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] | exact a1 | case mp.left
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
xs : List (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
a5 : Sum.inl q_0 ∈ List.map Sum.inl x.stop_state_list
⊢ { start_state := x.start_state, symbol := x.symbol, stop_state_list := x.stop_state_list } ∈ M_0.symbol_arrow_list | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp at a5 | case mp.right
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
xs : List (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
a5 : Sum.inl q_0 ∈ List.map Sum.inl x.stop_state_list
⊢ q_0 ∈ x.stop_state_list | case mp.right
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
xs : List (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
a5 : 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 a5 | case mp.right
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
xs : List (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
a5 : 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] | simp | case mpr
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 := p_0, symbol := c, stop_state_list := stop_state_list } ∈ M_0.symbol_arrow_list ∧
q_0 ∈ stop_state_list) →
∃ stop_state_list,
{ start_state := Sum.inl p_0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl 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
c : α
p_0 q_0 : σ_0
⊢ ∀ (x : List σ_0),
{ start_state := p_0, symbol := c, stop_state_list := x } ∈ M_0.symbol_arrow_list →
q_0 ∈ x →
∃ stop_state_list,
(∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro xs x 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
c : α
p_0 q_0 : σ_0
⊢ ∀ (x : List σ_0),
{ start_state := p_0, symbol := c, stop_state_list := x } ∈ M_0.symbol_arrow_list →
q_0 ∈ x →
∃ stop_state_list,
(∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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
c : α
p_0 q_0 : σ_0
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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.inl) | case mpr
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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
c : α
p_0 q_0 : σ_0
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ (∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl xs) ∧
Sum.inl q_0 ∈ List.map Sum.inl xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | constructor | case mpr
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ (∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl xs) ∧
Sum.inl q_0 ∈ List.map Sum.inl xs | case mpr.left
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ ∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl xs
case mpr.right
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ Sum.inl q_0 ∈ List.map Sum.inl 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, symbol := c, stop_state_list := xs } | case mpr.left
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ ∃ a ∈ M_0.symbol_arrow_list,
a.start_state = p_0 ∧ a.symbol = c ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl xs | case mpr.left
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list ∧
{ start_state := p_0, symbol := c, stop_state_list := xs }.start_state = p_0 ∧
{ start_state := p_0, symbol := c, stop_state_list := xs }.symbol = c ∧
List.map Sum.inl { start_state := p_0, symbol := c, stop_state_list := xs }.stop_state_list =
List.map Sum.inl xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp | case mpr.left
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list ∧
{ start_state := p_0, symbol := c, stop_state_list := xs }.start_state = p_0 ∧
{ start_state := p_0, symbol := c, stop_state_list := xs }.symbol = c ∧
List.map Sum.inl { start_state := p_0, symbol := c, stop_state_list := xs }.stop_state_list =
List.map Sum.inl xs | case mpr.left
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | exact x | case mpr.left
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_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 mpr.right
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : q_0 ∈ xs
⊢ Sum.inl q_0 ∈ List.map Sum.inl xs | case mpr.right
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : 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 a1 | case mpr.right
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
xs : List σ_0
x : { start_state := p_0, symbol := c, stop_state_list := xs } ∈ M_0.symbol_arrow_list
a1 : 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] | 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
q0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inr q0 ∈ stop_state_list) =
match (Sum.inl p_0, Sum.inr q0) with
| (Sum.inl p', 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 p', 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
q0 : σ_1
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_0.symbol_arrow_list,
x_1.start_state = p_0 → x_1.symbol = c → List.map Sum.inl x_1.stop_state_list = x → Sum.inr q0 ∉ x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro xs x _ _ _ 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
q0 : σ_1
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_0.symbol_arrow_list,
x_1.start_state = p_0 → x_1.symbol = c → List.map Sum.inl x_1.stop_state_list = x → Sum.inr q0 ∉ 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
q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_0
a✝² : x ∈ M_0.symbol_arrow_list
a✝¹ : x.start_state = p_0
a✝ : x.symbol = c
a4 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q0 ∉ xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | 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
q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_0
a✝² : x ∈ M_0.symbol_arrow_list
a✝¹ : x.start_state = p_0
a✝ : x.symbol = c
a4 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q0 ∉ 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
q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_0
a✝² : x ∈ M_0.symbol_arrow_list
a✝¹ : x.start_state = p_0
a✝ : x.symbol = c
a4 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q0 ∉ List.map 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] | 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
q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_0
a✝² : x ∈ M_0.symbol_arrow_list
a✝¹ : x.start_state = p_0
a✝ : x.symbol = c
a4 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q0 ∉ List.map Sum.inl 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] | 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 : σ_0 ⊕ σ_1
p0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
q ∈ stop_state_list) =
match (Sum.inr p0, q) with
| (Sum.inl p', 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 p', 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
p0 : σ_1
val✝ : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl val✝ ∈ stop_state_list) =
match (Sum.inr p0, Sum.inl val✝) with
| (Sum.inl p', 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 p', 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
p0 val✝ : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inr val✝ ∈ stop_state_list) =
match (Sum.inr p0, Sum.inr val✝) with
| (Sum.inl p', 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 p', 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_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp only [eq_iff_iff] | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) =
match (Sum.inr p0, Sum.inl q_0) with
| (Sum.inl p', 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 p', 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
p0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) ↔
False |
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
c : α
p0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) ↔
False | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) →
False
case mpr
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ False →
∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl 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 | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) →
False | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_1.symbol_arrow_list,
x_1.start_state = p0 → x_1.symbol = c → List.map 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_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro xs x _ _ _ a4 | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_1.symbol_arrow_list,
x_1.start_state = p0 → x_1.symbol = c → List.map Sum.inr x_1.stop_state_list = x → Sum.inl q_0 ∉ x | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a✝² : x ∈ M_1.symbol_arrow_list
a✝¹ : x.start_state = p0
a✝ : x.symbol = c
a4 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp only [← a4] | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a✝² : x ∈ M_1.symbol_arrow_list
a✝¹ : x.start_state = p0
a✝ : x.symbol = c
a4 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ xs | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a✝² : x ∈ M_1.symbol_arrow_list
a✝¹ : x.start_state = p0
a✝ : x.symbol = c
a4 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ List.map Sum.inr x.stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a✝² : x ∈ M_1.symbol_arrow_list
a✝¹ : x.start_state = p0
a✝ : x.symbol = c
a4 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ List.map Sum.inr 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] | simp | case mpr
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 : σ_1
q_0 : σ_0
⊢ False →
∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | 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
p0 q0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p0, symbol := c, stop_state_list := 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 })
M_1.symbol_arrow_list ∧
Sum.inr q0 ∈ stop_state_list) =
match (Sum.inr p0, Sum.inr q0) with
| (Sum.inl p', 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 p', 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
p0 q0 : σ_1
⊢ (∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list) ↔
∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
⊢ (∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list) ↔
∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
⊢ (∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list) →
∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list) →
∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
⊢ (∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list) →
∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
a1 :
∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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 mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
a1 :
∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list | case mp.intro
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
w✝ : List (σ_0 ⊕ σ_1)
h✝ :
(∃ a ∈ M_1.symbol_arrow_list, a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = w✝) ∧
Sum.inr q0 ∈ w✝
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2 :
(∃ a ∈ M_1.symbol_arrow_list, a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = xs) ∧
Sum.inr q0 ∈ xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
left✝ : ∃ a ∈ M_1.symbol_arrow_list, a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = xs
right✝ : Sum.inr q0 ∈ xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | cases a2_left | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_left : ∃ a ∈ M_1.symbol_arrow_list, a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = xs
a2_right : Sum.inr q0 ∈ xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
w✝ : SymbolArrow α σ_1
h✝ : w✝ ∈ M_1.symbol_arrow_list ∧ w✝.start_state = p0 ∧ w✝.symbol = c ∧ List.map Sum.inr w✝.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | cases a3 | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
a3 : x ∈ M_1.symbol_arrow_list ∧ x.start_state = p0 ∧ x.symbol = c ∧ List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
left✝ : x ∈ M_1.symbol_arrow_list
right✝ : x.start_state = p0 ∧ x.symbol = c ∧ List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right : x.start_state = p0 ∧ x.symbol = c ∧ List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
left✝ : x.start_state = p0
right✝ : x.symbol = c ∧ List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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_right | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right : x.symbol = c ∧ List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
left✝ : x.symbol = c
right✝ : List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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_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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q0 ∈ xs
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a3_right_right_right : List.map Sum.inr x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a3_right_right_right : List.map Sum.inr x.stop_state_list = xs
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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_right | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a3_right_right_right : List.map Sum.inr x.stop_state_list = xs
