module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Rat.Lemmas | {
"line": 104,
"column": 4
} | {
"line": 104,
"column": 15
} | {
"line": 104,
"column": 16
} | [
{
"pp": "case a\nq : ℚ\nn : ℤ\n⊢ q.den ∣ (q + ↑n).den",
"ppTerm": "?a✝",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case a\nq : ℚ\nn : ℤ\n⊢ q.den ∣ (q + ↑n).den"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Lemmas | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 47
} | {
"line": 118,
"column": 0
} | [
{
"pp": "n : ℤ\nq : ℚ\n⊢ (↑n - q).den = q.den",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Int.cast",
"Rat.instSub",
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"Rat",
"sub_eq_add_neg",
"HSub.hSub",
"Rat.den",
"AddZeroCla... | [] | rw [sub_eq_add_neg, intCast_add_den, neg_den] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Rat.Lemmas | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 47
} | {
"line": 118,
"column": 0
} | [
{
"pp": "n : ℤ\nq : ℚ\n⊢ (↑n - q).den = q.den",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Int.cast",
"Rat.instSub",
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"Rat",
"sub_eq_add_neg",
"HSub.hSub",
"Rat.den",
"AddZeroCla... | [] | rw [sub_eq_add_neg, intCast_add_den, neg_den] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Rat.Lemmas | {
"line": 116,
"column": 2
} | {
"line": 116,
"column": 47
} | {
"line": 118,
"column": 0
} | [
{
"pp": "n : ℤ\nq : ℚ\n⊢ (↑n - q).den = q.den",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Int.cast",
"Rat.instSub",
"Eq.mpr",
"congrArg",
"AddMonoid.toAddZeroClass",
"Rat",
"sub_eq_add_neg",
"HSub.hSub",
"Rat.den",
"AddZeroCla... | [] | rw [sub_eq_add_neg, intCast_add_den, neg_den] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rat.Lemmas | {
"line": 158,
"column": 76
} | {
"line": 162,
"column": 27
} | {
"line": 165,
"column": 0
} | [
{
"pp": "q r : ℚ\n⊢ q + r = (q.num * ↑r.den + ↑q.den * r.num) /. (↑q.den * ↑r.den)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Rat.num",
"NonUnitalCommRing.toNonUnitalNonAss... | [] | by
have hqd : (q.den : ℤ) ≠ 0 := Int.natCast_ne_zero_iff_pos.2 q.den_pos
have hrd : (r.den : ℤ) ≠ 0 := Int.natCast_ne_zero_iff_pos.2 r.den_pos
conv_lhs => rw [← num_divInt_den q, ← num_divInt_den r, divInt_add_divInt _ _ hqd hrd]
rw [mul_comm r.num q.den] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Rat.Cast.Defs | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 29
} | {
"line": 134,
"column": 30
} | [
{
"pp": "α : Type u_3\ninst✝ : DivisionRing α\nr : ℚ\na : α\n⊢ Commute (↑r) a",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Rat.num",
"instHDiv",
"DivisionRing.toRatCast",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
... | [
"α : Type u_3\ninst✝ : DivisionRing α\nr : ℚ\na : α\n⊢ Commute (↑r.num / ↑r.den) a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Inv | {
"line": 67,
"column": 49
} | {
"line": 67,
"column": 84
} | {
"line": 69,
"column": 0
} | [
{
"pp": "n✝¹ num✝ : ℤ\nn✝ denom✝ : ℕ\ninv✝ : Invertible ↑denom✝\nh : ↑n✝¹ / ↑n✝ = ↑num✝ * ⅟↑denom✝\n⊢ IsRat (mkRat ↑n✝¹ ↑n✝) num✝ denom✝",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Mathlib.Meta.NormNum.IsRat.mk",
"instHDiv",
"congrAr... | [] | rw [Rat.mkRat_eq_div]; exact ⟨_, h⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.NormNum.Inv | {
"line": 67,
"column": 49
} | {
"line": 67,
"column": 84
} | {
"line": 69,
"column": 0
} | [
{
"pp": "n✝¹ num✝ : ℤ\nn✝ denom✝ : ℕ\ninv✝ : Invertible ↑denom✝\nh : ↑n✝¹ / ↑n✝ = ↑num✝ * ⅟↑denom✝\n⊢ IsRat (mkRat ↑n✝¹ ↑n✝) num✝ denom✝",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"Mathlib.Meta.NormNum.IsRat.mk",
"instHDiv",
"congrAr... | [] | rw [Rat.mkRat_eq_div]; exact ⟨_, h⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Rat.Lemmas | {
"line": 328,
"column": 16
} | {
"line": 328,
"column": 41
} | {
"line": 328,
"column": 42
} | [
{
"pp": "p : ℚ → Prop\nh : ∀ (a b : ℤ), b ≠ 0 → p (↑a / ↑b)\nq : ℚ\n⊢ p q",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"p : ℚ → Prop\nh : ∀ (a b : ℤ), b ≠ 0 → p (↑a / ↑b)\nq : ℚ\n⊢ p q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Lemmas | {
"line": 331,
"column": 2
} | {
"line": 331,
"column": 13
} | {
"line": 331,
"column": 14
} | [
{
"pp": "p : ℚ → Prop\n⊢ (∃ r, p r) ↔ ∃ a b, b ≠ 0 ∧ p (↑a / ↑b)",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Int.cast",
"instHDiv",
"Rat",
"Exists",
"Rat.instIntCast",
"id",
"HDiv.hDiv",
"Ne",
"Int",
"And",
"Iff",
... | [
"p : ℚ → Prop\n⊢ (∃ r, p r) ↔ ∃ a b, ¬b = 0 ∧ p (↑a / ↑b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.Ring.Common | {
"line": 560,
"column": 2
} | {
"line": 560,
"column": 34
} | {
"line": 562,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\na b₂ c b₁ : R\nx✝ : a + b₂ = c\n⊢ a + (b₁ + b₂) = b₁ + c",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"add_left_comm",
"congrArg",
"CommSemiring.toSemiring",
"Distrib.toAdd",
"instDistribOfSemiring",
"ins... | [] | subst_vars; simp [add_left_comm] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.Ring.Common | {
"line": 560,
"column": 2
} | {
"line": 560,
"column": 34
} | {
"line": 562,
"column": 0
} | [
{
"pp": "R : Type u_1\ninst✝ : CommSemiring R\na b₂ c b₁ : R\nx✝ : a + b₂ = c\n⊢ a + (b₁ + b₂) = b₁ + c",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"add_left_comm",
"congrArg",
"CommSemiring.toSemiring",
"Distrib.toAdd",
"instDistribOfSemiring",
"ins... | [] | subst_vars; simp [add_left_comm] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 29
} | {
"line": 150,
"column": 30
} | [
{
"pp": "α : Type u\nminAx : MinimalAxioms α\ns : Set α\nb : α\n⊢ sSup s ⊓ b = ⨆ a ∈ s, a ⊓ b",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CompleteLattice.toLattice",
"Iff.of_eq",
"congrArg",
"iSup",
"Order.Frame.MinimalAxioms.toCompleteLat... | [
"α : Type u\nminAx : MinimalAxioms α\ns : Set α\nb : α\n⊢ b ⊓ sSup s = ⨆ a ∈ s, b ⊓ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 29
} | {
"line": 156,
"column": 30
} | [
{
