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pkuAI4M
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lean_github

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https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.mirror_IsFull
[124, 1]
[131, 15]
rw [mirror_mirror] at fmmt
α : Type t : BTree α fmt : IsFull (mirror t) fmmt : IsFull (mirror (mirror t)) ⊢ IsFull t
α : Type t : BTree α fmt : IsFull (mirror t) fmmt : IsFull t ⊢ IsFull t
Please generate a tactic in lean4 to solve the state. STATE: α : Type t : BTree α fmt : IsFull (mirror t) fmmt : IsFull (mirror (mirror t)) ⊢ IsFull t TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.mirror_IsFull
[124, 1]
[131, 15]
assumption
α : Type t : BTree α fmt : IsFull (mirror t) fmmt : IsFull t ⊢ IsFull t
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type t : BTree α fmt : IsFull (mirror t) fmmt : IsFull t ⊢ IsFull t TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_eq_empty_iff
[141, 1]
[144, 44]
simp [BTree.map]
α β : Type f : α → β ⊢ map f empty = empty ↔ empty = empty
no goals
Please generate a tactic in lean4 to solve the state. STATE: α β : Type f : α → β ⊢ map f empty = empty ↔ empty = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_eq_empty_iff
[141, 1]
[144, 44]
simp [BTree.map]
α β : Type f : α → β a✝² : α a✝¹ a✝ : BTree α ⊢ map f (node a✝² a✝¹ a✝) = empty ↔ node a✝² a✝¹ a✝ = empty
no goals
Please generate a tactic in lean4 to solve the state. STATE: α β : Type f : α → β a✝² : α a✝¹ a✝ : BTree α ⊢ map f (node a✝² a✝¹ a✝) = empty ↔ node a✝² a✝¹ a✝ = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
intro t hfull
α β : Type f : α → β ⊢ ∀ (t : BTree α), IsFull t → IsFull (map f t)
α β : Type f : α → β t : BTree α hfull : IsFull t ⊢ IsFull (map f t)
Please generate a tactic in lean4 to solve the state. STATE: α β : Type f : α → β ⊢ ∀ (t : BTree α), IsFull t → IsFull (map f t) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
induction hfull with | empty => simp [BTree.map] exact IsFull.empty | node a l r hl hr hiff ihl ihr => simp [BTree.map] apply IsFull.node { exact ihl } { exact ihr } { simp [BTree.map_eq_empty_iff] assumption }
α β : Type f : α → β t : BTree α hfull : IsFull t ⊢ IsFull (map f t)
no goals
Please generate a tactic in lean4 to solve the state. STATE: α β : Type f : α → β t : BTree α hfull : IsFull t ⊢ IsFull (map f t) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
simp [BTree.map]
case empty α β : Type f : α → β t : BTree α ⊢ IsFull (map f empty)
case empty α β : Type f : α → β t : BTree α ⊢ IsFull empty
Please generate a tactic in lean4 to solve the state. STATE: case empty α β : Type f : α → β t : BTree α ⊢ IsFull (map f empty) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
exact IsFull.empty
case empty α β : Type f : α → β t : BTree α ⊢ IsFull empty
no goals
Please generate a tactic in lean4 to solve the state. STATE: case empty α β : Type f : α → β t : BTree α ⊢ IsFull empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
simp [BTree.map]
case node α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f (node a l r))
case node α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (node (f a) (map f l) (map f r))
Please generate a tactic in lean4 to solve the state. STATE: case node α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f (node a l r)) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
apply IsFull.node
case node α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (node (f a) (map f l) (map f r))
case node.hl α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f l) case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
Please generate a tactic in lean4 to solve the state. STATE: case node α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (node (f a) (map f l) (map f r)) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
{ exact ihl }
case node.hl α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f l) case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
Please generate a tactic in lean4 to solve the state. STATE: case node.hl α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f l) case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
{ exact ihr }
case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