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := x.start_state, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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_left] | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := x.start_state, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := x.start_state, symbol := x.symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : Sum.inr q0 ∈ List.map Sum.inr x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := x.start_state, symbol := x.symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := x.start_state, symbol := x.symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := x.start_state, symbol := x.symbol, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ { start_state := x.start_state, symbol := x.symbol, stop_state_list := x.stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ { start_state := x.start_state, symbol := x.symbol, stop_state_list := x.stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ { start_state := x.start_state, symbol := x.symbol, stop_state_list := x.stop_state_list } ∈ M_1.symbol_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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ { start_state := x.start_state, symbol := x.symbol, stop_state_list := x.stop_state_list } ∈ M_1.symbol_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
c : α
p0 q0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : SymbolArrow α σ_1
a3_left : x ∈ M_1.symbol_arrow_list
a3_right_left : x.start_state = p0
a3_right_right_left : x.symbol = c
a2_right : q0 ∈ x.stop_state_list
⊢ q0 ∈ 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
c : α
p0 q0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list) →
∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
a1 :
∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list
⊢ ∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
a1 :
∃ stop_state_list,
{ start_state := p0, symbol := c, stop_state_list := stop_state_list } ∈ M_1.symbol_arrow_list ∧
q0 ∈ stop_state_list
⊢ ∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
w✝ : List σ_1
h✝ : { start_state := p0, symbol := c, stop_state_list := w✝ } ∈ M_1.symbol_arrow_list ∧ q0 ∈ w✝
⊢ ∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2 : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list ∧ q0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
left✝ : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
right✝ : q0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ (∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ (∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ List.map Sum.inr a.stop_state_list = List.map Sum.inr xs) ∧
Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ ∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ Sum.inr q0 ∈ 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 := p0, symbol := c, 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ ∃ a ∈ M_1.symbol_arrow_list,
a.start_state = p0 ∧ a.symbol = c ∧ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list ∧
{ start_state := p0, symbol := c, stop_state_list := xs }.start_state = p0 ∧
{ start_state := p0, symbol := c, stop_state_list := xs }.symbol = c ∧
List.map Sum.inr { start_state := p0, symbol := c, 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list ∧
{ start_state := p0, symbol := c, stop_state_list := xs }.start_state = p0 ∧
{ start_state := p0, symbol := c, stop_state_list := xs }.symbol = c ∧
List.map Sum.inr { start_state := p0, symbol := c, 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ Sum.inr q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ q0 ∈ 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
c : α
p0 q0 : σ_1
xs : List σ_1
a2_left : { start_state := p0, symbol := c, stop_state_list := xs } ∈ M_1.symbol_arrow_list
a2_right : q0 ∈ xs
⊢ q0 ∈ 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
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.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 })
M_1.epsilon_arrow_list ∧
stop_state ∈ stop_state_list) =
fun p q =>
match (p, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False) ∧
((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.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.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 })
M_1.epsilon_arrow_list ∧
stop_state ∈ stop_state_list) =
fun p q =>
match (p, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_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.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 |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | 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.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 })
M_1.epsilon_arrow_list ∧
stop_state ∈ stop_state_list) =
fun p q =>
match (p, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_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 : σ_0 ⊕ σ_1
⊢ (∃ stop_state_list,
{ start_state := p, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
q ∈ stop_state_list) =
match (p, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | 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 : σ_0 ⊕ σ_1
⊢ (∃ stop_state_list,
{ start_state := p, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
q ∈ stop_state_list) =
match (p, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_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 : σ_0 ⊕ σ_1
val✝ : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inl val✝, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
q ∈ stop_state_list) =
match (Sum.inl val✝, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_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 : σ_0 ⊕ σ_1
val✝ : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inr val✝, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
q ∈ stop_state_list) =
match (Sum.inr val✝, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | 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 : σ_0 ⊕ σ_1
p_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
q ∈ stop_state_list) =
match (Sum.inl p_0, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 val✝ : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inl val✝ ∈ stop_state_list) =
match (Sum.inl p_0, Sum.inl val✝) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 : σ_0
val✝ : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inr val✝ ∈ stop_state_list) =
match (Sum.inl p_0, Sum.inr val✝) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | case _ q_0 =>
simp
intro xs x _ _ a3
simp only [← a3]
simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_0
q_0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inr q_0 ∈ stop_state_list) =
match (Sum.inl p_0, Sum.inr q_0) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) =
match (Sum.inl p_0, Sum.inl q_0) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 q_0 : σ_0
⊢ (∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list) ↔
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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] | 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_0
⊢ (∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list) ↔
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_0
⊢ (∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list) →
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ 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_0
⊢ (∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list) →
∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_0
⊢ (∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list) →
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_0
a1 :
∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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] | cases a1 | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_0
a1 :
∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl q_0 ∈ stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list | case mp.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_0
w✝ : List (σ_0 ⊕ σ_1)
h✝ : (∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = w✝) ∧ Sum.inl q_0 ∈ w✝
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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] | 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_0
xs : List (σ_0 ⊕ σ_1)
a2 : (∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = xs) ∧ Sum.inl q_0 ∈ xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
left✝ : ∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = xs
right✝ : Sum.inl q_0 ∈ xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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] | cases a2_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_0
xs : List (σ_0 ⊕ σ_1)
a2_left : ∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = xs
a2_right : Sum.inl q_0 ∈ xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inl q_0 ∈ xs
w✝ : EpsilonArrow σ_0
h✝ : w✝ ∈ M_0.epsilon_arrow_list ∧ w✝.start_state = p_0 ∧ List.map Sum.inl w✝.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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] | cases a3 | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inl q_0 ∈ xs
x : EpsilonArrow σ_0
a3 : x ∈ M_0.epsilon_arrow_list ∧ x.start_state = p_0 ∧ List.map Sum.inl x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inl q_0 ∈ xs
x : EpsilonArrow σ_0
left✝ : x ∈ M_0.epsilon_arrow_list
right✝ : x.start_state = p_0 ∧ List.map Sum.inl x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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] | 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_0
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inl q_0 ∈ xs
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
a3_right : x.start_state = p_0 ∧ List.map Sum.inl x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inl q_0 ∈ xs
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
left✝ : x.start_state = p_0
right✝ : List.map Sum.inl x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inl q_0 ∈ xs
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
a3_right_left : x.start_state = p_0
a3_right_right : List.map Sum.inl x.stop_state_list = xs
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
a3_right_left : x.start_state = p_0
a3_right_right : List.map Sum.inl x.stop_state_list = xs
a2_right : Sum.inl q_0 ∈ List.map Sum.inl x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
a3_right_left : x.start_state = p_0
a3_right_right : List.map Sum.inl x.stop_state_list = xs
a2_right : Sum.inl q_0 ∈ List.map Sum.inl x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
a3_right_left : x.start_state = p_0
a2_right : Sum.inl q_0 ∈ List.map Sum.inl x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.epsilon_arrow_list
a3_right_left : x.start_state = p_0
a2_right : Sum.inl q_0 ∈ List.map Sum.inl x.stop_state_list
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0.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_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a3_left : x ∈ M_0.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_0
⊢ (∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list) →
∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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_0
a1 :
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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_0
a1 :
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ stop_state_list
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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_0
w✝ : List σ_0
h✝ : { start_state := p_0, stop_state_list := w✝ } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ w✝
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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_0
xs : List σ_0
a2 : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list ∧ q_0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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_0
xs : List σ_0
left✝ : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
right✝ : q_0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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.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 q_0 : σ_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ ∃ stop_state_list,
(∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = stop_state_list) ∧
Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ (∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl xs) ∧
Sum.inl q_0 ∈ List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ (∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl xs) ∧
Sum.inl q_0 ∈ List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ ∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ Sum.inl q_0 ∈ List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ ∃ a ∈ M_0.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inl a.stop_state_list = List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list ∧
{ start_state := p_0, stop_state_list := xs }.start_state = p_0 ∧
List.map Sum.inl { start_state := p_0, stop_state_list := xs }.stop_state_list = List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list ∧
{ start_state := p_0, stop_state_list := xs }.start_state = p_0 ∧
List.map Sum.inl { start_state := p_0, stop_state_list := xs }.stop_state_list = List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ { start_state := p_0, stop_state_list := xs } ∈ M_0.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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ { start_state := p_0, stop_state_list := xs } ∈ M_0.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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.epsilon_arrow_list
a2_right : q_0 ∈ xs
⊢ Sum.inl q_0 ∈ List.map Sum.inl 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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.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_0
xs : List σ_0
a2_left : { start_state := p_0, stop_state_list := xs } ∈ M_0.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] | simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_0
q_0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inl p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inr q_0 ∈ stop_state_list) =
match (Sum.inl p_0, Sum.inr q_0) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 : σ_0
q_0 : σ_1
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_0.epsilon_arrow_list, x_1.start_state = p_0 → List.map Sum.inl x_1.stop_state_list = x → Sum.inr q_0 ∉ x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro xs x _ _ a3 | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_0
q_0 : σ_1
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_0.epsilon_arrow_list, x_1.start_state = p_0 → List.map Sum.inl x_1.stop_state_list = x → 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
p_0 : σ_0
q_0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a✝¹ : x ∈ M_0.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q_0 ∉ xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp only [← a3] | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_0
q_0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a✝¹ : x ∈ M_0.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inl x.stop_state_list = xs
⊢ 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
p_0 : σ_0
q_0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a✝¹ : x ∈ M_0.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q_0 ∉ List.map 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] | simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_0
q_0 : σ_1
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_0
a✝¹ : x ∈ M_0.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inl x.stop_state_list = xs
⊢ Sum.inr q_0 ∉ List.map Sum.inl 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] | 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 : σ_0 ⊕ σ_1
p_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.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 })
M_1.epsilon_arrow_list ∧
q ∈ stop_state_list) =
match (Sum.inr p_0, q) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 : σ_1
val✝ : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inl val✝ ∈ stop_state_list) =
match (Sum.inr p_0, Sum.inl val✝) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 val✝ : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inr val✝ ∈ stop_state_list) =
match (Sum.inr p_0, Sum.inr val✝) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | case _ q_0 =>
simp
intro xs x _ _ a3
simp only [← a3]
simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) =
match (Sum.inr p_0, Sum.inl q_0) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q' ∈ stop_state_list
| x => False | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inl q_0 ∈ stop_state_list) =
match (Sum.inr p_0, Sum.inl q_0) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 : σ_1
q_0 : σ_0
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 → List.map 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_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro xs x _ _ a3 | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
⊢ ∀ (x : List (σ_0 ⊕ σ_1)),
∀ x_1 ∈ M_1.epsilon_arrow_list, x_1.start_state = p_0 → List.map Sum.inr x_1.stop_state_list = x → Sum.inl q_0 ∉ x | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_1
a✝¹ : x ∈ M_1.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ xs |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp only [← a3] | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_1
a✝¹ : x ∈ M_1.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ xs | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_1
a✝¹ : x ∈ M_1.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ List.map Sum.inr x.stop_state_list |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 : σ_1
q_0 : σ_0
xs : List (σ_0 ⊕ σ_1)
x : EpsilonArrow σ_1
a✝¹ : x ∈ M_1.epsilon_arrow_list
a✝ : x.start_state = p_0
a3 : List.map Sum.inr x.stop_state_list = xs
⊢ Sum.inl q_0 ∉ List.map Sum.inr 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] | simp | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_1
⊢ (∃ stop_state_list,
{ start_state := Sum.inr p_0, stop_state_list := 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 })
M_1.epsilon_arrow_list ∧
Sum.inr q_0 ∈ stop_state_list) =
match (Sum.inr p_0, Sum.inr q_0) with
| (Sum.inl p', 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 p', Sum.inr q') =>
∃ stop_state_list,
{ start_state := p', stop_state_list := stop_state_list } ∈ M_1.epsilon_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
p_0 q_0 : σ_1
⊢ (∃ 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) ↔
∃ 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] | 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
⊢ (∃ 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) ↔
∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_1
⊢ (∃ stop_state_list,
(∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q_0 ∈ 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
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 |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_union_EpsilonNFA_toAbstract | [312, 1] | [506, 17] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_1
⊢ (∃ stop_state_list,
(∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = stop_state_list) ∧
Sum.inr q_0 ∈ 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 | case mp
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,
(∃ 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
⊢ ∃ 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] | cases a1 | case mp
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,
(∃ 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
⊢ ∃ stop_state_list,
{ start_state := p_0, stop_state_list := stop_state_list } ∈ M_1.epsilon_arrow_list ∧ q_0 ∈ stop_state_list | case mp.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_0 ⊕ σ_1)
h✝ : (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = w✝) ∧ Sum.inr q_0 ∈ w✝
⊢ ∃ 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] | 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_0 ⊕ σ_1)
a2 : (∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = xs) ∧ Sum.inr q_0 ∈ 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)
left✝ : ∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = xs
right✝ : Sum.inr q_0 ∈ 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] | cases a2_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)
a2_left : ∃ a ∈ M_1.epsilon_arrow_list, a.start_state = p_0 ∧ List.map Sum.inr a.stop_state_list = xs
a2_right : Sum.inr q_0 ∈ 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
w✝ : EpsilonArrow σ_1
h✝ : w✝ ∈ M_1.epsilon_arrow_list ∧ w✝.start_state = p_0 ∧ List.map Sum.inr w✝.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] | cases a3 | α : Type
inst✝ : DecidableEq α
σ_0 σ_1 : Type
M_0 : EpsilonNFA α σ_0
M_1 : EpsilonNFA α σ_1
p_0 q_0 : σ_1
xs : List (σ_0 ⊕ σ_1)
a2_right : Sum.inr q_0 ∈ xs
x : EpsilonArrow σ_1
a3 : x ∈ M_1.epsilon_arrow_list ∧ 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
left✝ : x ∈ M_1.epsilon_arrow_list
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 |
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