Datasets:
pkuAI4M
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lean_github

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https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
visited_subset_dft_aux
[388, 1]
[409, 17]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† dft_aux g (x :: stack) visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† dft_aux g (x :: stack) visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
visited_subset_dft_aux
[388, 1]
[409, 17]
simp only [if_neg c1]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
visited_subset_dft_aux
[388, 1]
[409, 17]
trans (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† x :: visited Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
visited_subset_dft_aux
[388, 1]
[409, 17]
simp
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† x :: visited
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ visited βŠ† x :: visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
visited_subset_dft_aux
[388, 1]
[409, 17]
exact ih
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_1
[412, 1]
[424, 15]
simp
Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x :: zs βŠ† xs
Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x ∈ xs ∧ zs βŠ† xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x :: zs βŠ† xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_1
[412, 1]
[424, 15]
constructor
Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x ∈ xs ∧ zs βŠ† xs
case left Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x ∈ xs case right Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ zs βŠ† xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x ∈ xs ∧ zs βŠ† xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_1
[412, 1]
[424, 15]
apply Set.mem_of_subset_of_mem h3 h2
case left Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x ∈ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: case left Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ x ∈ xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_1
[412, 1]
[424, 15]
exact h1
case right Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ zs βŠ† xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right Ξ± : Type xs ys zs : List Ξ± x : Ξ± h1 : zs βŠ† xs h2 : x ∈ ys h3 : ys βŠ† xs ⊒ zs βŠ† xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_2
[427, 1]
[436, 10]
simp at *
Ξ± : Type ws xs ys zs : List Ξ± x : Ξ± h1 : ws ++ ys βŠ† zs h2 : x :: xs βŠ† zs ⊒ x :: ys βŠ† zs
Ξ± : Type ws xs ys zs : List Ξ± x : Ξ± h1 : ws βŠ† zs ∧ ys βŠ† zs h2 : x ∈ zs ∧ xs βŠ† zs ⊒ x ∈ zs ∧ ys βŠ† zs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type ws xs ys zs : List Ξ± x : Ξ± h1 : ws ++ ys βŠ† zs h2 : x :: xs βŠ† zs ⊒ x :: ys βŠ† zs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_2
[427, 1]
[436, 10]
tauto
Ξ± : Type ws xs ys zs : List Ξ± x : Ξ± h1 : ws βŠ† zs ∧ ys βŠ† zs h2 : x ∈ zs ∧ xs βŠ† zs ⊒ x ∈ zs ∧ ys βŠ† zs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type ws xs ys zs : List Ξ± x : Ξ± h1 : ws βŠ† zs ∧ ys βŠ† zs h2 : x ∈ zs ∧ xs βŠ† zs ⊒ x ∈ zs ∧ ys βŠ† zs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
induction stack, visited using dft_aux.induct g
Node : Type inst✝ : DecidableEq Node g : Graph Node stack visited : List Node ⊒ stack βŠ† dft_aux g stack visited
case case1 Node : Type inst✝ : DecidableEq Node g : Graph Node visited✝ : List Node ⊒ [] βŠ† dft_aux g [] visited✝ case case2 Node : Type inst✝ : DecidableEq Node g : Graph Node visited✝ : List Node x✝ : Node xs✝ : List Node h✝ : x✝ ∈ visited✝ ih1✝ : xs✝ βŠ† dft_aux g xs✝ visited✝ ⊒ x✝ :: xs✝ βŠ† dft_aux g (x✝ :: xs✝) visited✝ case case3 Node : Type inst✝ : DecidableEq Node g : Graph Node visited✝ : List Node x✝ : Node xs✝ : List Node h✝ : x✝ βˆ‰ visited✝ ih1✝ : direct_succ_list g x✝ ++ xs✝ βŠ† dft_aux g (direct_succ_list g x✝ ++ xs✝) (x✝ :: visited✝) ⊒ x✝ :: xs✝ βŠ† dft_aux g (x✝ :: xs✝) visited✝
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node stack visited : List Node ⊒ stack βŠ† dft_aux g stack visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
case _ visited => simp only [dft_aux] simp
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† dft_aux g [] visited
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† dft_aux g [] visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
case _ visited x stack c1 ih => simp only [dft_aux] simp only [if_pos c1] apply extracted_1 (dft_aux g stack visited) visited stack x ih c1 exact visited_subset_dft_aux g stack visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
case _ visited x stack c1 ih => simp only [dft_aux] simp only [if_neg c1] apply extracted_2 (direct_succ_list g x) visited stack (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) x ih apply visited_subset_dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† dft_aux g [] visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† visited
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† dft_aux g [] visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
simp
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† visited
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node ⊒ [] βŠ† visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
simp only [if_pos c1]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g stack visited
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
apply extracted_1 (dft_aux g stack visited) visited stack x ih c1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g stack visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ visited βŠ† dft_aux g stack visited
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ x :: stack βŠ† dft_aux g stack visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
exact visited_subset_dft_aux g stack visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ visited βŠ† dft_aux g stack visited
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : stack βŠ† dft_aux g stack visited ⊒ visited βŠ† dft_aux g stack visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (x :: stack) visited TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
simp only [if_neg c1]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
apply extracted_2 (direct_succ_list g x) visited stack (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) x ih
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
stack_subset_dft_aux
[439, 1]
[460, 84]
apply visited_subset_dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited)
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : direct_succ_list g x ++ stack βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) ⊒ x :: visited βŠ† dft_aux g (direct_succ_list g x ++ stack) (x :: visited) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
simp only [list_cons_to_set_union]
Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑(x :: ys).toFinset βˆͺ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βˆͺ ↑ys.toFinset βˆͺ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑(x :: ys).toFinset βˆͺ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
apply Set.union_subset
Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βˆͺ ↑ys.toFinset βˆͺ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
case sr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βˆͺ ↑ys.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset case tr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βˆͺ ↑ys.toFinset βˆͺ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
apply Set.union_subset
case sr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βˆͺ ↑ys.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
case sr.sr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset case sr.tr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑ys.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
Please generate a tactic in lean4 to solve the state. STATE: case sr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βˆͺ ↑ys.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
simp
case sr.sr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
case sr.sr α : Type inst : DecidableEq α xs ys : List α x : α h1 : x ∈ xs ⊒ x ∈ ys ∨ x ∈ xs
Please generate a tactic in lean4 to solve the state. STATE: case sr.sr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ {x} βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
right
case sr.sr α : Type inst : DecidableEq α xs ys : List α x : α h1 : x ∈ xs ⊒ x ∈ ys ∨ x ∈ xs
case sr.sr.h α : Type inst : DecidableEq α xs ys : List α x : α h1 : x ∈ xs ⊒ x ∈ xs
Please generate a tactic in lean4 to solve the state. STATE: case sr.sr α : Type inst : DecidableEq α xs ys : List α x : α h1 : x ∈ xs ⊒ x ∈ ys ∨ x ∈ xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
exact h1
case sr.sr.h α : Type inst : DecidableEq α xs ys : List α x : α h1 : x ∈ xs ⊒ x ∈ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: case sr.sr.h α : Type inst : DecidableEq α xs ys : List α x : α h1 : x ∈ xs ⊒ x ∈ xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
exact Set.subset_union_left ys.toFinset.toSet xs.toFinset.toSet
case sr.tr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑ys.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: case sr.tr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑ys.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_3
[463, 1]
[478, 71]
exact Set.subset_union_right ys.toFinset.toSet xs.toFinset.toSet
case tr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: case tr Ξ± : Type inst : DecidableEq Ξ± xs ys : List Ξ± x : Ξ± h1 : x ∈ xs ⊒ ↑xs.toFinset βŠ† ↑ys.toFinset βˆͺ ↑xs.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp only [list_cons_to_set_union] at h1
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : S βŠ† ↑(x :: zs).toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : S βŠ† {x} βˆͺ ↑zs.toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : S βŠ† ↑(x :: zs).toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp only [Set.subset_def] at h1
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : S βŠ† {x} βˆͺ ↑zs.toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, x_1 ∈ {x} βˆͺ ↑zs.toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : S βŠ† {x} βˆͺ ↑zs.toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp at h1
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, x_1 ∈ {x} βˆͺ ↑zs.toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, x_1 ∈ {x} βˆͺ ↑zs.toFinset βˆͺ ↑ys.toFinset ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp only [list_cons_to_set_union]
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ↑(x :: ys).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp only [list_append_to_set_union]
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset)
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑xs.toFinset βˆͺ ↑zs.toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑(xs ++ zs).toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp only [Set.subset_def]
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑xs.toFinset βˆͺ ↑zs.toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset)
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ βˆ€ x_1 ∈ ↑xs.toFinset βˆͺ S, x_1 ∈ ↑xs.toFinset βˆͺ ↑zs.toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ ↑xs.toFinset βˆͺ S βŠ† ↑xs.toFinset βˆͺ ↑zs.toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
simp
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ βˆ€ x_1 ∈ ↑xs.toFinset βˆͺ S, x_1 ∈ ↑xs.toFinset βˆͺ ↑zs.toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset)
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ βˆ€ (x_1 : Node), x_1 ∈ xs ∨ x_1 ∈ S β†’ x_1 = x ∨ (x_1 ∈ xs ∨ x_1 ∈ zs) ∨ x_1 ∈ ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ βˆ€ x_1 ∈ ↑xs.toFinset βˆͺ S, x_1 ∈ ↑xs.toFinset βˆͺ ↑zs.toFinset βˆͺ ({x} βˆͺ ↑ys.toFinset) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
intro a a1
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ βˆ€ (x_1 : Node), x_1 ∈ xs ∨ x_1 ∈ S β†’ x_1 = x ∨ (x_1 ∈ xs ∨ x_1 ∈ zs) ∨ x_1 ∈ ys
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys a : Node a1 : a ∈ xs ∨ a ∈ S ⊒ a = x ∨ (a ∈ xs ∨ a ∈ zs) ∨ a ∈ ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys ⊒ βˆ€ (x_1 : Node), x_1 ∈ xs ∨ x_1 ∈ S β†’ x_1 = x ∨ (x_1 ∈ xs ∨ x_1 ∈ zs) ∨ x_1 ∈ ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
specialize h1 a
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys a : Node a1 : a ∈ xs ∨ a ∈ S ⊒ a = x ∨ (a ∈ xs ∨ a ∈ zs) ∨ a ∈ ys
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x a : Node a1 : a ∈ xs ∨ a ∈ S h1 : a ∈ S β†’ (a = x ∨ a ∈ zs) ∨ a ∈ ys ⊒ a = x ∨ (a ∈ xs ∨ a ∈ zs) ∨ a ∈ ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x : Node h1 : βˆ€ x_1 ∈ S, (x_1 = x ∨ x_1 ∈ zs) ∨ x_1 ∈ ys a : Node a1 : a ∈ xs ∨ a ∈ S ⊒ a = x ∨ (a ∈ xs ∨ a ∈ zs) ∨ a ∈ ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
extracted_4
[481, 1]
[500, 10]
tauto
Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x a : Node a1 : a ∈ xs ∨ a ∈ S h1 : a ∈ S β†’ (a = x ∨ a ∈ zs) ∨ a ∈ ys ⊒ a = x ∨ (a ∈ xs ∨ a ∈ zs) ∨ a ∈ ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node xs ys zs : List Node S : Set Node x a : Node a1 : a ∈ xs ∨ a ∈ S h1 : a ∈ S β†’ (a = x ∨ a ∈ zs) ∨ a ∈ ys ⊒ a = x ∨ (a ∈ xs ∨ a ∈ zs) ∨ a ∈ ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
induction stack, visited using dft_aux.induct g
Node : Type inst✝ : DecidableEq Node g : Graph Node stack visited : List Node h1 : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset
case case1 Node : Type inst✝ : DecidableEq Node g : Graph Node visited✝ : List Node h1 : list_direct_succ_set g visited✝ βŠ† ↑[].toFinset βˆͺ ↑visited✝.toFinset ⊒ list_direct_succ_set g (dft_aux g [] visited✝) βŠ† ↑(dft_aux g [] visited✝).toFinset case case2 Node : Type inst✝ : DecidableEq Node g : Graph Node visited✝ : List Node x✝ : Node xs✝ : List Node h✝ : x✝ ∈ visited✝ ih1✝ : list_direct_succ_set g visited✝ βŠ† ↑xs✝.toFinset βˆͺ ↑visited✝.toFinset β†’ list_direct_succ_set g (dft_aux g xs✝ visited✝) βŠ† ↑(dft_aux g xs✝ visited✝).toFinset h1 : list_direct_succ_set g visited✝ βŠ† ↑(x✝ :: xs✝).toFinset βˆͺ ↑visited✝.toFinset ⊒ list_direct_succ_set g (dft_aux g (x✝ :: xs✝) visited✝) βŠ† ↑(dft_aux g (x✝ :: xs✝) visited✝).toFinset case case3 Node : Type inst✝ : DecidableEq Node g : Graph Node visited✝ : List Node x✝ : Node xs✝ : List Node h✝ : x✝ βˆ‰ visited✝ ih1✝ : list_direct_succ_set g (x✝ :: visited✝) βŠ† ↑(direct_succ_list g x✝ ++ xs✝).toFinset βˆͺ ↑(x✝ :: visited✝).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x✝ ++ xs✝) (x✝ :: visited✝)) βŠ† ↑(dft_aux g (direct_succ_list g x✝ ++ xs✝) (x✝ :: visited✝)).toFinset h1 : list_direct_succ_set g visited✝ βŠ† ↑(x✝ :: xs✝).toFinset βˆͺ ↑visited✝.toFinset ⊒ list_direct_succ_set g (dft_aux g (x✝ :: xs✝) visited✝) βŠ† ↑(dft_aux g (x✝ :: xs✝) visited✝).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node stack visited : List Node h1 : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
case _ visited => simp at h1 simp only [dft_aux] simp exact h1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† ↑[].toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† ↑[].toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
case _ visited x stack c1 ih => simp only [dft_aux] simp only [if_neg c1] apply ih simp only [list_direct_succ_set_cons] exact extracted_4 (direct_succ_list g x) visited stack (list_direct_succ_set g visited) x h1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (x :: stack) visited) βŠ† ↑(dft_aux g (x :: stack) visited).toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (x :: stack) visited) βŠ† ↑(dft_aux g (x :: stack) visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp at h1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† ↑[].toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† ↑[].toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g visited βŠ† ↑visited.toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g (dft_aux g [] visited) βŠ† ↑(dft_aux g [] visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g visited βŠ† ↑visited.toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g visited βŠ† {a | a ∈ visited}
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g visited βŠ† ↑visited.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
exact h1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g visited βŠ† {a | a ∈ visited}
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node h1 : list_direct_succ_set g visited βŠ† {a | a ∈ visited} ⊒ list_direct_succ_set g visited βŠ† {a | a ∈ visited} TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (x :: stack) visited) βŠ† ↑(dft_aux g (x :: stack) visited).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (x :: stack) visited) βŠ† ↑(dft_aux g (x :: stack) visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp only [if_pos c1]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
apply ih
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
trans (x :: stack).toFinset.toSet βˆͺ visited.toFinset.toSet
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
exact h1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
exact extracted_3 visited stack x c1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x ∈ visited ih : list_direct_succ_set g visited βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset β†’ list_direct_succ_set g (dft_aux g stack visited) βŠ† ↑(dft_aux g stack visited).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset βŠ† ↑stack.toFinset βˆͺ ↑visited.toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp only [dft_aux]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (x :: stack) visited) βŠ† ↑(dft_aux g (x :: stack) visited).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (x :: stack) visited) βŠ† ↑(dft_aux g (x :: stack) visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp only [if_neg c1]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(if x ∈ visited then dft_aux g stack visited else dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
apply ih
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
simp only [list_direct_succ_set_cons]
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ ↑(direct_succ_list g x).toFinset βˆͺ list_direct_succ_set g visited βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux_aux
[503, 1]
[531, 99]
exact extracted_4 (direct_succ_list g x) visited stack (list_direct_succ_set g visited) x h1
Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ ↑(direct_succ_list g x).toFinset βˆͺ list_direct_succ_set g visited βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node visited : List Node x : Node stack : List Node c1 : x βˆ‰ visited ih : list_direct_succ_set g (x :: visited) βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset β†’ list_direct_succ_set g (dft_aux g (direct_succ_list g x ++ stack) (x :: visited)) βŠ† ↑(dft_aux g (direct_succ_list g x ++ stack) (x :: visited)).toFinset h1 : list_direct_succ_set g visited βŠ† ↑(x :: stack).toFinset βˆͺ ↑visited.toFinset ⊒ ↑(direct_succ_list g x).toFinset βˆͺ list_direct_succ_set g visited βŠ† ↑(direct_succ_list g x ++ stack).toFinset βˆͺ ↑(x :: visited).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux
[534, 1]
[543, 9]
apply list_direct_succ_set_closed_dft_aux_aux
Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ list_direct_succ_set g (dft_aux g stack []) βŠ† ↑(dft_aux g stack []).toFinset
case h1 Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ list_direct_succ_set g [] βŠ† ↑stack.toFinset βˆͺ ↑[].toFinset
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ list_direct_succ_set g (dft_aux g stack []) βŠ† ↑(dft_aux g stack []).toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux
[534, 1]
[543, 9]
simp only [list_direct_succ_set]
case h1 Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ list_direct_succ_set g [] βŠ† ↑stack.toFinset βˆͺ ↑[].toFinset
case h1 Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ {y | βˆƒ x ∈ [], βˆƒ ys, y ∈ ys ∧ (x, ys) ∈ g} βŠ† ↑stack.toFinset βˆͺ ↑[].toFinset
Please generate a tactic in lean4 to solve the state. STATE: case h1 Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ list_direct_succ_set g [] βŠ† ↑stack.toFinset βˆͺ ↑[].toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
list_direct_succ_set_closed_dft_aux
[534, 1]
[543, 9]
simp
case h1 Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ {y | βˆƒ x ∈ [], βˆƒ ys, y ∈ ys ∧ (x, ys) ∈ g} βŠ† ↑stack.toFinset βˆͺ ↑[].toFinset
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h1 Node : Type inst✝ : DecidableEq Node g : Graph Node stack : List Node ⊒ {y | βˆƒ x ∈ [], βˆƒ ys, y ∈ ys ∧ (x, ys) ∈ g} βŠ† ↑stack.toFinset βˆͺ ↑[].toFinset TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
base_of_reachable_from_list_is_subset_of_reachable_from_list
[613, 1]
[623, 40]
simp only [Set.subset_def]
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node ⊒ ↑xs.toFinset βŠ† reachable_from_list g xs
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node ⊒ βˆ€ x ∈ ↑xs.toFinset, x ∈ reachable_from_list g xs
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node ⊒ ↑xs.toFinset βŠ† reachable_from_list g xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
base_of_reachable_from_list_is_subset_of_reachable_from_list
[613, 1]
[623, 40]
intro x a1
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node ⊒ βˆ€ x ∈ ↑xs.toFinset, x ∈ reachable_from_list g xs
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node x : Node a1 : x ∈ ↑xs.toFinset ⊒ x ∈ reachable_from_list g xs
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node ⊒ βˆ€ x ∈ ↑xs.toFinset, x ∈ reachable_from_list g xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
base_of_reachable_from_list_is_subset_of_reachable_from_list
[613, 1]
[623, 40]
simp at a1
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node x : Node a1 : x ∈ ↑xs.toFinset ⊒ x ∈ reachable_from_list g xs
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node x : Node a1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node x : Node a1 : x ∈ ↑xs.toFinset ⊒ x ∈ reachable_from_list g xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
base_of_reachable_from_list_is_subset_of_reachable_from_list
[613, 1]
[623, 40]
exact reachable_from_list.base x a1
Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node x : Node a1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs : List Node x : Node a1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
simp only [Set.subset_def]
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys ⊒ reachable_from_list g xs βŠ† reachable_from_list g ys
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys ⊒ βˆ€ x ∈ reachable_from_list g xs, x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys ⊒ reachable_from_list g xs βŠ† reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
intro x a1
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys ⊒ βˆ€ x ∈ reachable_from_list g xs, x ∈ reachable_from_list g ys
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x : Node a1 : x ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys ⊒ βˆ€ x ∈ reachable_from_list g xs, x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
induction a1
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x : Node a1 : x ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g ys
case base Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x x✝ : Node a✝ : x✝ ∈ xs ⊒ x✝ ∈ reachable_from_list g ys case step Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x x✝ : Node e✝ : Node Γ— List Node a✝² : e✝ ∈ g a✝¹ : x✝ ∈ e✝.2 a✝ : reachable_from_list g xs e✝.1 a_ih✝ : e✝.1 ∈ reachable_from_list g ys ⊒ x✝ ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x : Node a1 : x ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
case base a ih => apply reachable_from_list.base apply Set.mem_of_subset_of_mem h1 ih
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
case step x e ih_1 ih_2 _ ih_4 => exact reachable_from_list.step x e ih_1 ih_2 ih_4
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 a✝ : reachable_from_list g xs e.1 ih_4 : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 a✝ : reachable_from_list g xs e.1 ih_4 : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
apply reachable_from_list.base
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ reachable_from_list g ys
case a Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
apply Set.mem_of_subset_of_mem h1 ih
case a Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x a : Node ih : a ∈ xs ⊒ a ∈ ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_mono
[626, 1]
[641, 56]
exact reachable_from_list.step x e ih_1 ih_2 ih_4
Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 a✝ : reachable_from_list g xs e.1 ih_4 : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst✝ : DecidableEq Node g : Graph Node xs ys : List Node h1 : xs βŠ† ys x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 a✝ : reachable_from_list g xs e.1 ih_4 : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
simp only [Set.subset_def]
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ reachable_from_list g (xs ++ ys) βŠ† reachable_from_list g xs βˆͺ reachable_from_list g ys
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ βˆ€ x ∈ reachable_from_list g (xs ++ ys), x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ reachable_from_list g (xs ++ ys) βŠ† reachable_from_list g xs βˆͺ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
intro x a1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ βˆ€ x ∈ reachable_from_list g (xs ++ ys), x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g (xs ++ ys) ⊒ x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ βˆ€ x ∈ reachable_from_list g (xs ++ ys), x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
simp
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g (xs ++ ys) ⊒ x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g (xs ++ ys) ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g (xs ++ ys) ⊒ x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
induction a1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g (xs ++ ys) ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case base Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x x✝ : Node a✝ : x✝ ∈ xs ++ ys ⊒ x✝ ∈ reachable_from_list g xs ∨ x✝ ∈ reachable_from_list g ys case step Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x x✝ : Node e✝ : Node Γ— List Node a✝² : e✝ ∈ g a✝¹ : x✝ ∈ e✝.2 a✝ : reachable_from_list g (xs ++ ys) e✝.1 a_ih✝ : e✝.1 ∈ reachable_from_list g xs ∨ e✝.1 ∈ reachable_from_list g ys ⊒ x✝ ∈ reachable_from_list g xs ∨ x✝ ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g (xs ++ ys) ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
case _ x ih => simp at ih cases ih case inl c1 => left exact reachable_from_list.base x c1 case inr c1 => right exact reachable_from_list.base x c1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ++ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ++ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
case _ x e ih_1 ih_2 ih_3 ih_4 => cases ih_4 case _ left => left exact reachable_from_list.step x e ih_1 ih_2 left case _ right => right exact reachable_from_list.step x e ih_1 ih_2 right
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 ih_4 : e.1 ∈ reachable_from_list g xs ∨ e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 ih_4 : e.1 ∈ reachable_from_list g xs ∨ e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
simp at ih
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ++ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ∨ x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ++ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
cases ih
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ∨ x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case inl Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node h✝ : x ∈ xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys case inr Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node h✝ : x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node ih : x ∈ xs ∨ x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
case inl c1 => left exact reachable_from_list.base x c1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
case inr c1 => right exact reachable_from_list.base x c1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
left
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
exact reachable_from_list.base x c1
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ xs ⊒ x ∈ reachable_from_list g xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
right
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
exact reachable_from_list.base x c1
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node c1 : x ∈ ys ⊒ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
cases ih_4
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 ih_4 : e.1 ∈ reachable_from_list g xs ∨ e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case inl Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 h✝ : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys case inr Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 h✝ : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 ih_4 : e.1 ∈ reachable_from_list g xs ∨ e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
case _ left => left exact reachable_from_list.step x e ih_1 ih_2 left
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
case _ right => right exact reachable_from_list.step x e ih_1 ih_2 right
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
left
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
exact reachable_from_list.step x e ih_1 ih_2 left
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 left : e.1 ∈ reachable_from_list g xs ⊒ x ∈ reachable_from_list g xs TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
right
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_left
[644, 1]
[671, 59]
exact reachable_from_list.step x e ih_1 ih_2 right
case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x✝ x : Node e : Node Γ— List Node ih_1 : e ∈ g ih_2 : x ∈ e.2 ih_3 : reachable_from_list g (xs ++ ys) e.1 right : e.1 ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g ys TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_right
[674, 1]
[692, 20]
simp only [Set.subset_def]
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ reachable_from_list g xs βˆͺ reachable_from_list g ys βŠ† reachable_from_list g (xs ++ ys)
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ βˆ€ x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys, x ∈ reachable_from_list g (xs ++ ys)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ reachable_from_list g xs βˆͺ reachable_from_list g ys βŠ† reachable_from_list g (xs ++ ys) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_right
[674, 1]
[692, 20]
intro x a1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ βˆ€ x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys, x ∈ reachable_from_list g (xs ++ ys)
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys ⊒ x ∈ reachable_from_list g (xs ++ ys)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node ⊒ βˆ€ x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys, x ∈ reachable_from_list g (xs ++ ys) TACTIC:
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/DFT.lean
reachable_from_list_of_append_right
[674, 1]
[692, 20]
simp at a1
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys ⊒ x ∈ reachable_from_list g (xs ++ ys)
Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g xs ∨ x ∈ reachable_from_list g ys ⊒ x ∈ reachable_from_list g (xs ++ ys)
Please generate a tactic in lean4 to solve the state. STATE: Node : Type inst : DecidableEq Node g : Graph Node xs ys : List Node x : Node a1 : x ∈ reachable_from_list g xs βˆͺ reachable_from_list g ys ⊒ x ∈ reachable_from_list g (xs ++ ys) TACTIC: