path stringlengths 20 108 | imports listlengths 0 20 | full_name stringlengths 1 124 | code stringlengths 15 16.6k | start listlengths 2 2 | end listlengths 2 2 | kind stringclasses 3
values | pid int64 0 249k |
|---|---|---|---|---|---|---|---|
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | GT.gt | @[reducible] def GT.gt {α : Type u} [LT α] (a b : α) : Prop := LT.lt b a | [
1218,
1
] | [
1219,
73
] | commanddeclaration | 100 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | DecidableLT | abbrev DecidableLT (α : Type u) [LT α] := DecidableRel (LT.lt : α → α → Prop) | [
1221,
1
] | [
1222,
78
] | commanddeclaration | 101 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | DecidableLE | abbrev DecidableLE (α : Type u) [LE α] := DecidableRel (LE.le : α → α → Prop) | [
1223,
1
] | [
1224,
78
] | commanddeclaration | 102 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Max | class Max (α : Type u) where
max : α → α → α | [
1226,
1
] | [
1231,
18
] | commanddeclaration | 103 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | maxOfLe | @[inline]
def maxOfLe [LE α] [DecidableRel (@LE.le α _)] : Max α where
max x y := ite (LE.le x y) y x | [
1235,
1
] | [
1241,
33
] | commanddeclaration | 104 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Min | class Min (α : Type u) where
min : α → α → α | [
1243,
1
] | [
1248,
18
] | commanddeclaration | 105 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | minOfLe | @[inline]
def minOfLe [LE α] [DecidableRel (@LE.le α _)] : Min α where
min x y := ite (LE.le x y) x y | [
1252,
1
] | [
1258,
33
] | commanddeclaration | 106 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Trans | class Trans (r : α → β → Sort u) (s : β → γ → Sort v) (t : outParam (α → γ → Sort w)) where
trans : r a b → s b c → t a c | [
1260,
1
] | [
1271,
32
] | commanddeclaration | 107 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HAdd | class HAdd (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hAdd : α → β → γ | [
1281,
1
] | [
1288,
19
] | commanddeclaration | 108 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HSub | class HSub (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hSub : α → β → γ | [
1290,
1
] | [
1298,
19
] | commanddeclaration | 109 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HMul | class HMul (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hMul : α → β → γ | [
1300,
1
] | [
1307,
19
] | commanddeclaration | 110 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HDiv | class HDiv (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hDiv : α → β → γ | [
1309,
1
] | [
1325,
19
] | commanddeclaration | 111 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HMod | class HMod (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hMod : α → β → γ | [
1327,
1
] | [
1336,
19
] | commanddeclaration | 112 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HPow | class HPow (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hPow : α → β → γ | [
1338,
1
] | [
1345,
19
] | commanddeclaration | 113 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HAppend | class HAppend (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hAppend : α → β → γ | [
1347,
1
] | [
1354,
22
] | commanddeclaration | 114 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HOrElse | class HOrElse (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hOrElse : α → (Unit → β) → γ | [
1356,
1
] | [
1366,
31
] | commanddeclaration | 115 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HAndThen | class HAndThen (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hAndThen : α → (Unit → β) → γ | [
1368,
1
] | [
1378,
32
] | commanddeclaration | 116 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HAnd | class HAnd (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hAnd : α → β → γ | [
1380,
1
] | [
1384,
19
] | commanddeclaration | 117 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HXor | class HXor (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hXor : α → β → γ | [
1386,
1
] | [
1390,
19
] | commanddeclaration | 118 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HOr | class HOr (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hOr : α → β → γ | [
1392,
1
] | [
1396,
18
] | commanddeclaration | 119 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HShiftLeft | class HShiftLeft (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hShiftLeft : α → β → γ | [
1398,
1
] | [
1405,
25
] | commanddeclaration | 120 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HShiftRight | class HShiftRight (α : Type u) (β : Type v) (γ : outParam (Type w)) where
hShiftRight : α → β → γ | [
1407,
1
] | [
1413,
26
] | commanddeclaration | 121 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Zero | class Zero (α : Type u) where
zero : α | [
1415,
1
] | [
1418,
11
] | commanddeclaration | 122 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | One | class One (α : Type u) where
one : α | [
1420,
1
] | [
1423,
10
] | commanddeclaration | 123 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Add | class Add (α : Type u) where
add : α → α → α | [
1425,
1
] | [
1428,
18
] | commanddeclaration | 124 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Sub | class Sub (α : Type u) where
sub : α → α → α | [
1430,
1
] | [
1433,
18
] | commanddeclaration | 125 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Mul | class Mul (α : Type u) where
mul : α → α → α | [
1435,
1
] | [
1438,
18
] | commanddeclaration | 126 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Neg | class Neg (α : Type u) where
neg : α → α | [
1440,
1
] | [
1447,
14
] | commanddeclaration | 127 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Div | class Div (α : Type u) where
div : α → α → α | [
1449,
1
] | [
1452,
18
] | commanddeclaration | 128 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Mod | class Mod (α : Type u) where
mod : α → α → α | [
1454,
1
] | [
1457,
18
] | commanddeclaration | 129 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Dvd | class Dvd (α : Type _) where
dvd : α → α → Prop | [
1459,
1
] | [
1462,
21
] | commanddeclaration | 130 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Pow | class Pow (α : Type u) (β : Type v) where
pow : α → β → α | [
1464,
1
] | [
1476,
18
] | commanddeclaration | 131 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | NatPow | class NatPow (α : Type u) where
protected pow : α → Nat → α | [
1478,
1
] | [
1486,
30
] | commanddeclaration | 132 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HomogeneousPow | class HomogeneousPow (α : Type u) where
protected pow : α → α → α | [
1488,
1
] | [
1498,
28
] | commanddeclaration | 133 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Append | class Append (α : Type u) where
append : α → α → α | [
1500,
1
] | [
1503,
21
] | commanddeclaration | 134 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | OrElse | class OrElse (α : Type u) where
orElse : α → (Unit → α) → α | [
1505,
1
] | [
1512,
31
] | commanddeclaration | 135 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | AndThen | class AndThen (α : Type u) where
andThen : α → (Unit → α) → α | [
1514,
1
] | [
1521,
31
] | commanddeclaration | 136 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | AndOp | class AndOp (α : Type u) where
and : α → α → α | [
1523,
1
] | [
1529,
18
] | commanddeclaration | 137 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Xor | class Xor (α : Type u) where
xor : α → α → α | [
1531,
1
] | [
1534,
18
] | commanddeclaration | 138 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | OrOp | class OrOp (α : Type u) where
or : α → α → α | [
1536,
1
] | [
1542,
17
] | commanddeclaration | 139 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Complement | class Complement (α : Type u) where
complement : α → α | [
1544,
1
] | [
1547,
21
] | commanddeclaration | 140 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ShiftLeft | class ShiftLeft (α : Type u) where
shiftLeft : α → α → α | [
1549,
1
] | [
1552,
24
] | commanddeclaration | 141 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ShiftRight | class ShiftRight (α : Type u) where
shiftRight : α → α → α | [
1554,
1
] | [
1557,
