url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Int.zero_eq_mul | [136, 9] | [140, 26] | exact Int.mul_eq_zero | a b : ℤ
⊢ a * b = 0 ↔ a = 0 ∨ b = 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | have hxx : x + x = 2 * x :=
by linarith | x : ℚ
⊢ x / 2 + x / 2 = x | x : ℚ
hxx : x + x = 2 * x
⊢ x / 2 + x / 2 = x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | have hxx2 : (x + x) / 2 = (2 * x) / 2 :=
by rw [hxx] | x : ℚ
hxx : x + x = 2 * x
⊢ x / 2 + x / 2 = x | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | have hx2x2 : x / 2 + x / 2 = (2 * x) / 2 :=
by
rw [←hxx2]
rw [add_div] | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = x | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
hx2x2 : x / 2 + x / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | rw [hx2x2] | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
hx2x2 : x / 2 + x / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = x | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
hx2x2 : x / 2 + x / 2 = 2 * x / 2
⊢ 2 * x / 2 = x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | ring | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
hx2x2 : x / 2 + x / 2 = 2 * x / 2
⊢ 2 * x / 2 = x | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | linarith | x : ℚ
⊢ x + x = 2 * x | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | rw [hxx] | x : ℚ
hxx : x + x = 2 * x
⊢ (x + x) / 2 = 2 * x / 2 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | rw [←hxx2] | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = 2 * x / 2 | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = (x + x) / 2 |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Rat.div_two_add_div_two | [145, 9] | [157, 9] | rw [add_div] | x : ℚ
hxx : x + x = 2 * x
hxx2 : (x + x) / 2 = 2 * x / 2
⊢ x / 2 + x / 2 = (x + x) / 2 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_nil | [162, 9] | [164, 9] | rfl | α : Type
inst✝ : BEq α
x : α
⊢ List.count x [] = 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | induction as generalizing acc with
| nil => simp [List.countp.go, List.countp]
| cons a as' ih =>
simp [List.countp, List.countp.go]
cases Classical.em (p a) with
| inl hp =>
simp [hp, ih]
ac_rfl
| inr hp => simp [hp, ih] | α : Type
p : α → Bool
as : List α
acc : ℕ
⊢ List.countp.go p as acc = List.countp p as + acc | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | simp [List.countp.go, List.countp] | case nil
α : Type
p : α → Bool
acc : ℕ
⊢ List.countp.go p [] acc = List.countp p [] + acc | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | simp [List.countp, List.countp.go] | case cons
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
⊢ List.countp.go p (a :: as') acc = List.countp p (a :: as') + acc | case cons
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
⊢ (bif p a then List.countp.go p as' (acc + 1) else List.countp.go p as' acc) =
(bif p a then List.countp.go p as' 1 else List.countp.go p as' 0) + acc |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | cases Classical.em (p a) with
| inl hp =>
simp [hp, ih]
ac_rfl
| inr hp => simp [hp, ih] | case cons
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
⊢ (bif p a then List.countp.go p as' (acc + 1) else List.countp.go p as' acc) =
(bif p a then List.countp.go p as' 1 else List.countp.go p as' 0) + acc | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | simp [hp, ih] | case cons.inl
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
hp : p a = true
⊢ (bif p a then List.countp.go p as' (acc + 1) else List.countp.go p as' acc) =
(bif p a then List.countp.go p as' 1 else List.countp.go p as' 0) + acc | case cons.inl
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
hp : p a = true
⊢ List.countp p as' + (acc + 1) = List.countp p as' + 1 + acc |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | ac_rfl | case cons.inl
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
hp : p a = true
⊢ List.countp p as' + (acc + 1) = List.countp p as' + 1 + acc | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.countp.go_accum | [166, 1] | [177, 32] | simp [hp, ih] | case cons.inr
α : Type
p : α → Bool
a : α
as' : List α
ih : ∀ (acc : ℕ), List.countp.go p as' acc = List.countp p as' + acc
acc : ℕ
hp : ¬p a = true
⊢ (bif p a then List.countp.go p as' (acc + 1) else List.countp.go p as' acc) =
(bif p a then List.countp.go p as' 1 else List.countp.go p as' 0) + acc | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_cons | [179, 9] | [189, 16] | cases Classical.em (a == x) with
| inl hx =>
rw [List.count, List.countp, List.countp.go, List.countp.go_accum]
simp [hx]
ac_rfl
| inr hx =>
rw [List.count, List.countp, List.countp.go, List.countp]
simp [hx] | α : Type
inst✝ : BEq α
x a : α
as : List α
⊢ List.count x (a :: as) = (bif a == x then 1 else 0) + List.count x as | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_cons | [179, 9] | [189, 16] | rw [List.count, List.countp, List.countp.go, List.countp.go_accum] | case inl
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : (a == x) = true
⊢ List.count x (a :: as) = (bif a == x then 1 else 0) + List.count x as | case inl
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : (a == x) = true
⊢ (bif a == x then List.countp (fun x_1 => x_1 == x) as + (0 + 1) else List.countp.go (fun x_1 => x_1 == x) as 0) =
(bif a == x then 1 else 0) + List.countp (fun x_1 => x_1 == x) as |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_cons | [179, 9] | [189, 16] | simp [hx] | case inl
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : (a == x) = true
⊢ (bif a == x then List.countp (fun x_1 => x_1 == x) as + (0 + 1) else List.countp.go (fun x_1 => x_1 == x) as 0) =
(bif a == x then 1 else 0) + List.countp (fun x_1 => x_1 == x) as | case inl
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : (a == x) = true
⊢ List.countp (fun x_1 => x_1 == x) as + 1 = 1 + List.countp (fun x_1 => x_1 == x) as |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_cons | [179, 9] | [189, 16] | ac_rfl | case inl
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : (a == x) = true
⊢ List.countp (fun x_1 => x_1 == x) as + 1 = 1 + List.countp (fun x_1 => x_1 == x) as | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_cons | [179, 9] | [189, 16] | rw [List.count, List.countp, List.countp.go, List.countp] | case inr
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : ¬(a == x) = true
⊢ List.count x (a :: as) = (bif a == x then 1 else 0) + List.count x as | case inr
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : ¬(a == x) = true
⊢ (bif a == x then List.countp.go (fun x_1 => x_1 == x) as (0 + 1) else List.countp.go (fun x_1 => x_1 == x) as 0) =
(bif a == x then 1 else 0) + List.countp.go (fun x_1 => x_1 == x) as 0 |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_cons | [179, 9] | [189, 16] | simp [hx] | case inr
α : Type
inst✝ : BEq α
x a : α
as : List α
hx : ¬(a == x) = true
⊢ (bif a == x then List.countp.go (fun x_1 => x_1 == x) as (0 + 1) else List.countp.go (fun x_1 => x_1 == x) as 0) =
(bif a == x then 1 else 0) + List.countp.go (fun x_1 => x_1 == x) as 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_append | [191, 9] | [198, 13] | induction as with
| nil => simp
| cons a as' ih =>
simp [ih]
ac_rfl | α : Type
inst✝ : BEq α
x : α
as bs : List α
⊢ List.count x (as ++ bs) = List.count x as + List.count x bs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_append | [191, 9] | [198, 13] | simp | case nil
α : Type
inst✝ : BEq α
x : α
bs : List α
⊢ List.count x ([] ++ bs) = List.count x [] + List.count x bs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_append | [191, 9] | [198, 13] | simp [ih] | case cons
α : Type
inst✝ : BEq α
x : α
bs : List α
a : α
as' : List α
ih : List.count x (as' ++ bs) = List.count x as' + List.count x bs
⊢ List.count x (a :: as' ++ bs) = List.count x (a :: as') + List.count x bs | case cons
α : Type
inst✝ : BEq α
x : α
bs : List α
a : α
as' : List α
ih : List.count x (as' ++ bs) = List.count x as' + List.count x bs
⊢ (bif a == x then 1 else 0) + (List.count x as' + List.count x bs) =
(bif a == x then 1 else 0) + List.count x as' + List.count x bs |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.List.count_append | [191, 9] | [198, 13] | ac_rfl | case cons
α : Type
inst✝ : BEq α
x : α
bs : List α
a : α
as' : List α
ih : List.count x (as' ++ bs) = List.count x as' + List.count x bs
⊢ (bif a == x then 1 else 0) + (List.count x as' + List.count x bs) =
(bif a == x then 1 else 0) + List.count x as' + List.count x bs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.Mem_empty | [203, 9] | [205, 69] | simp [Membership.mem, Set.Mem, EmptyCollection.emptyCollection] | α : Type
a : α
⊢ a ∈ ∅ ↔ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.compreh_False | [207, 9] | [209, 9] | rfl | α : Type
⊢ {a | False} = ∅ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.subseteq_def | [211, 20] | [213, 9] | rfl | α : Type
A B : Set α
⊢ A ⊆ B ↔ ∀ (a : α), a ∈ A → a ∈ B | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.Mem_singleton | [215, 9] | [217, 9] | rfl | α : Type
a b : α
⊢ a ∈ {b} ↔ a = b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.Mem_compreh | [219, 9] | [221, 9] | rfl | α : Type
A : Set α
⊢ {a | a ∈ A} = A | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.compreh_Mem | [223, 9] | [225, 9] | rfl | α : Type
a : α
P : α → Prop
⊢ a ∈ {a | P a} ↔ P a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.empty_union | [227, 9] | [229, 35] | simp [Union.union, Set.union] | α : Type
A : Set α
⊢ ∅ ∪ A = A | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.union_empty | [231, 9] | [233, 35] | simp [Union.union, Set.union] | α : Type
A : Set α
⊢ A ∪ ∅ = A | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.Mem_union | [235, 9] | [237, 9] | rfl | α : Type
a : α
A B : Set α
⊢ a ∈ A ∪ B ↔ a ∈ A ∨ a ∈ B | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.unordered_pair_comm | [239, 1] | [244, 10] | apply Set.ext | α : Type
a b : α
⊢ {a, b} = {b, a} | case h
α : Type
a b : α
⊢ ∀ (x : α), x ∈ {a, b} ↔ x ∈ {b, a} |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.unordered_pair_comm | [239, 1] | [244, 10] | simp [insert, singleton, Set.insert, Set.singleton] | case h
α : Type
a b : α
⊢ ∀ (x : α), x ∈ {a, b} ↔ x ∈ {b, a} | case h
α : Type
a b : α
⊢ ∀ (x : α), x = a ∨ x = b ↔ x = b ∨ x = a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.unordered_pair_comm | [239, 1] | [244, 10] | aesop | case h
α : Type
a b : α
⊢ ∀ (x : α), x = a ∨ x = b ↔ x = b ∨ x = a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.le_def | [280, 9] | [282, 9] | rfl | α : Type
A B : Set α
⊢ A ≤ B ↔ A ⊆ B | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.Set.lt_def | [284, 9] | [286, 9] | rfl | α : Type
A B : Set α
⊢ A < B ↔ A ⊆ B ∧ A ≠ B | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.mem_Id | [298, 9] | [300, 9] | rfl | α : Type
a b : α
⊢ (a, b) ∈ Id ↔ b = a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.mem_comp | [307, 9] | [309, 9] | rfl | α : Type
r₁ r₂ : Set (α × α)
a b : α
⊢ (a, b) ∈ r₁ ◯ r₂ ↔ ∃ c, (a, c) ∈ r₁ ∧ (c, b) ∈ r₂ | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.mem_restrict | [317, 9] | [320, 9] | rfl | α : Type
r : Set (α × α)
P : α → Prop
a b : α
⊢ (a, b) ∈ r ⇃ P ↔ (a, b) ∈ r ∧ P a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.trans | [331, 1] | [340, 19] | induction hbc with
| refl =>
assumption
| tail c d hbc hcd hac =>
apply tail <;>
assumption | α : Type
R : α → α → Prop
a b c : α
hab : RTC R a b
hbc : RTC R b c
⊢ RTC R a c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.trans | [331, 1] | [340, 19] | assumption | case refl
α : Type
R : α → α → Prop
a b c : α
hab : RTC R a b
⊢ RTC R a b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.trans | [331, 1] | [340, 19] | apply tail <;>
assumption | case tail
α : Type
R : α → α → Prop
a b c✝ : α
hab : RTC R a b
c d : α
hbc : RTC R b c
hcd : R c d
hac : RTC R a c
⊢ RTC R a d | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head | [346, 1] | [355, 19] | induction hbc with
| refl =>
exact tail _ _ refl hab
| tail c d hbc hcd hac =>
apply tail <;>
assumption | α : Type
R : α → α → Prop
a b c : α
hab : R a b
hbc : RTC R b c
⊢ RTC R a c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head | [346, 1] | [355, 19] | exact tail _ _ refl hab | case refl
α : Type
R : α → α → Prop
a b c : α
hab : R a b
⊢ RTC R a b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head | [346, 1] | [355, 19] | apply tail <;>
assumption | case tail
α : Type
R : α → α → Prop
a b c✝ : α
hab : R a b
c d : α
hbc : RTC R b c
hcd : R c d
hac : RTC R a c
⊢ RTC R a d | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | induction h with
| refl =>
exact refl
| tail b' c _ hb'c ih =>
apply ih (P := fun a hab' ↦ P a (RTC.tail _ _ hab' hb'c))
{ exact head _ _ hb'c _ refl }
{ intro x y hxy hyb' hy
exact head _ _ hxy _ hy } | α : Type
R : α → α → Prop
b : α
P : (a : α) → RTC R a b → Prop
a : α
h : RTC R a b
refl : P b (_ : RTC R b b)
head : ∀ (a c : α) (h' : R a c) (h : RTC R c b), P c h → P a (_ : RTC R a b)
⊢ P a h | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | exact refl | case refl
α : Type
R : α → α → Prop
b a : α
P : (a_1 : α) → RTC R a_1 a → Prop
refl : P a (_ : RTC R a a)
head : ∀ (a_1 c : α) (h' : R a_1 c) (h : RTC R c a), P c h → P a_1 (_ : RTC R a_1 a)
⊢ P a (_ : RTC R a a) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | apply ih (P := fun a hab' ↦ P a (RTC.tail _ _ hab' hb'c)) | case tail
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ P a (_ : RTC R a c) | case tail.refl
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ P b' (_ : RTC R b' c)
case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 b'), P c_1 (_ : RTC R c_1 c) → P a (_ : RTC R a c) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | { exact head _ _ hb'c _ refl } | case tail.refl
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ P b' (_ : RTC R b' c)
case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 b'), P c_1 (_ : RTC R c_1 c) → P a (_ : RTC R a c) | case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 b'), P c_1 (_ : RTC R c_1 c) → P a (_ : RTC R a c) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | { intro x y hxy hyb' hy
exact head _ _ hxy _ hy } | case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 b'), P c_1 (_ : RTC R c_1 c) → P a (_ : RTC R a c) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | exact head _ _ hb'c _ refl | case tail.refl
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ P b' (_ : RTC R b' c) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | intro x y hxy hyb' hy | case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
⊢ ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 b'), P c_1 (_ : RTC R c_1 c) → P a (_ : RTC R a c) | case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
x y : α
hxy : R x y
hyb' : RTC R y b'
hy : P y (_ : RTC R y c)
⊢ P x (_ : RTC R x c) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.head_induction_on | [357, 1] | [371, 34] | exact head _ _ hxy _ hy | case tail.head
α : Type
R : α → α → Prop
b a b' c : α
hab : RTC R a b'
hb'c : R b' c
ih :
∀ {P : (a : α) → RTC R a b' → Prop},
P b' (_ : RTC R b' b') → (∀ (a c : α) (h' : R a c) (h : RTC R c b'), P c h → P a (_ : RTC R a b')) → P a hab
P : (a : α) → RTC R a c → Prop
refl : P c (_ : RTC R c c)
head : ∀ (a c_1 : α) (h' : R a c_1) (h : RTC R c_1 c), P c_1 h → P a (_ : RTC R a c)
x y : α
hxy : R x y
hyb' : RTC R y b'
hy : P y (_ : RTC R y c)
⊢ P x (_ : RTC R x c) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.lift | [373, 1] | [383, 16] | induction hab with
| refl => apply refl
| tail b c hab hbc ih =>
apply tail
apply ih
apply hf
exact hbc | α β : Type
R : α → α → Prop
S : β → β → Prop
a b : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
hab : RTC R a b
⊢ RTC S (f a) (f b) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.lift | [373, 1] | [383, 16] | apply refl | case refl
α β : Type
R : α → α → Prop
S : β → β → Prop
a b : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
⊢ RTC S (f a) (f a) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.lift | [373, 1] | [383, 16] | apply tail | case tail
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ RTC S (f a) (f c) | case tail.hab
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ RTC S (f a) ?tail.b
case tail.hbc
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ S ?tail.b (f c)
case tail.b
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ β |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.lift | [373, 1] | [383, 16] | apply ih | case tail.hab
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ RTC S (f a) ?tail.b
case tail.hbc
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ S ?tail.b (f c)
case tail.b
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ β | case tail.hbc
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ S (f b) (f c) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.lift | [373, 1] | [383, 16] | apply hf | case tail.hbc
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ S (f b) (f c) | case tail.hbc.a
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ R b c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.lift | [373, 1] | [383, 16] | exact hbc | case tail.hbc.a
α β : Type
R : α → α → Prop
S : β → β → Prop
a b✝ : α
f : α → β
hf : ∀ (a b : α), R a b → S (f a) (f b)
b c : α
hab : RTC R a b
hbc : R b c
ih : RTC S (f a) (f b)
⊢ R b c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.RTC_RTC_eq | [389, 1] | [405, 26] | induction h with
| refl => exact refl
| tail b c hab' hbc ih =>
apply trans <;>
assumption | α : Type
R : α → α → Prop
a b : α
h : RTC (RTC R) a b
⊢ RTC R a b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.RTC_RTC_eq | [389, 1] | [405, 26] | exact refl | case refl
α : Type
R : α → α → Prop
a b : α
⊢ RTC R a a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.RTC.RTC_RTC_eq | [389, 1] | [405, 26] | apply trans <;>
assumption | case tail
α : Type
R : α → α → Prop
a b✝ b c : α
hab' : RTC (RTC R) a b
hbc : RTC R b c
ih : RTC R a b
⊢ RTC R a c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_apply | [438, 9] | [442, 8] | apply if_pos | name : String
val : ℕ
s : State
⊢ State.update name val s name = val | case hc
name : String
val : ℕ
s : State
⊢ name = name |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_apply | [438, 9] | [442, 8] | rfl | case hc
name : String
val : ℕ
s : State
⊢ name = name | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_apply_neq | [444, 9] | [449, 15] | apply if_neg | name name' : String
val : ℕ
s : State
hneq : name' ≠ name
⊢ State.update name val s name' = s name' | case hnc
name name' : String
val : ℕ
s : State
hneq : name' ≠ name
⊢ ¬name' = name |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_apply_neq | [444, 9] | [449, 15] | assumption | case hnc
name name' : String
val : ℕ
s : State
hneq : name' ≠ name
⊢ ¬name' = name | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_override | [451, 9] | [458, 24] | apply funext | name : String
val₁ val₂ : ℕ
s : State
⊢ State.update name val₁ (State.update name val₂ s) = State.update name val₁ s | case h
name : String
val₁ val₂ : ℕ
s : State
⊢ ∀ (x : String), State.update name val₁ (State.update name val₂ s) x = State.update name val₁ s x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_override | [451, 9] | [458, 24] | intro name' | case h
name : String
val₁ val₂ : ℕ
s : State
⊢ ∀ (x : String), State.update name val₁ (State.update name val₂ s) x = State.update name val₁ s x | case h
name : String
val₁ val₂ : ℕ
s : State
name' : String
⊢ State.update name val₁ (State.update name val₂ s) name' = State.update name val₁ s name' |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_override | [451, 9] | [458, 24] | cases Classical.em (name' = name) with
| inl h => simp [h]
| inr h => simp [h] | case h
name : String
val₁ val₂ : ℕ
s : State
name' : String
⊢ State.update name val₁ (State.update name val₂ s) name' = State.update name val₁ s name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_override | [451, 9] | [458, 24] | simp [h] | case h.inl
name : String
val₁ val₂ : ℕ
s : State
name' : String
h : name' = name
⊢ State.update name val₁ (State.update name val₂ s) name' = State.update name val₁ s name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_override | [451, 9] | [458, 24] | simp [h] | case h.inr
name : String
val₁ val₂ : ℕ
s : State
name' : String
h : ¬name' = name
⊢ State.update name val₁ (State.update name val₂ s) name' = State.update name val₁ s name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | apply funext | name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) = State.update name₂ val₂ (State.update name₁ val₁ s) | case h
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
⊢ ∀ (x : String),
State.update name₁ val₁ (State.update name₂ val₂ s) x = State.update name₂ val₂ (State.update name₁ val₁ s) x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | intro name' | case h
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
⊢ ∀ (x : String),
State.update name₁ val₁ (State.update name₂ val₂ s) x = State.update name₂ val₂ (State.update name₁ val₁ s) x | case h
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
name' : String
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) name' = State.update name₂ val₂ (State.update name₁ val₁ s) name' |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | cases Classical.em (name' = name₁) with
| inl h => simp [*]
| inr h =>
cases Classical.em (name' = name₁) with
| inl h => simp [*]
| inr h => simp [State.update, *] | case h
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
name' : String
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) name' = State.update name₂ val₂ (State.update name₁ val₁ s) name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | simp [*] | case h.inl
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
name' : String
h : name' = name₁
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) name' = State.update name₂ val₂ (State.update name₁ val₁ s) name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | cases Classical.em (name' = name₁) with
| inl h => simp [*]
| inr h => simp [State.update, *] | case h.inr
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
name' : String
h : ¬name' = name₁
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) name' = State.update name₂ val₂ (State.update name₁ val₁ s) name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | simp [*] | case h.inr.inl
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
name' : String
h✝ : ¬name' = name₁
h : name' = name₁
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) name' = State.update name₂ val₂ (State.update name₁ val₁ s) name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_swap | [460, 9] | [471, 40] | simp [State.update, *] | case h.inr.inr
name₁ name₂ : String
val₁ val₂ : ℕ
s : State
hneq : name₁ ≠ name₂
name' : String
h✝ h : ¬name' = name₁
⊢ State.update name₁ val₁ (State.update name₂ val₂ s) name' = State.update name₂ val₂ (State.update name₁ val₁ s) name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_id | [473, 9] | [480, 13] | apply funext | name : String
s : State
⊢ State.update name (s name) s = s | case h
name : String
s : State
⊢ ∀ (x : String), State.update name (s name) s x = s x |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_id | [473, 9] | [480, 13] | intro name' | case h
name : String
s : State
⊢ ∀ (x : String), State.update name (s name) s x = s x | case h
name : String
s : State
name' : String
⊢ State.update name (s name) s name' = s name' |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_id | [473, 9] | [480, 13] | simp [State.update] | case h
name : String
s : State
name' : String
⊢ State.update name (s name) s name' = s name' | case h
name : String
s : State
name' : String
⊢ name' = name → s name = s name' |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_id | [473, 9] | [480, 13] | intro heq | case h
name : String
s : State
name' : String
⊢ name' = name → s name = s name' | case h
name : String
s : State
name' : String
heq : name' = name
⊢ s name = s name' |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_id | [473, 9] | [480, 13] | simp [*] | case h
name : String
s : State
name' : String
heq : name' = name
⊢ s name = s name' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_same_const | [482, 9] | [486, 24] | apply funext | name : String
val : ℕ
⊢ (State.update name val fun x => val) = fun x => val | case h
name : String
val : ℕ
⊢ ∀ (x : String), State.update name val (fun x => val) x = val |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/LoVelib.lean | LoVe.update_same_const | [482, 9] | [486, 24] | simp [State.update] | case h
name : String
val : ℕ
⊢ ∀ (x : String), State.update name val (fun x => val) x = val | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe07_EffectfulProgramming_Demo.lean | LoVe.mmap_append | [449, 1] | [460, 30] | simp [mmap, LawfulMonad.bind_pure, LawfulMonad.pure_bind] | m : Type → Type
inst✝ : LawfulMonad m
α β : Type
f : α → m β
x✝ : List α
⊢ mmap f ([] ++ x✝) = do
let bs ← mmap f []
let bs' ← mmap f x✝
pure (bs ++ bs') | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe07_EffectfulProgramming_Demo.lean | LoVe.mmap_append | [449, 1] | [460, 30] | simp [mmap, mmap_append _ as as', LawfulMonad.pure_bind,
LawfulMonad.bind_assoc] | m : Type → Type
inst✝ : LawfulMonad m
α β : Type
f : α → m β
a : α
as as' : List α
⊢ mmap f (a :: as ++ as') = do
let bs ← mmap f (a :: as)
let bs' ← mmap f as'
pure (bs ++ bs') | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | simp [List.add] | ⊢ List.length [] = List.length [] → List.length (add [] []) = List.length [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | simp [List.add, List.length] | x : ℤ
xs : List ℤ
y : ℤ
ys : List ℤ
⊢ List.length (x :: xs) = List.length (y :: ys) → List.length (add (x :: xs) (y :: ys)) = List.length (x :: xs) | x : ℤ
xs : List ℤ
y : ℤ
ys : List ℤ
⊢ List.length xs = List.length ys → List.length (add xs ys) = List.length xs |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | intro hsame | x : ℤ
xs : List ℤ
y : ℤ
ys : List ℤ
⊢ List.length xs = List.length ys → List.length (add xs ys) = List.length xs | x : ℤ
xs : List ℤ
y : ℤ
ys : List ℤ
hsame : List.length xs = List.length ys
⊢ List.length (add xs ys) = List.length xs |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | rw [List.length_add xs ys hsame] | x : ℤ
xs : List ℤ
y : ℤ
ys : List ℤ
hsame : List.length xs = List.length ys
⊢ List.length (add xs ys) = List.length xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | intro hsame | y : ℤ
ys : List ℤ
⊢ List.length [] = List.length (y :: ys) → List.length (add [] (y :: ys)) = List.length [] | y : ℤ
ys : List ℤ
hsame : List.length [] = List.length (y :: ys)
⊢ List.length (add [] (y :: ys)) = List.length [] |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | cases hsame | y : ℤ
ys : List ℤ
hsame : List.length [] = List.length (y :: ys)
⊢ List.length (add [] (y :: ys)) = List.length [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Labs/Lab8Solution.lean | LoVe.List.length_add | [31, 1] | [48, 18] | intro hsame | x : ℤ
xs : List ℤ
⊢ List.length (x :: xs) = List.length [] → List.length (add (x :: xs) []) = List.length (x :: xs) | x : ℤ
xs : List ℤ
hsame : List.length (x :: xs) = List.length []
⊢ List.length (add (x :: xs) []) = List.length (x :: xs) |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.