Please generate a tactic in lean4 to solve the state. STATE: case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
{ simp [BTree.map_eq_empty_iff] assumption }
case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
no goals
Please generate a tactic in lean4 to solve the state. STATE: case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
exact ihl
case node.hl α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f l)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case node.hl α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f l) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
exact ihr
case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case node.hr α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ IsFull (map f r) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
simp [BTree.map_eq_empty_iff]
case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty
case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ l = empty ↔ r = empty
Please generate a tactic in lean4 to solve the state. STATE: case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ map f l = empty ↔ map f r = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab5Solution.lean
LoVe.BTree.map_mirror
[148, 1]
[162, 21]
assumption
case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ l = empty ↔ r = empty
no goals
Please generate a tactic in lean4 to solve the state. STATE: case node.hiff α β : Type f : α → β t : BTree α a : α l r : BTree α hl : IsFull l hr : IsFull r hiff : l = empty ↔ r = empty ihl : IsFull (map f l) ihr : IsFull (map f r) ⊢ l = empty ↔ r = empty TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.proof_irrel
[148, 1]
[150, 9]
rfl
a : Prop h₁ h₂ : a ⊢ h₁ = h₂
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : Prop h₁ h₂ : a ⊢ h₁ = h₂ TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.FullBTree.mirror_mirror
[388, 1]
[392, 48]
apply Subtype.eq
α : Type t : FullBTree α ⊢ mirror (mirror t) = t
case a α : Type t : FullBTree α ⊢ ↑(mirror (mirror t)) = ↑t
Please generate a tactic in lean4 to solve the state. STATE: α : Type t : FullBTree α ⊢ mirror (mirror t) = t TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.FullBTree.mirror_mirror
[388, 1]
[392, 48]
simp [FullBTree.mirror, LoVe.mirror_mirror]
case a α : Type t : FullBTree α ⊢ ↑(mirror (mirror t)) = ↑t
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a α : Type t : FullBTree α ⊢ ↑(mirror (mirror t)) = ↑t TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Vector.neg_neg
[411, 1]
[415, 22]
apply Subtype.eq
n : ℕ v : Vector ℤ n ⊢ neg (neg v) = v
case a n : ℕ v : Vector ℤ n ⊢ ↑(neg (neg v)) = ↑v
Please generate a tactic in lean4 to solve the state. STATE: n : ℕ v : Vector ℤ n ⊢ neg (neg v) = v TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Vector.neg_neg
[411, 1]
[415, 22]
simp [Vector.neg]
case a n : ℕ v : Vector ℤ n ⊢ ↑(neg (neg v)) = ↑v
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a n : ℕ v : Vector ℤ n ⊢ ↑(neg (neg v)) = ↑v TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.Setoid_Iff
[481, 1]
[484, 9]
rfl
pn₁ pn₂ : ℕ × ℕ ⊢ pn₁ ≈ pn₂ ↔ pn₁.fst + pn₂.snd = pn₂.fst + pn₁.snd
no goals
Please generate a tactic in lean4 to solve the state. STATE: pn₁ pn₂ : ℕ × ℕ ⊢ pn₁ ≈ pn₂ ↔ pn₁.fst + pn₂.snd = pn₂.fst + pn₁.snd TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.zero_Eq
[492, 1]
[498, 9]
rw [Int.zero]
m : ℕ ⊢ zero = Quotient.mk Setoid (m, m)
m : ℕ ⊢ Quotient.mk Setoid (0, 0) = Quotient.mk Setoid (m, m)
Please generate a tactic in lean4 to solve the state. STATE: m : ℕ ⊢ zero = Quotient.mk Setoid (m, m) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.zero_Eq
[492, 1]
[498, 9]
apply Quotient.sound
m : ℕ ⊢ Quotient.mk Setoid (0, 0) = Quotient.mk Setoid (m, m)
case a m : ℕ ⊢ (0, 0) ≈ (m, m)
Please generate a tactic in lean4 to solve the state. STATE: m : ℕ ⊢ Quotient.mk Setoid (0, 0) = Quotient.mk Setoid (m, m) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.zero_Eq
[492, 1]
[498, 9]
rw [Int.Setoid_Iff]
case a m : ℕ ⊢ (0, 0) ≈ (m, m)
case a m : ℕ ⊢ (0, 0).fst + (m, m).snd = (m, m).fst + (0, 0).snd
Please generate a tactic in lean4 to solve the state. STATE: case a m : ℕ ⊢ (0, 0) ≈ (m, m) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.zero_Eq
[492, 1]
[498, 9]
simp
case a m : ℕ ⊢ (0, 0).fst + (m, m).snd = (m, m).fst + (0, 0).snd
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a m : ℕ ⊢ (0, 0).fst + (m, m).snd = (m, m).fst + (0, 0).snd TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.add_Eq
[511, 1]
[513, 9]
rfl
p₁ n₁ p₂ n₂ : ℕ ⊢ add (Quotient.mk Setoid (p₁, n₁)) (Quotient.mk Setoid (p₂, n₂)) = Quotient.mk Setoid (p₁ + p₂, n₁ + n₂)
no goals
Please generate a tactic in lean4 to solve the state. STATE: p₁ n₁ p₂ n₂ : ℕ ⊢ add (Quotient.mk Setoid (p₁, n₁)) (Quotient.mk Setoid (p₂, n₂)) = Quotient.mk Setoid (p₁ + p₂, n₁ + n₂) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.add_zero
[515, 1]
[521, 46]
induction i using Quotient.inductionOn with | h pn => cases pn with | mk p n => simp [Int.zero, Int.add_Eq]
i : Int ⊢ add zero i = i
no goals
Please generate a tactic in lean4 to solve the state. STATE: i : Int ⊢ add zero i = i TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.add_zero
[515, 1]
[521, 46]
cases pn with | mk p n => simp [Int.zero, Int.add_Eq]
case h pn : ℕ × ℕ ⊢ add zero (Quotient.mk Setoid pn) = Quotient.mk Setoid pn
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h pn : ℕ × ℕ ⊢ add zero (Quotient.mk Setoid pn) = Quotient.mk Setoid pn TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Int.add_zero
[515, 1]
[521, 46]
simp [Int.zero, Int.add_Eq]
case h.mk p n : ℕ ⊢ add zero (Quotient.mk Setoid (p, n)) = Quotient.mk Setoid (p, n)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h.mk p n : ℕ ⊢ add zero (Quotient.mk Setoid (p, n)) = Quotient.mk Setoid (p, n) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.UPair.Setoid_Iff
[567, 1]
[571, 9]
rfl
α : Type ab₁ ab₂ : α × α ⊢ ab₁ ≈ ab₂ ↔ {ab₁.fst, ab₁.snd} = {ab₂.fst, ab₂.snd}
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type ab₁ ab₂ : α × α ⊢ ab₁ ≈ ab₂ ↔ {ab₁.fst, ab₁.snd} = {ab₂.fst, ab₂.snd} TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.UPair.mk_symm
[580, 1]
[585, 35]
apply Quotient.sound
α : Type a b : α ⊢ Quotient.mk (Setoid α) (a, b) = Quotient.mk (Setoid α) (b, a)
case a α : Type a b : α ⊢ (a, b) ≈ (b, a)
Please generate a tactic in lean4 to solve the state. STATE: α : Type a b : α ⊢ Quotient.mk (Setoid α) (a, b) = Quotient.mk (Setoid α) (b, a) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.UPair.mk_symm
[580, 1]
[585, 35]
rw [UPair.Setoid_Iff]
case a α : Type a b : α ⊢ (a, b) ≈ (b, a)
case a α : Type a b : α ⊢ {(a, b).fst, (a, b).snd} = {(b, a).fst, (b, a).snd}
Please generate a tactic in lean4 to solve the state. STATE: case a α : Type a b : α ⊢ (a, b) ≈ (b, a) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.UPair.mk_symm
[580, 1]
[585, 35]
simp [Set.unordered_pair_comm]
case a α : Type a b : α ⊢ {(a, b).fst, (a, b).snd} = {(b, a).fst, (b, a).snd}
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a α : Type a b : α ⊢ {(a, b).fst, (a, b).snd} = {(b, a).fst, (b, a).snd} TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
cases pn with | mk p n => simp [Int.normalize] cases Classical.em (p ≥ n) with | inl hpn => simp [*] exact Int.IsCanonical.nonneg | inr hpn => simp [*] exact Int.IsCanonical.nonpos
pn : ℕ × ℕ ⊢ IsCanonical (normalize pn)
no goals
Please generate a tactic in lean4 to solve the state. STATE: pn : ℕ × ℕ ⊢ IsCanonical (normalize pn) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
simp [Int.normalize]
case mk p n : ℕ ⊢ IsCanonical (normalize (p, n))
case mk p n : ℕ ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p))
Please generate a tactic in lean4 to solve the state. STATE: case mk p n : ℕ ⊢ IsCanonical (normalize (p, n)) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
cases Classical.em (p ≥ n) with | inl hpn => simp [*] exact Int.IsCanonical.nonneg | inr hpn => simp [*] exact Int.IsCanonical.nonpos
case mk p n : ℕ ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p))
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mk p n : ℕ ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p)) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
simp [*]
case mk.inl p n : ℕ hpn : p ≥ n ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p))
case mk.inl p n : ℕ hpn : p ≥ n ⊢ IsCanonical (p - n, 0)
Please generate a tactic in lean4 to solve the state. STATE: case mk.inl p n : ℕ hpn : p ≥ n ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p)) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
exact Int.IsCanonical.nonneg
case mk.inl p n : ℕ hpn : p ≥ n ⊢ IsCanonical (p - n, 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mk.inl p n : ℕ hpn : p ≥ n ⊢ IsCanonical (p - n, 0) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
simp [*]
case mk.inr p n : ℕ hpn : ¬p ≥ n ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p))
case mk.inr p n : ℕ hpn : ¬p ≥ n ⊢ IsCanonical (0, n - p)
Please generate a tactic in lean4 to solve the state. STATE: case mk.inr p n : ℕ hpn : ¬p ≥ n ⊢ IsCanonical (if n ≤ p then (p - n, 0) else (0, n - p)) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe12_LogicalFoundationsOfMathematics_Demo.lean
LoVe.Alternative.Int.IsCanonical_normalize
[622, 1]
[635, 37]
exact Int.IsCanonical.nonpos
case mk.inr p n : ℕ hpn : ¬p ≥ n ⊢ IsCanonical (0, n - p)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case mk.inr p n : ℕ hpn : ¬p ≥ n ⊢ IsCanonical (0, n - p) TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_example
[63, 1]
[68, 18]
repeat' apply And.intro
⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_example
[63, 1]
[68, 18]
repeat' apply Even.add_two
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
case left.a.a ⊢ Even 0 case right.left.a.a.a ⊢ Even 1 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_example
[63, 1]
[68, 18]
repeat' sorry
case left.a.a ⊢ Even 0 case right.left.a.a.a ⊢ Even 1 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case left.a.a ⊢ Even 0 case right.left.a.a.a ⊢ Even 1 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_example
[63, 1]
[68, 18]
apply And.intro
case right.right ⊢ Even 3 ∧ Even 0
case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case right.right ⊢ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_example
[63, 1]
[68, 18]
apply Even.add_two
case right.right.left ⊢ Even 3
case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_example
[63, 1]
[68, 18]
sorry
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
repeat' apply And.intro
⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
repeat' first | apply Even.add_two | apply Even.zero
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
case right.left.a.a.a ⊢ Even 1 case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
repeat' sorry
case right.left.a.a.a ⊢ Even 1 case right.right.left.a ⊢ Even 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.left.a.a.a ⊢ Even 1 case right.right.left.a ⊢ Even 1 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
apply And.intro
case right.right ⊢ Even 3 ∧ Even 0
case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case right.right ⊢ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
first | apply Even.add_two | apply Even.zero
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
apply Even.add_two
case right.right.left ⊢ Even 3
case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
apply Even.zero
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.repeat'_first_example
[74, 1]
[82, 18]
sorry
case right.right.left.a ⊢ Even 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left.a ⊢ Even 1 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
repeat' apply And.intro
⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
all_goals try apply Even.add_two
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
case left.a ⊢ Even 2 case right.left.a ⊢ Even 5 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
repeat sorry
case left.a ⊢ Even 2 case right.left.a ⊢ Even 5 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case left.a ⊢ Even 2 case right.left.a ⊢ Even 5 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
apply And.intro
case right.right ⊢ Even 3 ∧ Even 0
case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case right.right ⊢ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
try apply Even.add_two
case right.right.left ⊢ Even 3
case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
apply Even.add_two
case right.right.left ⊢ Even 3
case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.all_goals_try_example
[96, 1]
[101, 17]
sorry
