internlm/Lean-Github · Datasets at Hugging Face

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	cases a3_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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) a2_right : Sum.inr q_0 ∈ xs x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right : x.start_state = p_0 ∧ List.map Sum.inr x.stop_state_list = xs ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list	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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) a2_right : Sum.inr q_0 ∈ xs x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list left✝ : x.start_state = p_0 right✝ : List.map Sum.inr x.stop_state_list = xs ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp only [← a3_right_right] at 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) a2_right : Sum.inr q_0 ∈ xs x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a3_right_right : List.map Sum.inr x.stop_state_list = xs ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a3_right_right : List.map Sum.inr x.stop_state_list = xs a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	clear a3_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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a3_right_right : List.map Sum.inr x.stop_state_list = xs a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp at 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	apply Exists.intro x.stop_state_list	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := p_0, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp only [← a3_right_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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := p_0, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	constructor	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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list	case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ q_0 ∈ x.stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	exact a3_left	case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	exact a2_right	case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ q_0 ∈ x.stop_state_list	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	intro a1	case mpr 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 := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list) → ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list	case mpr 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 a1 : ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	cases a1	case mpr 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 a1 : ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list	case mpr.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 q_0 : σ_1 w✝ : List σ_1 h✝ : { start_state := p_0, stop_state_list := w✝ } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ w✝ ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	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 q_0 : σ_1 xs : List σ_1 a2 : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ xs ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list	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 q_0 : σ_1 xs : List σ_1 left✝ : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list right✝ : q_0 ∈ xs ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	apply Exists.intro (xs.map Sum.inr)	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 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list	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 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs) ∧ Sum.inr q_0 ∈ List.map Sum.inr xs
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	constructor	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 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs) ∧ Sum.inr q_0 ∈ List.map Sum.inr xs	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ ∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ Sum.inr q_0 ∈ List.map Sum.inr xs
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	apply Exists.intro { start_state := p_0, stop_state_list := xs }	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ ∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list ∧ { start_state := p_0, stop_state_list := xs }.start_state = p_0 ∧ List.map Sum.inr { start_state := p_0, stop_state_list := xs }.stop_state_list = List.map Sum.inr xs
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list ∧ { start_state := p_0, stop_state_list := xs }.start_state = p_0 ∧ List.map Sum.inr { start_state := p_0, stop_state_list := xs }.stop_state_list = List.map Sum.inr xs	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	exact a2_left	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ Sum.inr q_0 ∈ List.map Sum.inr xs	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ q_0 ∈ xs
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	exact a2_right	case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ q_0 ∈ xs	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	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.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = fun p => match p with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list) ∧ (fun state => state ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = fun p => match p with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list	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.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = fun p => match p with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list 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.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = fun p => match p with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	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.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = fun p => match p with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list	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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match p with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match p with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list	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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inl val✝ with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list case right.right.left.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inr val✝ with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp	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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inl val✝ with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp	case right.right.left.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inr val✝ with \| Sum.inl p' => p' ∈ M_0.starting_state_list \| Sum.inr p' => p' ∈ M_1.starting_state_list	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	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.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = fun p => match p with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list	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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match p with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match p with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list	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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inl val✝ with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list case right.right.right.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inr val✝ with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp	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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inl val✝ with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.accepting_state_list	no goals
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_union_EpsilonNFA_toAbstract	[312, 1]	[506, 17]	simp	case right.right.right.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inr val✝ with \| Sum.inl p' => p' ∈ M_0.accepting_state_list \| Sum.inr p' => p' ∈ M_1.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 only [match_concat_EpsilonNFA]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (match_concat_EpsilonNFA α σ_0 σ_1 M_0 M_1).toAbstract = match_concat_AbstractEpsilonNFA α σ_0 σ_1 M_0.toAbstract M_1.toAbstract	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list, epsilon_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list, starting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list }.toAbstract = match_concat_AbstractEpsilonNFA α σ_0 σ_1 M_0.toAbstract M_1.toAbstract
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	simp only [EpsilonNFA.toAbstract]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list, epsilon_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list, starting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list }.toAbstract = match_concat_AbstractEpsilonNFA α σ_0 σ_1 M_0.toAbstract M_1.toAbstract	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = match_concat_AbstractEpsilonNFA α σ_0 σ_1 { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_0.starting_state_list, accepting := fun state => state ∈ M_0.accepting_state_list } { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_1.starting_state_list, accepting := fun state => state ∈ M_1.accepting_state_list }
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	simp only [match_concat_AbstractEpsilonNFA]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = match_concat_AbstractEpsilonNFA α σ_0 σ_1 { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_0.starting_state_list, accepting := fun state => state ∈ M_0.accepting_state_list } { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_1.starting_state_list, accepting := fun state => state ∈ M_1.accepting_state_list }	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = { symbol := fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False, epsilon := fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False, start := fun p => match p with \| Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list \| x => False, accepting := fun p => 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]	simp only [AbstractEpsilonNFA.mk.injEq]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = { symbol := fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False, epsilon := fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False, start := fun p => match p with \| Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list \| x => False, accepting := fun p => match p with \| Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list \| x => False }	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list) = fun p => match p with \| Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list \| x => False) ∧ (fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => 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]	simp only [EpsilonNFA.wrapLeft]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list) = fun p => match p with \| Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list \| x => False) ∧ (fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => match p with \| Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.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 state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => 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]	simp only [EpsilonNFA.wrapRight]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.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 state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => match p with \| Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).starting_state_list }) (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((fun state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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 state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	simp only [EpsilonNFA.map]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).starting_state_list }) (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((fun state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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 state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((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 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
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	constructor	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((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 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 left α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case right α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((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 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
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	funext p c q	case left α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	case left.h.h.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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 left.h.h.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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	case left.h.h.h.inl α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl val✝, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inl val✝, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case left.h.h.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr val✝, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr val✝, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 => cases q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ p_0 => cases q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] 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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl val✝), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl val✝), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr val✝), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr val✝), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 => cases q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] 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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 q	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_0 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl val✝) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr val✝) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False
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 a4 simp only [← a4] simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_0 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) 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 a4	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) 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 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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]	simp only [← a4]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inl q_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]	simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inl q_0 ∉ List.map (Sum.inr ∘ Sum.inl) x.stop_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_0	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inl val✝)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inr val✝)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False
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 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inl q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inr q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inl q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, (∃ a ∈ M_0.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ 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 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, (∃ a ∈ M_0.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ 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]	simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inr q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) x_1.stop_state_list = x → Sum.inr (Sum.inr 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 a4	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) x_1.stop_state_list = x → Sum.inr (Sum.inr 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 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr q_0) ∉ xs
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	simp only [← a4]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr 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 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr q_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]	simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr q_0) ∉ List.map (Sum.inr ∘ Sum.inl) x.stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inl val✝) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr val✝) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False
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 a4 simp only [← a4] simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inl q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] 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 c : α p_0 : σ_1 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inl q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 a4	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 [← a4]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inl q_0 ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_state_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 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inl q_0 ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_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_0	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inl val✝)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inr val✝)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False
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 a4 simp only [← a4] simp	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inl q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ 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 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inr q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inl q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 a4	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 [← a4]	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inr (Sum.inl q_0) ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_state_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 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inr (Sum.inl q_0) ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_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 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inr q_0)) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list \| x => False	α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, (∃ a ∈ M_1.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ 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 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, (∃ a ∈ M_1.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ 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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False) ∧ ((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 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.left α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False 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 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
https://github.com/pthomas505/FOL.git	097a4abea51b641d144539b9a0f7516f3b9d818c	FOL/Parsing/RegExpToEpsilonNFA.lean	match_concat_EpsilonNFA_toAbstract	[557, 1]	[690, 19]	funext p q	case 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 start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False	case right.left.h.h α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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.left.h.h α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (p, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False	case right.left.h.h.inl 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 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl val✝, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inl val✝, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False case right.left.h.h.inr 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 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr val✝, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr val✝, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 => cases q 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 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp sorry case _ p_0 => cases q case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp 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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl val✝), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl val✝), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False case inr 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 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr val✝), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr val✝), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_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 => cases q 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 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp 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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp 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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inl val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl val✝) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False case inr 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✝ : 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inr val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr val✝) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False
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 => 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 ⊢ (∃ 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_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 _ 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 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_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list \| (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list \| x => False	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.inr ∘ Sum.inr) M_1.starting_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 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.inr ∘ Sum.inr) M_1.starting_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_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.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]	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.inr) M_1.starting_state_list = xs ⊢ Sum.inl q_0 ∉ xs	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_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.accepting_state_list, a = 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 _ 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.map (Sum.inr ∘ Sum.inl) x.stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

cases a3_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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) a2_right : Sum.inr q_0 ∈ xs x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right : x.start_state = p_0 ∧ List.map Sum.inr x.stop_state_list = xs ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) a2_right : Sum.inr q_0 ∈ xs x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list left✝ : x.start_state = p_0 right✝ : List.map Sum.inr x.stop_state_list = xs ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp only [← a3_right_right] at 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) a2_right : Sum.inr q_0 ∈ xs x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a3_right_right : List.map Sum.inr x.stop_state_list = xs ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a3_right_right : List.map Sum.inr x.stop_state_list = xs a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

clear a3_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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a3_right_right : List.map Sum.inr x.stop_state_list = xs a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp at 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : Sum.inr q_0 ∈ List.map Sum.inr x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

apply Exists.intro x.stop_state_list

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := p_0, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp only [← a3_right_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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := p_0, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

constructor

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 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ x.stop_state_list

case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ q_0 ∈ x.stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

exact a3_left

case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ { start_state := x.start_state, stop_state_list := x.stop_state_list } ∈ M_1.epsilon_arrow_list

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

exact a2_right

case 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 q_0 : σ_1 xs : List (σ_0 ⊕ σ_1) x : EpsilonArrow σ_1 a3_left : x ∈ M_1.epsilon_arrow_list a3_right_left : x.start_state = p_0 a2_right : q_0 ∈ x.stop_state_list ⊢ q_0 ∈ x.stop_state_list

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

intro a1

case mpr 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 := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list) → ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

case mpr 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 a1 : ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

cases a1

case mpr 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 a1 : ∃ stop_state_list, { start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

case mpr.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 q_0 : σ_1 w✝ : List σ_1 h✝ : { start_state := p_0, stop_state_list := w✝ } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ w✝ ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

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 q_0 : σ_1 xs : List σ_1 a2 : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ xs ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

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 q_0 : σ_1 xs : List σ_1 left✝ : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list right✝ : q_0 ∈ xs ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

apply Exists.intro (xs.map Sum.inr)

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 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ ∃ stop_state_list, (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧ Sum.inr q_0 ∈ stop_state_list

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 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs) ∧ Sum.inr q_0 ∈ List.map Sum.inr xs

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

constructor

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 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs) ∧ Sum.inr q_0 ∈ List.map Sum.inr xs

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ ∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ Sum.inr q_0 ∈ List.map Sum.inr xs

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

apply Exists.intro { start_state := p_0, stop_state_list := xs }

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ ∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list ∧ { start_state := p_0, stop_state_list := xs }.start_state = p_0 ∧ List.map Sum.inr { start_state := p_0, stop_state_list := xs }.stop_state_list = List.map Sum.inr xs

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list ∧ { start_state := p_0, stop_state_list := xs }.start_state = p_0 ∧ List.map Sum.inr { start_state := p_0, stop_state_list := xs }.stop_state_list = List.map Sum.inr xs

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

exact a2_left

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ Sum.inr q_0 ∈ List.map Sum.inr xs

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ q_0 ∈ xs

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

exact a2_right

case 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 q_0 : σ_1 xs : List σ_1 a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_1.epsilon_arrow_list a2_right : q_0 ∈ xs ⊢ q_0 ∈ xs

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

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.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = fun p => match p with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list) ∧ (fun state => state ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = fun p => match p with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

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.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = fun p => match p with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list 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.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = fun p => match p with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

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.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = fun p => match p with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list

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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match p with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match p with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list

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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inl val✝ with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list case right.right.left.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inr val✝ with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp

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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inl val✝ with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp

case right.right.left.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.starting_state_list ++ List.map Sum.inr M_1.starting_state_list) = match Sum.inr val✝ with | Sum.inl p' => p' ∈ M_0.starting_state_list | Sum.inr p' => p' ∈ M_1.starting_state_list

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

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.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = fun p => match p with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match p with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

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 : σ_0 ⊕ σ_1 ⊢ (p ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match p with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inl val✝ with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list case right.right.right.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inr val✝ with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp

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✝ : σ_0 ⊢ (Sum.inl val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inl val✝ with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.accepting_state_list

no goals

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_union_EpsilonNFA_toAbstract

[312, 1]

[506, 17]

simp

case right.right.right.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 val✝ : σ_1 ⊢ (Sum.inr val✝ ∈ List.map Sum.inl M_0.accepting_state_list ++ List.map Sum.inr M_1.accepting_state_list) = match Sum.inr val✝ with | Sum.inl p' => p' ∈ M_0.accepting_state_list | Sum.inr p' => p' ∈ M_1.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 only [match_concat_EpsilonNFA]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (match_concat_EpsilonNFA α σ_0 σ_1 M_0 M_1).toAbstract = match_concat_AbstractEpsilonNFA α σ_0 σ_1 M_0.toAbstract M_1.toAbstract

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list, epsilon_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list, starting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list }.toAbstract = match_concat_AbstractEpsilonNFA α σ_0 σ_1 M_0.toAbstract M_1.toAbstract

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

simp only [EpsilonNFA.toAbstract]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list, epsilon_arrow_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list, starting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list }.toAbstract = match_concat_AbstractEpsilonNFA α σ_0 σ_1 M_0.toAbstract M_1.toAbstract

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = match_concat_AbstractEpsilonNFA α σ_0 σ_1 { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_0.starting_state_list, accepting := fun state => state ∈ M_0.accepting_state_list } { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_1.starting_state_list, accepting := fun state => state ∈ M_1.accepting_state_list }

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

simp only [match_concat_AbstractEpsilonNFA]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = match_concat_AbstractEpsilonNFA α σ_0 σ_1 { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_0.starting_state_list, accepting := fun state => state ∈ M_0.accepting_state_list } { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ M_1.starting_state_list, accepting := fun state => state ∈ M_1.accepting_state_list }

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = { symbol := fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False, epsilon := fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False, start := fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False, accepting := fun p => 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]

simp only [AbstractEpsilonNFA.mk.injEq]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ { symbol := fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list, epsilon := fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list, start := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list, accepting := fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list } = { symbol := fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False, epsilon := fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False, start := fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False, accepting := fun p => match p with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False }

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list) = fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False) ∧ (fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => 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]

simp only [EpsilonNFA.wrapLeft]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapLeft σ_1 M_0)).starting_state_list) = fun p => match p with | Sum.inr (Sum.inl p') => p' ∈ M_0.starting_state_list | x => False) ∧ (fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => match p with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.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 state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => 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]

simp only [EpsilonNFA.wrapRight]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).starting_state_list }) (EpsilonNFA.wrapRight ℕ (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((fun state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.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 state => state ∈ (EpsilonNFA.wrapRight ℕ (EpsilonNFA.wrapRight σ_0 M_1)).accepting_state_list) = fun p => match p with | Sum.inr (Sum.inr p') => p' ∈ M_1.accepting_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).starting_state_list }) (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((fun state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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 state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

simp only [EpsilonNFA.map]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).symbol_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).symbol_arrow_list ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).epsilon_arrow_list ++ (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).epsilon_arrow_list ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inr M_1)).starting_state_list }) (EpsilonNFA.map Sum.inr (EpsilonNFA.map Sum.inl M_0)).accepting_state_list ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((fun state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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 state => state ∈ (EpsilonNFA.map Sum.inr (EpsilonNFA.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

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((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 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

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

constructor

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False) ∧ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((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 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 left α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case right α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((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 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

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

funext p c q

case left α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (fun start_state symbol stop_state => ∃ stop_state_list, { start_state := start_state, symbol := symbol, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ stop_state ∈ stop_state_list) = fun p c q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

case left.h.h.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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 left.h.h.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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

case left.h.h.h.inl α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl val✝, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inl val✝, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case left.h.h.h.inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr val✝, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr val✝, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 => cases q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ p_0 => cases q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] 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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl val✝), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl val✝), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr val✝), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr val✝), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 => cases q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 q case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp case _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] 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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 q

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_0 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl val✝) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr val✝) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

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 a4 simp only [← a4] simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_0 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) 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 a4

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) 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 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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]

simp only [← a4]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inl q_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]

simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inl q_0 ∉ List.map (Sum.inr ∘ Sum.inl) x.stop_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_0

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inl val✝)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inr val✝)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

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 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inl q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inr q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inl q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, (∃ a ∈ M_0.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ 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 c : α p_0 q_0 : σ_0 ⊢ (∃ stop_state_list, (∃ a ∈ M_0.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inl) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ 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]

simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr (Sum.inr q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) x_1.stop_state_list = x → Sum.inr (Sum.inr 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 a4

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_0.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → List.map (Sum.inr ∘ Sum.inl) x_1.stop_state_list = x → Sum.inr (Sum.inr 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 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr q_0) ∉ xs

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

simp only [← a4]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr 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 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr q_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]

simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_0 q_0 : σ_1 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_0 a1 : x ∈ M_0.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inl) x.stop_state_list = xs ⊢ Sum.inr (Sum.inr q_0) ∉ List.map (Sum.inr ∘ Sum.inl) x.stop_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 c : α q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inl val✝) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr val✝) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

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 a4 simp only [← a4] simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inl q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ q_0 => cases q_0 case _ q_0 => simp intro xs x a1 a2 a3 a4 simp only [← a4] 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 c : α p_0 : σ_1 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 q_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inl q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 a4

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 [← a4]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inl q_0 ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_state_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 c : α p_0 : σ_1 q_0 : ℕ xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inl q_0 ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_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_0

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inl val✝)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False case inr α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr val✝) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inr val✝)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

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 a4 simp only [← a4] simp

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inl q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 _ 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 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inr q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_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 c : α p_0 : σ_1 q_0 : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inl q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inl q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 a4

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 ⊢ ∀ (x : List (ℕ ⊕ σ_0 ⊕ σ_1)), ∀ x_1 ∈ M_1.symbol_arrow_list, x_1.start_state = p_0 → x_1.symbol = c → 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 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 [← a4]

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : 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 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inr (Sum.inl q_0) ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_state_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 c : α p_0 : σ_1 q_0 : σ_0 xs : List (ℕ ⊕ σ_0 ⊕ σ_1) x : SymbolArrow α σ_1 a1 : x ∈ M_1.symbol_arrow_list a2 : x.start_state = p_0 a3 : x.symbol = c a4 : List.map (Sum.inr ∘ Sum.inr) x.stop_state_list = xs ⊢ Sum.inr (Sum.inl q_0) ∉ List.map (Sum.inr ∘ Sum.inr) x.stop_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 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr p_0), symbol := c, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.symbol_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, symbol := arrow.symbol, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.symbol_arrow_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), Sum.inr (Sum.inr q_0)) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ q' ∈ stop_state_list | x => False

α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, (∃ a ∈ M_1.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ 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 c : α p_0 q_0 : σ_1 ⊢ (∃ stop_state_list, (∃ a ∈ M_1.symbol_arrow_list, a.start_state = p_0 ∧ a.symbol = c ∧ List.map (Sum.inr ∘ Sum.inr) a.stop_state_list = stop_state_list) ∧ Sum.inr (Sum.inr q_0) ∈ stop_state_list) ↔ ∃ stop_state_list, { start_state := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧ 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 α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ ((fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False) ∧ ((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 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.left α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 ⊢ (fun start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False 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 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

https://github.com/pthomas505/FOL.git

097a4abea51b641d144539b9a0f7516f3b9d818c

FOL/Parsing/RegExpToEpsilonNFA.lean

match_concat_EpsilonNFA_toAbstract

[557, 1]

[690, 19]

funext p q

case 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 start_state stop_state => ∃ stop_state_list, { start_state := start_state, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ stop_state ∈ stop_state_list) = fun p q => match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False

case right.left.h.h α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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.left.h.h α : Type inst✝ : DecidableEq α σ_0 σ_1 : Type M_0 : EpsilonNFA α σ_0 M_1 : EpsilonNFA α σ_1 p q : ℕ ⊕ σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := p, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (p, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False

case right.left.h.h.inl 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 val✝ : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl val✝, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inl val✝, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False case right.left.h.h.inr 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 val✝ : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr val✝, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr val✝, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 => cases q 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 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp case _ q_0 => cases q_0 case _ q_0 => simp sorry case _ q_0 => simp sorry case _ p_0 => cases q case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp 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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : ℕ ⊢ (∃ stop_state_list, { start_state := Sum.inl p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inl p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q : ℕ ⊕ σ_0 ⊕ σ_1 p_0 : σ_0 ⊕ σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr p_0, stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr p_0, q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q : ℕ ⊕ σ_0 ⊕ σ_1 val✝ : σ_0 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inl val✝), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl val✝), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False case inr 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 val✝ : σ_1 ⊢ (∃ stop_state_list, { start_state := Sum.inr (Sum.inr val✝), stop_state_list := stop_state_list } ∈ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr val✝), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_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 => cases q 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 => cases a2 case _ a2_left a2_right => cases a2_right case _ a2_right_left a2_right_right => simp only [← a2_right_right] simp 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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 q case _ q_0 => simp intro xs x a1 a2 a3 simp only [← a3] simp 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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inr p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ q ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), q) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inl val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl val✝) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False case inr 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✝ : 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inr val✝ ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr val✝) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False

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 => 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 ⊢ (∃ 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_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 _ 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 arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inr q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inr q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.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 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_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inl arrow.start_state, stop_state_list := List.map Sum.inl arrow.stop_state_list }) M_0.epsilon_arrow_list) ++ List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) (List.map (fun arrow => { start_state := Sum.inr arrow.start_state, stop_state_list := List.map Sum.inr arrow.stop_state_list }) M_1.epsilon_arrow_list) ++ List.map (fun accepting_state => { start_state := accepting_state, stop_state_list := List.map Sum.inr (List.map Sum.inr M_1.starting_state_list) }) (List.map Sum.inr (List.map Sum.inl M_0.accepting_state_list)) ∧ Sum.inl q_0 ∈ stop_state_list) = match (Sum.inr (Sum.inl p_0), Sum.inl q_0) with | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inl q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inr p'), Sum.inr (Sum.inr q')) => ∃ stop_state_list, { start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list | (Sum.inr (Sum.inl p'), Sum.inr (Sum.inr q')) => p' ∈ M_0.accepting_state_list ∧ q' ∈ M_1.starting_state_list | x => False

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.inr ∘ Sum.inr) M_1.starting_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 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.inr ∘ Sum.inr) M_1.starting_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_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.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]

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.inr) M_1.starting_state_list = xs ⊢ Sum.inl q_0 ∉ xs

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_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.accepting_state_list, a = 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 _ 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.map (Sum.inr ∘ Sum.inl) x.stop_state_list