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https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 q : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 p_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr a...
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 val✝ : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr a...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 q : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 p_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp intro xs a1 cases a1 case _ left => cases left case _ x a2 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp case _ right => cases right case _ x a2 =...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun ar...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arr...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = x) ∨ βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.in...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun ar...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
intro xs a1
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = x) ∨ βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.in...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) a1 : (βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs) ∨ βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = x) ∨ ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a1
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) a1 : (βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs) ∨ βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum...
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) h✝ : βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs case inr Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) a1 : (βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs) ∨ βˆƒ a ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ left => cases left case _ x a2 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) left : βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) left : βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs ⊒ Sum.inl q_...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ right => cases right case _ x a2 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) right : βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) right : βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases left
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) left : βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
case intro Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) w✝ : EpsilonArrow Οƒ_0 h✝ : w✝ ∈ M_0.epsilon_arrow_list ∧ w✝.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) w✝.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) left : βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs ⊒ Sum.inl q_...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ x a2 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2 : x ∈ M_0.epsilon_arrow_list ∧ x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2 : x ∈ M_0.epsilon_arrow_list ∧ x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2 : x ∈ M_0.epsilon_arrow_list ∧ x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
case intro Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 left✝ : x ∈ M_0.epsilon_arrow_list right✝ : x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2 : x ∈ M_0.epsilon_arrow_list ∧ x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right : x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right : x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.s...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2_right
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right : x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
case intro Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list left✝ : x.start_state = p_0 right✝ : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right : x.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) x.s...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Su...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a2_right_right]
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ List....
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Su...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ List....
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_0 a2_left : x ∈ M_0.epsilon_arrow_list a2_right_left : x.start_state = p_0 a2_right_right : List.map (Su...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases right
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) right : βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
case intro Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) w✝ : Οƒ_0 h✝ : w✝ ∈ M_0.accepting_state_list ∧ w✝ = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) right : βˆƒ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ x a2 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2 : x ∈ M_0.accepting_state_list ∧ x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2 : x ∈ M_0.accepting_state_list ∧ x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2 : x ∈ M_0.accepting_state_list ∧ x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
case intro Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 left✝ : x ∈ M_0.accepting_state_list right✝ : x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2 : x ∈ M_0.accepting_state_list ∧ x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right : x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right : x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2_right
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right : x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
case intro Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list left✝ : x = p_0 right✝ : List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right : x = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a2_right_right]
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ List.map (Sum.inr ∘ Su...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.starting_state_list = xs ⊒ Sum.inl q_0 βˆ‰ List.map (Sum.inr ∘ Su...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : Οƒ_0 a2_left : x ∈ M_0.accepting_state_list a2_right_left : x = p_0 a2_right_right : List.map (Sum.inr ∘ Sum.inr) M_1.st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q_0
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arr...
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 val✝ : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_sta...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.sta...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_sta...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ βˆƒ a ∈ M_0.accepting_state_list, ...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ βˆƒ a ∈ M_0.accepting_state_list, ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.sta...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ βˆƒ a ∈ M_0.accepting_state_list, ...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } ∈ List.map (fun ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ βˆƒ a ∈ M_0.accepting_state_list, ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, ((βˆƒ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 q : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 p_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr a...
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 val✝ : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr a...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 q : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 p_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun ar...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp case _ q_0 => simp sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arr...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), βˆ€ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 β†’ List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x β†’ Sum.inl q_0 βˆ‰ x
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun ar...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
intro xs x a1 a2 a3
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), βˆ€ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 β†’ List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x β†’ Sum.inl q_0 βˆ‰ x
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), βˆ€ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 β†’ List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a3]
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ xs
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ List.map (Sum.inr ∘ Sum.inr) x.st...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_stat...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inl q_0 βˆ‰ List.map (Sum.inr ∘ Sum.inr) x.st...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : β„• xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_stat...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q_0
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arr...
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 val✝ : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.sta...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_sta...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.sta...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), βˆ€ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 β†’ List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x β†’ Sum.inr (Sum.inl q_0) βˆ‰ x
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
intro xs x a1 a2 a3
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), βˆ€ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 β†’ List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x β†’ Sum.inr (Sum.inl q_0) βˆ‰ x
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inr (Sum.inl q_0) βˆ‰ xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 ⊒ βˆ€ (x : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1)), βˆ€ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 β†’ List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a3]
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inr (Sum.inl q_0) βˆ‰ xs
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inr (Sum.inl q_0) βˆ‰ List.map (Sum.inr ∘ S...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊒ Sum.inr (Sum.inl q_0) βˆ‰ List.map (Sum.inr ∘ S...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 q_0 : Οƒ_0 xs : List (β„• βŠ• Οƒ_0 βŠ• Οƒ_1) x : EpsilonArrow Οƒ_1 a1 : x ∈ M_1.epsilon_arrow_list a2 : x.start_state = p_0 a3 : List.map (Sum.inr ∘ Sum.inr) x.stop_st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_sta...
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, (βˆƒ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) ↔ ...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } ∈ List.map (fun arrow ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
sorry
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, (βˆƒ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) ↔ ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 q_0 : Οƒ_1 ⊒ (βˆƒ stop_state_list, (βˆƒ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_li...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
constructor
case right.right Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ ((fun state => state ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False) ∧ (fun sta...
case right.right.left Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ (fun state => state ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False case right.right...
Please generate a tactic in lean4 to solve the state. STATE: case right.right Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ ((fun state => state ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p => match p with | Sum.inr (Sum.inl p') => p'...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
funext p
case right.right.left Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ (fun state => state ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
case right.right.left.h Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 ⊒ (p ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ (fun state => state ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p => match p with | Sum.inr (Sum.inl p') => p'...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases p
case right.right.left.h Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 ⊒ (p ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
case right.right.left.h.inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 val✝ : β„• ⊒ (Sum.inl val✝ ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inl val✝ with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False case ...
Please generate a tactic in lean4 to solve the state. STATE: case right.right.left.h Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 ⊒ (p ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match p with | Sum.inr (Sum.inl p') => p' ∈ M_0...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_stat...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => cases p_0 case _ p_0 => simp case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.start...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_stat...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases p_0
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 val✝ : Οƒ_0 ⊒ (Sum.inr (Sum.inl val✝) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inl val✝) with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False ca...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inl p') => p' ∈ M_0.start...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inl p') => ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inl p') => ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inl p') => ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inl p') => ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
funext p
case right.right.right Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ (fun state => state ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = fun p => match p with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
case right.right.right.h Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 ⊒ (p ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match p with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 ⊒ (fun state => state ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = fun p => match p with | Sum.inr (Sum.inr p') => ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases p
case right.right.right.h Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 ⊒ (p ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match p with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
case right.right.right.h.inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 val✝ : β„• ⊒ (Sum.inl val✝ ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inl val✝ with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False ca...
Please generate a tactic in lean4 to solve the state. STATE: case right.right.right.h Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p : β„• βŠ• Οƒ_0 βŠ• Οƒ_1 ⊒ (p ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match p with | Sum.inr (Sum.inr p') => p' ∈ M...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => cases p_0 case _ p_0 => simp case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.acce...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : β„• ⊒ (Sum.inl p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inl p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases p_0
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
case inl Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 val✝ : Οƒ_0 ⊒ (Sum.inr (Sum.inl val✝) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inl val✝) with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False ...
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 βŠ• Οƒ_1 ⊒ (Sum.inr p_0 ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr p_0 with | Sum.inr (Sum.inr p') => p' ∈ M_1.acce...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inr p') =>...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inr p') =>...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_0 ⊒ (Sum.inr (Sum.inl p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inl p_0) with | Sum.inr (Sum.inr p') =>...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type inst✝ : DecidableEq Ξ± Οƒ_0 Οƒ_1 : Type M_0 : EpsilonNFA Ξ± Οƒ_0 M_1 : EpsilonNFA Ξ± Οƒ_1 p_0 : Οƒ_1 ⊒ (Sum.inr (Sum.inr p_0) ∈ List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = match Sum.inr (Sum.inr p_0) with | Sum.inr (Sum.inr p') =>...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
induction h1 generalizing V
D : Type I J : Interpretation D V : VarAssignment D E : Env A : Formula P : PredName zs : List VarName H B : Formula h1 : IsSub P zs H A B h2 : βˆ€ (Q : PredName) (ds : List D), Q = P ∧ ds.length = zs.length β†’ (Holds D I (Function.updateListITE V zs ds) E H ↔ J.pred_var_ P ds) h3_const : I.pred_const_ = J.pred_cons...
case pred_const_ D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) X✝ : PredName xs✝ : List VarName V : VarAssignment ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D V : VarAssignment D E : Env A : Formula P : PredName zs : List VarName H B : Formula h1 : IsSub P zs H A B h2 : βˆ€ (Q : PredName) (ds : List D), Q = P ∧ ds.length = zs.length β†’ (Holds D I (Function.updateListITE V zs ds) E...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
case pred_const_ h1_X h1_ts => simp only [Holds] simp only [h3_const]
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
case pred_occurs_in h1_X h1_ts h1_1 h1_2 => obtain s1 := Sub.Var.All.Rec.substitution_theorem D I V E (Function.updateListITE id zs h1_ts) H h1_2 obtain s2 := Function.updateListITE_comp id V zs h1_ts simp only [s2] at s1 simp at s1 specialize h2 h1_X (List.map V h1_ts) simp only [s1] at h2 simp only [Hol...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
case eq_ h1_x h1_y => simp only [Holds]
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_x h1_y : VarName V : VarAssignment D h2 : βˆ€ (Q : PredName) (ds ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_x h1...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
case true_ | false_ => simp only [Holds]
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) V : VarAssignment D h2 : βˆ€ (Q : PredName) (ds : List D), Q = P...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) V : Var...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
case not_ h1_phi h1_phi' _ h1_ih => simp only [Holds] congr! 1 exact h1_ih V h2
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_phi h1_phi' : Formula a✝ : IsSub P zs H h1_phi h1_phi' h1_ih : ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_phi ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
case forall_ h1_x h1_phi h1_phi' h1_1 _ h1_ih | exists_ h1_x h1_phi h1_phi' h1_1 _ h1_ih => simp only [Holds] first | apply forall_congr' | apply exists_congr intro d apply h1_ih intro Q ds a1 specialize h2 Q ds a1 have s1 : Holds D I (Function.updateListITE (Function.updateITE V h1_x d) zs ds) E H ...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_x : VarName h1_phi h1_phi' : Formula h1_1 : Β¬isFreeIn h1_x H a✝ :...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_x : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp only [Holds]
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp only [h3_const]
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp at h1_1
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : Β¬(h1_X = P ∧ h1_ts.lengt...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
apply Holds_coincide_PredVar
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
case h1 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
exact h3_const
case h1 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
no goals
Please generate a tactic in lean4 to solve the state. STATE: case h1 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
intro X ds a1
case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
Please generate a tactic in lean4 to solve the state. STATE: case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp only [predVarOccursIn] at a1
case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
Please generate a tactic in lean4 to solve the state. STATE: case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
cases a1
case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
case h2.intro D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment...
Please generate a tactic in lean4 to solve the state. STATE: case h2 D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
subst a1_left
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredName) (ds...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
apply h3_var
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredName) (ds...
case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredNa...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts :...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp
case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredNa...
case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredNa...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
intro a2
case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredNa...
case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredNa...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
subst a2
case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : βˆ€ (Q : PredNa...
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp at h1_1
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
intro contra
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
apply h1_1
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
trans List.length ds
case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_va...
D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds...
Please generate a tactic in lean4 to solve the state. STATE: case a D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName)...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp only [eq_comm]
D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds...
D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
exact a1_right
D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
exact contra
D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = X ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds...
no goals
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h1_ts : List VarName V : VarAssignment D X : PredName ds : List D a1_right : ds.length = h1_ts.length h3_var : βˆ€ (Q : PredName) (ds : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
obtain s1 := Sub.Var.All.Rec.substitution_theorem D I V E (Function.updateListITE id zs h1_ts) H h1_2
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
obtain s2 := Function.updateListITE_comp id V zs h1_ts
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp only [s2] at s1
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
simp at s1
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/NV/Sub/Pred/One/Ind/Sub.lean
FOL.NV.Sub.Pred.One.Ind.substitution_theorem
[131, 1]
[245, 15]
specialize h2 h1_X (List.map V h1_ts)
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : h1_X = P ∧ h1_ts.length ...
Please generate a tactic in lean4 to solve the state. STATE: D : Type I J : Interpretation D E : Env A : Formula P : PredName zs : List VarName H B : Formula h3_const : I.pred_const_ = J.pred_const_ h3_var : βˆ€ (Q : PredName) (ds : List D), Β¬(Q = P ∧ ds.length = zs.length) β†’ (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : ...