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.Data.Ordmap.Ordnode | {
"line": 219,
"column": 6
} | {
"line": 219,
"column": 15
} | {
"line": 220,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Ordmap.Ordnode | {
"line": 219,
"column": 6
} | {
"line": 219,
"column": 15
} | {
"line": 220,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordnode | {
"line": 219,
"column": 6
} | {
"line": 219,
"column": 15
} | {
"line": 220,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Ordnode | {
"line": 253,
"column": 6
} | {
"line": 253,
"column": 15
} | {
"line": 254,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Ordmap.Ordnode | {
"line": 253,
"column": 6
} | {
"line": 253,
"column": 15
} | {
"line": 254,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordnode | {
"line": 253,
"column": 6
} | {
"line": 253,
"column": 15
} | {
"line": 254,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Ordnode | {
"line": 287,
"column": 6
} | {
"line": 287,
"column": 15
} | {
"line": 288,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Ordmap.Ordnode | {
"line": 287,
"column": 6
} | {
"line": 287,
"column": 15
} | {
"line": 288,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordnode | {
"line": 287,
"column": 6
} | {
"line": 287,
"column": 15
} | {
"line": 288,
"column": 4
} | [
{
"pp": "case nil.nil\nα : Type u_1\nl : Ordnode α\nx : α\nr : Ordnode α\n⊢ Ordnode α",
"ppTerm": "?nil.nil",
"assigned": true,
"usedConstants": [
"Ordnode.singleton"
],
"usedFVars": [
"α",
"x"
],
"usedGoals": []
}
] | [] | exact ι x | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Nat.Nth | {
"line": 517,
"column": 18
} | {
"line": 517,
"column": 29
} | {
"line": 517,
"column": 30
} | [
{
"pp": "p : ℕ → Prop\nn n' : ℕ\nhn' : n' ∈ Set.ofPred p\nhp : n' ∉ ↑(range n)\n⊢ n' ≥ n",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"GE.ge",
"id",
"LE.le",
"instLENat",
"ge_iff_le._simp_1",
"Nat",
"Eq"
],
"usedFVars": [... | [
"p : ℕ → Prop\nn n' : ℕ\nhn' : n' ∈ Set.ofPred p\nhp : n' ∉ ↑(range n)\n⊢ n ≤ n'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 125,
"column": 6
} | {
"line": 125,
"column": 17
} | {
"line": 125,
"column": 18
} | [
{
"pp": "case pos\nα : Type u_1\ninst✝ : AddGroupWithOne α\na : PosNum\ne : a.succ.pred' = Num.pos a\nthis : ↑(-↑a) = -1 + ↑(-↑a + 1)\n⊢ -↑(Num.casesOn (Num.pos a) 1 bit1) = -↑a.succ + -↑a.succ + 1",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtra... | [
"case pos\nα : Type u_1\ninst✝ : AddGroupWithOne α\na : PosNum\ne : a.succ.pred' = Num.pos a\nthis : ↑(-↑a) = -1 + ↑(-↑a + 1)\n⊢ -↑a = -1 + (-↑a + 1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 30
} | {
"line": 134,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ZNum\nthis : ↑(-1 + ↑n + ↑n) = ↑(↑n + ↑n + -1)\n⊢ -(↑(-n) + ↑(-n) + 1) = ↑n + ↑n - 1",
"ppTerm": "?m.56",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"Neg... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\nn : ZNum\nthis : ↑(-1 + ↑n + ↑n) = ↑(↑n + ↑n + -1)\n⊢ -1 + (↑n + ↑n) = ↑n + (↑n + -1)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 171,
"column": 4
} | {
"line": 171,
"column": 32
} | {
"line": 171,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(↑a + -↑b + (↑a + -↑b)) = ↑a + ↑a + (-↑b + -↑b)\n⊢ ↑a - ↑b + (↑a - ↑b) = ↑a.bit0 - ↑b.bit0",
"ppTerm": "?m.160",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(↑a + -↑b + (↑a + -↑b)) = ↑a + ↑a + (-↑b + -↑b)\n⊢ -↑b + (↑a + -↑b) = ↑a + (-↑b + -↑b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 176,
"column": 4
} | {
"line": 176,
"column": 32
} | {
"line": 176,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + -1))) = ↑(↑a + -1 + (-↑b + -↑b))\n⊢ ↑a - ↑b + (↑a - ↑b) - 1 = ↑a.bit0 - ↑b.bit1",
"ppTerm": "?m.223",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + -1))) = ↑(↑a + -1 + (-↑b + -↑b))\n⊢ -↑b + (↑a + (-↑b + -1)) = ↑a + (-1 + (-↑b + -↑b))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 44
} | {
"line": 179,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\n⊢ ↑(a.bit1.sub' b.bit0) = ↑a.bit1 - ↑b.bit0",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"castPosNum",
"ZNum.bi... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\n⊢ ↑a - ↑b + (↑a - ↑b) + 1 = ↑a.bit1 - ↑b.bit0"
] | rw [sub', ZNum.cast_bit1, cast_sub' a b] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Num.ZNum | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 32
} | {
"line": 181,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + 1))) = ↑(↑a + 1 + (-↑b + -↑b))\n⊢ ↑a - ↑b + (↑a - ↑b) + 1 = ↑a.bit1 - ↑b.bit0",
"ppTerm": "?m.282",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mp... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + (-↑b + 1))) = ↑(↑a + 1 + (-↑b + -↑b))\n⊢ -↑b + (↑a + (-↑b + 1)) = ↑a + (1 + (-↑b + -↑b))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 185,
"column": 4
} | {
"line": 185,
"column": 32
} | {
"line": 185,
"column": 33
} | [
{
"pp": "α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + -↑b)) = ↑a + (-↑b + -↑b)\n⊢ ↑a - ↑b + (↑a - ↑b) = ↑a.bit1 - ↑b.bit1",
"ppTerm": "?m.329",
"assigned": true,
"usedConstants": [
"neg_add_rev",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castPo... | [
"α : Type u_1\ninst✝ : AddGroupWithOne α\na b : PosNum\nthis : ↑(-↑b + (↑a + -↑b)) = ↑a + (-↑b + -↑b)\n⊢ -↑b + (↑a + -↑b) = ↑a + (-↑b + -↑b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 307,
"column": 60
} | {
"line": 307,
"column": 71
} | {
"line": 307,
"column": 71
} | [
{
"pp": "α : Type u_1\ninst✝ : NonAssocRing α\nm n : ZNum\n⊢ ↑m * ↑↑n = ↑m * ↑n",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"HMul.hMul",
"AddMonoid.toAddSem... | [
"α : Type u_1\ninst✝ : NonAssocRing α\nm n : ZNum\n⊢ ↑m * ↑n = ↑m * ↑n"
] | cast_to_int | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Ordmap.Invariants | {
"line": 64,
"column": 4
} | {
"line": 64,
"column": 27
} | {
"line": 64,
"column": 28
} | [
{
"pp": "a b : ℕ\nh₁ : delta * a < b\nh₂ : delta * b < a\n⊢ a ≤ delta * (delta * a)",
"ppTerm": "?m.31",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℕ\nh₁ : delta * a < b\nh₂ : delta * b < a\n⊢ a ≤ delta * (delta * a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 356,
"column": 27
} | {
"line": 357,
"column": 40
} | {
"line": 359,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Ring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nm n : ZNum\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"castZNum",
"NegZeroClass.toNeg",
"Preorder.toLT",
"congrArg",
"PartialO... | [] | by
rw [← not_lt]; exact not_congr cast_lt | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Num.ZNum | {
"line": 559,
"column": 6
} | {
"line": 559,
"column": 17
} | {
"line": 559,
"column": 18
} | [
{
"pp": "case bit0.h₂\nd n : PosNum\nq r : Num\nIH : ↑r + ↑d * ↑q = ↑n ∧ ↑r < ↑d\n⊢ ↑r.bit0 < 2 * ↑d",
"ppTerm": "?bit0.h₂",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"castPosNum",
"Nat.instMulZeroClass",
"Preorder.toLT",
... | [
"case bit0.h₂\nd n : PosNum\nq r : Num\nIH : ↑r + ↑d * ↑q = ↑n ∧ ↑r < ↑d\n⊢ ↑r < ↑d"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.ZNum | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 20
} | {
"line": 594,
"column": 0
} | [
{
"pp": "case pos\na✝ : PosNum\n⊢ (pos a✝).mod 0 = pos a✝",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Num",
"eq_self",
"Num.pos",
"of_eq_true",
"Eq"
],
"usedFVars": [
"a✝"
],
"usedGoals": []
}
] | [] | simp [Num.mod] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Num.ZNum | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 20
} | {
"line": 594,
"column": 0
} | [
{
"pp": "case pos\na✝ : PosNum\n⊢ (pos a✝).mod 0 = pos a✝",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Num",
"eq_self",
"Num.pos",
"of_eq_true",
"Eq"
],
"usedFVars": [
"a✝"
],
"usedGoals": []
}
] | [] | simp [Num.mod] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.ZNum | {
"line": 592,
"column": 6
} | {
"line": 592,
"column": 20
} | {
"line": 594,
"column": 0
} | [
{
"pp": "case pos\na✝ : PosNum\n⊢ (pos a✝).mod 0 = pos a✝",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"Num",
"eq_self",
"Num.pos",
"of_eq_true",
"Eq"
],
"usedFVars": [
"a✝"
],
"usedGoals": []
}
] | [] | simp [Num.mod] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Num.ZNum | {
"line": 681,
"column": 10
} | {
"line": 681,
"column": 30
} | {
"line": 681,
"column": 31
} | [
{
"pp": "n : PosNum\nd : ZNum\n⊢ ↑(Num.pos n % d.abs) = ↑(pos n) % ↑d",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"castZNum",
"Nat.instMulZeroClass",
"Nat.instOne",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"ZNum.abs",
"... | [
"n : PosNum\nd : ZNum\n⊢ ↑↑(Num.pos n % d.abs) = ↑(pos n) % ↑d"
] | ← Num.to_nat_to_int, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.ZNum | {
"line": 685,
"column": 10
} | {
"line": 685,
"column": 30
} | {
"line": 685,
"column": 31
} | [
{
"pp": "n : PosNum\nd : ZNum\n⊢ ↑d.abs - ↑(n.pred' % d.abs).succ = ↑(neg n) % ↑d",
"ppTerm": "?m.45",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"Nat.instMulZeroClass",
"Nat.instOne",
"AddMonoid.toAddSemigroup",
... | [
"n : PosNum\nd : ZNum\n⊢ ↑↑d.abs - ↑(n.pred' % d.abs).succ = ↑(neg n) % ↑d"
] | ← Num.to_nat_to_int, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Num.ZNum | {
"line": 685,
"column": 41
} | {
"line": 685,
"column": 61
} | {
"line": 685,
"column": 62
} | [
{
"pp": "n : PosNum\nd : ZNum\n⊢ ↑↑d.abs - ↑(n.pred' % d.abs).succ = -↑n % ↑d",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"castZNum",
"castPosNum",
"Nat.instMulZeroClass",
"Nat.instOne",
"AddMonoid.toAd... | [
"n : PosNum\nd : ZNum\n⊢ ↑↑d.abs - ↑↑(n.pred' % d.abs).succ = -↑n % ↑d"
] | ← Num.to_nat_to_int, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Ordmap.Ordset | {
"line": 324,
"column": 4
} | {
"line": 325,
"column": 86
} | {
"line": 327,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u_2\nl r : Ordnode α\nr' : ℕ\nhr : r.size.dist r' ≤ 1\nleft✝ : l.size ≤ delta * r'\nh₂ : r' ≤ delta * l.size\n⊢ r.size ≤ 3 * (l.size + 1)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.mul_succ",
"Nat.instIsOrderedAddMono... | [] | rw [Nat.mul_succ]
exact le_trans (Nat.dist_tri_right' _ _) (add_le_add h₂ (le_trans hr (by decide))) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Ordset | {
"line": 324,
"column": 4
} | {
"line": 325,
"column": 86
} | {
"line": 327,
"column": 0
} | [
{
"pp": "case inr.inr\nα : Type u_2\nl r : Ordnode α\nr' : ℕ\nhr : r.size.dist r' ≤ 1\nleft✝ : l.size ≤ delta * r'\nh₂ : r' ≤ delta * l.size\n⊢ r.size ≤ 3 * (l.size + 1)",
"ppTerm": "?inr.inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.mul_succ",
"Nat.instIsOrderedAddMono... | [] | rw [Nat.mul_succ]
exact le_trans (Nat.dist_tri_right' _ _) (add_le_add h₂ (le_trans hr (by decide))) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Ordmap.Invariants | {
"line": 548,
"column": 4
} | {
"line": 551,
"column": 69
} | {
"line": 553,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : LE α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ (Ordnode.insert x (node size✝ l y r)).dual = Ordnode.insert x (node size✝ l y r).dual",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": ... | [] | have : @cmpLE αᵒᵈ _ _ x y = cmpLE y x := rfl
rw [Ordnode.insert, dual, Ordnode.insert, this, ← cmpLE_swap x y]
cases cmpLE x y <;>
simp [Ordering.swap, dual_balanceL, dual_balanceR, dual_insert] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Ordmap.Invariants | {
"line": 548,
"column": 4
} | {
"line": 551,
"column": 69
} | {
"line": 553,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : LE α\ninst✝¹ : Std.Total fun x1 x2 ↦ x1 ≤ x2\ninst✝ : DecidableLE α\nx : α\nsize✝ : ℕ\nl : Ordnode α\ny : α\nr : Ordnode α\n⊢ (Ordnode.insert x (node size✝ l y r)).dual = Ordnode.insert x (node size✝ l y r).dual",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": ... | [] | have : @cmpLE αᵒᵈ _ _ x y = cmpLE y x := rfl
rw [Ordnode.insert, dual, Ordnode.insert, this, ← cmpLE_swap x y]
cases cmpLE x y <;>
simp [Ordering.swap, dual_balanceL, dual_balanceR, dual_insert] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.PNat.Factors | {
"line": 319,
"column": 4
} | {
"line": 319,
"column": 46
} | {
"line": 320,
"column": 4
} | [
{
"pp": "case mpr\nm n : ℕ+\nh : m ∣ n\n⊢ m.factorMultiset ≤ n.factorMultiset",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PNat.factorMultiset_mul",
"HMul.hMul",
"instDistribLatticePrimeMultiset",
"congrArg",
"instAddCommMonoidPrimeMultiset"... | [
"case mpr\nm n : ℕ+\nh : m ∣ n\n⊢ m.factorMultiset ≤ m.factorMultiset + (n.divExact m).factorMultiset"
] | rw [← mul_div_exact h, factorMultiset_mul] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.PNat.Xgcd | {
"line": 292,
"column": 4
} | {
"line": 292,
"column": 17
} | {
"line": 293,
"column": 4
} | [
{
"pp": "case fst\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (u.y * u.q + ↑u.z) * ↑u.b + u.y * (u.r - 1 + 1) = u.y * ↑u.a + ↑u.z * ↑u.b",
"ppTerm": "?fst",
"assigned"... | [
"case fst\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (u.y * u.q + ↑u.z) * ↑u.b + u.y * u.r = u.y * (u.r + ↑u.b * u.q) + ↑u.z * ↑u.b"
] | rw [← ha, hr] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.PNat.Xgcd | {
"line": 295,
"column": 4
} | {
"line": 295,
"column": 17
} | {
"line": 296,
"column": 4
} | [
{
"pp": "case snd\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (↑u.w * u.q + u.x) * ↑u.b + ↑u.w * (u.r - 1 + 1) = ↑u.w * ↑u.a + u.x * ↑u.b",
"ppTerm": "?snd",
"assigned... | [
"case snd\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := rq_eq u\nhr : u.r - 1 + 1 = u.r := Eq.trans (add_comm (u.r - 1) 1) (add_tsub_cancel_of_le (Nat.pos_of_ne_zero hr✝))\n⊢ (↑u.w * u.q + u.x) * ↑u.b + ↑u.w * u.r = ↑u.w * (u.r + ↑u.b * u.q) + u.x * ↑u.b"
] | rw [← ha, hr] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.PNat.Xgcd | {
"line": 294,
"column": 2
} | {
"line": 296,
"column": 8
} | {
"line": 298,
"column": 0
} | [
{
"pp": "case snd\nu : XgcdType\nhr✝ : u.r ≠ 0\nha : u.r + ↑u.b * u.q = ↑u.a := ⋯\nhr : u.r - 1 + 1 = u.r := ⋯\n⊢ u.step.v.2 = u.v.swap.2",
"ppTerm": "?snd",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"PNat.val",
"Eq.mpr",
"NonAssocSemiring... | [] | · change ((u.w * u.q + u.x) * u.b + u.w * (u.r - 1 + 1) : ℕ) = u.w * u.a + u.x * u.b
rw [← ha, hr]
ring | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Ordmap.Invariants | {
"line": 686,
"column": 24
} | {
"line": 686,
"column": 33
} | {
"line": 686,
"column": 33
} | [
{
"pp": "α : Type u_1\nl : Ordnode α\nx₁ x₂ : α\nr₁ r₂ : Ordnode α\nH : Raised r₁.size r₂.size\n⊢ Raised (l.size + r₁.size + 1) (l.node' x₂ r₂).size",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Ordnode.node'",
"Eq.mpr",
"Ordnode.size_node",
"congrArg",
"id... | [
"α : Type u_1\nl : Ordnode α\nx₁ x₂ : α\nr₁ r₂ : Ordnode α\nH : Raised r₁.size r₂.size\n⊢ Raised (l.size + r₁.size + 1) (l.size + r₂.size + 1)"
] | size_node | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 101,
"column": 6
} | {
"line": 101,
"column": 35
} | {
"line": 101,
"column": 35
} | [
{
"pp": "n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\n⊢ ∀ (a b : (P F).M α), Mcongr a b → Quot.mk Mcongr (g <$$> a) = Quot.mk Mcongr (g <$$> b)",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"instOfNatNat",
"And.casesOn",
"instHAd... | [
"n : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\naa₁ aa₂ : (P F).M α\nr : (P F).M α → (P F).M α → Prop\npr : IsPrecongr r\nra₁a₂ : r aa₁ aa₂\n⊢ Quot.mk Mcongr (g <$$> aa₁) = Quot.mk Mcongr (g <$$> aa₂)"
] | rintro aa₁ aa₂ ⟨r, pr, ra₁a₂⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Data.QPF.Multivariate.Constructions.Cofix | {
"line": 115,
"column": 64
} | {
"line": 115,
"column": 78
} | {
"line": 115,
"column": 78
} | [
{
"pp": "case h.left\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\naa₁ aa₂ : (P F).M α\nr : (P F).M α → (P F).M α → Prop\npr : IsPrecongr r\nra₁a₂✝ : r aa₁ aa₂\nr' : (P F).M β → (P F).M β → Prop := fun b₁ b₂ ↦ ∃ a₁ a₂, r a₁ a₂ ∧ b₁ = g <$$> a₁ ∧ b₂ = g <$$> a₂\nb₁ b₂ : (... | [
"case h.left\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u\nq : MvQPF F\nα β : TypeVec.{u} n\ng : α ⟹ β\naa₁ aa₂ : (P F).M α\nr : (P F).M α → (P F).M α → Prop\npr : IsPrecongr r\nra₁a₂✝ : r aa₁ aa₂\nr' : (P F).M β → (P F).M β → Prop := fun b₁ b₂ ↦ ∃ a₁ a₂, r a₁ a₂ ∧ b₁ = g <$$> a₁ ∧ b₂ = g <$$> a₂\nb₁ b₂ : (P F).M β\na₁... | ← q.P.comp_map | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 105,
"column": 4
} | {
"line": 105,
"column": 29
} | {
"line": 106,
"column": 4
} | [
{
"pp": "case mp\nF : Type u → Type v\nq : QPF F\nα : Type u\np : α → Prop\nx : F α\ny : F (Subtype p)\nhy : Subtype.val <$> y = x\na : (P F).A\nf : (P F).B a → Subtype p\nh : repr y = ⟨a, f⟩\n⊢ ∃ a f, x = abs ⟨a, f⟩ ∧ ∀ (i : (P F).B a), p (f i)",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": ... | [
"case h\nF : Type u → Type v\nq : QPF F\nα : Type u\np : α → Prop\nx : F α\ny : F (Subtype p)\nhy : Subtype.val <$> y = x\na : (P F).A\nf : (P F).B a → Subtype p\nh : repr y = ⟨a, f⟩\n⊢ x = abs ⟨a, fun i ↦ ↑(f i)⟩ ∧ ∀ (i : (P F).B a), p ((fun i ↦ ↑(f i)) i)"
] | use a, fun i => (f i).val | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 202,
"column": 2
} | {
"line": 206,
"column": 67
} | {
"line": 208,
"column": 0
} | [
{
"pp": "F : Type u → Type v\nq : QPF F\nx y : (P F).W\n⊢ Wequiv x y → Wequiv y x",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"QPF.Wequiv.trans",
"PFunctor.A",
"QPF.Wequiv.rec",
"PFunctor.B",
"PFunctor.W",
"QPF.Wequiv",
"QPF.P",
"QPF.Wequi... | [] | intro h
induction h with
| ind a f f' _ ih => exact Wequiv.ind _ _ _ ih
| abs a f a' f' h => exact Wequiv.abs _ _ _ _ h.symm
| trans x y z _ _ ih₁ ih₂ => exact QPF.Wequiv.trans _ _ _ ih₂ ih₁ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 202,
"column": 2
} | {
"line": 206,
"column": 67
} | {
"line": 208,
"column": 0
} | [
{
"pp": "F : Type u → Type v\nq : QPF F\nx y : (P F).W\n⊢ Wequiv x y → Wequiv y x",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"QPF.Wequiv.trans",
"PFunctor.A",
"QPF.Wequiv.rec",
"PFunctor.B",
"PFunctor.W",
"QPF.Wequiv",
"QPF.P",
"QPF.Wequi... | [] | intro h
induction h with
| ind a f f' _ ih => exact Wequiv.ind _ _ _ ih
| abs a f a' f' h => exact Wequiv.abs _ _ _ _ h.symm
| trans x y z _ _ ih₁ ih₂ => exact QPF.Wequiv.trans _ _ _ ih₂ ih₁ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 257,
"column": 4
} | {
"line": 257,
"column": 21
} | {
"line": 258,
"column": 2
} | [
{
"pp": "case mk\nF : Type u → Type u\nq : QPF F\nα : Type u\ng : F α → α\nx✝¹ : F (Fix F)\nx✝ : Fix F\nx : (P F).W\n⊢ Wequiv (Quotient.lift Wrepr ⋯ (Quot.mk (⇑Wsetoid) x)) x",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"QPF.Wrepr_equiv"
],
"usedFVars": [
"F",
"q... | [] | apply Wrepr_equiv | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 276,
"column": 2
} | {
"line": 276,
"column": 19
} | {
"line": 278,
"column": 0
} | [
{
"pp": "F : Type u → Type u\nq : QPF F\na : (P F).A\nf : (P F).B a → (P F).W\nthis : mk (abs ⟨a, fun x ↦ ⟦f x⟧⟩) = ⟦Wrepr (WType.mk a f)⟧\n⊢ Wsetoid (Wrepr (WType.mk a f)) (WType.mk a f)",
"ppTerm": "?m.86",
"assigned": true,
"usedConstants": [
"PFunctor.A",
"PFunctor.B",
"QPF.Wre... | [] | apply Wrepr_equiv | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.Rat.Star | {
"line": 41,
"column": 2
} | {
"line": 41,
"column": 23
} | {
"line": 41,
"column": 24
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = ⊤",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ closure (range fun x ↦ x * x) = ⊤"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Star | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 23
} | {
"line": 60,
"column": 24
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = nonneg ℚ",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"⊢ closure (range fun x ↦ x * x) = nonneg ℚ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Rat.Star | {
"line": 59,
"column": 92
} | {
"line": 60,
"column": 75
} | {
"line": 62,
"column": 0
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = nonneg ℚ",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Nat.instMulZeroClass",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"even_two",
"AddMonoid.toAddZeroClass",
"Rat",
"Rat.instAddLeftMono",... | [] | by
simpa only [sq] using addSubmonoid_closure_range_pow two_ne_zero even_two | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.QPF.Univariate.Basic | {
"line": 619,
"column": 2
} | {
"line": 623,
"column": 12
} | {
"line": 624,
"column": 2
} | [
{
"pp": "case mp\nF : Type u → Type u\nq : QPF F\nh : IsUniform\nα : Type u\nx : F α\np : α → Prop\na : (P F).A\nf : (P F).B a → α\n⊢ (∃ a_1 f_1, abs ⟨a, f⟩ = abs ⟨a_1, f_1⟩ ∧ ∀ (i : (P F).B a_1), p (f_1 i)) → ∀ u ∈ supp (abs ⟨a, f⟩), p u",
"ppTerm": "?mp",
"assigned": true,
"usedConstants": [
... | [
"case mpr\nF : Type u → Type u\nq : QPF F\nh : IsUniform\nα : Type u\nx : F α\np : α → Prop\na : (P F).A\nf : (P F).B a → α\n⊢ (∀ u ∈ supp (abs ⟨a, f⟩), p u) → ∃ a_2 f_1, abs ⟨a, f⟩ = abs ⟨a_2, f_1⟩ ∧ ∀ (i : (P F).B a_2), p (f_1 i)"
] | · rintro ⟨a', f', abseq, hf⟩ u
rw [supp_eq_of_isUniform h, h _ _ _ _ abseq]
rintro ⟨i, _, hi⟩
rw [← hi]
apply hf | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Set.Enumerate | {
"line": 68,
"column": 6
} | {
"line": 70,
"column": 17
} | {
"line": 72,
"column": 0
} | [
{
"pp": "case some\nα : Type u_1\nsel : Set α → Option α\nh_sel : ∀ (s : Set α) (a : α), sel s = some a → a ∈ s\ns : Set α\nn : ℕ\na a' : α\nh : sel s = some a'\n⊢ (do\n let a ← some a'\n enumerate sel (s \\ {a}) n) =\n some a →\n a ∈ s",
"ppTerm": "?some",
"assigned": true,
"u... | [] | exact fun h' : enumerate sel (s \ {a'}) n = some a ↦
have : a ∈ s \ {a'} := enumerate_mem h_sel h'
this.left | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.WSeq.Basic | {
"line": 250,
"column": 20
} | {
"line": 250,
"column": 31
} | {
"line": 250,
"column": 32
} | [
{
"pp": "case think\nα : Type u\nc : Computation (WSeq α)\nc1 c2 : Computation (Option (α × WSeq α))\nh : c1 = c2 ∨ ∃ c, c1 = (flatten c).destruct ∧ c2 = c.bind destruct\nc' : Computation (WSeq α)\n⊢ BisimO (fun c1 c2 ↦ c1 = c2 ∨ ∃ c, c1 = (flatten c).destruct ∧ c2 = c.bind destruct)\n (flatten c'.think).des... | [
"case think\nα : Type u\nc : Computation (WSeq α)\nc1 c2 : Computation (Option (α × WSeq α))\nh : c1 = c2 ∨ ∃ c, c1 = (flatten c).destruct ∧ c2 = c.bind destruct\nc' : Computation (WSeq α)\n⊢ (flatten c').destruct = c'.bind destruct ∨\n ∃ c, (flatten c').destruct = (flatten c).destruct ∧ c'.bind destruct = c.bin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.List | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 31
} | {
"line": 35,
"column": 32
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\nn : ℕ\n⊢ {l | l.length ≤ n}.Finite",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Finite α\nn : ℕ\n⊢ {l | l.length ≤ n}.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 204,
"column": 48
} | {
"line": 204,
"column": 70
} | {
"line": 204,
"column": 71
} | [
{
"pp": "α : Type u\nβ : Type v\nR : α → β → Prop\ns✝ : WSeq α\nt✝ : WSeq β\nH : LiftRel R s✝ t✝\nn : ℕ\na✝ : Option (α × WSeq α)\nb✝ : Option (β × WSeq β)\no : LiftRelO R (LiftRel R) a✝ b✝\na : α\ns : WSeq α\nb : β\nt : WSeq β\nleft✝ : R a b\nh2 : LiftRel R s t\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) (... | [
"α : Type u\nβ : Type v\nR : α → β → Prop\ns✝ : WSeq α\nt✝ : WSeq β\nH : LiftRel R s✝ t✝\nn : ℕ\na✝ : Option (α × WSeq α)\nb✝ : Option (β × WSeq β)\no : LiftRelO R (LiftRel R) a✝ b✝\na : α\ns : WSeq α\nb : β\nt : WSeq β\nleft✝ : R a b\nh2 : LiftRel R s t\n⊢ Computation.LiftRel (LiftRelO R (LiftRel R)) s.destruct t.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 468,
"column": 30
} | {
"line": 468,
"column": 41
} | {
"line": 468,
"column": 42
} | [
{
"pp": "α : Type u\na : α\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get 0\n⊢ a ∈ nil",
"ppTerm": "?m.61",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\na : α\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get 0\n⊢ a ∈ nil"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 468,
"column": 30
} | {
"line": 468,
"column": 41
} | {
"line": 468,
"column": 42
} | [
{
"pp": "α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get (n✝ + 1)\n⊢ a ∈ nil",
"ppTerm": "?m.85",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nm : a ∈ nil.tail\ne : some (some a) = (↑nil.tail).get (n✝ + 1)\n⊢ a ∈ nil"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 469,
"column": 80
} | {
"line": 469,
"column": 91
} | {
"line": 469,
"column": 92
} | [
{
"pp": "α : Type u\na x✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get 0\n⊢ a ∈ s✝",
"ppTerm": "?m.122",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\na x✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get 0\n⊢ a ∈ s✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 469,
"column": 80
} | {
"line": 469,
"column": 91
} | {
"line": 469,
"column": 92
} | [
{
"pp": "α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nx✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get (n✝ + 1)\n⊢ a ∈ s✝",
"ppTerm": "?m.140",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"α : Type u\na : α\nn✝ : ℕ\na✝ : ∀ {s : WSeq α}, a ∈ s.tail → some (some a) = (↑s.tail).get n✝ → a ∈ s\nx✝ : α\ns✝ : WSeq α\nm : a ∈ (cons x✝ s✝).tail\ne : some (some a) = (↑(cons x✝ s✝).tail).get (n✝ + 1)\n⊢ a ∈ s✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Setoid.Partition.Card | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 14
} | {
"line": 66,
"column": 2
} | [
{
"pp": "α : Type u_1\nP : Set (Set α)\nhP : IsPartition P\ns : Set α\nhs : s.Finite\nhst : ∀ (t : Set α), (s ∩ t).Finite\nhst' : ∀ (t : Set α), Nat.card ↑(s ∩ t) = ⋯.toFinset.card\nf : ↑(Function.support fun t ↦ (s ∩ ↑t).ncard) → ↑s := ⋯\nhf : ∀ (t : ↑(Function.support fun t ↦ (s ∩ ↑t).ncard)), ↑↑t ∈ P ∧ ↑(f t... | [
"α : Type u_1\nP : Set (Set α)\nhP : IsPartition P\ns : Set α\nhs : s.Finite\nhst : ∀ (t : Set α), (s ∩ t).Finite\nhst' : ∀ (t : Set α), Nat.card ↑(s ∩ t) = ⋯.toFinset.card\nf : ↑(Function.support fun t ↦ (s ∩ ↑t).ncard) → ↑s :=\n fun x ↦\n match x with\n | ⟨t, ht⟩ => ⟨Exists.choose ⋯, ⋯⟩\nhf : ∀ (t : ↑(Func... | intro t t' h | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Data.WSeq.Relation | {
"line": 376,
"column": 8
} | {
"line": 376,
"column": 19
} | {
"line": 376,
"column": 20
} | [
{
"pp": "case some.some\nα : Type u\nβ : Type v\nR : α → β → Prop\ns1✝ s2 : WSeq α\nt1✝ t2 : WSeq β\nh1 : LiftRel R s1✝ t1✝\nh2 : LiftRel R s2 t2\ns✝ : WSeq α\nt✝ : WSeq β\nh✝¹ : (fun s t ↦ LiftRel R s t ∨ ∃ s1 t1, s = s1.append s2 ∧ t = t1.append t2 ∧ LiftRel R s1 t1) s✝ t✝\ns1 : WSeq α\nt1 : WSeq β\nh✝ : Lift... | [
"case some.some\nα : Type u\nβ : Type v\nR : α → β → Prop\ns1✝ s2 : WSeq α\nt1✝ t2 : WSeq β\nh1 : LiftRel R s1✝ t1✝\nh2 : LiftRel R s2 t2\ns✝ : WSeq α\nt✝ : WSeq β\nh✝¹ : (fun s t ↦ LiftRel R s t ∨ ∃ s1 t1, s = s1.append s2 ∧ t = t1.append t2 ∧ LiftRel R s1 t1) s✝ t✝\ns1 : WSeq α\nt1 : WSeq β\nh✝ : LiftRel R s1 t1\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sigma.Interval | {
"line": 132,
"column": 4
} | {
"line": 132,
"column": 24
} | {
"line": 134,
"column": 0
} | [
{
"pp": "case inr\nι : Type u_1\nα : ι → Type u_2\ninst✝¹ : (i : ι) → Preorder (α i)\ninst✝ : (i : ι) → LocallyFiniteOrderTop (α i)\nx✝¹ x✝ : (i : ι) × α i\ni : ι\na : α i\nj : ι\nb : α j\nhij : i ≠ j\n⊢ (⟨j, b⟩ ∈\n match ⟨i, a⟩ with\n | ⟨i, a⟩ => Finset.map (Embedding.sigmaMk i) (Ioi a)) ↔\n ⟨i, a... | [] | · simp [hij, lt_def] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.String.Basic | {
"line": 63,
"column": 17
} | {
"line": 63,
"column": 28
} | {
"line": 63,
"column": 29
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := ofList s₂.s.toList, i... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := s₂.s, i := s₂.i }.hasNext = true"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 63,
"column": 45
} | {
"line": 63,
"column": 56
} | {
"line": 63,
"column": 57
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := ofList s₁.s.toList, i... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := s₁.s, i := s₁.i }.hasNext = true"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 66,
"column": 6
} | {
"line": 66,
"column": 78
} | {
"line": 66,
"column": 79
} | [
{
"pp": "case case1.hc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ { s := ofList... | [
"case case1.hc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : s₁.curr = s₂.curr\nih :\n ltb { s := ofList (c :: s₁.next.s.toList), i := s₁.next.i + c }\n { s := ofList (c :: s₂.next.s.toList), i := s₂.next.i + c } =\n ltb s₁.next s₂.next\n⊢ Pos.Raw.get s₁.s s₁.i = P... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 69,
"column": 17
} | {
"line": 69,
"column": 28
} | {
"line": 69,
"column": 29
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := ofList s₂.s.toList, i := s₂.i }.hasNext = true",
"ppTerm": "?m.131",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := s₂.s, i := s₂.i }.hasNext = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 69,
"column": 45
} | {
"line": 69,
"column": 56
} | {
"line": 69,
"column": 57
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := ofList s₁.s.toList, i := s₁.i }.hasNext = true",
"ppTerm": "?m.144",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ { s := s₁.s, i := s₁.i }.hasNext = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 71,
"column": 6
} | {
"line": 71,
"column": 78
} | {
"line": 71,
"column": 79
} | [
{
"pp": "case case2.hnc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ ¬{ s := ofList (c :: s₁.s.toList), i := s₁.i + c }.curr = { s := ofList (c :: s₂.s.toList), i := s₂.i + c }.curr",
"ppTerm": "?case2.hnc",
"assigned": true,
"usedCons... | [
"case case2.hnc\nc : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : s₁.hasNext = true\nh : ¬s₁.curr = s₂.curr\n⊢ ¬Pos.Raw.get s₁.s s₁.i = Pos.Raw.get s₂.s s₂.i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 74,
"column": 17
} | {
"line": 74,
"column": 28
} | {
"line": 74,
"column": 29
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ { s := ofList s₂.s.toList, i := s₂.i }.hasNext = true",
"ppTerm": "?m.186",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
"String",
"... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ { s := s₂.s, i := s₂.i }.hasNext = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 74,
"column": 45
} | {
"line": 74,
"column": 56
} | {
"line": 74,
"column": 57
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ ¬{ s := ofList s₁.s.toList, i := s₁.i }.hasNext = true",
"ppTerm": "?m.199",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
"String",
... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : s₂.hasNext = true\nh₂ : ¬s₁.hasNext = true\n⊢ { s := s₁.s, i := s₁.i }.hasNext = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.String.Basic | {
"line": 76,
"column": 62
} | {
"line": 76,
"column": 73
} | {
"line": 76,
"column": 74
} | [
{
"pp": "c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : ¬s₂.hasNext = true\n⊢ ¬{ s := ofList s₂.s.toList, i := s₂.i }.hasNext = true",
"ppTerm": "?m.227",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"String.Legacy.Iterator.mk",
"String",
"String.Legacy.Iterator.... | [
"c : Char\ns₁ s₂ : Legacy.Iterator\nh₁ : ¬s₂.hasNext = true\n⊢ { s := s₂.s, i := s₂.i }.hasNext = false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 812,
"column": 20
} | {
"line": 812,
"column": 31
} | {
"line": 812,
"column": 32
} | [
{
"pp": "case bisim.nil.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct (nil.append (map f (cons s S).join))) (Seq.destruct (nil.append (map (map f) ... | [
"case bisim.nil.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ ∃ s_1 S_1,\n (map f s).append (map f S.join) = s_1.append (map f S_1.join) ∧\n (map f s).append (map (map f) S).join = s_1.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 813,
"column": 19
} | {
"line": 813,
"column": 30
} | {
"line": 813,
"column": 31
} | [
{
"pp": "case bisim.nil.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct (nil.append (map f S.think.join))) (Seq.destruct (nil.append (map (map f) S.think).join))",
"ppTerm":... | [
"case bisim.nil.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\n⊢ ∃ s S_1, map f S.join = s.append (map f S_1.join) ∧ (map (map f) S).join = s.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 814,
"column": 6
} | {
"line": 814,
"column": 17
} | {
"line": 814,
"column": 18
} | [
{
"pp": "case bisim.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\nx✝ : β\ns✝ : WSeq β\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct ((cons x✝ s✝).append (map f S.join))) (Seq.destruct ((cons x✝ s✝).append (map (map f) S).... | [
"case bisim.cons\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\nx✝ : β\ns✝ : WSeq β\n⊢ ∃ s S_1,\n s✝.append (map f S.join) = s.append (map f S_1.join) ∧\n s✝.append (map (map f) S).join = s.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Basic | {
"line": 815,
"column": 6
} | {
"line": 815,
"column": 17
} | {
"line": 815,
"column": 18
} | [
{
"pp": "case bisim.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\ns✝ : WSeq β\n⊢ Seq.BisimO (fun s1 s2 ↦ ∃ s S, s1 = s.append (map f S.join) ∧ s2 = s.append (map (map f) S).join)\n (Seq.destruct (s✝.think.append (map f S.join))) (Seq.destruct (s✝.think.append (map (map f) S).join))",
"p... | [
"case bisim.think\nα : Type u\nβ : Type v\nf : α → β\nS✝ S : WSeq (WSeq α)\ns✝ : WSeq β\n⊢ ∃ s S_1,\n s✝.append (map f S.join) = s.append (map f S_1.join) ∧\n s✝.append (map (map f) S).join = s.append (map (map f) S_1).join"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 440,
"column": 8
} | {
"line": 440,
"column": 19
} | {
"line": 440,
"column": 20
} | [
{
"pp": "α : Type u\nβ : Type v\nR : α → β → Prop\nS✝ : WSeq (WSeq α)\nT✝ : WSeq (WSeq β)\nh✝ : LiftRel (LiftRel R) S✝ T✝\ns1 : WSeq α\ns2 : WSeq β\nx✝ :\n (fun s1 s2 ↦ ∃ s t S T, s1 = s.append S.join ∧ s2 = t.append T.join ∧ LiftRel R s t ∧ LiftRel (LiftRel R) S T) s1 s2\ns✝ : WSeq α\nt✝ : WSeq β\nS : WSeq (W... | [
"α : Type u\nβ : Type v\nR : α → β → Prop\nS✝ : WSeq (WSeq α)\nT✝ : WSeq (WSeq β)\nh✝ : LiftRel (LiftRel R) S✝ T✝\ns1 : WSeq α\ns2 : WSeq β\nx✝ :\n (fun s1 s2 ↦ ∃ s t S T, s1 = s.append S.join ∧ s2 = t.append T.join ∧ LiftRel R s t ∧ LiftRel (LiftRel R) S T) s1 s2\ns✝ : WSeq α\nt✝ : WSeq β\nS : WSeq (WSeq α)\nT : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 468,
"column": 56
} | {
"line": 468,
"column": 73
} | {
"line": 468,
"column": 74
} | [
{
"pp": "α : Type u\ns : WSeq α\n⊢ (ret s).join ~ʷ s",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Stream'.WSeq.join",
"congrArg",
"Stream'.WSeq.cons",
"Stream'.WSeq.ofList_cons",
"id",
"Stream'.WSeq.join_cons",
"Stream'.WSeq.thin... | [
"α : Type u\ns : WSeq α\n⊢ s.think ~ʷ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Parallel | {
"line": 277,
"column": 39
} | {
"line": 277,
"column": 50
} | {
"line": 277,
"column": 51
} | [
{
"pp": "case inr.nil\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (L... | [
"case inr.nil\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (List.map (map... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Parallel | {
"line": 277,
"column": 39
} | {
"line": 277,
"column": 50
} | {
"line": 277,
"column": 51
} | [
{
"pp": "case inr.cons\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (... | [
"case inr.cons\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (List.map (ma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Seq.Parallel | {
"line": 277,
"column": 39
} | {
"line": 277,
"column": 50
} | {
"line": 277,
"column": 51
} | [
{
"pp": "case inr.think\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap ... | [
"case inr.think\nα : Type u\nβ : Type v\nf : α → β\nS : WSeq (Computation α)\nc1 c2 : Computation β\nh : ∃ l S, c1 = map f (corec parallel.aux1 (l, S)) ∧ c2 = corec parallel.aux1 (List.map (map f) l, WSeq.map (map f) S)\nl : List (Computation α)\nthis : parallel.aux2 (List.map (map f) l) = lmap f (rmap (List.map (m... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Sym.Sym2.Finsupp | {
"line": 33,
"column": 2
} | {
"line": 33,
"column": 13
} | {
"line": 33,
"column": 14
} | [
{
"pp": "case mk\nα : Type u_1\nM₀ : Type u_2\ninst✝ : CommMonoidWithZero M₀\nf : α →₀ M₀\np : Sym2 α\na b : α\nhp : ¬f a * f b = 0\n⊢ Quot.mk (Rel α) (a, b) ∈ f.support.sym2",
"ppTerm": "?mk",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Sym2.Rel",
... | [
"case mk\nα : Type u_1\nM₀ : Type u_2\ninst✝ : CommMonoidWithZero M₀\nf : α →₀ M₀\np : Sym2 α\na b : α\nhp : ¬f a * f b = 0\n⊢ ¬f a = 0 ∧ ¬f b = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 515,
"column": 18
} | {
"line": 515,
"column": 29
} | {
"line": 515,
"column": 30
} | [
{
"pp": "case nil.cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nT : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ LiftRelAux (LiftRelO Eq fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join... | [
"case nil.cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nT : WSeq (WSeq α)\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ ∃ s_1 S_1 T_1,\n (s.append (S.append T).join).destruct = (s_1.append (S_1.append T_1).join).destruct ∧\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 517,
"column": 16
} | {
"line": 517,
"column": 27
} | {
"line": 517,
"column": 28
} | [
{
"pp": "case cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\na : α\ns : WSeq α\n⊢ LiftRelAux (LiftRelO Eq fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join... | [
"case cons\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\na : α\ns : WSeq α\n⊢ ∃ s_1 S_1 T_1,\n s.append (S.append T).join = s_1.append (S_1.append T_1).join ∧\n s.append (S.join.append T.join) = s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 518,
"column": 15
} | {
"line": 518,
"column": 26
} | {
"line": 518,
"column": 27
} | [
{
"pp": "case think\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\ns : WSeq α\n⊢ LiftRelAux (LiftRelO Eq fun s1 s2 ↦ ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join))\n ... | [
"case think\nα : Type u\nS✝ T✝ : WSeq (WSeq α)\ns1 s2 : WSeq α\nh : ∃ s S T, s1 = s.append (S.append T).join ∧ s2 = s.append (S.join.append T.join)\nS T : WSeq (WSeq α)\ns : WSeq α\n⊢ ∃ s_1 S_1 T_1,\n (s.append (S.append T).join).destruct = (s_1.append (S_1.append T_1).join).destruct ∧\n (s.append (S.join.a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 561,
"column": 22
} | {
"line": 561,
"column": 33
} | {
"line": 561,
"column": 34
} | [
{
"pp": "case nil.cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ LiftRelAux\n (LiftRelO... | [
"case nil.cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\nS : WSeq (WSeq α)\n⊢ ∃ s_1 S_1 SS_1,\n (s.append (S.app... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 563,
"column": 20
} | {
"line": 563,
"column": 31
} | {
"line": 563,
"column": 32
} | [
{
"pp": "case cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\na : α\ns : WSeq α\n⊢ LiftRelAux\n (LiftR... | [
"case cons\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\na : α\ns : WSeq α\n⊢ ∃ s_1 S_1 SS_1,\n s.append (S.a... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Relation | {
"line": 564,
"column": 19
} | {
"line": 564,
"column": 30
} | {
"line": 564,
"column": 31
} | [
{
"pp": "case think\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\n⊢ LiftRelAux\n (LiftRelO Eq... | [
"case think\nα : Type u\nSS✝ : WSeq (WSeq (WSeq α))\ns1 s2 : WSeq α\nh : ∃ s S SS, s1 = s.append (S.append SS.join).join ∧ s2 = s.append (S.join.append (map join SS).join)\nc1 c2 : Computation (Option (α × WSeq α))\nS : WSeq (WSeq α)\nSS : WSeq (WSeq (WSeq α))\ns : WSeq α\n⊢ ∃ s_1 S_1 SS_1,\n (s.append (S.append... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.Mem | {
"line": 71,
"column": 2
} | {
"line": 71,
"column": 71
} | {
"line": 71,
"column": 72
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nb : β\nv : Vector α 0\nf : α → β\n⊢ ¬b ∈ (map f v).toList",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.Vector.map",
"List.Vector.eq_nil",
"List.Vector",
"Membership.mem",
"id",
... | [
"α : Type u_1\nβ : Type u_2\nb : β\nv : Vector α 0\nf : α → β\n⊢ ¬b ∈ []"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.MapLemmas | {
"line": 64,
"column": 67
} | {
"line": 64,
"column": 78
} | {
"line": 64,
"column": 79
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ : Type u_5\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\ns : σ\ns₁ : σ₁\ns₂ : σ₂\nxs : Vector α n\nf₁✝ : β → σ₁ → σ₁ × γ\nf₂✝ : α → σ₂ → σ₂ × β\np : β → Prop\nf₁ : (b : β) → p b → γ\nf₂ : α → β\nH : ∀ (x : β), x ∈ (map f₂ xs).toList → p x\... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nζ : Type u_4\nσ : Type u_5\nσ₁ : Type u_6\nσ₂ : Type u_7\nφ : Type u_8\nn : ℕ\ns : σ\ns₁ : σ₁\ns₂ : σ₂\nxs : Vector α n\nf₁✝ : β → σ₁ → σ₁ × γ\nf₂✝ : α → σ₂ → σ₂ × β\np : β → Prop\nf₁ : (b : β) → p b → γ\nf₂ : α → β\nH : ∀ (x : β), x ∈ (map f₂ xs).toList → p x\n⊢ ∀ (x : α)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 55
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f xs = (mapAccumr (fun x x_1 ↦ ((), f x)) xs ()).2",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unit.unit",
"List.Vector.mapAccumr",
"List.Vector.mapAccumr_snoc",
"congrArg",
"Li... | [] | induction xs using Vector.revInductionOn <;> simp_all | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 55
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f xs = (mapAccumr (fun x x_1 ↦ ((), f x)) xs ()).2",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unit.unit",
"List.Vector.mapAccumr",
"List.Vector.mapAccumr_snoc",
"congrArg",
"Li... | [] | induction xs using Vector.revInductionOn <;> simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Vector.MapLemmas | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 55
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nn : ℕ\nxs : Vector α n\nf : α → β\n⊢ map f xs = (mapAccumr (fun x x_1 ↦ ((), f x)) xs ()).2",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Unit.unit",
"List.Vector.mapAccumr",
"List.Vector.mapAccumr_snoc",
"congrArg",
"Li... | [] | induction xs using Vector.revInductionOn <;> simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Vector.MapLemmas | {
"line": 252,
"column": 2
} | {
"line": 252,
"column": 26
} | {
"line": 253,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (s : σ), s ∈ S → (f a s).1 ∈ S\nout : ∀ (a : α) (s s' : σ), s ∈ S → s' ∈ S → (f a s).2 = (f a s').2\n⊢ ∃ R, R s₀ () ∧ ∀ {s : σ} {q : Unit} (a : α), R s q → R (f a s).... | [
"case right\nα : Type u_1\nβ : Type u_2\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nf : α → σ → σ × β\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (s : σ), s ∈ S → (f a s).1 ∈ S\nout : ∀ (a : α) (s s' : σ), s ∈ S → s' ∈ S → (f a s).2 = (f a s').2\n⊢ ∀ {s : σ} {q : Unit} (a : α), s ∈ S → (f a s).1 ∈ S ∧ (f a s).2... | use fun s _ => s ∈ S, h₀ | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Data.Vector.MapLemmas | {
"line": 270,
"column": 2
} | {
"line": 270,
"column": 26
} | {
"line": 271,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × γ\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (b : β) (s : σ), s ∈ S → (f a b s).1 ∈ S\nout : ∀ (a : α) (b : β) (s s' : σ), s ∈ S → s' ∈ S → (f a b s).2 = (f a b s').2\n⊢ ∃ R,\n... | [
"case right\nα : Type u_1\nβ : Type u_2\nγ : Type u_3\nσ : Type u_5\nn : ℕ\nxs : Vector α n\nys : Vector β n\nf : α → β → σ → σ × γ\ns₀ : σ\nS : Set σ\nh₀ : s₀ ∈ S\nclosure : ∀ (a : α) (b : β) (s : σ), s ∈ S → (f a b s).1 ∈ S\nout : ∀ (a : α) (b : β) (s s' : σ), s ∈ S → s' ∈ S → (f a b s).2 = (f a b s').2\n⊢ ∀ {s :... | use fun s _ => s ∈ S, h₀ | Mathlib.Tactic._aux_Mathlib_Tactic_Use___elabRules_Mathlib_Tactic_useSyntax_1 | Mathlib.Tactic.useSyntax |
Mathlib.Data.Sum.Interval | {
"line": 189,
"column": 2
} | {
"line": 189,
"column": 28
} | {
"line": 190,
"column": 2
} | [
{
"pp": "case refine_4.inl.inr\nα₁ : Type u_1\nα₂ : Type u_2\nβ₁ : Type u_3\nβ₂ : Type u_4\nγ₁ : Type u_5\nγ₂ : Type u_6\nf₁ : α₁ → β₁ → Finset γ₁\nf₂ : α₂ → β₂ → Finset γ₂\ng₁ : α₁ → β₂ → Finset γ₁\ng₂ : α₁ → β₂ → Finset γ₂\nval✝¹ : α₁\nval✝ : β₂\nh :\n (∀ (a₁ : α₁) (b₁ : β₁), inl val✝¹ = inl a₁ → inr val✝ = ... | [
"case refine_4.inr.inl\nα₁ : Type u_1\nα₂ : Type u_2\nβ₁ : Type u_3\nβ₂ : Type u_4\nγ₁ : Type u_5\nγ₂ : Type u_6\nf₁ : α₁ → β₁ → Finset γ₁\nf₂ : α₂ → β₂ → Finset γ₂\ng₁ : α₁ → β₂ → Finset γ₁\ng₂ : α₁ → β₂ → Finset γ₂\nval✝¹ : α₂\nval✝ : β₁\nh :\n (∀ (a₁ : α₁) (b₁ : β₁), inr val✝¹ = inl a₁ → inl val✝ = inl b₁ → f₁ ... | · simp [h.2.1 _ _ rfl rfl] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Vector3 | {
"line": 190,
"column": 2
} | {
"line": 190,
"column": 18
} | {
"line": 190,
"column": 19
} | [
{
"pp": "case refine_2\nα : Type u_1\nm n : ℕ\na : α\nt✝ : Vector3 α m\nv : Vector3 α n\ni : Fin2 (n + 1)\ne : n + 1 + m = n + m + 1\nk : ℕ\nb : α\nt : Vector3 α k\nIH : ∀ (x : n + 1 + k = n + k + 1), insert a (t +-+ v) (Eq.recOn x (i.add k)) = Eq.recOn x (t +-+ insert a v i)\nx✝ : n + 1 + (k + 1) = n + (k + 1)... | [
"case refine_2\nα : Type u_1\nm n : ℕ\na : α\nt✝ : Vector3 α m\nv : Vector3 α n\ni : Fin2 (n + 1)\ne : n + 1 + m = n + m + 1\nk : ℕ\nb : α\nt : Vector3 α k\nIH : ∀ (x : n + 1 + k = n + k + 1), insert a (t +-+ v) (Eq.recOn x (i.add k)) = Eq.recOn x (t +-+ insert a v i)\nx✝ : n + 1 + (k + 1) = n + (k + 1) + 1\ne' : n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector3 | {
"line": 254,
"column": 6
} | {
"line": 254,
"column": 17
} | {
"line": 254,
"column": 18
} | [
{
"pp": "case refine_2.refine_1\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\n⊢ p a",
"ppTerm": "?refine_2.refine_1",
"assigned": false,
"usedConstants": [],
"usedFVa... | [
"case refine_2.refine_1\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\n⊢ p a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Vector3 | {
"line": 255,
"column": 6
} | {
"line": 255,
"column": 17
} | {
"line": 255,
"column": 18
} | [
{
"pp": "case refine_2.refine_2\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\ni : Fin2 n\n⊢ p (v i)",
"ppTerm": "?refine_2.refine_2",
"assigned": false,
"usedConstants": ... | [
"case refine_2.refine_2\nα : Type u_1\nn✝ : ℕ\np : α → Prop\nv✝ : Vector3 α n✝\nn : ℕ\na : α\nv : Vector3 α n\nIH : VectorAllP p v ↔ ∀ (i : Fin2 n), p (v i)\nh : ∀ (i : Fin2 (n + 1)), p ((a :: v) i)\ni : Fin2 n\n⊢ p (v i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SemiconjSup | {
"line": 68,
"column": 14
} | {
"line": 68,
"column": 43
} | {
"line": 68,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → α\nh : IsOrderRightAdjoint f g\ne : β ≃o γ\ny : γ\n⊢ IsLUB {x | (⇑e ∘ f) x ≤ y} ((g ∘ ⇑e.symm) y)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Set.o... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : Preorder β\ninst✝ : Preorder γ\nf : α → β\ng : β → α\nh : IsOrderRightAdjoint f g\ne : β ≃o γ\ny : γ\n⊢ IsLUB {x | e (f x) ≤ y} (g (e.symm y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SemiconjSup | {
"line": 102,
"column": 2
} | {
"line": 102,
"column": 24
} | {
"line": 102,
"column": 25
} | [
{
"pp": "α : Type u_1\nG : Type u_4\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' ↦ (f₁ g')⁻¹ ((f₂ g') x)) (h x)\ng : G\ny : α\nthis : IsLUB (range ((⇑(f₁ g) ∘ fun g' ↦ (f₁ g')⁻¹ ((f₂ g') y)) ∘ ⇑(Equiv.mulRight g))) ((f₁ g) (h y))\n⊢ IsLUB (range f... | [
"α : Type u_1\nG : Type u_4\ninst✝¹ : PartialOrder α\ninst✝ : Group G\nf₁ f₂ : G →* α ≃o α\nh : α → α\nH : ∀ (x : α), IsLUB (range fun g' ↦ (f₁ g')⁻¹ ((f₂ g') x)) (h x)\ng : G\ny : α\nthis : IsLUB (range ((⇑(f₁ g) ∘ fun g' ↦ (f₁ g')⁻¹ ((f₂ g') y)) ∘ ⇑(Equiv.mulRight g))) ((f₁ g) (h y))\n⊢ IsLUB (range fun g' ↦ (f₁ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Defs | {
"line": 243,
"column": 16
} | {
"line": 243,
"column": 27
} | {
"line": 243,
"column": 28
} | [
{
"pp": "case cons\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\na : α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.i... | [
"case cons\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\na : α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.inr (n, s')\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.WSeq.Defs | {
"line": 244,
"column": 15
} | {
"line": 244,
"column": 26
} | {
"line": 244,
"column": 27
} | [
{
"pp": "case think\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.inr (n,... | [
"case think\nα : Type u\ns✝ : WSeq α\ns1 s2 : Computation ℕ\nl : List α\ns : WSeq α\nh :\n s1 =\n Computation.corec\n (fun x ↦\n match x with\n | (n, s) =>\n match Seq.destruct s with\n | none => Sum.inl n\n | some (none, s') => Sum.inr (n, s')\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Ergodic | {
"line": 63,
"column": 2
} | {
"line": 63,
"column": 41
} | {
"line": 63,
"column": 42
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhfs : f ⁻¹' s = s\n⊢ s =ᵐ[μ] ∅ ∨ s =ᵐ[μ] univ",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhfs : f ⁻¹' s = s\n⊢ s =ᵐ[μ] ∅ ∨ s =ᵐ[μ] univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Dynamics.Ergodic.Ergodic | {
"line": 67,
"column": 2
} | {
"line": 67,
"column": 13
} | {
"line": 67,
"column": 14
} | [
{
"pp": "α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ μ s = 0 ∨ μ sᶜ = 0",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nm : MeasurableSpace α\ns : Set α\nf : α → α\nμ : Measure α\nhf : PreErgodic f μ\nhs : MeasurableSet s\nhs' : f ⁻¹' s = s\n⊢ μ s = 0 ∨ μ sᶜ = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.