file stringlengths 21 79 | dependencies listlengths 1 16 | definitions listlengths 1 625 | theorem_idx int64 0 574 | theorem stringlengths 3 121 | theorem_loc listlengths 2 2 | tactic_idx int64 0 155 | tactic_len int64 1 156 | tactic stringlengths 3 5.76k | state_before stringlengths 7 13.6k | state_after stringlengths 7 13.6k |
|---|---|---|---|---|---|---|---|---|---|---|
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 326 | List.length_merge | [
[
1586,
51
],
[
1594,
43
]
] | 4 | 9 | split | α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
⊢ (if s a b = true then a :: merge s l (b :: r) else b :: merge s (a :: l) r).length = (a :: l).length + (b :: r).length | case isTrue
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : s a b = true
⊢ (a :: merge s l (b :: r)).length = (a :: l).length + (b :: r).length
case isFalse
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ (b :: merge s (a :: l) r).... |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 326 | List.length_merge | [
[
1586,
51
],
[
1594,
43
]
] | 5 | 9 | · simp_arith [length_merge s l (b::r)] | case isTrue
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : s a b = true
⊢ (a :: merge s l (b :: r)).length = (a :: l).length + (b :: r).length
case isFalse
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ (b :: merge s (a :: l) r).... | case isFalse
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ (b :: merge s (a :: l) r).length = (a :: l).length + (b :: r).length |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 326 | List.length_merge | [
[
1586,
51
],
[
1594,
43
]
] | 6 | 9 | · simp_arith [length_merge s (a::l) r] | case isFalse
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ (b :: merge s (a :: l) r).length = (a :: l).length + (b :: r).length | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 326 | List.length_merge | [
[
1586,
51
],
[
1594,
43
]
] | 7 | 9 | simp_arith [length_merge s l (b::r)] | case isTrue
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : s a b = true
⊢ (a :: merge s l (b :: r)).length = (a :: l).length + (b :: r).length | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 326 | List.length_merge | [
[
1586,
51
],
[
1594,
43
]
] | 8 | 9 | simp_arith [length_merge s (a::l) r] | case isFalse
α : Type u_1
s : α → α → Bool
l✝ r✝ : List α
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ (b :: merge s (a :: l) r).length = (a :: l).length + (b :: r).length | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 0 | 9 | match l, r with
| l, [] => simp
| [], l => simp
| a::l, b::r =>
rw [cons_merge_cons]
split
· simp [mem_merge (l := l) (r := b::r), or_assoc]
· simp [mem_merge (l := a::l) (r := r), or_assoc, or_left_comm] | α : Type u_1
x : α
l r : List α
s : α → α → Bool
⊢ x ∈ merge s l r ↔ x ∈ l ∨ x ∈ r | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 1 | 9 | simp | α : Type u_1
x : α
l✝ r : List α
s : α → α → Bool
l : List α
⊢ x ∈ merge s l [] ↔ x ∈ l ∨ x ∈ [] | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 2 | 9 | simp | α : Type u_1
x : α
l✝ r : List α
s : α → α → Bool
l : List α
⊢ x ∈ merge s [] l ↔ x ∈ [] ∨ x ∈ l | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 3 | 9 | rw [cons_merge_cons] | α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
⊢ x ∈ merge s (a :: l) (b :: r) ↔ x ∈ a :: l ∨ x ∈ b :: r | α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
⊢ (x ∈ if s a b = true then a :: merge s l (b :: r) else b :: merge s (a :: l) r) ↔ x ∈ a :: l ∨ x ∈ b :: r |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 4 | 9 | split | α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
⊢ (x ∈ if s a b = true then a :: merge s l (b :: r) else b :: merge s (a :: l) r) ↔ x ∈ a :: l ∨ x ∈ b :: r | case isTrue
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : s a b = true
⊢ x ∈ a :: merge s l (b :: r) ↔ x ∈ a :: l ∨ x ∈ b :: r
case isFalse
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ x ∈ b :: merge s (a :: l) r ↔... |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 5 | 9 | · simp [mem_merge (l := l) (r := b::r), or_assoc] | case isTrue
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : s a b = true
⊢ x ∈ a :: merge s l (b :: r) ↔ x ∈ a :: l ∨ x ∈ b :: r
case isFalse
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ x ∈ b :: merge s (a :: l) r ↔... | case isFalse
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ x ∈ b :: merge s (a :: l) r ↔ x ∈ a :: l ∨ x ∈ b :: r |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 6 | 9 | · simp [mem_merge (l := a::l) (r := r), or_assoc, or_left_comm] | case isFalse
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ x ∈ b :: merge s (a :: l) r ↔ x ∈ a :: l ∨ x ∈ b :: r | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 7 | 9 | simp [mem_merge (l := l) (r := b::r), or_assoc] | case isTrue
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : s a b = true
⊢ x ∈ a :: merge s l (b :: r) ↔ x ∈ a :: l ∨ x ∈ b :: r | no goals |
.lake/packages/batteries/Batteries/Data/List/Lemmas.lean | [
[
"Batteries.Tactic.Alias",
".lake/packages/batteries/Batteries/Tactic/Alias.lean"
],
[
"Init",
".lake/packages/lean4/src/lean/Init.lean"
],
[
"Batteries.Control.ForInStep.Lemmas",
".lake/packages/batteries/Batteries/Control/ForInStep/Lemmas.lean"
],
[
"Batteries.Tactic.Init"... | [
{
"code": "@[simp] theorem mem_toArray {a : α} {l : List α} : a ∈ l.toArray ↔ a ∈ l",
"end": [
18,
23
],
"full_name": "List.mem_toArray",
"kind": "commanddeclaration",
"start": [
17,
1
]
},
{
"code": "@[simp]\ntheorem drop_one : ∀ l : List α, drop 1 l = ta... | 327 | List.mem_merge | [
[
1597,
75
],
[
1605,
68
]
] | 8 | 9 | simp [mem_merge (l := a::l) (r := r), or_assoc, or_left_comm] | case isFalse
α : Type u_1
x : α
l✝ r✝ : List α
s : α → α → Bool
a : α
l : List α
b : α
r : List α
h✝ : ¬s a b = true
⊢ x ∈ b :: merge s (a :: l) r ↔ x ∈ a :: l ∨ x ∈ b :: r | no goals |
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