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_example
[106, 1]
[111, 18]
repeat' apply And.intro
⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_example
[106, 1]
[111, 18]
any_goals apply Even.add_two
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
case left.a ⊢ Even 2 case right.left.a ⊢ Even 5 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_example
[106, 1]
[111, 18]
repeat' sorry
case left.a ⊢ Even 2 case right.left.a ⊢ Even 5 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case left.a ⊢ Even 2 case right.left.a ⊢ Even 5 case right.right.left.a ⊢ Even 1 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_example
[106, 1]
[111, 18]
apply And.intro
case right.right ⊢ Even 3 ∧ Even 0
case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case right.right ⊢ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_example
[106, 1]
[111, 18]
apply Even.add_two
case right.right.left ⊢ Even 3
case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_example
[106, 1]
[111, 18]
sorry
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
repeat' apply And.intro
⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
any_goals solve | repeat' first | apply Even.add_two | apply Even.zero
case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
case right.left ⊢ Even 7 case right.right.left ⊢ Even 3
Please generate a tactic in lean4 to solve the state. STATE: case left ⊢ Even 4 case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
repeat' sorry
case right.left ⊢ Even 7 case right.right.left ⊢ Even 3
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
apply And.intro
case right.right ⊢ Even 3 ∧ Even 0
case right.right.left ⊢ Even 3 case right.right.right ⊢ Even 0
Please generate a tactic in lean4 to solve the state. STATE: case right.right ⊢ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
solve | repeat' first | apply Even.add_two | apply Even.zero
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
repeat' first | apply Even.add_two | apply Even.zero
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
first | apply Even.add_two | apply Even.zero
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
apply Even.add_two
case right.right.left ⊢ Even 3
case right.right.left.a ⊢ Even 1
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
apply Even.zero
case right.right.right ⊢ Even 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right ⊢ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.any_goals_solve_repeat_first_example
[116, 1]
[126, 18]
sorry
case right.right.left ⊢ Even 3
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.intro_and_even_example
[157, 1]
[161, 18]
intro_and_even
⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0
case right.left ⊢ Even 7 case right.right.left ⊢ Even 3
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Even 4 ∧ Even 7 ∧ Even 3 ∧ Even 0 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.intro_and_even_example
[157, 1]
[161, 18]
repeat' sorry
case right.left ⊢ Even 7 case right.right.left ⊢ Even 3
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.left ⊢ Even 7 case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.intro_and_even_example
[157, 1]
[161, 18]
sorry
case right.right.left ⊢ Even 3
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left ⊢ Even 3 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.Even_18_and_Even_20
[199, 1]
[204, 19]
apply And.intro
α : Type a : α ⊢ Even 18 ∧ Even 20
case left α : Type a : α ⊢ Even 18 case right α : Type a : α ⊢ Even 20
Please generate a tactic in lean4 to solve the state. STATE: α : Type a : α ⊢ Even 18 ∧ Even 20 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.Even_18_and_Even_20
[199, 1]
[204, 19]
intro_and_even
case left α : Type a : α ⊢ Even 18 case right α : Type a : α ⊢ Even 20
no goals
Please generate a tactic in lean4 to solve the state. STATE: case left α : Type a : α ⊢ Even 18 case right α : Type a : α ⊢ Even 20 TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.hypothesis_example
[229, 1]
[232, 16]
hypothesis
α : Type p : α → Prop a : α hpa : p a ⊢ p a
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type p : α → Prop a : α hpa : p a ⊢ p a TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.abc_a_again