25
] | commanddeclaration | 142 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instHAdd | @[default_instance]
instance instHAdd [Add α] : HAdd α α α where
hAdd a b := Add.add a b | [
1559,
1
] | [
1561,
26
] | commanddeclaration | 143 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instHSub | @[default_instance]
instance instHSub [Sub α] : HSub α α α where
hSub a b := Sub.sub a b | [
1563,
1
] | [
1565,
26
] | commanddeclaration | 144 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instHMul | @[default_instance]
instance instHMul [Mul α] : HMul α α α where
hMul a b := Mul.mul a b | [
1567,
1
] | [
1569,
26
] | commanddeclaration | 145 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instHDiv | @[default_instance]
instance instHDiv [Div α] : HDiv α α α where
hDiv a b := Div.div a b | [
1571,
1
] | [
1573,
26
] | commanddeclaration | 146 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instHMod | @[default_instance]
instance instHMod [Mod α] : HMod α α α where
hMod a b := Mod.mod a b | [
1575,
1
] | [
1577,
26
] | commanddeclaration | 147 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instHPow | @[default_instance]
instance instHPow [Pow α β] : HPow α β α where
hPow a b := Pow.pow a b | [
1579,
1
] | [
1581,
26
] | commanddeclaration | 148 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instPowNat | @[default_instance]
instance instPowNat [NatPow α] : Pow α Nat where
pow a n := NatPow.pow a n | [
1583,
1
] | [
1585,
28
] | commanddeclaration | 149 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Membership | class Membership (α : outParam (Type u)) (γ : Type v) where
mem : γ → α → Prop | [
1629,
1
] | [
1636,
21
] | commanddeclaration | 150 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.add | @[extern "lean_nat_add"]
protected def Nat.add : (@& Nat) → (@& Nat) → Nat
| a, Nat.zero => a
| a, Nat.succ b => Nat.succ (Nat.add a b) | [
1639,
1
] | [
1648,
44
] | commanddeclaration | 151 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instAddNat | instance instAddNat : Add Nat where
add := Nat.add | [
1650,
1
] | [
1651,
17
] | commanddeclaration | 152 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.mul | @[extern "lean_nat_mul"]
protected def Nat.mul : (@& Nat) → (@& Nat) → Nat
| _, 0 => 0
| a, Nat.succ b => Nat.add (Nat.mul a b) a | [
1658,
1
] | [
1667,
45
] | commanddeclaration | 153 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instMulNat | instance instMulNat : Mul Nat where
mul := Nat.mul | [
1669,
1
] | [
1670,
17
] | commanddeclaration | 154 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.pow | @[extern "lean_nat_pow"]
protected def Nat.pow (m : @& Nat) : (@& Nat) → Nat
| 0 => 1
| succ n => Nat.mul (Nat.pow m n) m | [
1673,
1
] | [
1682,
38
] | commanddeclaration | 155 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instNatPowNat | instance instNatPowNat : NatPow Nat := ⟨Nat.pow⟩ | [
1684,
1
] | [
1684,
49
] | commanddeclaration | 156 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.beq | @[extern "lean_nat_dec_eq"]
def Nat.beq : (@& Nat) → (@& Nat) → Bool
| zero, zero => true
| zero, succ _ => false
| succ _, zero => false
| succ n, succ m => beq n m | [
1687,
1
] | [
1698,
30
] | commanddeclaration | 157 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.eq_of_beq_eq_true | theorem Nat.eq_of_beq_eq_true : {n m : Nat} → Eq (beq n m) true → Eq n m | [
1700,
1
] | [
1707,
15
] | commanddeclaration | 158 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.ne_of_beq_eq_false | theorem Nat.ne_of_beq_eq_false : {n m : Nat} → Eq (beq n m) false → Not (Eq n m) | [
1709,
1
] | [
1715,
71
] | commanddeclaration | 159 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.decEq | @[reducible, extern "lean_nat_dec_eq"]
protected def Nat.decEq (n m : @& Nat) : Decidable (Eq n m) :=
match h:beq n m with
| true => isTrue (eq_of_beq_eq_true h)
| false => isFalse (ne_of_beq_eq_false h) | [
1717,
1
] | [
1733,
44
] | commanddeclaration | 160 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.ble | @[extern "lean_nat_dec_le"]
def Nat.ble : @& Nat → @& Nat → Bool
| zero, zero => true
| zero, succ _ => true
| succ _, zero => false
| succ n, succ m => ble n m | [
1738,
1
] | [
1754,
30
] | commanddeclaration | 161 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le | protected inductive Nat.le (n : Nat) : Nat → Prop
| refl : Nat.le n n
| step {m} : Nat.le n m → Nat.le n (succ m) | [
1756,
1
] | [
1763,
46
] | commanddeclaration | 162 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instLENat | instance instLENat : LE Nat where
le := Nat.le | [
1765,
1
] | [
1766,
15
] | commanddeclaration | 163 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.lt | protected def Nat.lt (n m : Nat) : Prop :=
Nat.le (succ n) m | [
1768,
1
] | [
1774,
20
] | commanddeclaration | 164 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instLTNat | instance instLTNat : LT Nat where
lt := Nat.lt | [
1776,
1
] | [
1777,
15
] | commanddeclaration | 165 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.not_succ_le_zero | theorem Nat.not_succ_le_zero : ∀ (n : Nat), LE.le (succ n) 0 → False | [
1779,
1
] | [
1781,
20
] | commanddeclaration | 166 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.not_lt_zero | theorem Nat.not_lt_zero (n : Nat) : Not (LT.lt n 0) | [
1783,
1
] | [
1784,
21
] | commanddeclaration | 167 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.zero_le | theorem Nat.zero_le : (n : Nat) → LE.le 0 n | [
1786,
1
] | [
1788,
38
] | commanddeclaration | 168 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.succ_le_succ | theorem Nat.succ_le_succ : LE.le n m → LE.le (succ n) (succ m) | [
1790,
1
] | [
1792,
50
] | commanddeclaration | 169 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.zero_lt_succ | theorem Nat.zero_lt_succ (n : Nat) : LT.lt 0 (succ n) | [
1794,
1
] | [
1795,
27
] | commanddeclaration | 170 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_step | theorem Nat.le_step (h : LE.le n m) : LE.le n (succ m) | [
1797,
1
] | [
1798,
16
] | commanddeclaration | 171 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_trans | protected theorem Nat.le_trans {n m k : Nat} : LE.le n m → LE.le m k → LE.le n k | [
1800,
1
] | [
1802,
59
] | commanddeclaration | 172 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.lt_trans | protected theorem Nat.lt_trans {n m k : Nat} (h₁ : LT.lt n m) : LT.lt m k → LT.lt n k | [
1804,
1
] | [
1805,
28
] | commanddeclaration | 173 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_succ | theorem Nat.le_succ (n : Nat) : LE.le n (succ n) | [
1807,
1
] | [
1808,
26
] | commanddeclaration | 174 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_succ_of_le | theorem Nat.le_succ_of_le {n m : Nat} (h : LE.le n m) : LE.le n (succ m) | [
1810,
1
] | [
1811,
29
] | commanddeclaration | 175 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_refl | protected theorem Nat.le_refl (n : Nat) : LE.le n n | [
1813,
1
] | [
1814,
14
] | commanddeclaration | 176 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.succ_pos | theorem Nat.succ_pos (n : Nat) : LT.lt 0 (succ n) | [
1816,
1
] | [
1817,
17
] | commanddeclaration | 177 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.pred | @[extern "lean_nat_pred"]
def Nat.pred : (@& Nat) → Nat
| 0 => 0
| succ a => a | [
1820,
1
] | [
1830,
16
] | commanddeclaration | 178 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.pred_le_pred | theorem Nat.pred_le_pred : {n m : Nat} → LE.le n m → LE.le (pred n) (pred m) | [
1832,
1
] | [
1835,
64
] | commanddeclaration | 179 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_of_succ_le_succ | theorem Nat.le_of_succ_le_succ {n m : Nat} : LE.le (succ n) (succ m) → LE.le n m | [
1837,
1
] | [
1838,
15
] | commanddeclaration | 180 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_of_lt_succ | theorem Nat.le_of_lt_succ {m n : Nat} : LT.lt m (succ n) → LE.le m n | [
1840,
1
] | [
1841,
21
] | commanddeclaration | 181 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.eq_or_lt_of_le | protected def Nat.eq_or_lt_of_le : {n m: Nat} → LE.le n m → Or (Eq n m) (LT.lt n m)
| zero, zero, _ => Or.inl rfl
| zero, succ _, _ => Or.inr (Nat.succ_le_succ (Nat.zero_le _))
| succ _, zero, h => absurd h (not_succ_le_zero _)
| succ n, succ m, h =>
have : LE.le n m := Nat.le_of_succ_le_succ h
match Nat.eq_or_lt_of_le this with
| Or.inl h => Or.inl (h ▸ rfl)
| Or.inr h => Or.inr (succ_le_succ h) | [
1845,
1
] | [
1853,
42
] | commanddeclaration | 182 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.lt_or_ge | protected theorem Nat.lt_or_ge (n m : Nat) : Or (LT.lt n m) (GE.ge n m) | [
1855,
1
] | [
1864,
31
] | commanddeclaration | 183 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.not_succ_le_self | theorem Nat.not_succ_le_self : (n : Nat) → Not (LE.le (succ n) n) | [
1866,
1
] | [
1868,
74
] | commanddeclaration | 184 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.lt_irrefl | protected theorem Nat.lt_irrefl (n : Nat) : Not (LT.lt n n) | [
1870,
1
] | [
1871,
25
] | commanddeclaration | 185 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.lt_of_le_of_lt | protected theorem Nat.lt_of_le_of_lt {n m k : Nat} (h₁ : LE.le n m) (h₂ : LT.lt m k) : LT.lt n k | [
1873,
1
] | [
1874,
40
] | commanddeclaration | 186 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_antisymm | protected theorem Nat.le_antisymm {n m : Nat} (h₁ : LE.le n m) (h₂ : LE.le m n) : Eq n m | [
1876,
1
] | [
1879,
72
] | commanddeclaration | 187 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.lt_of_le_of_ne | protected theorem Nat.lt_of_le_of_ne {n m : Nat} (h₁ : LE.le n m) (h₂ : Not (Eq n m)) : LT.lt n m | [
1881,
1
] | [
1884,
51
] | commanddeclaration | 188 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.le_of_ble_eq_true | theorem Nat.le_of_ble_eq_true (h : Eq (Nat.ble n m) true) : LE.le n m | [
1886,
1
] | [
1889,
61
] | commanddeclaration | 189 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.ble_self_eq_true | theorem Nat.ble_self_eq_true : (n : Nat) → Eq (Nat.ble n n) true | [
1891,
1
] | [
1893,
33
] | commanddeclaration | 190 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.ble_succ_eq_true | theorem Nat.ble_succ_eq_true : {n m : Nat} → Eq (Nat.ble n m) true → Eq (Nat.ble n (succ m)) true | [
1895,
1
] | [
1897,
53
] | commanddeclaration | 191 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.ble_eq_true_of_le | theorem Nat.ble_eq_true_of_le (h : LE.le n m) : Eq (Nat.ble n m) true | [
1899,
1
] | [
1902,
64
] | commanddeclaration | 192 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.not_le_of_not_ble_eq_true | theorem Nat.not_le_of_not_ble_eq_true (h : Not (Eq (Nat.ble n m) true)) : Not (LE.le n m) | [
1904,
1
] | [
1905,
48
] | commanddeclaration | 193 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.decLe | @[extern "lean_nat_dec_le"]
instance Nat.decLe (n m : @& Nat) : Decidable (LE.le n m) :=
dite (Eq (Nat.ble n m) true) (fun h => isTrue (Nat.le_of_ble_eq_true h)) (fun h => isFalse (Nat.not_le_of_not_ble_eq_true h)) | [
1907,
1
] | [
1919,
128
] | commanddeclaration | 194 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.decLt | @[extern "lean_nat_dec_lt"]
instance Nat.decLt (n m : @& Nat) : Decidable (LT.lt n m) :=
decLe (succ n) m | [
1921,
1
] | [
1933,
19
] | commanddeclaration | 195 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat.sub | @[extern "lean_nat_sub"]
protected def Nat.sub : (@& Nat) → (@& Nat) → Nat
| a, 0 => a
| a, succ b => pred (Nat.sub a b) | [
1938,
1
] | [
1955,
36
] | commanddeclaration | 196 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instSubNat | instance instSubNat : Sub Nat where
sub := Nat.sub | [
1957,
1
] | [
1958,
17
] | commanddeclaration | 197 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | System.Platform.getNumBits | @[extern "lean_system_platform_nbits"] opaque System.Platform.getNumBits : Unit → Subtype fun (n : Nat) => Or (Eq n 32) (Eq n 64) :=
fun _ => ⟨64, Or.inr rfl⟩ | [
1960,
1
] | [
1969,
28
] | commanddeclaration | 198 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | System.Platform.numBits | def System.Platform.numBits : Nat :=
(getNumBits ()).val | [
1971,
1
] | [
1975,
22
] | commanddeclaration | 199 |
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