblenWith f o a = a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 558,
"column": 75
} | {
"line": 558,
"column": 86
} | {
"line": 558,
"column": 87
} | [
{
"pp": "x y : ZFSet.{u}\nhxy : x ⊆ y\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ x ∩ y ↔ z✝ ∈ x",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ZFSet",
"Membership.mem",
"ZFSet.mem_inter._simp_1",
"id",
"Inter.inter",
"And",
"Iff",
... | [
"x y : ZFSet.{u}\nhxy : x ⊆ y\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ x → z✝ ∈ y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 13
} | {
"line": 226,
"column": 14
} | [
{
"pp": "f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ f a < veblenWith f o (f a) ↔ a < veblenWith f o a",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : Ordinal.{u} → Ordinal.{u}\no a : Ordinal.{u}\nhf : IsNormal f\n⊢ f a < veblenWith f o (f a) ↔ a < veblenWith f o a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 559,
"column": 76
} | {
"line": 559,
"column": 87
} | {
"line": 559,
"column": 88
} | [
{
"pp": "x y : ZFSet.{u}\nhyx : y ⊆ x\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ x ∩ y ↔ z✝ ∈ y",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"ZFSet",
"Membership.mem",
"ZFSet.mem_inter._simp_1",
"id",
"Inter.inter",
"And",
"Iff",
... | [
"x y : ZFSet.{u}\nhyx : y ⊆ x\nz✝ : ZFSet.{u}\n⊢ z✝ ∈ y → z✝ ∈ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 651,
"column": 6
} | {
"line": 651,
"column": 22
} | {
"line": 651,
"column": 23
} | [
{
"pp": "case h\nα : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\nx : ZFSet.{u}\ny : PSet.{u}\nz : α\nhz : f z = ⟦y⟧\n⊢ y.Equiv ((PSet.mk (Shrink.{u, u_1} α) (Quotient.out ∘ f ∘ ⇑(equivShrink α).symm)).Func ((equivShrink α) z))",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"... | [
"case h\nα : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\nx : ZFSet.{u}\ny : PSet.{u}\nz : α\nhz : f z = ⟦y⟧\n⊢ y.Equiv (Quotient.out (mk y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 444,
"column": 8
} | {
"line": 444,
"column": 19
} | {
"line": 444,
"column": 20
} | [
{
"pp": "case oadd.lt.h₂\ne : ONote\nn : ℕ+\na o : ONote\nh₁ : (e.oadd n a).NF\nh₂ : o.NF\nthis✝¹ : a.NF\nh' : (a.add o).repr = a.repr + o.repr\ne' : ONote\nn' : ℕ+\na' : ONote\nh : a.add o = e'.oadd n' a'\nnf : (e'.oadd n' a').NF\nthis✝ : e.NF\nthis : e'.NF\nhe : e.cmp e' = Ordering.lt\nee : e < e'\n⊢ ω ^ e'.r... | [
"case oadd.lt.h₂\ne : ONote\nn : ℕ+\na o : ONote\nh₁ : (e.oadd n a).NF\nh₂ : o.NF\nthis✝¹ : a.NF\nh' : (a.add o).repr = a.repr + o.repr\ne' : ONote\nn' : ℕ+\na' : ONote\nh : a.add o = e'.oadd n' a'\nnf : (e'.oadd n' a').NF\nthis✝ : e.NF\nthis : e'.NF\nhe : e.cmp e' = Ordering.lt\nee : e < e'\n⊢ ω ^ e'.repr ≤ ω ^ e'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 675,
"column": 2
} | {
"line": 675,
"column": 13
} | {
"line": 675,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\ni : α\nx : ZFSet.{u}\nhx : x ∈ f i\n⊢ x ∈ ⋃ (i : α), f i",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ZFSet",
"Membership.mem",
"Exists",
"id",
"ZFSet.mem_iUnion._simp_1",
... | [
"α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\ni : α\nx : ZFSet.{u}\nhx : x ∈ f i\n⊢ ∃ i, x ∈ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 699,
"column": 40
} | {
"line": 699,
"column": 65
} | {
"line": 699,
"column": 66
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 699,
"column": 40
} | {
"line": 699,
"column": 88
} | {
"line": 700,
"column": 2
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"ZFSet",
"Eq.mp",
"Insert.insert",
"_private.Mathlib.SetTheory.ZFC.Basic.0.Z... | [] | simpa [or_and_left] using (H {x}).1 (Or.inl rfl) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.SetTheory.ZFC.Basic | {
"line": 699,
"column": 40
} | {
"line": 699,
"column": 88
} | {
"line": 700,
"column": 2
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"ZFSet",
"Eq.mp",
"Insert.insert",
"_private.Mathlib.SetTheory.ZFC.Basic.0.Z... | [] | simpa [or_and_left] using (H {x}).1 (Or.inl rfl) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.ZFC.Basic | {
"line": 699,
"column": 40
} | {
"line": 699,
"column": 88
} | {
"line": 700,
"column": 2
} | [
{
"pp": "x x' y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x'} ∨ z = {x', y'}\n⊢ x = x' ∧ ?m.27",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"congrArg",
"ZFSet",
"Eq.mp",
"Insert.insert",
"_private.Mathlib.SetTheory.ZFC.Basic.0.Z... | [] | simpa [or_and_left] using (H {x}).1 (Or.inl rfl) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.ZFC.Basic | {
"line": 702,
"column": 4
} | {
"line": 702,
"column": 25
} | {
"line": 702,
"column": 26
} | [
{
"pp": "y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {y} ∨ z = {y, y} ↔ z = {y} ∨ z = {y, y'}\n⊢ y = y'",
"ppTerm": "?m.71",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {y} ∨ z = {y, y} ↔ z = {y} ∨ z = {y, y'}\n⊢ y = y'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 433,
"column": 2
} | {
"line": 433,
"column": 13
} | {
"line": 433,
"column": 14
} | [
{
"pp": "o x : Ordinal.{u}\nh : o < x.invVeblen₁\n⊢ veblen o x = x",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o x : Ordinal.{u}\nh : o < x.invVeblen₁\n⊢ veblen o x = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Basic | {
"line": 706,
"column": 2
} | {
"line": 706,
"column": 13
} | {
"line": 706,
"column": 14
} | [
{
"pp": "x y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x} ∨ z = {x, y'}\nhe : y = x → y = y'\nhx : y = x ∨ {x, y} = {x, y'}\nhy : {x, y} = {x, y'}\n⊢ y = x ∨ y = y'",
"ppTerm": "?m.128",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}... | [
"x y y' : ZFSet.{u_1}\nH : ∀ (z : ZFSet.{u_1}), z = {x} ∨ z = {x, y} ↔ z = {x} ∨ z = {x, y'}\nhe : y = x → y = y'\nhx : y = x ∨ {x, y} = {x, y'}\nhy : {x, y} = {x, y'}\n⊢ y = x ∨ y = y'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 109,
"column": 72
} | {
"line": 117,
"column": 10
} | {
"line": 119,
"column": 0
} | [
{
"pp": "x : PSet.{u_1}\n⊢ x.rank ≤ succ (⋃₀ x).rank",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Order.succ",
"PSet.instMembership",
"Ordinal.partialOrder",
"PSet.rank_mono",
"congrArg",
"PSet.powerset",
"PartialOrder.toPreorder... | [] | by
rw [← rank_powerset]
apply rank_mono
rw [subset_iff]
intro z _
rw [mem_powerset, subset_iff]
intro _ _
rw [mem_sUnion]
exists z | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 457,
"column": 6
} | {
"line": 457,
"column": 21
} | {
"line": 458,
"column": 6
} | [
{
"pp": "case eq\ne₁ : ONote\nn₁ : ℕ+\na₁ e₂ : ONote\nn₂ : ℕ+\na₂ : ONote\nb : Ordinal.{0}\nh₁ : (e₁.oadd n₁ a₁).NFBelow b\nh₂ : (e₂.oadd n₂ a₂).NF\nh' : (a₁.sub a₂).NFBelow e₁.repr\nthis : (e₁.cmp e₂).Compares e₁ e₂\nh : e₁.cmp e₂ = Ordering.eq\n⊢ (match Ordering.eq with\n | Ordering.lt => 0\n | Orde... | [
"case eq\ne₁ : ONote\nn₁ : ℕ+\na₁ e₂ : ONote\nn₂ : ℕ+\na₂ : ONote\nb : Ordinal.{0}\nh₁ : (e₁.oadd n₁ a₁).NFBelow b\nh₂ : (e₂.oadd n₂ a₂).NF\nh' : (a₁.sub a₂).NFBelow e₁.repr\nthis : (e₁.cmp e₂).Compares e₁ e₂\nh : e₁.cmp e₂ = Ordering.eq\n⊢ (match Ordering.eq with\n | Ordering.lt => 0\n | Ordering.gt => e... | rw [Nat.sub_eq] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.SetTheory.ZFC.Rank | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 37
} | {
"line": 127,
"column": 38
} | [
{
"pp": "x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ lift.{u + 1, u} o < ⨆ i, succ (lift.{u + 1, u} (↑i).rank)",
"ppTerm": "?m.66",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLinea... | [
"x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ ∃ a ∈ x, o ≤ a.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 549,
"column": 2
} | {
"line": 549,
"column": 23
} | {
"line": 549,
"column": 24
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ ε_ o = deriv (fun a ↦ ω ^ a) o",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Ordinal.omega0",
"id",
"HPow.hPow",
"Ordinal.deriv",
"Ordinal.epsilon",
"instHPow",
"Ordinal.instPow",
"Eq",
"Ordinal"
],
... | [
"o : Ordinal.{u_1}\n⊢ veblen 1 o = deriv (fun a ↦ ω ^ a) o"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 128,
"column": 4
} | {
"line": 128,
"column": 15
} | {
"line": 128,
"column": 16
} | [
{
"pp": "x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : { b // b ∈ x }\n⊢ succ (lift.{u + 1, u} (↑h).rank) ≤ lift.{u + 1, u} x.rank",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.s... | [
"x✝ x : PSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : { b // b ∈ x }\n⊢ (↑h).rank < x.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 589,
"column": 2
} | {
"line": 589,
"column": 13
} | {
"line": 589,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ ω < veblen 1 0",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ ω < veblen 1 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Veblen | {
"line": 681,
"column": 2
} | {
"line": 681,
"column": 13
} | {
"line": 681,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ ε_ 0 < Γ_ 0",
"ppTerm": "?m.20",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ ε_ 0 < Γ_ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 207,
"column": 4
} | {
"line": 207,
"column": 47
} | {
"line": 207,
"column": 48
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ (range f).rank ≤ ⨆ i, succ (f i).rank",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.SetTheory.ZFC.Rank.0.ZFSet.rank_range._simp_1_1",
"ZFSet.mem_range._simp_1",
"Preo... | [
"α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ ∀ (a : α), (f a).rank + 1 ≤ ⨆ i, (f i).rank + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Class | {
"line": 265,
"column": 2
} | {
"line": 265,
"column": 39
} | {
"line": 265,
"column": 40
} | [
{
"pp": "x : Class.{u}\nz : ZFSet.{u}\nhz : z ∈ x\ny : ZFSet.{u}\nright✝ : ↑z y\nH : ∀ z ∈ x, ↑y ∈ z\nw : ZFSet.{u}\nhxw : x w\n⊢ y ∈ w",
"ppTerm": "?m.70",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"x : Class.{u}\nz : ZFSet.{u}\nhz : z ∈ x\ny : ZFSet.{u}\nright✝ : ↑z y\nH : ∀ z ∈ x, ↑y ∈ z\nw : ZFSet.{u}\nhxw : x w\n⊢ y ∈ w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 206,
"column": 2
} | {
"line": 208,
"column": 25
} | {
"line": 210,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ (range f).rank = ⨆ i, succ (f i).rank",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.SetTheory.ZFC.Rank.0.ZFSet.rank_range._simp_1_1",
"_private.Mathlib.SetTheory.ZFC.Rank.0... | [] | apply (Ordinal.iSup_le _).antisymm'
· simpa [rank_le_iff, ← add_one_le_iff] using Ordinal.le_iSup _
· simp [rank_lt_of_mem] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.ZFC.Rank | {
"line": 206,
"column": 2
} | {
"line": 208,
"column": 25
} | {
"line": 210,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : Small.{u, u_1} α\nf : α → ZFSet.{u}\n⊢ (range f).rank = ⨆ i, succ (f i).rank",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.SetTheory.ZFC.Rank.0.ZFSet.rank_range._simp_1_1",
"_private.Mathlib.SetTheory.ZFC.Rank.0... | [] | apply (Ordinal.iSup_le _).antisymm'
· simpa [rank_le_iff, ← add_one_le_iff] using Ordinal.le_iSup _
· simp [rank_lt_of_mem] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.ZFC.Rank | {
"line": 227,
"column": 4
} | {
"line": 227,
"column": 37
} | {
"line": 227,
"column": 38
} | [
{
"pp": "x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ lift.{u + 1, u} o < ⨆ i, succ (lift.{u + 1, u} (↑i).rank)",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Ordinal.instLine... | [
"x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\no : Ordinal.{u}\nh : o < x.rank\n⊢ ∃ a ∈ x, o ≤ a.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Rank | {
"line": 228,
"column": 4
} | {
"line": 228,
"column": 15
} | {
"line": 228,
"column": 16
} | [
{
"pp": "x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : ↥x\n⊢ succ (lift.{u + 1, u} (↑h).rank) ≤ lift.{u + 1, u} x.rank",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Order.succ",
... | [
"x✝ x : ZFSet.{u}\nih : ∀ y ∈ x, lift.{u + 1, u} y.rank = IsWellFounded.rank (fun x1 x2 ↦ x1 ∈ x2) y\nh : ↥x\n⊢ (↑h).rank < x.rank"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 211,
"column": 4
} | {
"line": 211,
"column": 15
} | {
"line": 211,
"column": 16
} | [
{
"pp": "x : ZFSet.{u}\nh : x.IsOrdinal\na : ZFSet.{u}\nha : a ∈ x\nb : ZFSet.{u}\nhb : b ∈ x\n⊢ Subrel (fun x1 x2 ↦ x1 ∈ x2) (fun x_1 ↦ x_1 ∈ x) ⟨a, ha⟩ ⟨b, hb⟩ ∨\n ⟨a, ha⟩ = ⟨b, hb⟩ ∨ Subrel (fun x1 x2 ↦ x1 ∈ x2) (fun x_1 ↦ x_1 ∈ x) ⟨b, hb⟩ ⟨a, ha⟩",
"ppTerm": "?m.51",
"assigned": true,
"usedCo... | [
"x : ZFSet.{u}\nh : x.IsOrdinal\na : ZFSet.{u}\nha : a ∈ x\nb : ZFSet.{u}\nhb : b ∈ x\n⊢ a ∈ b ∨ a = b ∨ b ∈ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.VonNeumann | {
"line": 129,
"column": 17
} | {
"line": 129,
"column": 45
} | {
"line": 129,
"column": 46
} | [
{
"pp": "o : Ordinal.{u}\nh : IsSuccPrelimit o\nz : ZFSet.{u}\n⊢ z ∈ V_ o ↔ z ∈ ⋃ (a : ↑(Set.Iio o)), V_ ↑a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"Ordinal.partialOrder",
"Iff.of_eq",
"congrArg",
"ZFSet",
"Partia... | [
"o : Ordinal.{u}\nh : IsSuccPrelimit o\nz : ZFSet.{u}\n⊢ z.rank < o ↔ ∃ a < o, z.rank < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.VonNeumann | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 13
} | {
"line": 138,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ o.card ≤ (V_ o).card",
"ppTerm": "?m.3",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ o.card ≤ (V_ o).card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 293,
"column": 2
} | {
"line": 293,
"column": 13
} | {
"line": 293,
"column": 14
} | [
{
"pp": "o : Ordinal.{u_1}\nx : PSet.{u_1}\n⊢ (∃ b, x.Equiv ((PSet.mk o.ToType fun a ↦ (↑a.toOrd).toPSet).Func b)) ↔ ∃ a < o, x.Equiv a.toPSet",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"Ordinal.ToType.toOrd",
"Ordinal.partialOrder",
"PartialOr... | [
"o : Ordinal.{u_1}\nx : PSet.{u_1}\n⊢ (∃ b, x.Equiv (↑b.toOrd).toPSet) ↔ ∃ a < o, x.Equiv a.toPSet"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 371,
"column": 2
} | {
"line": 371,
"column": 88
} | {
"line": 372,
"column": 4
} | [
{
"pp": "o : Ordinal.{u_1}\n⊢ o.toZFSet.card = o.card",
"ppTerm": "?m.2",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"o : Ordinal.{u_1}\n⊢ o.toZFSet.card = o.card"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.ZFC.Ordinal | {
"line": 406,
"column": 32
} | {
"line": 406,
"column": 43
} | {
"line": 406,
"column": 44
} | [
{
"pp": "x✝¹ y z w : ZFSet.{u}\nx✝ : { x // x.IsOrdinal }\nx : ZFSet.{?u.18}\nhx : x.IsOrdinal\n⊢ (fun o ↦ ⟨o.toZFSet, ⋯⟩) ((fun x ↦ (↑x).rank) ⟨x, hx⟩) = ⟨x, hx⟩",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ZFSet",
"ZFSet.IsOrdinal",
"id",
"Subt... | [
"x✝¹ y z w : ZFSet.{u}\nx✝ : { x // x.IsOrdinal }\nx : ZFSet.{?u.18}\nhx : x.IsOrdinal\n⊢ x.rank.toZFSet = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 721,
"column": 2
} | {
"line": 721,
"column": 13
} | {
"line": 721,
"column": 14
} | [
{
"pp": "o e : ONote\nn : ℕ+\na : ONote\nm : ℕ\ninst✝ : o.NF\nh : o.split = (e.oadd n a, m)\nh₁ : (e.oadd n a).NF\nh₂ : o.repr = (e.oadd n a).repr + ↑m\ne0 : e.repr ≠ 0\nd : ω ∣ a.repr\n⊢ ω ≤ ω ^ e.repr",
"ppTerm": "?m.65",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"o e : ONote\nn : ℕ+\na : ONote\nm : ℕ\ninst✝ : o.NF\nh : o.split = (e.oadd n a, m)\nh₁ : (e.oadd n a).NF\nh₂ : o.repr = (e.oadd n a).repr + ↑m\ne0 : e.repr ≠ 0\nd : ω ∣ a.repr\n⊢ ω ≤ ω ^ e.repr"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 726,
"column": 58
} | {
"line": 726,
"column": 69
} | {
"line": 726,
"column": 70
} | [
{
"pp": "o : ONote\ninst✝ : o.NF\nn : ℕ\n⊢ (o.mulNat n).NF",
"ppTerm": "?m.3",
"assigned": true,
"usedConstants": [
"ONote.NF",
"Eq.mpr",
"ONote.instMul",
"HMul.hMul",
"congrArg",
"ONote.ofNat",
"id",
"ONote.mulNat",
"ONote.mulNat_eq_mul",
... | [
"o : ONote\ninst✝ : o.NF\nn : ℕ\n⊢ (o * ↑n).NF"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 811,
"column": 6
} | {
"line": 811,
"column": 17
} | {
"line": 811,
"column": 18
} | [
{
"pp": "case inr\ne a : ONote\nNe : e.NF\nNa : a.NF\ne0 : e.repr ≠ 0\nn : ℕ+\nh✝ : a.repr < ω ^ e.repr\nNo : (e.oadd n a).NF\nthis✝ : ω ^ e.repr ≤ ω ^ e.repr * ↑↑n + a.repr\nb : Ordinal.{0}\nl : b < ω\nthis : ω ^ e.repr * ↑↑n + a.repr < ω ^ succ e.repr\nh : e.repr < ω\n⊢ ω ^ ω ≤ ω ^ (e.repr * ω)",
"ppTerm"... | [
"case inr\ne a : ONote\nNe : e.NF\nNa : a.NF\ne0 : e.repr ≠ 0\nn : ℕ+\nh✝ : a.repr < ω ^ e.repr\nNo : (e.oadd n a).NF\nthis✝ : ω ^ e.repr ≤ ω ^ e.repr * ↑↑n + a.repr\nb : Ordinal.{0}\nl : b < ω\nthis : ω ^ e.repr * ↑↑n + a.repr < ω ^ succ e.repr\nh : e.repr < ω\n⊢ ω ≤ e.repr * ω"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 841,
"column": 25
} | {
"line": 841,
"column": 51
} | {
"line": 841,
"column": 52
} | [
{
"pp": "a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0... | [
"a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0} := ω ^ a0.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 849,
"column": 8
} | {
"line": 849,
"column": 29
} | {
"line": 849,
"column": 30
} | [
{
"pp": "case pos.succ\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ω ^ a0.repr\nα' : Ordinal.{0} := ω0 * ↑↑n + a'.repr\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nk0 : k = 0\nm : ℕ\nh : a'.repr + ↑(m + 1) < ω ^ a0.repr\nR' : Ordinal... | [
"case pos.succ\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ω ^ a0.repr\nα' : Ordinal.{0} := ω0 * ↑↑n + a'.repr\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nk0 : k = 0\nm : ℕ\nh : a'.repr + ↑(m + 1) < ω ^ a0.repr\nR' : Ordinal.{0} := (opo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Lemmas | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 62
} | {
"line": 44,
"column": 63
} | [
{
"pp": "α : Type u_1\n𝕜 : 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 : 𝕜 → α\nc : 𝕜\nh : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ Tendsto f (𝓝[>] c) l",
"ppTerm": "?m.23",
"assigned":... | [
"α : Type u_1\n𝕜 : 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 : 𝕜 → α\nc : 𝕜\nh : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ map f (𝓝[>] c) ≤ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Lemmas | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 41
} | {
"line": 51,
"column": 42
} | [
{
"pp": "α : Type u_1\n𝕜 : 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 : 𝕜 → α\nc : 𝕜\nh : Tendsto (f ∘ (fun x ↦ c + x) ∘ Neg.neg ∘ Inv.inv) atTop l\n⊢ Tendsto f (𝓝[<] c) l",
"ppTerm": "?m.... | [
"α : Type u_1\n𝕜 : 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 : 𝕜 → α\nc : 𝕜\nh : Tendsto (f ∘ (fun x ↦ c + x) ∘ Neg.neg ∘ Inv.inv) atTop l\n⊢ map f (𝓝[<] c) ≤ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Lemmas | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 44
} | {
"line": 57,
"column": 4
} | [
{
"pp": "α : Type u_1\n𝕜 : 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 : 𝕜 → α\nc : 𝕜\nh_neg : Tendsto (fun x ↦ f (c - x⁻¹)) atTop l\nh_pos : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ Tendsto f (... | [
"α : Type u_1\n𝕜 : 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 : 𝕜 → α\nc : 𝕜\nh_neg : Tendsto (fun x ↦ f (c - x⁻¹)) atTop l\nh_pos : Tendsto (fun x ↦ f (c + x⁻¹)) atTop l\n⊢ map f (𝓝[<] c) ≤ l ∧ m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized | {
"line": 68,
"column": 2
} | {
"line": 68,
"column": 42
} | {
"line": 70,
"column": 0
} | [
{
"pp": "f b : ℝ → ℝ\nexp1 exp2 : ℝ\nh_lt : exp1 ≤ exp2\nh : ∀ exp' > exp1, f =o[atTop] (b ^ exp')\n⊢ ∀ exp' > exp2, f =o[atTop] (b ^ exp')",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"Neg... | [] | exact fun exp' h_exp ↦ h _ (by linarith) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized | {
"line": 73,
"column": 2
} | {
"line": 73,
"column": 37
} | {
"line": 73,
"column": 38
} | [
{
"pp": "f b : ℝ → ℝ\nexp : ℝ\nh_lt : exp < 0\nh : Majorized f b exp\n⊢ Tendsto f atTop (𝓝 0)",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f b : ℝ → ℝ\nexp : ℝ\nh_lt : exp < 0\nh : Majorized f b exp\n⊢ Tendsto f atTop (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 862,
"column": 8
} | {
"line": 862,
"column": 19
} | {
"line": 862,
"column": 20
} | [
{
"pp": "case hbc.refine_1\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0✝ : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).r... | [
"case hbc.refine_1\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0✝ : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Or... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 876,
"column": 39
} | {
"line": 876,
"column": 50
} | {
"line": 876,
"column": 51
} | [
{
"pp": "a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0... | [
"a0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nm : ℕ\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nh : a'.repr + ↑m < ω ^ a0.repr\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nR' : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) (k + 1) m).repr\nR : Ordinal.{0} := (opowAux 0 a0 (a0.oadd n a' * ↑m) k m).repr\nω0 : Ordinal.{0} := ω ^ a0.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 94,
"column": 4
} | {
"line": 94,
"column": 55
} | {
"line": 94,
"column": 56
} | [
{
"pp": "case left\nleft right : Basis\nh_left : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) left ∧ ∀ f ∈ left, Tendsto f atTop atTop\nh_right : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) right ∧ ∀ f ∈ right, Tendsto f atTop atTop\nh : ∀ f ∈ left, ∀ g ∈ right, (Real.... | [
"case left\nleft right : Basis\nh_left : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) left ∧ ∀ f ∈ left, Tendsto f atTop atTop\nh_right : List.Pairwise (fun x y ↦ (Real.log ∘ y) =o[atTop] (Real.log ∘ x)) right ∧ ∀ f ∈ right, Tendsto f atTop atTop\nh : ∀ f ∈ left, ∀ g ∈ right, (Real.log ∘ g) =o[... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 224,
"column": 2
} | {
"line": 224,
"column": 13
} | {
"line": 224,
"column": 14
} | [
{
"pp": "α : Type u_1\nop : Stream'.Seq α → Stream'.Seq α\nh : ∀ (x y : Stream'.Seq α), dist (op x) (op y) ≤ ↑1 * dist x y\ns t : Stream'.Seq α\n⊢ dist (op s) (op t) ≤ dist s t",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nop : Stream'.Seq α → Stream'.Seq α\nh : ∀ (x y : Stream'.Seq α), dist (op x) (op y) ≤ ↑1 * dist x y\ns t : Stream'.Seq α\n⊢ dist (op s) (op t) ≤ dist s t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 62
} | {
"line": 104,
"column": 0
} | [
{
"pp": "basis : Basis\nf : ℝ → ℝ\nh_basis : WellFormedBasis basis\nhf_tendsto : Tendsto f atTop atTop\nhf : ∀ g ∈ basis, (Real.log ∘ g) =o[atTop] (Real.log ∘ f)\n⊢ WellFormedBasis ([f] ++ basis)",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Real",
... | [] | exact append (by simpa [WellFormedBasis]) h_basis (by simpa) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 251,
"column": 4
} | {
"line": 251,
"column": 38
} | {
"line": 252,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\n⊢ Lipschi... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\n⊢ ∀ (x y : β →ᵤ Strea... | rw [lipschitzWith_iff_dist_le_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 267,
"column": 10
} | {
"line": 267,
"column": 21
} | {
"line": 267,
"column": 22
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\nf g : β →... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nF : β → Option (α × γ × β)\nop : γ → Stream'.Seq α → Stream'.Seq α\nh : FriendlyOperationClass op\nT : (β →ᵤ Stream'.Seq α) → β →ᵤ Stream'.Seq α :=\n fun f b ↦\n match F b with\n | none => nil\n | some (a, c, b') => Seq.cons a (op c (f b'))\nf g : β →ᵤ Stream'.Se... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 898,
"column": 6
} | {
"line": 898,
"column": 24
} | {
"line": 898,
"column": 25
} | [
{
"pp": "case h₂\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ⋯\nα' : Ordinal.{0} := ⋯\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nn✝ : ℕ\nh : a'.repr + ↑(n✝ + 1) < ω ^ a0.repr\nR' : Ordinal.{0} := ⋯\nR : Ordinal.{0} := ⋯\nIH : (k ≠ ... | [
"case h₂\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ⋯\nα' : Ordinal.{0} := ⋯\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nn✝ : ℕ\nh : a'.repr + ↑(n✝ + 1) < ω ^ a0.repr\nR' : Ordinal.{0} := ⋯\nR : Ordinal.{0} := ⋯\nIH : (k ≠ 0 → R < ω0 ^... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 155,
"column": 4
} | {
"line": 155,
"column": 53
} | {
"line": 155,
"column": 54
} | [
{
"pp": "case hf_comp\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\ng : ℝ → ℝ\nhg : (basis_hd :: basis_tl).getLast? = some g\n⊢ (Real.log ∘ Real.log ∘ (basis_hd :: basis_tl).getLast ⋯) =o[atTop] (Real.log ∘ g)",
"ppTerm": "?hf_comp",
"assigned": true,
"usedCo... | [
"case hf_comp\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\ng : ℝ → ℝ\nhg : (basis_hd :: basis_tl).getLast? = some g\n⊢ (Real.log ∘ Real.log ∘ g) =o[atTop] (Real.log ∘ g)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 216,
"column": 20
} | {
"line": 216,
"column": 42
} | {
"line": 216,
"column": 43
} | [
{
"pp": "case keep\nbasis : Basis\nbasis_hd✝ : ℝ → ℝ\nbasis_tl✝ : Basis\nex : BasisExtension basis_tl✝\nih : List.Sublist basis_tl✝ ex.getBasis\n⊢ (basis_hd✝ :: basis_tl✝).Sublist (keep basis_hd✝ ex).getBasis",
"ppTerm": "?keep",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.cons_... | [
"case keep\nbasis : Basis\nbasis_hd✝ : ℝ → ℝ\nbasis_tl✝ : Basis\nex : BasisExtension basis_tl✝\nih : List.Sublist basis_tl✝ ex.getBasis\n⊢ List.Sublist basis_tl✝ ex.getBasis"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 59
} | {
"line": 162,
"column": 60
} | [
{
"pp": "case cons\nc : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (const (basis_hd :: basis_tl) c).Sorted",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.Sorted",
"id",
"... | [
"case cons\nc : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (Multiseries.const basis_hd basis_tl c).Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | {
"line": 232,
"column": 4
} | {
"line": 232,
"column": 62
} | {
"line": 232,
"column": 63
} | [
{
"pp": "case cons\nn : ℕ\nr : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (monomialRpow (basis_hd :: basis_tl) n r).Sorted",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"congrArg",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.monomialRpow... | [
"case cons\nn : ℕ\nr : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\n⊢ (Multiseries.monomialRpow basis_hd basis_tl n r).Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 36
} | {
"line": 149,
"column": 0
} | [
{
"pp": "case cons.cons\nexp : ℝ\nexps : List ℝ\nih✝ :\n ∀ {basis : Basis},\n WellFormedBasis basis →\n (fun a ↦ (List.zipWith (fun exp b ↦ b a ^ exp) (List.map (fun x ↦ -x) exps) basis).prod) =ᶠ[atTop] fun a ↦\n (List.zipWith (fun exp b ↦ b a ^ exp) exps basis).prod⁻¹\nbasis_hd : ℝ → ℝ\nbasis_t... | [] | grind [Real.rpow_neg h_pos.le] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | {
"line": 453,
"column": 6
} | {
"line": 453,
"column": 58
} | {
"line": 453,
"column": 59
} | [
{
"pp": "case succ.some\nα : Type u_1\nmotive : (Stream'.Seq α → Stream'.Seq α) → Prop\nh_step :\n ∀ (op : Stream'.Seq α → Stream'.Seq α),\n motive op →\n ∃ T,\n ∀ (s : Stream'.Seq α),\n (op s).destruct =\n Option.map\n (fun x ↦\n match x with\n ... | [
"case succ.some\nα : Type u_1\nmotive : (Stream'.Seq α → Stream'.Seq α) → Prop\nh_step :\n ∀ (op : Stream'.Seq α → Stream'.Seq α),\n motive op →\n ∃ T,\n ∀ (s : Stream'.Seq α),\n (op s).destruct =\n Option.map\n (fun x ↦\n match x with\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 407,
"column": 2
} | {
"line": 407,
"column": 24
} | {
"line": 407,
"column": 25
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : Multiseries basis_hd basis_tl\nh : ms.destruct = none\n⊢ Seq.destruct ms = none",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"basis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : Multiseries basis_hd basis_tl\nh : ms.destruct = none\n⊢ Seq.destruct ms = none"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 546,
"column": 10
} | {
"line": 546,
"column": 43
} | {
"line": 547,
"column": 2
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\ns t : Multiseries basis_hd basis_tl\nf g : ℝ → ℝ\nh : mk s f = mk t g\n⊢ s = t ∧ f = g",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Stream'.Seq",
"Real",
"congrArg",
"Tactic.ComputeAsymptotics.MultiseriesExpansion.mk.... | [] | by rwa [mk, mk, Prod.mk_inj] at h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 679,
"column": 6
} | {
"line": 679,
"column": 17
} | {
"line": 679,
"column": 18
} | [
{
"pp": "case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted",
"ppTerm": "?seq.h_coef",
"assigned": true,
"usedConstants... | [
"case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ ∀ (a : ℝ) (b : MultiseriesExpansion basis_tl), (a, b) ∈ ms.seq → b.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 680,
"column": 6
} | {
"line": 680,
"column": 17
} | {
"line": 680,
"column": 18
} | [
{
"pp": "case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq",
"ppTerm": "?seq.h_Pairwise",
"assigned":... | [
"case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ ms.seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x2 < x1) ms.seq"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 684,
"column": 6
} | {
"line": 684,
"column": 17
} | {
"line": 684,
"column": 18
} | [
{
"pp": "case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ ∀ x ∈ ms.seq, x.2.Sorted",
"ppTerm": "?seq.h_coef",
"assigned": true,
"us... | [
"case seq.h_coef\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ ∀ (a : ℝ) (b : MultiseriesExpansion basis_tl), (a, b) ∈ ms.seq → b.Sorted"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 685,
"column": 6
} | {
"line": 685,
"column": 17
} | {
"line": 685,
"column": 18
} | [
{
"pp": "case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x1 > x2) ms.seq",
"ppTerm": "?seq.h_Pairwise",
... | [
"case seq.h_Pairwise\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\nms : MultiseriesExpansion (basis_hd :: basis_tl)\nh_coef : ∀ x ∈ (mk ms.seq 0).seq, x.2.Sorted\nh_Pairwise : Seq.Pairwise (fun x1 x2 ↦ x1 > x2) (mk ms.seq 0).seq\n⊢ Seq.Pairwise (fun x1 x2 ↦ x2 < x1) ms.seq"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 713,
"column": 43
} | {
"line": 713,
"column": 66
} | {
"line": 713,
"column": 67
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\nh_coef : coef.Sorted\nexp✝ : ℝ\ncoef✝ : MultiseriesExpansion basis_tl\ntl✝ : Multiseries basis_hd basis_tl\nh_comp : (Multiseries.cons exp✝ coef✝ tl✝).leadingExp < ↑exp\nh_tl_coef : ∀ x ∈ (mk (Multiseries.cons exp✝ coef✝... | [
"basis_hd : ℝ → ℝ\nbasis_tl : Basis\nexp : ℝ\ncoef : MultiseriesExpansion basis_tl\nh_coef : coef.Sorted\nexp✝ : ℝ\ncoef✝ : MultiseriesExpansion basis_tl\ntl✝ : Multiseries basis_hd basis_tl\nh_comp : (Multiseries.cons exp✝ coef✝ tl✝).leadingExp < ↑exp\nh_tl_coef : ∀ x ∈ (mk (Multiseries.cons exp✝ coef✝ tl✝) 0).seq... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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