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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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊢ (∃ 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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 val✝ : ℕ ⊢ (∃ 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...
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 =...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ ⊢ (∃ 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
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ ⊢ (∃ 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...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ((∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = x) ∨ ∃ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.in...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
intro xs a1
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ((∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = x) ∨ ∃ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.in...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) a1 : (∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs) ∨ ∃ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a1
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) a1 : (∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = xs) ∨ ∃ a ∈ M_0.accepting_state_list, a = p_0 ∧ List.map (Sum.inr ∘ Sum...
case inl α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) h✝ : ∃ 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 ∉ xs case inr α : Type inst✝ : DecidableEq α σ_0 σ_...
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) left : ∃ 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 ∉ xs
no goals
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) right : ∃ 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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases left
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) left : ∃ 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 ∉ xs
case intro α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) w✝ : EpsilonArrow σ_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 ∉ xs
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
case intro α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2_right
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
case intro α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a2_right_right]
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ List....
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ List....
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases right
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) right : ∃ 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 ∉ xs
case intro α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) w✝ : σ_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 ∉ xs
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
case intro α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases a2_right
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
case intro α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a2_right_right]
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ xs
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ List.map (Sum.inr ∘ Su...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : σ_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 ∉ List.map (Sum.inr ∘ Su...
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q_0
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ 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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 val✝ : σ_0 ⊢ (∃ 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...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp sorry
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_0 ⊢ (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp sorry
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : σ_1 ⊢ (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_0 ⊢ (∃ 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...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, ((∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ ∃ a ∈ M_0.accepting_state_list, ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
sorry
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, ((∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ ∃ a ∈ M_0.accepting_state_list, ...
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : σ_1 ⊢ (∃ 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...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : σ_1 ⊢ (∃ stop_state_list, ((∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ ∃ a ∈ M_0.accepting_state_list, ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
sorry
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 q_0 : σ_1 ⊢ (∃ stop_state_list, ((∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∨ ∃ a ∈ M_0.accepting_state_list, ...
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_1 ⊢ (∃ 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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 val✝ : ℕ ⊢ (∃ 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...
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ ⊢ (∃ 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
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ ⊢ (∃ 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...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 → List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x → Sum.inl q_0 ∉ x
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 → List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x → Sum.inl q_0 ∉ x
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a3]
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ xs
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ List.map (Sum.inr ∘ Sum.inr) x.st...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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 ∉ List.map (Sum.inr ∘ Sum.inr) x.st...
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases q_0
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ 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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 val✝ : σ_0 ⊢ (∃ 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...
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 ⊢ (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ q_0 => simp sorry
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_1 ⊢ (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 ⊢ (∃ 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...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 → List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x → Sum.inr (Sum.inl q_0) ∉ x
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 → List.map (Sum.inr ∘ Sum.inr) x_1.stop_state_list = x → Sum.inr (Sum.inl q_0) ∉ x
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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) ∉ xs
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp only [← a3]
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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) ∉ xs
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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) ∉ List.map (Sum.inr ∘ S...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : EpsilonArrow σ_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) ∉ List.map (Sum.inr ∘ S...
no goals
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_1 ⊢ (∃ 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...
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, (∃ 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) ↔ ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
sorry
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, (∃ 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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
constructor
case right.right α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_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...
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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p : ℕ ⊕ σ_0 ⊕ σ_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
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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p : ℕ ⊕ σ_0 ⊕ σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : ℕ ⊢ (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 ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : ℕ ⊢ (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
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 ⊕ σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : ℕ ⊢ (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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases p_0
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 ⊕ σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_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...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p : ℕ ⊕ σ_0 ⊕ σ_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
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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p : ℕ ⊕ σ_0 ⊕ σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : ℕ ⊢ (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...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : ℕ ⊢ (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
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
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 ⊕ σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : ℕ ⊢ (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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
cases p_0
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_0 ⊕ σ_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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_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 ...
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
case _ p_0 => simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
https://github.com/pthomas505/FOL.git
097a4abea51b641d144539b9a0f7516f3b9d818c
FOL/Parsing/RegExpToEpsilonNFA.lean
match_concat_EpsilonNFA_toAbstract
[557, 1]
[690, 19]
simp
α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p_0 : σ_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
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 : ∀ (Q : PredName) (ds : List D), Q = P ∧ ds.length = zs.length → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) X✝ : PredName xs✝ : List VarName V : VarAssignment ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_x h1_y : VarName V : VarAssignment D h2 : ∀ (Q : PredName) (ds ...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) V : VarAssignment D h2 : ∀ (Q : PredName) (ds : List D), Q = P...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_x : VarName h1_phi h1_phi' : Formula h1_1 : ¬isFreeIn h1_x H a✝ :...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName h1_1 : ¬(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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_X : PredName h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (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]
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q : PredNa...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q : PredNa...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (Q : PredNa...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (I.pred_var_ Q ds ↔ J.pred_var_ Q ds) h1_ts : List VarName V : VarAssignment D h2 : ∀ (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.pred_va...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.pred_va...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.pred_va...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.pred_va...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.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 [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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.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]
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.pred_var_ Q ds...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = X ∧ ds.length = zs.length) → (I.pred_var_ Q ds...
no goals
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 ...
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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 : ∀ (Q : PredName) (ds : List D), ¬(Q = P ∧ ds.length = zs.length) → (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 ...