"pp": "α : Type u\nι : Sort w\nminAx : MinimalAxioms α\na : α\nf : ι → α\n⊢ a ⊓ ⨆ i, f i = ⨆ i, a ⊓ f i",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nι : Sort w\nminAx : MinimalAxioms α\na : α\nf : ι → α\n⊢ a ⊓ ⨆ i, f i = ⨆ i, a ⊓ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteLattice.Basic | {
"line": 513,
"column": 2
} | {
"line": 513,
"column": 29
} | {
"line": 513,
"column": 30
} | [
{
"pp": "α : Type u_1\nι : Sort u_4\ninst✝ : CompleteLattice α\np : ι → Prop\nf : (i : ι) → p i → α\na : α\nh : ∃ i, p i\n⊢ a ⊔ ⨆ i, ⨆ (h : p i), f i h = ⨆ i, ⨆ (h : p i), a ⊔ f i h",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Sort u_4\ninst✝ : CompleteLattice α\np : ι → Prop\nf : (i : ι) → p i → α\na : α\nh : ∃ i, p i\n⊢ a ⊔ ⨆ i, ⨆ (h : p i), f i h = ⨆ i, ⨆ (h : p i), a ⊔ f i h"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 190,
"column": 2
} | {
"line": 190,
"column": 29
} | {
"line": 190,
"column": 30
} | [
{
"pp": "α : Type u\nminAx : MinimalAxioms α\ns : Set α\nb : α\n⊢ sInf s ⊔ b = ⨅ a ∈ s, a ⊔ b",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Order.Coframe.MinimalAxioms.toCompleteLattice",
"Eq.mpr",
"Lattice.toSemilatticeSup",
"iInf",
"CompleteLattice.toLatt... | [
"α : Type u\nminAx : MinimalAxioms α\ns : Set α\nb : α\n⊢ b ⊔ sInf s = ⨅ a ∈ s, b ⊔ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 196,
"column": 2
} | {
"line": 196,
"column": 29
} | {
"line": 196,
"column": 30
} | [
{
"pp": "α : Type u\nι : Sort w\nminAx : MinimalAxioms α\na : α\nf : ι → α\n⊢ a ⊔ ⨅ i, f i = ⨅ i, a ⊔ f i",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nι : Sort w\nminAx : MinimalAxioms α\na : α\nf : ι → α\n⊢ a ⊔ ⨅ i, f i = ⨅ i, a ⊔ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteLattice.Basic | {
"line": 644,
"column": 2
} | {
"line": 644,
"column": 28
} | {
"line": 644,
"column": 29
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\nf : β → α\np : β → Prop\n⊢ ⨆ i, f i = (⨆ i, ⨆ (_ : p i), f i) ⊔ ⨆ i, ⨆ (_ : ¬p i), f i",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\ninst✝ : CompleteLattice α\nf : β → α\np : β → Prop\n⊢ ⨆ i, f i = (⨆ i, ⨆ (_ : p i), f i) ⊔ ⨆ i, ⨆ (_ : ¬p i), f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteLattice.Basic | {
"line": 686,
"column": 2
} | {
"line": 686,
"column": 23
} | {
"line": 686,
"column": 24
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : CompleteLattice α\ns : Set β\nt : Set γ\nf : β → α\ng : γ → α\nh : β → γ\nh1 : BijOn h s t\nh2 : ∀ (x : β), g (h x) = f x\n⊢ ⨆ x ∈ s, f x = ⨆ y ∈ t, g y",
"ppTerm": "?m.28",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"u... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : CompleteLattice α\ns : Set β\nt : Set γ\nf : β → α\ng : γ → α\nh : β → γ\nh1 : BijOn h s t\nh2 : ∀ (x : β), g (h x) = f x\n⊢ ⨆ x ∈ s, f x = ⨆ y ∈ t, g y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 377,
"column": 8
} | {
"line": 377,
"column": 65
} | {
"line": 377,
"column": 66
} | [
{
"pp": "α✝ : Type u\nβ✝ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝ : CompleteLinearOrder α✝\nα : Type u\nβ : α → Type u\ng : (a : α) → β a → α✝\nlhs : α✝ := ⨅ a, ⨆ b, g a b\nrhs : α✝ := ⨆ h, ⨅ a, g a (h a)\nh : ¬∃ x, rhs < x ∧ x < lhs\nhrl : rhs < lhs\n⊢ ∀ (x : α✝), x ≤ rhs ∨ lhs ≤ x",
"ppTerm": "?m.170"... | [
"α✝ : Type u\nβ✝ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝ : CompleteLinearOrder α✝\nα : Type u\nβ : α → Type u\ng : (a : α) → β a → α✝\nlhs : α✝ := ⨅ a, ⨆ b, g a b\nrhs : α✝ := ⨆ h, ⨅ a, g a (h a)\nh : ¬∃ x, rhs < x ∧ x < lhs\nhrl : rhs < lhs\n⊢ ∀ (x : α✝), x ≤ rhs ∨ lhs ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 382,
"column": 41
} | {
"line": 382,
"column": 52
} | {
"line": 382,
"column": 53
} | [
{
"pp": "α✝ : Type u\nβ✝ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝ : CompleteLinearOrder α✝\nα : Type u\nβ : α → Type u\ng : (a : α) → β a → α✝\nlhs : α✝ := ⨅ a, ⨆ b, g a b\nrhs : α✝ := ⨆ h, ⨅ a, g a (h a)\nhrl : rhs < lhs\nh : ∀ (x : α✝), x ≤ rhs ∨ lhs ≤ x\nf : (a : α) → β a\nhf : ∀ (a : α), rhs < g a (f a)... | [
"α✝ : Type u\nβ✝ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝ : CompleteLinearOrder α✝\nα : Type u\nβ : α → Type u\ng : (a : α) → β a → α✝\nlhs : α✝ := ⨅ a, ⨆ b, g a b\nrhs : α✝ := ⨆ h, ⨅ a, g a (h a)\nhrl : rhs < lhs\nh : ∀ (x : α✝), x ≤ rhs ∨ lhs ≤ x\nf : (a : α) → β a\nhf : ∀ (a : α), rhs < g a (f a)\na : α\n⊢ r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 395,
"column": 2
} | {
"line": 395,
"column": 29
} | {
"line": 395,
"column": 30
} | [
{
"pp": "α : Type u\ninst✝ : Frame α\ns : Set α\nb : α\n⊢ sSup s ⊓ b = ⨆ a ∈ s, a ⊓ b",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"CompleteLattice.toLattice",
"Iff.of_eq",
"congrArg",
"iSup",
"Membership.mem",
"id",
"Semilattice... | [
"α : Type u\ninst✝ : Frame α\ns : Set α\nb : α\n⊢ b ⊓ sSup s = ⨆ a ∈ s, b ⊓ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 401,
"column": 2
} | {
"line": 401,
"column": 29
} | {
"line": 401,
"column": 30
} | [
{
"pp": "α : Type u\nι : Sort w\ninst✝ : Frame α\na : α\nf : ι → α\n⊢ a ⊓ ⨆ i, f i = ⨆ i, a ⊓ f i",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nι : Sort w\ninst✝ : Frame α\na : α\nf : ι → α\n⊢ a ⊓ ⨆ i, f i = ⨆ i, a ⊓ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Lattice | {
"line": 120,
"column": 2
} | {
"line": 120,
"column": 13
} | {
"line": 120,
"column": 14
} | [
{
"pp": "β : Type u_2\nι : Type u_12\nt : Set ι\ns : ι → Set β\nw : ⋃ i ∈ t, s i = ⊤\nx : β\np : ∃ i, x ∈ ⋃ (_ : i ∈ t), s i\n⊢ ∃ i ∈ t, x ∈ s i",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"β : Type u_2\nι : Type u_12\nt : Set ι\ns : ι → Set β\nw : ⋃ i ∈ t, s i = ⊤\nx : β\np : ∃ i, x ∈ ⋃ (_ : i ∈ t), s i\n⊢ ∃ i ∈ t, x ∈ s i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Lattice | {
"line": 134,
"column": 43
} | {
"line": 134,
"column": 69
} | {
"line": 134,
"column": 70
} | [
{
"pp": "α : Type u_1\nι : Sort u_5\ns : ι → Set α\ninst✝ : Nonempty α\nh_Union : ⋃ i, s i = univ\n⊢ (⋃ i, s i).Nonempty",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.univ",
"id",
"Set.Nonempty",
"Eq",
"Set.iUnion",
... | [
"α : Type u_1\nι : Sort u_5\ns : ι → Set α\ninst✝ : Nonempty α\nh_Union : ⋃ i, s i = univ\n⊢ univ.Nonempty"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Lattice | {
"line": 782,
"column": 56
} | {
"line": 782,
"column": 80
} | {
"line": 784,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_5\nκ : ι → Sort u_8\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ s ∩ ⋃ i, ⋃ j, t i j = ⋃ i, ⋃ j, s ∩ t i j",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.instInter",
"Inter.inter",
"funext",
"True",
"eq_sel... | [] | simp only [inter_iUnion] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Set.Lattice | {
"line": 782,
"column": 56
} | {
"line": 782,
"column": 80
} | {
"line": 784,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_5\nκ : ι → Sort u_8\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ s ∩ ⋃ i, ⋃ j, t i j = ⋃ i, ⋃ j, s ∩ t i j",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.instInter",
"Inter.inter",
"funext",
"True",
"eq_sel... | [] | simp only [inter_iUnion] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Lattice | {
"line": 782,
"column": 56
} | {
"line": 782,
"column": 80
} | {
"line": 784,
"column": 0
} | [
{
"pp": "α : Type u_1\nι : Sort u_5\nκ : ι → Sort u_8\ns : Set α\nt : (i : ι) → κ i → Set α\n⊢ s ∩ ⋃ i, ⋃ j, t i j = ⋃ i, ⋃ j, s ∩ t i j",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.instInter",
"Inter.inter",
"funext",
"True",
"eq_sel... | [] | simp only [inter_iUnion] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 444,
"column": 2
} | {
"line": 444,
"column": 34
} | {
"line": 444,
"column": 35
} | [
{
"pp": "α : Type u\nι : Sort w\ninst✝ : Frame α\na : α\nf : ι → α\n⊢ Disjoint a (⨆ i, f i) ↔ ∀ (i : ι), Disjoint a (f i)",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nι : Sort w\ninst✝ : Frame α\na : α\nf : ι → α\n⊢ Disjoint a (⨆ i, f i) ↔ ∀ (i : ι), Disjoint a (f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 458,
"column": 2
} | {
"line": 458,
"column": 34
} | {
"line": 458,
"column": 35
} | [
{
"pp": "α : Type u\ninst✝ : Frame α\na : α\ns : Set α\n⊢ Disjoint a (sSup s) ↔ ∀ b ∈ s, Disjoint a b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : Frame α\na : α\ns : Set α\n⊢ Disjoint a (sSup s) ↔ ∀ b ∈ s, Disjoint a b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Lattice | {
"line": 1048,
"column": 2
} | {
"line": 1048,
"column": 21
} | {
"line": 1050,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nx : β\n⊢ x ∈ ⋃ x, {f x} ↔ x ∈ range f",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.mem_iUnion._simp_1",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"eq_comm",
"Set.mem_rang... | [] | simp [@eq_comm _ x] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 673,
"column": 2
} | {
"line": 673,
"column": 26
} | {
"line": 673,
"column": 27
} | [
{
"pp": "α : Type u\nι : Sort w\ninst✝¹ : CompleteBooleanAlgebra α\nf : ι → α\ninst✝ : Nonempty ι\na : α\n⊢ (⨆ i, f i) ∆ a ≤ ⨆ i, f i ∆ a",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nι : Sort w\ninst✝¹ : CompleteBooleanAlgebra α\nf : ι → α\ninst✝ : Nonempty ι\na : α\n⊢ (⨆ i, f i) ∆ a ≤ ⨆ i, f i ∆ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 676,
"column": 2
} | {
"line": 676,
"column": 29
} | {
"line": 676,
"column": 30
} | [
{
"pp": "α : Type u\nι : Sort w\ninst✝¹ : CompleteBooleanAlgebra α\nf : ι → α\ninst✝ : Nonempty ι\na : α\n⊢ a ∆ ⨆ i, f i ≤ ⨆ i, a ∆ f i",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nι : Sort w\ninst✝¹ : CompleteBooleanAlgebra α\nf : ι → α\ninst✝ : Nonempty ι\na : α\n⊢ a ∆ ⨆ i, f i ≤ ⨆ i, a ∆ f i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 684,
"column": 2
} | {
"line": 684,
"column": 29
} | {
"line": 684,
"column": 30
} | [
{
"pp": "α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns : Set α\nhs : s.Nonempty\na : α\n⊢ a ∆ sSup s ≤ sSup ((fun x ↦ a ∆ x) '' s)",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns : Set α\nhs : s.Nonempty\na : α\n⊢ a ∆ sSup s ≤ sSup ((fun x ↦ a ∆ x) '' s)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Lattice | {
"line": 1298,
"column": 40
} | {
"line": 1298,
"column": 82
} | {
"line": 1298,
"column": 83
} | [
{
"pp": "α : Type u_1\nι : Type u_12\nEs : ι → Set α\nEs_union : ⋃ i, Es i = univ\nEs_disj : Pairwise fun i j ↦ Disjoint (Es i) (Es j)\nI : Set ι\nx : α\ni : ι\nhix : x ∈ Es i\nJ : Set ι\ni_in_J : i ∈ J\n⊢ x ∈ ⋃ j ∈ J, Es j",
"ppTerm": "?m.82",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"α : Type u_1\nι : Type u_12\nEs : ι → Set α\nEs_union : ⋃ i, Es i = univ\nEs_disj : Pairwise fun i j ↦ Disjoint (Es i) (Es j)\nI : Set ι\nx : α\ni : ι\nhix : x ∈ Es i\nJ : Set ι\ni_in_J : i ∈ J\n⊢ ∃ i ∈ J, x ∈ Es i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 690,
"column": 32
} | {
"line": 690,
"column": 56
} | {
"line": 690,
"column": 57
} | [
{
"pp": "α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns t : Set α\nhs : s.Nonempty\nht : t.Nonempty\n⊢ sSup s ∆ sSup t ≤ ⨆ a ∈ s, a ∆ sSup t",
"ppTerm": "?m.55",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns t : Set α\nhs : s.Nonempty\nht : t.Nonempty\n⊢ sSup s ∆ sSup t ≤ ⨆ a ∈ s, a ∆ sSup t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 691,
"column": 50
} | {
"line": 691,
"column": 74
} | {
"line": 691,
"column": 75
} | [
{
"pp": "α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns t : Set α\nhs : s.Nonempty\nht : t.Nonempty\na : α\nx✝ : a ∈ s\n⊢ a ∆ sSup t ≤ ⨆ b ∈ t, a ∆ b",
"ppTerm": "?m.75",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : CompleteBooleanAlgebra α\ns t : Set α\nhs : s.Nonempty\nht : t.Nonempty\na : α\nx✝ : a ∈ s\n⊢ a ∆ sSup t ≤ ⨆ b ∈ t, a ∆ b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 729,
"column": 32
} | {
"line": 729,
"column": 44
} | {
"line": 729,
"column": 44
} | [
{
"pp": "α : Type u\nβ : Type v\nι✝¹ : Sort w\nκ : ι✝¹ → Sort w'\nι : Type u_1\nπ : ι → Type u_2\ninst✝ : (i : ι) → CompleteAtomicBooleanAlgebra (π i)\nι✝ : Type (max u_1 u_2)\nκ✝ : ι✝ → Type (max u_1 u_2)\nf : (a : ι✝) → κ✝ a → (i : ι) → π i\nx✝ : ι\n⊢ (⨅ a, ⨆ b, f a b) x✝ = (⨆ g, ⨅ a, f a (g a)) x✝",
"ppT... | [
"α : Type u\nβ : Type v\nι✝¹ : Sort w\nκ : ι✝¹ → Sort w'\nι : Type u_1\nπ : ι → Type u_2\ninst✝ : (i : ι) → CompleteAtomicBooleanAlgebra (π i)\nι✝ : Type (max u_1 u_2)\nκ✝ : ι✝ → Type (max u_1 u_2)\nf : (a : ι✝) → κ✝ a → (i : ι) → π i\nx✝ : ι\n⊢ (⨆ g, ⨅ a, f a (g a)) x✝ = (⨆ g, ⨅ a, f a (g a)) x✝"
] | iInf_iSup_eq | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Set.Lattice | {
"line": 1304,
"column": 15
} | {
"line": 1304,
"column": 60
} | {
"line": 1304,
"column": 61
} | [
{
"pp": "α : Type u_1\nι : Type u_12\nEs : ι → Set α\nEs_union : ⋃ i, Es i = univ\nEs_disj : Pairwise fun i j ↦ Disjoint (Es i) (Es j)\nI : Set ι\nx : α\ni : ι\nhix : x ∈ Es i\nobs : ∀ (J : Set ι), x ∈ ⋃ j ∈ J, Es j ↔ i ∈ J\nJ : Set ι\n⊢ x ∈ (⋃ j ∈ J, Es j)ᶜ ↔ i ∉ J",
"ppTerm": "?m.154",
"assigned": tru... | [
"α : Type u_1\nι : Type u_12\nEs : ι → Set α\nEs_union : ⋃ i, Es i = univ\nEs_disj : Pairwise fun i j ↦ Disjoint (Es i) (Es j)\nI : Set ι\nx : α\ni : ι\nhix : x ∈ Es i\nobs : ∀ (J : Set ι), x ∈ ⋃ j ∈ J, Es j ↔ i ∈ J\nJ : Set ι\n⊢ x ∈ ⋃ j ∈ J, Es j ↔ i ∈ J"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Lattice | {
"line": 1366,
"column": 30
} | {
"line": 1366,
"column": 41
} | {
"line": 1366,
"column": 42
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nt : α → Set β\nb : β\nhb : b ∈ ⋃ i, t i\n⊢ ∃ a, b ∈ t a",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\nt : α → Set β\nb : β\nhb : b ∈ ⋃ i, t i\n⊢ ∃ a, b ∈ t a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 361,
"column": 4
} | {
"line": 361,
"column": 15
} | {
"line": 361,
"column": 16
} | [
{
"pp": "α : Type u_1\ninst✝² : ConditionallyCompleteLattice α\na : α\ninst✝¹ : NoMaxOrder α\ninst✝ : DenselyOrdered α\nw : α\nhw : a < w\n⊢ ∃ a_1 ∈ Ioi a, a_1 < w",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Set.Ioi",
"Preorder.toLT",
"congrArg",
... | [
"α : Type u_1\ninst✝² : ConditionallyCompleteLattice α\na : α\ninst✝¹ : NoMaxOrder α\ninst✝ : DenselyOrdered α\nw : α\nhw : a < w\n⊢ ∃ a_1, a < a_1 ∧ a_1 < w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 374,
"column": 4
} | {
"line": 374,
"column": 26
} | {
"line": 374,
"column": 27
} | [
{
"pp": "α : Type u_1\ninst✝² : ConditionallyCompleteLattice α\na : α\ninst✝¹ : NoMinOrder α\ninst✝ : DenselyOrdered α\nw : α\nhw : w < a\n⊢ ∃ a_1 ∈ Iio a, w < a_1",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder.t... | [
"α : Type u_1\ninst✝² : ConditionallyCompleteLattice α\na : α\ninst✝¹ : NoMinOrder α\ninst✝ : DenselyOrdered α\nw : α\nhw : w < a\n⊢ ∃ a_1, w < a_1 ∧ a_1 < a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 452,
"column": 61
} | {
"line": 452,
"column": 72
} | {
"line": 452,
"column": 73
} | [
{
"pp": "α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrder α\nt : Set α\nhs : ∀ x ∈ ∅, ∃ y ∈ t, x ≤ y\nht : ∀ y ∈ t, ∃ x ∈ ∅, y ≤ x\ny : α\nyt : y ∈ t\n⊢ False",
"ppTerm": "?m.59",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrder α\nt : Set α\nhs : ∀ x ∈ ∅, ∃ y ∈ t, x ≤ y\nht : ∀ y ∈ t, ∃ x ∈ ∅, y ≤ x\ny : α\nyt : y ∈ t\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 455,
"column": 61
} | {
"line": 455,
"column": 72
} | {
"line": 455,
"column": 73
} | [
{
"pp": "α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Set α\ns_ne : s.Nonempty\nhs : ∀ x ∈ s, ∃ y ∈ ∅, x ≤ y\nht : ∀ y ∈ ∅, ∃ x ∈ s, y ≤ x\nx : α\nxs : x ∈ s\n⊢ False",
"ppTerm": "?m.98",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Set α\ns_ne : s.Nonempty\nhs : ∀ x ∈ s, ∃ y ∈ ∅, x ≤ y\nht : ∀ y ∈ ∅, ∃ x ∈ s, y ≤ x\nx : α\nxs : x ∈ s\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 870,
"column": 6
} | {
"line": 870,
"column": 18
} | {
"line": 870,
"column": 18
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ninst✝¹² : Max α\ninst✝¹¹ : Min α\ninst✝¹⁰ : LE α\ninst✝⁹ : LT α\ninst✝⁸ : SupSet α\ninst✝⁷ : InfSet α\ninst✝⁶ : Top α\ninst✝⁵ : Bot α\ninst✝⁴ : Compl α\ninst✝³ : HImp α\ninst✝² : HNot α\ninst✝¹ : SDiff α\ninst✝ : CompletelyDistribLattice β\nf : α → β... | [] | iInf_iSup_eq | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 581,
"column": 2
} | {
"line": 581,
"column": 53
} | {
"line": 581,
"column": 54
} | [
{
"pp": "α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Set α\na : α\nhb : BddAbove s\n⊢ a < sSup s ↔ ∃ b ∈ s, a < b",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : ConditionallyCompleteLinearOrderBot α\ns : Set α\na : α\nhb : BddAbove s\n⊢ a < sSup s ↔ ∃ b ∈ s, a < b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteBooleanAlgebra | {
"line": 929,
"column": 2
} | {
"line": 929,
"column": 44
} | {
"line": 929,
"column": 45
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ne : α ≃ β\ninst✝ : CompletelyDistribLattice β\ncompleteDistribLattice : CompleteDistribLattice α := e.completeDistribLattice\n⊢ CompletelyDistribLattice α",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"BiheytingAlgebra.to... | [
"case le\nα : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ne : α ≃ β\ninst✝ : CompletelyDistribLattice β\ncompleteDistribLattice : CompleteDistribLattice α := ⋯\n⊢ ∀ {x y : α}, e x ≤ e y ↔ x ≤ y",
"case lt\nα : Type u\nβ : Type v\nι : Sort w\nκ : ι → Sort w'\ne : α ≃ β\ninst✝ : CompletelyDistribLattice β\ncom... | apply e.injective.completelyDistribLattice | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Order.ConditionallyCompleteLattice.Basic | {
"line": 791,
"column": 29
} | {
"line": 791,
"column": 73
} | {
"line": 791,
"column": 74
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : ConditionallyCompleteLattice β\nf : α → β\nt : Set α\nht : BddBelow (f '' t)\nhf : MonotoneOn f t\nhst : ∅ ⊆ t\nh : ∀ y ∈ t, ∃ x ∈ ∅, x ≤ y\n⊢ t = ∅",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Memb... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : Preorder α\ninst✝ : ConditionallyCompleteLattice β\nf : α → β\nt : Set α\nht : BddBelow (f '' t)\nhf : MonotoneOn f t\nhst : ∅ ⊆ t\nh : ∀ y ∈ t, ∃ x ∈ ∅, x ≤ y\n⊢ ∀ (x : α), x ∉ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 32
} | {
"line": 150,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : DistribLattice α\na b c : α\n⊢ b ∈ [[a, c]] → c ∈ [[a, b]] → b = c",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.uIcc_comm",
"Membership.mem",
"DistribLattice.toLattice",
"id",
"implies_co... | [
"α : Type u_1\ninst✝ : DistribLattice α\na b c : α\n⊢ b ∈ [[c, a]] → c ∈ [[b, a]] → b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 157,
"column": 2
} | {
"line": 157,
"column": 30
} | {
"line": 157,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : DistribLattice α\na : α\n⊢ Injective (uIcc a)",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : DistribLattice α\na : α\n⊢ Injective (uIcc a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Pairwise.Basic | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 40
} | {
"line": 44,
"column": 41
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝ : Std.Symm r\na b : α\n⊢ Pairwise (r on fun c ↦ bif c then a else b) ↔ r a b",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"cond",
"Eq.mpr",
"False",
"and_true",
"Function.onFun",
"Bool.not_eq_false",
... | [
"α : Type u_1\nr : α → α → Prop\ninst✝ : Std.Symm r\na b : α\n⊢ r a b → r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Pairwise.Basic | {
"line": 196,
"column": 2
} | {
"line": 196,
"column": 60
} | {
"line": 198,
"column": 0
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\n⊢ univ.Pairwise r ↔ Pairwise r",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.univ",
"instInhabitedTrue",
"Membership.mem",
"Ne",
"Set.Pairwise",
"iff_self",
"Iff",
"implies_cong... | [] | simp only [Set.Pairwise, Pairwise, mem_univ, forall_const] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Set.Pairwise.Basic | {
"line": 196,
"column": 2
} | {
"line": 196,
"column": 60
} | {
"line": 198,
"column": 0
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\n⊢ univ.Pairwise r ↔ Pairwise r",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.univ",
"instInhabitedTrue",
"Membership.mem",
"Ne",
"Set.Pairwise",
"iff_self",
"Iff",
"implies_cong... | [] | simp only [Set.Pairwise, Pairwise, mem_univ, forall_const] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Pairwise.Basic | {
"line": 196,
"column": 2
} | {
"line": 196,
"column": 60
} | {
"line": 198,
"column": 0
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\n⊢ univ.Pairwise r ↔ Pairwise r",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"congrArg",
"Set.univ",
"instInhabitedTrue",
"Membership.mem",
"Ne",
"Set.Pairwise",
"iff_self",
"Iff",
"implies_cong... | [] | simp only [Set.Pairwise, Pairwise, mem_univ, forall_const] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Pairwise.Basic | {
"line": 382,
"column": 23
} | {
"line": 382,
"column": 84
} | {
"line": 383,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf : α → β → γ\ns : Set α\nt : Set β\nhf : ∀ (a : α), a ∈ s → Injective (f a)\nhs : s.PairwiseDisjoint fun a ↦ f a '' t\nx : α × β\nhx : x ∈ s ×ˢ t\ny : α × β\nhy : y ∈ s ×ˢ t\nh : f x.1 x.2 = (fun p ↦ f p.1 p.2) y\nthis : x.1 = y.1\n⊢ x = y",
"ppTerm": "?m.... | [] | by exact Prod.ext this (hf _ hx.1 <| h.trans <| by rw [this]) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 287,
"column": 2
} | {
"line": 287,
"column": 32
} | {
"line": 287,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b c : α\n⊢ b ∈ Ι a c → c ∈ Ι a b → b = c",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.uIoc",
"Set.uIoc_comm",
"Membership.mem",
"id",
"implies_congr",
"Eq.refl",
... | [
"α : Type u_1\ninst✝ : LinearOrder α\na b c : α\n⊢ b ∈ Ι c a → c ∈ Ι b a → b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 301,
"column": 4
} | {
"line": 301,
"column": 80
} | {
"line": 301,
"column": 81
} | [
{
"pp": "case inl\nα : Type u_1\ninst✝ : LinearOrder α\na b c : α\nh : ∀ (x : α), x ∈ (fun b ↦ Ι b a) b ↔ x ∈ (fun b ↦ Ι b a) c\nha : b ≤ a\nhb : b ≤ c\nhc : b < c\n⊢ False",
"ppTerm": "?inl",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inl\nα : Type u_1\ninst✝ : LinearOrder α\na b c : α\nh : ∀ (x : α), x ∈ (fun b ↦ Ι b a) b ↔ x ∈ (fun b ↦ Ι b a) c\nha : b ≤ a\nhb : b ≤ c\nhc : b < c\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 305,
"column": 4
} | {
"line": 305,
"column": 41
} | {
"line": 305,
"column": 42
} | [
{
"pp": "case inr\nα : Type u_1\ninst✝ : LinearOrder α\na b c : α\nh : ∀ (x : α), x ∈ (fun b ↦ Ι b a) b ↔ x ∈ (fun b ↦ Ι b a) c\nha : a < b\n⊢ b ≤ c",
"ppTerm": "?inr",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inr\nα : Type u_1\ninst✝ : LinearOrder α\na b c : α\nh : ∀ (x : α), x ∈ (fun b ↦ Ι b a) b ↔ x ∈ (fun b ↦ Ι b a) c\nha : a < b\n⊢ b ≤ c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Interval.Set.UnorderedInterval | {
"line": 308,
"column": 2
} | {
"line": 308,
"column": 30
} | {
"line": 308,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na : α\n⊢ Injective (Ι a)",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : LinearOrder α\na : α\n⊢ Injective (Ι a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.SetLike.Basic | {
"line": 208,
"column": 2
} | {
"line": 208,
"column": 91
} | {
"line": 208,
"column": 92
} | [
{
"pp": "A : Type u_1\nB : Type u_2\ni : SetLike A B\ninst✝¹ : LE A\ninst✝ : OrderTop A\ns : A\nhs : s ≠ ⊤\nh_top : ↑⊤ = Set.univ\n⊢ ∃ b, ¬b ∈ s",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"A : Type u_1\nB : Type u_2\ni : SetLike A B\ninst✝¹ : LE A\ninst✝ : OrderTop A\ns : A\nhs : s ≠ ⊤\nh_top : ↑⊤ = Set.univ\n⊢ ∃ b, ¬b ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Antichain | {
"line": 195,
"column": 2
} | {
"line": 195,
"column": 13
} | {
"line": 195,
"column": 14
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\n⊢ IsAntichain (fun x1 x2 ↦ r ↑x1 ↑x2) univ ↔ IsAntichain r s",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr : α → α → Prop\ns : Set α\n⊢ IsAntichain (fun x1 x2 ↦ r ↑x1 ↑x2) univ ↔ IsAntichain r s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Chain | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 13
} | {
"line": 142,
"column": 14
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\n⊢ IsChain (fun x1 x2 ↦ r ↑x1 ↑x2) univ ↔ IsChain r s",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr : α → α → Prop\ns : Set α\n⊢ IsChain (fun x1 x2 ↦ r ↑x1 ↑x2) univ ↔ IsChain r s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Chain | {
"line": 246,
"column": 14
} | {
"line": 246,
"column": 48
} | {
"line": 246,
"column": 49
} | [
{
"pp": "case inl\nα : Type u_1\ns : Set α\ninst✝ : Preorder α\nhs : IsChain (fun x1 x2 ↦ x1 ≤ x2) s\nx y : α\nhx : x ∈ s\nhy : y ∈ s\nh : ¬x < y\nh' : x ≤ y\n⊢ y ≤ x",
"ppTerm": "?inl",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case inl\nα : Type u_1\ns : Set α\ninst✝ : Preorder α\nhs : IsChain (fun x1 x2 ↦ x1 ≤ x2) s\nx y : α\nhx : x ∈ s\nhy : y ∈ s\nh : ¬x < y\nh' : x ≤ y\n⊢ y ≤ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Antichain | {
"line": 399,
"column": 23
} | {
"line": 399,
"column": 66
} | {
"line": 399,
"column": 67
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\nh : IsMaxAntichain r s\n⊢ ¬Nonempty α ↔ ¬s.Nonempty",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"IsEmpty",
"Iff",
"Set.Nonempty",
"congr",
"_private.Mathlib.Or... | [
"α : Type u_1\nr : α → α → Prop\ns : Set α\nh : IsMaxAntichain r s\n⊢ IsEmpty α ↔ s = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Chain | {
"line": 287,
"column": 23
} | {
"line": 287,
"column": 66
} | {
"line": 287,
"column": 67
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\nh : IsMaxChain r s\n⊢ ¬Nonempty α ↔ ¬s.Nonempty",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"IsEmpty",
"Iff",
"Set.Nonempty",
"congr",
"Set.instEmptyCollection... | [
"α : Type u_1\nr : α → α → Prop\ns : Set α\nh : IsMaxChain r s\n⊢ IsEmpty α ↔ s = ∅"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Chain | {
"line": 301,
"column": 2
} | {
"line": 301,
"column": 56
} | {
"line": 301,
"column": 57
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\nh : ∃ t, IsChain r s ∧ SuperChain r s t\nthis : IsChain r s ∧ SuperChain r s h.choose\n⊢ SuperChain r s (SuccChain r s)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"dite_cond_eq_true",
"Eq.mpr",
"SuperChain",
"... | [
"α : Type u_1\nr : α → α → Prop\ns : Set α\nh : ∃ t, IsChain r s ∧ SuperChain r s t\nthis : IsChain r s ∧ SuperChain r s h.choose\n⊢ SuperChain r s ⋯.choose"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.Preorder.Chain | {
"line": 308,
"column": 4
} | {
"line": 308,
"column": 39
} | {
"line": 308,
"column": 40
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ns : Set α\nhs : IsChain r s\nh : ¬(IsChain r s ∧ ∃ x, SuperChain r s x)\n⊢ IsChain r (SuccChain r s)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"SuperChain",
"eq_false",
"congrArg",
"Classi... | [
"α : Type u_1\nr : α → α → Prop\ns : Set α\nhs : IsChain r s\nh : ¬(IsChain r s ∧ ∃ x, SuperChain r s x)\n⊢ IsChain r s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Monoid.Basic | {
"line": 59,
"column": 38
} | {
"line": 59,
"column": 71
} | {
"line": 59,
"column": 72
} | [
{
"pp": "α : Type u\nβ : Type u_1\ninst✝⁴ : CommMonoid α\ninst✝³ : Preorder α\ninst✝² : IsOrderedCancelMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : LinearOrder β\nf : β → α\nhf : StrictMono f\nmul : ∀ (x y : β), f (x * y) = f x * f y\na b c : β\nh : a * b ≤ a * c\n⊢ b ≤ c",
"ppTerm": "?m.34",
"assigned": tr... | [
"α : Type u\nβ : Type u_1\ninst✝⁴ : CommMonoid α\ninst✝³ : Preorder α\ninst✝² : IsOrderedCancelMonoid α\ninst✝¹ : CommMonoid β\ninst✝ : LinearOrder β\nf : β → α\nhf : StrictMono f\nmul : ∀ (x y : β), f (x * y) = f x * f y\na b c : β\nh : a * b ≤ a * c\n⊢ f b ≤ f c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.CompleteLatticeIntervals | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 63
} | {
"line": 157,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Set α\nhs : s.OrdConnected\nt : Set ↑s\nc : ↑s\nhct : c ∈ t\nB : ↑s\nhB : B ∈ lowerBounds t\n⊢ ↑B ≤ sInf (Subtype.val '' t)",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"PartialOrder.toPreord... | [
"case refine_2\nα : Type u_2\ninst✝ : ConditionallyCompleteLinearOrder α\ns : Set α\nhs : s.OrdConnected\nt : Set ↑s\nc : ↑s\nhct : c ∈ t\nB : ↑s\nhB : B ∈ lowerBounds t\n⊢ sInf (Subtype.val '' t) ≤ ↑c"
] | · exact (Subtype.mono_coe (· ∈ s)).le_csInf_image ⟨c, hct⟩ hB | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.CompleteLatticeIntervals | {
"line": 228,
"column": 33
} | {
"line": 228,
"column": 44
} | {
"line": 228,
"column": 45
} | [
{
"pp": "ι : Sort u_1\nα : Type u_2\ns : Set α\ninst✝ : CompleteLattice α\na : α\nS : Set ↑(Iic a)\n⊢ sSup (Subtype.val '' S) ∈ Iic a",
"ppTerm": "?m.129",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"sSup_le_iff._simp_2",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"S... | [
"ι : Sort u_1\nα : Type u_2\ns : Set α\ninst✝ : CompleteLattice α\na : α\nS : Set ↑(Iic a)\n⊢ ∀ (b : α) (x : b ≤ a), ⟨b, ⋯⟩ ∈ S → b ≤ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Eq | {
"line": 24,
"column": 38
} | {
"line": 24,
"column": 49
} | {
"line": 24,
"column": 50
} | [
{
"pp": "α : Type u_1\ninst✝¹ : AddMonoidWithOne α\ninst✝ : CharZero α\nn✝¹ n✝ : ℕ\nh : n✝¹.beq n✝ = false\n⊢ ¬↑n✝¹ = ↑n✝",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"Nat",
"... | [
"α : Type u_1\ninst✝¹ : AddMonoidWithOne α\ninst✝ : CharZero α\nn✝¹ n✝ : ℕ\nh : n✝¹.beq n✝ = false\n⊢ ¬n✝¹ = n✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.Eq | {
"line": 28,
"column": 38
} | {
"line": 28,
"column": 49
} | {
"line": 28,
"column": 50
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Ring α\ninst✝ : CharZero α\nn✝¹ n✝ : ℤ\nh : decide (n✝¹ = n✝) = false\n⊢ ¬↑n✝¹ = ↑n✝",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Int.cast",
"Eq.mpr",
"congrArg",
"id",
"Int",
"AddGroupWithOne.toIntCast",
"Int.ca... | [
"α : Type u_1\ninst✝¹ : Ring α\ninst✝ : CharZero α\nn✝¹ n✝ : ℤ\nh : decide (n✝¹ = n✝) = false\n⊢ ¬n✝¹ = n✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Cast.Order | {
"line": 37,
"column": 2
} | {
"line": 37,
"column": 38
} | {
"line": 37,
"column": 39
} | [
{
"pp": "K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\np q : ℚ\n⊢ p < q → ↑p < ↑q",
"ppTerm": "?m.9",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"K : Type u_5\ninst✝² : Field K\ninst✝¹ : LinearOrder K\ninst✝ : IsStrictOrderedRing K\np q : ℚ\n⊢ p < q → ↑p < ↑q"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.DivMod | {
"line": 36,
"column": 51
} | {
"line": 36,
"column": 62
} | {
"line": 36,
"column": 63
} | [
{
"pp": "case H2\na q m : ℤ\nb' r : ℕ\nhm : q * ↑b' = m\nh : ↑r + m = a\nh₂ : r < b'\n⊢ ↑r < ↑b'",
"ppTerm": "?H2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.cast_lt._simp_1",
"AddGroupWithOne.toAddMonoidWithOne",
"SemilatticeInf.toPartialOrder",
"id",
"... | [
"case H2\na q m : ℤ\nb' r : ℕ\nhm : q * ↑b' = m\nh : ↑r + m = a\nh₂ : r < b'\n⊢ r < b'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Tactic.NormNum.DivMod | {
"line": 98,
"column": 36
} | {
"line": 98,
"column": 47
} | {
"line": 98,
"column": 48
} | [
{
"pp": "case H2\na q m : ℤ\nb' r : ℕ\nhm : q * ↑b' = m\nh₂ : r.blt b' = true\nh : ↑r + m = a\n⊢ ↑r < ↑b'",
"ppTerm": "?H2",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.cast_lt._simp_1",
"AddGroupWithOne.toAddMonoidWithOne",
"SemilatticeInf.toPartialOrder",
"id"... | [
"case H2\na q m : ℤ\nb' r : ℕ\nhm : q * ↑b' = m\nh₂ : r.blt b' = true\nh : ↑r + m = a\n⊢ r < b'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 104,
"column": 50
} | {
"line": 104,
"column": 66
} | {
"line": 106,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : DivInvMonoid α\na : α\n⊢ a⁻ᵐ ≤ 1 ↔ a⁻¹ ≤ 1",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"and_true",
"instLeOnePart",
"Monoid.toMulOneC... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 104,
"column": 50
} | {
"line": 104,
"column": 66
} | {
"line": 106,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : DivInvMonoid α\na : α\n⊢ a⁻ᵐ ≤ 1 ↔ a⁻¹ ≤ 1",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"and_true",
"instLeOnePart",
"Monoid.toMulOneC... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 104,
"column": 50
} | {
"line": 104,
"column": 66
} | {
"line": 106,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : DivInvMonoid α\na : α\n⊢ a⁻ᵐ ≤ 1 ↔ a⁻¹ ≤ 1",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"and_true",
"instLeOnePart",
"Monoid.toMulOneC... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 119,
"column": 72
} | {
"line": 119,
"column": 88
} | {
"line": 121,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : Group α\n⊢ 1⁻ᵐ = 1",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"instLeOnePart",
... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 119,
"column": 72
} | {
"line": 119,
"column": 88
} | {
"line": 121,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : Group α\n⊢ 1⁻ᵐ = 1",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"instLeOnePart",
... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 119,
"column": 72
} | {
"line": 119,
"column": 88
} | {
"line": 121,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Lattice α\ninst✝ : Group α\n⊢ 1⁻ᵐ = 1",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"instLeOnePart",
... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 127,
"column": 79
} | {
"line": 127,
"column": 95
} | {
"line": 129,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\na : α\ninst✝ : MulLeftMono α\n⊢ a⁻ᵐ = a⁻¹ ↔ a ≤ 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMono... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 127,
"column": 79
} | {
"line": 127,
"column": 95
} | {
"line": 129,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\na : α\ninst✝ : MulLeftMono α\n⊢ a⁻ᵐ = a⁻¹ ↔ a ≤ 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMono... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 127,
"column": 79
} | {
"line": 127,
"column": 95
} | {
"line": 129,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\na : α\ninst✝ : MulLeftMono α\n⊢ a⁻ᵐ = a⁻¹ ↔ a ≤ 1",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMono... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 135,
"column": 62
} | {
"line": 135,
"column": 78
} | {
"line": 137,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\na : α\ninst✝ : MulLeftMono α\n⊢ a⁻ᵐ ≤ 1 ↔ 1 ≤ a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Left.inv_le_one_iff._simp_2",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOn... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 135,
"column": 62
} | {
"line": 135,
"column": 78
} | {
"line": 137,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\na : α\ninst✝ : MulLeftMono α\n⊢ a⁻ᵐ ≤ 1 ↔ 1 ≤ a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Left.inv_le_one_iff._simp_2",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOn... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 135,
"column": 62
} | {
"line": 135,
"column": 78
} | {
"line": 137,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\na : α\ninst✝ : MulLeftMono α\n⊢ a⁻ᵐ ≤ 1 ↔ 1 ≤ a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Left.inv_le_one_iff._simp_2",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"InvOn... | [] | simp [leOnePart] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 142,
"column": 2
} | {
"line": 143,
"column": 28
} | {
"line": 145,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\ninst✝ : MulLeftMono α\na : α\n⊢ a⁺ᵐ / a⁻ᵐ = a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"instHDiv",
"HMul.hMul"... | [] | rw [div_eq_mul_inv, mul_inv_eq_iff_eq_mul, leOnePart_def, mul_sup, mul_one, mul_inv_cancel,
sup_comm, oneLePart_def] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 142,
"column": 2
} | {
"line": 143,
"column": 28
} | {
"line": 145,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\ninst✝ : MulLeftMono α\na : α\n⊢ a⁺ᵐ / a⁻ᵐ = a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"instHDiv",
"HMul.hMul"... | [] | rw [div_eq_mul_inv, mul_inv_eq_iff_eq_mul, leOnePart_def, mul_sup, mul_one, mul_inv_cancel,
sup_comm, oneLePart_def] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 142,
"column": 2
} | {
"line": 143,
"column": 28
} | {
"line": 145,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Lattice α\ninst✝¹ : Group α\ninst✝ : MulLeftMono α\na : α\n⊢ a⁺ᵐ / a⁻ᵐ = a",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"DivInvMonoid.toInv",
"Lattice.toSemilatticeSup",
"instHDiv",
"HMul.hMul"... | [] | rw [div_eq_mul_inv, mul_inv_eq_iff_eq_mul, leOnePart_def, mul_sup, mul_one, mul_inv_cancel,
sup_comm, oneLePart_def] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 170,
"column": 6
} | {
"line": 170,
"column": 20
} | {
"line": 170,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝³ : Lattice α\ninst✝² : Group α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\na : α\n⊢ a⁺ᵐ * a⁻ᵐ = |a|ₘ",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"instLeOne... | [
"α : Type u_1\ninst✝³ : Lattice α\ninst✝² : Group α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\na : α\n⊢ (a ⊔ 1) * a⁻ᵐ = |a|ₘ"
] | oneLePart_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 175,
"column": 6
} | {
"line": 175,
"column": 20
} | {
"line": 175,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝³ : Lattice α\ninst✝² : Group α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\na : α\n⊢ a⁻ᵐ * a⁺ᵐ = |a|ₘ",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"instLeOne... | [
"α : Type u_1\ninst✝³ : Lattice α\ninst✝² : Group α\ninst✝¹ : MulLeftMono α\ninst✝ : MulRightMono α\na : α\n⊢ a⁻ᵐ * (a ⊔ 1) = |a|ₘ"
] | oneLePart_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 247,
"column": 6
} | {
"line": 247,
"column": 20
} | {
"line": 247,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : Group α\na : α\n⊢ a⁺ᵐ = if 1 ≤ a then a else 1",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"MulOne.toOne",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
... | [
"α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : Group α\na : α\n⊢ max a 1 = if 1 ≤ a then a else 1"
] | oneLePart_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Order.Group.PosPart | {
"line": 257,
"column": 6
} | {
"line": 257,
"column": 20
} | {
"line": 257,
"column": 21
} | [
{
"pp": "α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : Group α\na : α\nha : 1 < a⁺ᵐ\n⊢ a⁺ᵐ = a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"MulOne.toOne",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
... | [
"α : Type u_1\ninst✝¹ : LinearOrder α\ninst✝ : Group α\na : α\nha : 1 < max a 1\n⊢ a⁺ᵐ = a"
] | oneLePart_def, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Notation.Support | {
"line": 188,
"column": 25
} | {
"line": 188,
"column": 36
} | {
"line": 188,
"column": 37
} | [
{
"pp": "ι : Type u_1\nκ : Type u_2\nM : Type u_3\ninst✝ : One M\nf : ι × κ → M\ni : ι\nj : κ\nhj : j ∈ mulSupport fun j ↦ f (i, j)\n⊢ (i, j) ∈ mulSupport f ∧ (i, j).2 = j",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Function.mem_mulSupport._simp_2",
"and_tr... | [
"ι : Type u_1\nκ : Type u_2\nM : Type u_3\ninst✝ : One M\nf : ι × κ → M\ni : ι\nj : κ\nhj : j ∈ mulSupport fun j ↦ f (i, j)\n⊢ ¬f (i, j) = 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Nat.Factorial.Basic | {
"line": 180,
"column": 16
} | {
"line": 180,
"column": 33
} | {
"line": 180,
"column": 34
} | [
{
"pp": "n m : ℕ\nhnm : n ≤ m\n⊢ n ! * (n + 1) ^ (m - n) ≤ m !",
"ppTerm": "?m.52",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n m : ℕ\nhnm : n ≤ m\n⊢ n ! * (n + 1) ^ (m - n) ≤ m !"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Hom.Basic | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 45
} | {
"line": 130,
"column": 46
} | [
{
"pp": "F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : CommMagma β\ninst✝¹ : LE β\ninst✝ : SubmultiplicativeHomClass F α β\nf : F\na b : α\n⊢ f a ≤ f b * f (a / b)",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"us... | [
"F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : CommMagma β\ninst✝¹ : LE β\ninst✝ : SubmultiplicativeHomClass F α β\nf : F\na b : α\n⊢ f a ≤ f b * f (a / b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Hom.Basic | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 45
} | {
"line": 135,
"column": 46
} | [
{
"pp": "F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : AddCommMagma β\ninst✝¹ : LE β\ninst✝ : MulLEAddHomClass F α β\nf : F\na b : α\n⊢ f a ≤ f b + f (a / b)",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoal... | [
"F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : AddCommMagma β\ninst✝¹ : LE β\ninst✝ : MulLEAddHomClass F α β\nf : F\na b : α\n⊢ f a ≤ f b + f (a / b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Hom.Basic | {
"line": 140,
"column": 2
} | {
"line": 140,
"column": 39
} | {
"line": 140,
"column": 40
} | [
{
"pp": "F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : Mul β\ninst✝¹ : LE β\ninst✝ : SubmultiplicativeHomClass F α β\nf : F\na b c : α\n⊢ f (a / c) ≤ f (a / b) * f (b / c)",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],... | [
"F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : Mul β\ninst✝¹ : LE β\ninst✝ : SubmultiplicativeHomClass F α β\nf : F\na b c : α\n⊢ f (a / c) ≤ f (a / b) * f (b / c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Algebra.Order.Hom.Basic | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 41
} | {
"line": 145,
"column": 42
} | [
{
"pp": "F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : Add β\ninst✝¹ : LE β\ninst✝ : MulLEAddHomClass F α β\nf : F\na b c : α\n⊢ f (a / c) ≤ f (a / b) + f (b / c)",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"use... | [
"F : Type u_2\nα : Type u_3\nβ : Type u_4\ninst✝⁴ : FunLike F α β\ninst✝³ : Group α\ninst✝² : Add β\ninst✝¹ : LE β\ninst✝ : MulLEAddHomClass F α β\nf : F\na b c : α\n⊢ f (a / c) ≤ f (a / b) + f (b / c)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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