[393, 1]
[395, 20]
destruct_and h
a b c : Prop h : a ∧ b ∧ c ⊢ a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c : Prop h : a ∧ b ∧ c ⊢ a TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.abc_b_again
[397, 1]
[399, 20]
destruct_and h
a b c : Prop h : a ∧ b ∧ c ⊢ b
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c : Prop h : a ∧ b ∧ c ⊢ b TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.abc_bc_again
[401, 1]
[403, 20]
destruct_and h
a b c : Prop h : a ∧ b ∧ c ⊢ b ∧ c
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c : Prop h : a ∧ b ∧ c ⊢ b ∧ c TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.abc_c_again
[408, 1]
[410, 20]
destruct_and h
a b c : Prop h : a ∧ b ∧ c ⊢ c
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c : Prop h : a ∧ b ∧ c ⊢ c TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.Nat.Eq_symm
[477, 1]
[479, 18]
prove_direct
x y : ℕ h : x = y ⊢ y = x
no goals
Please generate a tactic in lean4 to solve the state. STATE: x y : ℕ h : x = y ⊢ y = x TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.Nat.Eq_symm_manual
[481, 1]
[485, 15]
apply symm
x y : ℕ h : x = y ⊢ y = x
case a x y : ℕ h : x = y ⊢ x = y
Please generate a tactic in lean4 to solve the state. STATE: x y : ℕ h : x = y ⊢ y = x TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.Nat.Eq_symm_manual
[481, 1]
[485, 15]
hypothesis
case a x y : ℕ h : x = y ⊢ x = y
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a x y : ℕ h : x = y ⊢ x = y TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.Nat.Eq_trans
[487, 1]
[489, 18]
prove_direct
x y z : ℕ hxy : x = y hyz : y = z ⊢ x = z
no goals
Please generate a tactic in lean4 to solve the state. STATE: x y z : ℕ hxy : x = y hyz : y = z ⊢ x = z TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.List.reverse_twice
[491, 1]
[493, 18]
prove_direct
xs : List ℕ ⊢ List.reverse (List.reverse xs) = xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: xs : List ℕ ⊢ List.reverse (List.reverse xs) = xs TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Lectures/LoVe08_Metaprogramming_Demo.lean
LoVe.List.reverse_twice_library_search
[497, 1]
[499, 20]
library_search
xs : List ℕ ⊢ List.reverse (List.reverse xs) = xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: xs : List ℕ ⊢ List.reverse (List.reverse xs) = xs TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab4Solution.lean
LoVe.reverseAccu_Eq_reverse_append
[30, 1]
[34, 71]
rfl
α : Type as : List α ⊢ reverseAccu as [] = reverse [] ++ as
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type as : List α ⊢ reverseAccu as [] = reverse [] ++ as TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab4Solution.lean
LoVe.reverseAccu_Eq_reverse_append
[30, 1]
[34, 71]
simp [reverse, reverseAccu, reverseAccu_Eq_reverse_append _ xs]
α : Type as : List α x : α xs : List α ⊢ reverseAccu as (x :: xs) = reverse (x :: xs) ++ as
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type as : List α x : α xs : List α ⊢ reverseAccu as (x :: xs) = reverse (x :: xs) ++ as TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab4Solution.lean
LoVe.reverseAccu_eq_reverse
[38, 1]
[40, 42]
simp [reverseAccu_Eq_reverse_append]
α : Type xs : List α ⊢ reverseAccu [] xs = reverse xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type xs : List α ⊢ reverseAccu [] xs = reverse xs TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab4Solution.lean
LoVe.reverseAccu_reverseAccu
[46, 1]
[48, 52]
simp [reverseAccu_eq_reverse, reverse_reverse]
α : Type xs : List α ⊢ reverseAccu [] (reverseAccu [] xs) = xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: α : Type xs : List α ⊢ reverseAccu [] (reverseAccu [] xs) = xs TACTIC:
https://github.com/BrownCS1951x/fpv2023.git
9aaf6b5c454aa9a70fc4e6807adf3123b001ea66
LoVe/Labs/Lab4Solution.lean
LoVe.Vec.meld_append
[167, 1]
[180, 73]
simp [append, meld]
α β γ : Type m n : ℕ f : α → β → γ xs : Vec α m ys : Vec β m ⊢ meld f (append V[] xs) (append V[] ys) = append (meld f V[] V[]) (meld f xs ys)
no goals
Please generate a tactic in lean4 to solve the state. STATE: α β γ : Type m n : ℕ f : α → β → γ xs : Vec α m ys : Vec β m ⊢ meld f (append V[] xs) (append V[] ys) = append (meld f V[] V[]) (meld f xs ys) TACTIC: