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 | [] | id | @[inline] def id {α : Sort u} (a : α) : α := a | [
23,
1
] | [
35,
47
] | commanddeclaration | 0 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Function.comp | @[inline] def Function.comp {α : Sort u} {β : Sort v} {δ : Sort w} (f : β → δ) (g : α → β) : α → δ :=
fun x => f (g x) | [
37,
1
] | [
46,
19
] | commanddeclaration | 1 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Function.const | @[inline] def Function.const {α : Sort u} (β : Sort v) (a : α) : β → α :=
fun _ => a | [
48,
1
] | [
60,
13
] | commanddeclaration | 2 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | letFun | @[irreducible] def letFun {α : Sort u} {β : α → Sort v} (v : α) (f : (x : α) → β x) : β v := f v | [
62,
1
] | [
73,
97
] | commanddeclaration | 3 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | inferInstance | abbrev inferInstance {α : Sort u} [i : α] : α := i | [
76,
1
] | [
92,
51
] | commanddeclaration | 4 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | inferInstanceAs | abbrev inferInstanceAs (α : Sort u) [i : α] : α := i | [
95,
1
] | [
106,
53
] | commanddeclaration | 5 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | PUnit | inductive PUnit : Sort u where
| unit : PUnit | [
109,
1
] | [
117,
17
] | commanddeclaration | 6 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Unit | abbrev Unit : Type := PUnit | [
119,
1
] | [
129,
28
] | commanddeclaration | 7 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Unit.unit | @[match_pattern] abbrev Unit.unit : Unit := PUnit.unit | [
131,
1
] | [
136,
55
] | commanddeclaration | 8 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | lcErased | unsafe axiom lcErased : Type | [
138,
1
] | [
139,
29
] | commanddeclaration | 9 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | lcAny | unsafe axiom lcAny : Type | [
141,
1
] | [
142,
26
] | commanddeclaration | 10 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | lcProof | unsafe axiom lcProof {α : Prop} : α | [
144,
1
] | [
153,
36
] | commanddeclaration | 11 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | lcCast | unsafe axiom lcCast {α : Sort u} {β : Sort v} (a : α) : β | [
155,
1
] | [
158,
58
] | commanddeclaration | 12 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | lcUnreachable | unsafe axiom lcUnreachable {α : Sort u} : α | [
161,
1
] | [
173,
44
] | commanddeclaration | 13 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | True | inductive True : Prop where
| intro : True | [
175,
1
] | [
183,
17
] | commanddeclaration | 14 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | False | inductive False : Prop | [
185,
1
] | [
193,
23
] | commanddeclaration | 15 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Empty | inductive Empty : Type | [
195,
1
] | [
200,
23
] | commanddeclaration | 16 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | PEmpty | inductive PEmpty : Sort u where | [
203,
1
] | [
210,
32
] | commanddeclaration | 17 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Not | def Not (a : Prop) : Prop := a → False | [
212,
1
] | [
219,
39
] | commanddeclaration | 18 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | False.elim | @[macro_inline] def False.elim {C : Sort u} (h : False) : C :=
h.rec | [
221,
1
] | [
232,
8
] | commanddeclaration | 19 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | absurd | @[macro_inline] def absurd {a : Prop} {b : Sort v} (h₁ : a) (h₂ : Not a) : b :=
(h₂ h₁).rec | [
234,
1
] | [
242,
14
] | commanddeclaration | 20 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Eq | inductive Eq : α → α → Prop where
| refl (a : α) : Eq a a | [
244,
1
] | [
274,
26
] | commanddeclaration | 21 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Eq.ndrec | @[simp] abbrev Eq.ndrec.{u1, u2} {α : Sort u2} {a : α} {motive : α → Sort u1} (m : motive a) {b : α} (h : Eq a b) : motive b :=
h.rec m | [
276,
1
] | [
278,
10
] | commanddeclaration | 22 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | rfl | @[match_pattern] def rfl {α : Sort u} {a : α} : Eq a a := Eq.refl a | [
280,
1
] | [
289,
68
] | commanddeclaration | 23 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | id_eq | @[simp] theorem id_eq (a : α) : Eq (id a) a | [
291,
1
] | [
292,
51
] | commanddeclaration | 24 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Eq.subst | theorem Eq.subst {α : Sort u} {motive : α → Prop} {a b : α} (h₁ : Eq a b) (h₂ : motive a) : motive b | [
294,
1
] | [
308,
17
] | commanddeclaration | 25 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Eq.symm | @[symm] theorem Eq.symm {α : Sort u} {a b : α} (h : Eq a b) : Eq b a | [
310,
1
] | [
319,
10
] | commanddeclaration | 26 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Eq.trans | theorem Eq.trans {α : Sort u} {a b c : α} (h₁ : Eq a b) (h₂ : Eq b c) : Eq a c | [
321,
1
] | [
331,
10
] | commanddeclaration | 27 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | cast | @[macro_inline] def cast {α β : Sort u} (h : Eq α β) (a : α) : β :=
h.rec a | [
333,
1
] | [
345,
10
] | commanddeclaration | 28 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | congrArg | theorem congrArg {α : Sort u} {β : Sort v} {a₁ a₂ : α} (f : α → β) (h : Eq a₁ a₂) : Eq (f a₁) (f a₂) | [
347,
1
] | [
358,
10
] | commanddeclaration | 29 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | congr | theorem congr {α : Sort u} {β : Sort v} {f₁ f₂ : α → β} {a₁ a₂ : α} (h₁ : Eq f₁ f₂) (h₂ : Eq a₁ a₂) : Eq (f₁ a₁) (f₂ a₂) | [
360,
1
] | [
368,
16
] | commanddeclaration | 30 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | congrFun | theorem congrFun {α : Sort u} {β : α → Sort v} {f g : (x : α) → β x} (h : Eq f g) (a : α) : Eq (f a) (g a) | [
370,
1
] | [
372,
10
] | commanddeclaration | 31 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Quot.lcInv | unsafe axiom Quot.lcInv {α : Sort u} {r : α → α → Prop} (q : Quot r) : α | [
463,
1
] | [
466,
73
] | commanddeclaration | 32 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HEq | inductive HEq : {α : Sort u} → α → {β : Sort u} → β → Prop where
| refl (a : α) : HEq a a | [
468,
1
] | [
482,
27
] | commanddeclaration | 33 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | HEq.rfl | @[match_pattern] protected def HEq.rfl {α : Sort u} {a : α} : HEq a a :=
HEq.refl a | [
484,
1
] | [
486,
13
] | commanddeclaration | 34 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | eq_of_heq | theorem eq_of_heq {α : Sort u} {a a' : α} (h : HEq a a') : Eq a a' | [
488,
1
] | [
493,
22
] | commanddeclaration | 35 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Prod | structure Prod (α : Type u) (β : Type v) where
mk ::
fst : α
snd : β | [
495,
1
] | [
510,
10
] | commanddeclaration | 36 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | PProd | structure PProd (α : Sort u) (β : Sort v) where
fst : α
snd : β | [
514,
1
] | [
524,
10
] | commanddeclaration | 37 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | MProd | structure MProd (α β : Type u) where
fst : α
snd : β | [
526,
1
] | [
535,
10
] | commanddeclaration | 38 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | And | @[pp_using_anonymous_constructor]
structure And (a b : Prop) : Prop where
intro ::
left : a
right : b | [
537,
1
] | [
551,
12
] | commanddeclaration | 39 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or | inductive Or (a b : Prop) : Prop where
| inl (h : a) : Or a b
| inr (h : b) : Or a b | [
553,
1
] | [
563,
25
] | commanddeclaration | 40 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.intro_left | theorem Or.intro_left (b : Prop) (h : a) : Or a b | [
565,
1
] | [
567,
11
] | commanddeclaration | 41 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.intro_right | theorem Or.intro_right (a : Prop) (h : b) : Or a b | [
569,
1
] | [
571,
11
] | commanddeclaration | 42 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.elim | theorem Or.elim {c : Prop} (h : Or a b) (left : a → c) (right : b → c) : c | [
573,
1
] | [
580,
24
] | commanddeclaration | 43 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.resolve_left | theorem Or.resolve_left (h: Or a b) (na : Not a) : b | [
582,
1
] | [
582,
81
] | commanddeclaration | 44 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.resolve_right | theorem Or.resolve_right (h: Or a b) (nb : Not b) : a | [
583,
1
] | [
583,
81
] | commanddeclaration | 45 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.neg_resolve_left | theorem Or.neg_resolve_left (h : Or (Not a) b) (ha : a) : b | [
584,
1
] | [
584,
86
] | commanddeclaration | 46 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Or.neg_resolve_right | theorem Or.neg_resolve_right (h : Or a (Not b)) (nb : b) : a | [
585,
1
] | [
585,
86
] | commanddeclaration | 47 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Bool | inductive Bool : Type where
| false : Bool
| true : Bool | [
587,
1
] | [
599,
16
] | commanddeclaration | 48 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Subtype | @[pp_using_anonymous_constructor]
structure Subtype {α : Sort u} (p : α → Prop) where
val : α
property : p val | [
603,
1
] | [
628,
19
] | commanddeclaration | 49 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | optParam | @[reducible] def optParam (α : Sort u) (default : α) : Sort u := α | [
631,
1
] | [
638,
67
] | commanddeclaration | 50 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | outParam | @[reducible] def outParam (α : Sort u) : Sort u := α | [
640,
1
] | [
656,
53
] | commanddeclaration | 51 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | semiOutParam | @[reducible] def semiOutParam (α : Sort u) : Sort u := α | [
658,
1
] | [
679,
57
] | commanddeclaration | 52 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | namedPattern | @[reducible] def namedPattern {α : Sort u} (x a : α) (h : Eq x a) : α := a | [
682,
1
] | [
683,
75
] | commanddeclaration | 53 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | sorryAx | @[extern "lean_sorry", never_extract]
axiom sorryAx (α : Sort u) (synthetic : Bool) : α | [
685,
1
] | [
701,
50
] | commanddeclaration | 54 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | eq_false_of_ne_true | theorem eq_false_of_ne_true : {b : Bool} → Not (Eq b true) → Eq b false | [
703,
1
] | [
705,
20
] | commanddeclaration | 55 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | eq_true_of_ne_false | theorem eq_true_of_ne_false : {b : Bool} → Not (Eq b false) → Eq b true | [
707,
1
] | [
709,
35
] | commanddeclaration | 56 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ne_false_of_eq_true | theorem ne_false_of_eq_true : {b : Bool} → Eq b true → Not (Eq b false) | [
711,
1
] | [
713,
35
] | commanddeclaration | 57 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ne_true_of_eq_false | theorem ne_true_of_eq_false : {b : Bool} → Eq b false → Not (Eq b true) | [
715,
1
] | [
717,
44
] | commanddeclaration | 58 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Inhabited | class Inhabited (α : Sort u) where
default : α | [
719,
1
] | [
734,
14
] | commanddeclaration | 59 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nonempty | class inductive Nonempty (α : Sort u) : Prop where
| intro (val : α) : Nonempty α | [
738,
1
] | [
748,
33
] | commanddeclaration | 60 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Classical.choice | axiom Classical.choice {α : Sort u} : Nonempty α → α | [
750,
1
] | [
772,
53
] | commanddeclaration | 61 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nonempty.elim | protected theorem Nonempty.elim {α : Sort u} {p : Prop} (h₁ : Nonempty α) (h₂ : α → p) : p | [
774,
1
] | [
782,
20
] | commanddeclaration | 62 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Classical.ofNonempty | noncomputable def Classical.ofNonempty {α : Sort u} [Nonempty α] : α :=
Classical.choice inferInstance | [
787,
1
] | [
792,
33
] | commanddeclaration | 63 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Pi.instNonempty | instance Pi.instNonempty {α : Sort u} {β : α → Sort v} [(a : α) → Nonempty (β a)] :
Nonempty ((a : α) → β a) :=
Nonempty.intro fun _ => Classical.ofNonempty | [
797,
1
] | [
799,
47
] | commanddeclaration | 64 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Pi.instInhabited | instance Pi.instInhabited {α : Sort u} {β : α → Sort v} [(a : α) → Inhabited (β a)] :
Inhabited ((a : α) → β a) where
default := fun _ => default | [
807,
1
] | [
809,
30
] | commanddeclaration | 65 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | PLift | structure PLift (α : Sort u) : Type u where
up ::
down : α | [
813,
1
] | [
832,
11
] | commanddeclaration | 66 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | PLift.up_down | theorem PLift.up_down {α : Sort u} (b : PLift α) : Eq (up (down b)) b | [
834,
1
] | [
835,
77
] | commanddeclaration | 67 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | PLift.down_up | theorem PLift.down_up {α : Sort u} (a : α) : Eq (down (up a)) a | [
837,
1
] | [
838,
71
] | commanddeclaration | 68 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | NonemptyType | def NonemptyType := Subtype fun α : Type u => Nonempty α | [
840,
1
] | [
846,
57
] | commanddeclaration | 69 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | NonemptyType.type | abbrev NonemptyType.type (type : NonemptyType.{u}) : Type u :=
type.val | [
848,
1
] | [
850,
11
] | commanddeclaration | 70 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ULift | structure ULift.{r, s} (α : Type s) : Type (max s r) where
up ::
down : α | [
856,
1
] | [
881,
11
] | commanddeclaration | 71 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ULift.up_down | theorem ULift.up_down {α : Type u} (b : ULift.{v} α) : Eq (up (down b)) b | [
883,
1
] | [
884,
81
] | commanddeclaration | 72 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ULift.down_up | theorem ULift.down_up {α : Type u} (a : α) : Eq (down (up.{v} a)) a | [
886,
1
] | [
887,
75
] | commanddeclaration | 73 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Decidable | class inductive Decidable (p : Prop) where
| isFalse (h : Not p) : Decidable p
| isTrue (h : p) : Decidable p | [
889,
1
] | [
907,
33
] | commanddeclaration | 74 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Decidable.decide | @[inline_if_reduce, nospecialize] def Decidable.decide (p : Prop) [h : Decidable p] : Bool :=
h.casesOn (fun _ => false) (fun _ => true) | [
909,
1
] | [
916,
45
] | commanddeclaration | 75 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | DecidablePred | abbrev DecidablePred {α : Sort u} (r : α → Prop) :=
(a : α) → Decidable (r a) | [
920,
1
] | [
926,
28
] | commanddeclaration | 76 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | DecidableRel | abbrev DecidableRel {α : Sort u} {β : Sort v} (r : α → β → Prop) :=
(a : α) → (b : β) → Decidable (r a b) | [
928,
1
] | [
934,
40
] | commanddeclaration | 77 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | DecidableEq | abbrev DecidableEq (α : Sort u) :=
(a b : α) → Decidable (Eq a b) | [
936,
1
] | [
943,
33
] | commanddeclaration | 78 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | decEq | def decEq {α : Sort u} [inst : DecidableEq α] (a b : α) : Decidable (Eq a b) :=
inst a b | [
945,
1
] | [
949,
11
] | commanddeclaration | 79 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | decide_eq_true | theorem decide_eq_true : [inst : Decidable p] → p → Eq (decide p) true | [
952,
1
] | [
954,
35
] | commanddeclaration | 80 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | decide_eq_false | theorem decide_eq_false : [Decidable p] → Not p → Eq (decide p) false | [
956,
1
] | [
958,
26
] | commanddeclaration | 81 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | of_decide_eq_true | theorem of_decide_eq_true [inst : Decidable p] : Eq (decide p) true → p | [
960,
1
] | [
963,
70
] | commanddeclaration | 82 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | of_decide_eq_false | theorem of_decide_eq_false [inst : Decidable p] : Eq (decide p) false → Not p | [
965,
1
] | [
968,
21
] | commanddeclaration | 83 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | of_decide_eq_self_eq_true | theorem of_decide_eq_self_eq_true [inst : DecidableEq α] (a : α) : Eq (decide (Eq a a)) true | [
970,
1
] | [
973,
32
] | commanddeclaration | 84 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Bool.decEq | @[inline] def Bool.decEq (a b : Bool) : Decidable (Eq a b) :=
match a, b with
| false, false => isTrue rfl
| false, true => isFalse (fun h => Bool.noConfusion h)
| true, false => isFalse (fun h => Bool.noConfusion h)
| true, true => isTrue rfl | [
975,
1
] | [
986,
32
] | commanddeclaration | 85 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | BEq | class BEq (α : Type u) where
beq : α → α → Bool | [
991,
1
] | [
1004,
21
] | commanddeclaration | 86 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | dite | @[macro_inline] def dite {α : Sort u} (c : Prop) [h : Decidable c] (t : c → α) (e : Not c → α) : α :=
h.casesOn e t | [
1012,
1
] | [
1027,
16
] | commanddeclaration | 87 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | ite | @[macro_inline] def ite {α : Sort u} (c : Prop) [h : Decidable c] (t e : α) : α :=
h.casesOn (fun _ => e) (fun _ => t) | [
1031,
1
] | [
1052,
38
] | commanddeclaration | 88 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | cond | @[macro_inline] def cond {α : Sort u} (c : Bool) (x y : α) : α :=
match c with
| true => x
| false => y | [
1081,
1
] | [
1094,
15
] | commanddeclaration | 89 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Bool.dcond | @[macro_inline]
protected def Bool.dcond {α : Sort u} (c : Bool) (x : Eq c true → α) (y : Eq c false → α) : α :=
match c with
| true => x rfl
| false => y rfl | [
1097,
1
] | [
1115,
19
] | commanddeclaration | 90 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Bool.or | @[macro_inline] def Bool.or (x y : Bool) : Bool :=
match x with
| true => true
| false => y | [
1117,
1
] | [
1129,
15
] | commanddeclaration | 91 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Bool.and | @[macro_inline] def Bool.and (x y : Bool) : Bool :=
match x with
| false => false
| true => y | [
1131,
1
] | [
1143,
15
] | commanddeclaration | 92 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Bool.not | @[inline] def Bool.not : Bool → Bool
| true => false
| false => true | [
1145,
1
] | [
1153,
18
] | commanddeclaration | 93 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | Nat | inductive Nat where
| zero : Nat
| succ (n : Nat) : Nat | [
1157,
1
] | [
1178,
25
] | commanddeclaration | 94 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | OfNat | class OfNat (α : Type u) (_ : Nat) where
ofNat : α | [
1183,
1
] | [
1200,
12
] | commanddeclaration | 95 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | instOfNatNat | @[default_instance 100]
instance instOfNatNat (n : Nat) : OfNat Nat n where
ofNat := n | [
1202,
1
] | [
1204,
13
] | commanddeclaration | 96 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | LE | class LE (α : Type u) where
le : α → α → Prop | [
1206,
1
] | [
1209,
20
] | commanddeclaration | 97 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | LT | class LT (α : Type u) where
lt : α → α → Prop | [
1211,
1
] | [
1214,
20
] | commanddeclaration | 98 |
.lake/packages/lean4/src/lean/Init/Prelude.lean | [] | GE.ge | @[reducible] def GE.ge {α : Type u} [LE α] (a b : α) : Prop := LE.le b a | [
1216,
1
] | [
1217,
73
] | commanddeclaration | 99 |
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