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/Lectures/LoVe00_Preface_Demo.lean | biggerPrimeIsBigger | [156, 1] | [165, 7] | have h1 : (biggerPrime M) ∣ M ! + 1 := minFac_dvd _ | M : ℕ
hqM : ¬biggerPrime M ≥ M
⊢ False | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | biggerPrimeIsBigger | [156, 1] | [165, 7] | have hqM2 : biggerPrime M ≤ M := by linarith | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
⊢ False | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
hqM2 : biggerPrime M ≤ M
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | biggerPrimeIsBigger | [156, 1] | [165, 7] | have hqM3 : biggerPrime M ∣ M ! :=
Iff.mpr (Prime.dvd_factorial (biggerPrimeIsPrime _)) hqM2 | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
hqM2 : biggerPrime M ≤ M
⊢ False | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
hqM2 : biggerPrime M ≤ M
hqM3 : biggerPrime M ∣ M !
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | biggerPrimeIsBigger | [156, 1] | [165, 7] | have hq1 : biggerPrime M ∣ 1 := Iff.mp (Nat.dvd_add_right hqM3) h1 | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
hqM2 : biggerPrime M ≤ M
hqM3 : biggerPrime M ∣ M !
⊢ False | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
hqM2 : biggerPrime M ≤ M
hqM3 : biggerPrime M ∣ M !
hq1 : biggerPrime M ∣ 1
⊢ False |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | biggerPrimeIsBigger | [156, 1] | [165, 7] | apply Nat.Prime.not_dvd_one (biggerPrimeIsPrime _) hq1 | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
hqM2 : biggerPrime M ≤ M
hqM3 : biggerPrime M ∣ M !
hq1 : biggerPrime M ∣ 1
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | biggerPrimeIsBigger | [156, 1] | [165, 7] | linarith | M : ℕ
hqM : ¬biggerPrime M ≥ M
h1 : biggerPrime M ∣ M ! + 1
⊢ biggerPrime M ≤ M | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | intro N | ⊢ ∀ (N : ℕ), ∃ p, p ≥ N ∧ Nat.Prime p | N : ℕ
⊢ ∃ p, p ≥ N ∧ Nat.Prime p |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | use biggerPrime N | N : ℕ
⊢ ∃ p, p ≥ N ∧ Nat.Prime p | case h
N : ℕ
⊢ biggerPrime N ≥ N ∧ Nat.Prime (biggerPrime N) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | apply And.intro | case h
N : ℕ
⊢ biggerPrime N ≥ N ∧ Nat.Prime (biggerPrime N) | case h.left
N : ℕ
⊢ biggerPrime N ≥ N
case h.right
N : ℕ
⊢ Nat.Prime (biggerPrime N) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | { exact biggerPrimeIsBigger _ } | case h.left
N : ℕ
⊢ biggerPrime N ≥ N
case h.right
N : ℕ
⊢ Nat.Prime (biggerPrime N) | case h.right
N : ℕ
⊢ Nat.Prime (biggerPrime N) |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | { exact biggerPrimeIsPrime _ } | case h.right
N : ℕ
⊢ Nat.Prime (biggerPrime N) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | exact biggerPrimeIsBigger _ | case h.left
N : ℕ
⊢ biggerPrime N ≥ N | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe00_Preface_Demo.lean | infinitude_of_primes2 | [169, 1] | [175, 7] | exact biggerPrimeIsPrime _ | case h.right
N : ℕ
⊢ Nat.Prime (biggerPrime N) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVeXX_ALookUnderTheHood_Demo.lean | a_silly_theorem | [101, 1] | [102, 39] | simp | ⊢ True | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.Nat.succ_neq_self | [68, 1] | [73, 28] | induction n with
| zero => simp
| succ n' ih => simp [ih] | n : ℕ
⊢ Nat.succ n ≠ n | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.Nat.succ_neq_self | [68, 1] | [73, 28] | simp | case zero
⊢ Nat.succ Nat.zero ≠ Nat.zero | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.Nat.succ_neq_self | [68, 1] | [73, 28] | simp [ih] | case succ
n' : ℕ
ih : Nat.succ n' ≠ n'
⊢ Nat.succ (Nat.succ n') ≠ Nat.succ n' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.proof_of_False | [108, 1] | [118, 21] | rw [←hi] | hi : immoral 0 = immoral 0 + 1
⊢ immoral 0 - immoral 0 = immoral 0 + 1 - immoral 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.proof_of_False | [108, 1] | [118, 21] | simp at him | hi : immoral 0 = immoral 0 + 1
him : immoral 0 - immoral 0 = immoral 0 + 1 - immoral 0
⊢ 0 = 1 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.proof_of_False | [108, 1] | [118, 21] | simp at h0eq1 | hi : immoral 0 = immoral 0 + 1
him : immoral 0 - immoral 0 = immoral 0 + 1 - immoral 0
h0eq1 : 0 = 1
⊢ False | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.shuffle_shuffle_shuffle | [245, 1] | [247, 9] | rfl | c : RGB
⊢ shuffle (shuffle (shuffle c)) = c | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.head_head | [272, 1] | [275, 9] | rfl | α : Type
inst✝ : Inhabited α
xs : List α
⊢ head [head xs] = head xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.head_head_cases | [308, 1] | [314, 24] | cases xs with
| nil => rfl
| cons x xs' => rfl | α : Type
inst✝ : Inhabited α
xs : List α
⊢ head [head xs] = head xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.head_head_cases | [308, 1] | [314, 24] | rfl | case nil
α : Type
inst✝ : Inhabited α
⊢ head [head []] = head [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.head_head_cases | [308, 1] | [314, 24] | rfl | case cons
α : Type
inst✝ : Inhabited α
x : α
xs' : List α
⊢ head [head (x :: xs')] = head (x :: xs') | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.head_head_match | [318, 1] | [323, 30] | rfl | α : Type
inst✝ : Inhabited α
xs : List α
⊢ head [head []] = head [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.head_head_match | [318, 1] | [323, 30] | rfl | α : Type
inst✝ : Inhabited α
xs : List α
x : α
xs' : List α
⊢ head [head (x :: xs')] = head (x :: xs') | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.injection_example | [329, 1] | [334, 9] | cases h | α : Type
x y : α
xs ys : List α
h : x :: xs = y :: ys
⊢ x = y ∧ xs = ys | case refl
α : Type
x : α
xs : List α
⊢ x = x ∧ xs = xs |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.injection_example | [329, 1] | [334, 9] | simp | case refl
α : Type
x : α
xs : List α
⊢ x = x ∧ xs = xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.distinctness_example | [338, 1] | [341, 13] | cases h | α : Type
y : α
ys : List α
h : [] = y :: ys
⊢ false = true | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_ident | [353, 1] | [358, 38] | induction xs with
| nil => rfl
| cons x xs' ih => simp [map, ih] | α : Type
xs : List α
⊢ map (fun x => x) xs = xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_ident | [353, 1] | [358, 38] | rfl | case nil
α : Type
⊢ map (fun x => x) [] = [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_ident | [353, 1] | [358, 38] | simp [map, ih] | case cons
α : Type
x : α
xs' : List α
ih : map (fun x => x) xs' = xs'
⊢ map (fun x => x) (x :: xs') = x :: xs' | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_comp | [360, 1] | [366, 38] | induction xs with
| nil => rfl
| cons x xs' ih => simp [map, ih] | α β γ : Type
f : α → β
g : β → γ
xs : List α
⊢ map g (map f xs) = map (fun x => g (f x)) xs | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_comp | [360, 1] | [366, 38] | rfl | case nil
α β γ : Type
f : α → β
g : β → γ
⊢ map g (map f []) = map (fun x => g (f x)) [] | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_comp | [360, 1] | [366, 38] | simp [map, ih] | case cons
α β γ : Type
f : α → β
g : β → γ
x : α
xs' : List α
ih : map g (map f xs') = map (fun x => g (f x)) xs'
⊢ map g (map f (x :: xs')) = map (fun x => g (f x)) (x :: xs') | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_append | [368, 1] | [374, 38] | induction xs with
| nil => rfl
| cons x xs' ih => simp [map, ih] | α β : Type
f : α → β
xs ys : List α
⊢ map f (xs ++ ys) = map f xs ++ map f ys | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_append | [368, 1] | [374, 38] | rfl | case nil
α β : Type
f : α → β
ys : List α
⊢ map f ([] ++ ys) = map f [] ++ map f ys | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_append | [368, 1] | [374, 38] | simp [map, ih] | case cons
α β : Type
f : α → β
ys : List α
x : α
xs' : List α
ih : map f (xs' ++ ys) = map f xs' ++ map f ys
⊢ map f (x :: xs' ++ ys) = map f (x :: xs') ++ map f ys | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add | [410, 1] | [415, 29] | cases Classical.em (m ≤ n) with
| inl h => simp [min, h]
| inr h => simp [min, h] | l m n : ℕ
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add | [410, 1] | [415, 29] | simp [min, h] | case inl
l m n : ℕ
h : m ≤ n
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add | [410, 1] | [415, 29] | simp [min, h] | case inr
l m n : ℕ
h : ¬m ≤ n
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add_match | [417, 1] | [421, 33] | simp [min, h] | l m n : ℕ
h : m ≤ n
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add_match | [417, 1] | [421, 33] | simp [min, h] | l m n : ℕ
h : ¬m ≤ n
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add_if | [423, 1] | [428, 21] | simp [min, h] | l m n : ℕ
h : m ≤ n
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.min_add_add_if | [423, 1] | [428, 21] | simp [min, h] | l m n : ℕ
h : ¬m ≤ n
⊢ min (m + l) (n + l) = min m n + l | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_zip | [430, 1] | [438, 62] | induction xs generalizing ys with
| nil => simp [min, length]
| cons x xs' ih =>
cases ys with
| nil => rfl
| cons y ys' => simp [zip, length, ih ys', min_add_add] | α β : Type
xs : List α
ys : List β
⊢ length (zip xs ys) = min (length xs) (length ys) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_zip | [430, 1] | [438, 62] | simp [min, length] | case nil
α β : Type
ys : List β
⊢ length (zip [] ys) = min (length []) (length ys) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_zip | [430, 1] | [438, 62] | cases ys with
| nil => rfl
| cons y ys' => simp [zip, length, ih ys', min_add_add] | case cons
α β : Type
x : α
xs' : List α
ih : ∀ (ys : List β), length (zip xs' ys) = min (length xs') (length ys)
ys : List β
⊢ length (zip (x :: xs') ys) = min (length (x :: xs')) (length ys) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_zip | [430, 1] | [438, 62] | rfl | case cons.nil
α β : Type
x : α
xs' : List α
ih : ∀ (ys : List β), length (zip xs' ys) = min (length xs') (length ys)
⊢ length (zip (x :: xs') []) = min (length (x :: xs')) (length []) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_zip | [430, 1] | [438, 62] | simp [zip, length, ih ys', min_add_add] | case cons.cons
α β : Type
x : α
xs' : List α
ih : ∀ (ys : List β), length (zip xs' ys) = min (length xs') (length ys)
y : β
ys' : List β
⊢ length (zip (x :: xs') (y :: ys')) = min (length (x :: xs')) (length (y :: ys')) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_zip | [440, 1] | [448, 31] | simp [zip, map, map_zip f g xs ys] | α α' β β' : Type
f : α → α'
g : β → β'
x : α
xs : List α
y : β
ys : List β
⊢ map (fun ab => (f ab.fst, g ab.snd)) (zip (x :: xs) (y :: ys)) = zip (map f (x :: xs)) (map g (y :: ys)) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_zip | [440, 1] | [448, 31] | rfl | α α' β β' : Type
f : α → α'
g : β → β'
x✝ : List β
⊢ map (fun ab => (f ab.fst, g ab.snd)) (zip [] x✝) = zip (map f []) (map g x✝) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.map_zip | [440, 1] | [448, 31] | rfl | α α' β β' : Type
f : α → α'
g : β → β'
head✝ : α
tail✝ : List α
⊢ map (fun ab => (f ab.fst, g ab.snd)) (zip (head✝ :: tail✝) []) = zip (map f (head✝ :: tail✝)) (map g []) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror | [478, 1] | [483, 56] | induction t with
| empty => rfl
| node a l r ih_l ih_r => simp [mirror, ih_l, ih_r] | α : Type
t : BTree α
⊢ mirror (mirror t) = t | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror | [478, 1] | [483, 56] | rfl | case empty
α : Type
⊢ mirror (mirror BTree.empty) = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror | [478, 1] | [483, 56] | simp [mirror, ih_l, ih_r] | case node
α : Type
a : α
l r : BTree α
ih_l : mirror (mirror l) = l
ih_r : mirror (mirror r) = r
⊢ mirror (mirror (BTree.node a l r)) = BTree.node a l r | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror_calc | [485, 1] | [499, 37] | rfl | α : Type
⊢ mirror (mirror BTree.empty) = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror_calc | [485, 1] | [499, 37] | rfl | α : Type
a : α
l r : BTree α
⊢ mirror (mirror (BTree.node a l r)) = mirror (BTree.node a (mirror r) (mirror l)) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror_calc | [485, 1] | [499, 37] | rfl | α : Type
a : α
l r : BTree α
⊢ mirror (BTree.node a (mirror r) (mirror l)) = BTree.node a (mirror (mirror l)) (mirror (mirror r)) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror_calc | [485, 1] | [499, 37] | rw [mirror_mirror_calc l] | α : Type
a : α
l r : BTree α
⊢ BTree.node a (mirror (mirror l)) (mirror (mirror r)) = BTree.node a l (mirror (mirror r)) | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_mirror_calc | [485, 1] | [499, 37] | rw [mirror_mirror_calc r] | α : Type
a : α
l r : BTree α
⊢ BTree.node a l (mirror (mirror r)) = BTree.node a l r | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_Eq_empty_Iff | [501, 1] | [504, 41] | simp [mirror] | α : Type
⊢ mirror BTree.empty = BTree.empty ↔ BTree.empty = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.mirror_Eq_empty_Iff | [501, 1] | [504, 41] | simp [mirror] | α : Type
a✝² : α
a✝¹ a✝ : BTree α
⊢ mirror (BTree.node a✝² a✝¹ a✝) = BTree.empty ↔ BTree.node a✝² a✝¹ a✝ = BTree.empty | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_listOfVec | [525, 1] | [529, 46] | rfl | α : Type
⊢ List.length (listOfVec Vec.nil) = 0 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe05_FunctionalProgramming_Demo.lean | LoVe.length_listOfVec | [525, 1] | [529, 46] | simp [listOfVec, length_listOfVec _ v] | α : Type
a : α
n✝ : ℕ
v : Vec α n✝
⊢ List.length (listOfVec (Vec.cons a v)) = n✝ + 1 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.fst_of_two_props | [31, 1] | [36, 13] | intro a b | ⊢ ∀ (a b : Prop), a → b → a | a b : Prop
⊢ a → b → a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.fst_of_two_props | [31, 1] | [36, 13] | intro ha hb | a b : Prop
⊢ a → b → a | a b : Prop
ha : a
hb : b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.fst_of_two_props | [31, 1] | [36, 13] | apply ha | a b : Prop
ha : a
hb : b
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.fst_of_two_props_params | [60, 1] | [62, 14] | apply ha | a b : Prop
ha : a
hb : b
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.prop_comp | [66, 1] | [72, 13] | intro ha | a b c : Prop
hab : a → b
hbc : b → c
⊢ a → c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ c |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.prop_comp | [66, 1] | [72, 13] | apply hbc | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ c | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.prop_comp | [66, 1] | [72, 13] | apply hab | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ b | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.prop_comp | [66, 1] | [72, 13] | apply ha | a b c : Prop
hab : a → b
hbc : b → c
ha : a
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.fst_of_two_props_exact | [86, 1] | [88, 14] | exact ha | a b : Prop
ha : a
hb : b
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.fst_of_two_props_assumption | [93, 1] | [96, 16] | assumption | a b : Prop
ha : a
hb : b
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap | [130, 1] | [138, 14] | intro hab | a b : Prop
⊢ a ∧ b → b ∧ a | a b : Prop
hab : a ∧ b
⊢ b ∧ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap | [130, 1] | [138, 14] | apply And.intro | a b : Prop
hab : a ∧ b
⊢ b ∧ a | case left
a b : Prop
hab : a ∧ b
⊢ b
case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap | [130, 1] | [138, 14] | apply And.right | case left
a b : Prop
hab : a ∧ b
⊢ b
case right
a b : Prop
hab : a ∧ b
⊢ a | case left.self
a b : Prop
hab : a ∧ b
⊢ ?left.a ∧ b
case left.a
a b : Prop
hab : a ∧ b
⊢ Prop
case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap | [130, 1] | [138, 14] | exact hab | case left.self
a b : Prop
hab : a ∧ b
⊢ ?left.a ∧ b
case left.a
a b : Prop
hab : a ∧ b
⊢ Prop
case right
a b : Prop
hab : a ∧ b
⊢ a | case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap | [130, 1] | [138, 14] | apply And.left | case right
a b : Prop
hab : a ∧ b
⊢ a | case right.self
a b : Prop
hab : a ∧ b
⊢ a ∧ ?right.b
case right.b
a b : Prop
hab : a ∧ b
⊢ Prop |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap | [130, 1] | [138, 14] | exact hab | case right.self
a b : Prop
hab : a ∧ b
⊢ a ∧ ?right.b
case right.b
a b : Prop
hab : a ∧ b
⊢ Prop | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap_braces | [155, 1] | [161, 27] | intro a b hab | ⊢ ∀ (a b : Prop), a ∧ b → b ∧ a | a b : Prop
hab : a ∧ b
⊢ b ∧ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap_braces | [155, 1] | [161, 27] | apply And.intro | a b : Prop
hab : a ∧ b
⊢ b ∧ a | case left
a b : Prop
hab : a ∧ b
⊢ b
case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap_braces | [155, 1] | [161, 27] | { exact And.right hab } | case left
a b : Prop
hab : a ∧ b
⊢ b
case right
a b : Prop
hab : a ∧ b
⊢ a | case right
a b : Prop
hab : a ∧ b
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap_braces | [155, 1] | [161, 27] | { exact And.left hab } | case right
a b : Prop
hab : a ∧ b
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap_braces | [155, 1] | [161, 27] | exact And.right hab | case left
a b : Prop
hab : a ∧ b
⊢ b | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.And_swap_braces | [155, 1] | [161, 27] | exact And.left hab | case right
a b : Prop
hab : a ∧ b
⊢ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.f5_if | [172, 1] | [174, 15] | exact h 5 | h : ∀ (n : ℕ), f n = n
⊢ f 5 = 5 | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | intro hab | a b : Prop
⊢ a ∨ b → b ∨ a | a b : Prop
hab : a ∨ b
⊢ b ∨ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | apply Or.elim hab | a b : Prop
hab : a ∨ b
⊢ b ∨ a | case left
a b : Prop
hab : a ∨ b
⊢ a → b ∨ a
case right
a b : Prop
hab : a ∨ b
⊢ b → b ∨ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | { intro ha
exact Or.inr ha } | case left
a b : Prop
hab : a ∨ b
⊢ a → b ∨ a
case right
a b : Prop
hab : a ∨ b
⊢ b → b ∨ a | case right
a b : Prop
hab : a ∨ b
⊢ b → b ∨ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | { intro hb
exact Or.inl hb } | case right
a b : Prop
hab : a ∨ b
⊢ b → b ∨ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | intro ha | case left
a b : Prop
hab : a ∨ b
⊢ a → b ∨ a | case left
a b : Prop
hab : a ∨ b
ha : a
⊢ b ∨ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | exact Or.inr ha | case left
a b : Prop
hab : a ∨ b
ha : a
⊢ b ∨ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | intro hb | case right
a b : Prop
hab : a ∨ b
⊢ b → b ∨ a | case right
a b : Prop
hab : a ∨ b
hb : b
⊢ b ∨ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.Or_swap | [177, 1] | [185, 24] | exact Or.inl hb | case right
a b : Prop
hab : a ∨ b
hb : b
⊢ b ∨ a | no goals |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.modus_ponens | [187, 1] | [192, 13] | intro hab ha | a b : Prop
⊢ (a → b) → a → b | a b : Prop
hab : a → b
ha : a
⊢ b |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.modus_ponens | [187, 1] | [192, 13] | apply hab | a b : Prop
hab : a → b
ha : a
⊢ b | a b : Prop
hab : a → b
ha : a
⊢ a |
https://github.com/BrownCS1951x/fpv2023.git | 9aaf6b5c454aa9a70fc4e6807adf3123b001ea66 | LoVe/Lectures/LoVe03_BackwardProofs_Demo.lean | LoVe.BackwardProofs.modus_ponens | [187, 1] | [192, 13] | exact ha | a b : Prop
hab : a → b
ha : a
⊢ a | no goals |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.