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 | input stringlengths 73 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.st... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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_l... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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.st... |
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_sta... | 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,
... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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,
... | 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 ∧... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 ∧... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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,
... |
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 ... | 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.ma... | Please generate a tactic in lean4 to solve the state.
STATE:
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_arr... |
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.ma... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :=... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :=... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 ∈ L... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC... |
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... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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 ar... | 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.... | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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.... | 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.... | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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.... | 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.in... | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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.in... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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.in... | Please generate a tactic in lean4 to solve the state.
STATE:
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 S... |
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.in... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 S... |
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_sta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 } ∈
Lis... |
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_s... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ar... |
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... | 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) →
... | Please generate a tactic in lean4 to solve the state.
STATE:
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_sta... |
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) →
... | 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
⊢ ∃ sto... | Please generate a tactic in lean4 to solve the state.
STATE:
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 = ... |
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
⊢ ∃ sto... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 = ... |
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... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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, ... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 : S... |
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,
{ sta... | 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_... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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_l... | 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
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
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 =... |
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 =... | 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_sta... | Please generate a tactic in lean4 to solve the state.
STATE:
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_righ... |
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 S... | 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 = ... | Please generate a tactic in lean4 to solve the state.
STATE:
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_righ... |
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 = ... | 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
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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
⊢... | 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
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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
⊢... | 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
⊢... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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
⊢... | 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,
{... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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,
{... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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.... |
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_s... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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.symb... | 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_arro... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ∈ st... |
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_arro... | 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 ∧ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ∈ st... |
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 ∧ ... | 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 =... | Please generate a tactic in lean4 to solve the state.
STATE:
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.sy... |
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... | 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 Su... | Please generate a tactic in lean4 to solve the state.
STATE:
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,
... |
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 Su... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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_arro... |
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... | 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_ar... | Please generate a tactic in lean4 to solve the state.
STATE:
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.sy... |
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_ar... | 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_ar... | Please generate a tactic in lean4 to solve the state.
STATE:
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_stat... |
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_ar... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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_stat... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TAC... |
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 =>
{ ... | 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_... | Please generate a tactic in lean4 to solve the state.
STATE:
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 } ∈
Li... |
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_... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | 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 := S... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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, ... | 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, ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>
... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>
... |
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... | 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,
... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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,
... | 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,
{ star... | Please generate a tactic in lean4 to solve the state.
STATE:
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) ∧
... |
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,
{ star... | 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_li... | Please generate a tactic in lean4 to solve the state.
STATE:
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) ∧
... |
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_sta... | 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_sta... | Please generate a tactic in lean4 to solve the state.
STATE:
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_stat... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢... |
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, ... | 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,
{... | Please generate a tactic in lean4 to solve the state.
STATE:
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_st... |
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_... | 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_lis... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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_stat... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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.s... |
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... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 ... | 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 } ... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ ... |
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 } ... | 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_sta... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ ... |
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_sta... | 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 := ... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ ... |
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 := ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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_sta... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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_st... |
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.star... | 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_sta... | Please generate a tactic in lean4 to solve the state.
STATE:
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) →
∃... |
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_sta... | 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.s... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ ∃ st... |
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 ... | 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.i... | Please generate a tactic in lean4 to solve the state.
STATE:
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_li... |
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.st... | 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.ma... | Please generate a tactic in lean4 to solve the state.
STATE:
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.ep... |
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.ma... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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.sta... |
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 ... | 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_st... | Please generate a tactic in lean4 to solve the state.
STATE:
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_li... |
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_st... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 Su... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>
... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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] | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢... |
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, ... | 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_s... | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>
... |
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... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>
... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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] | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 =>
... |
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... | 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,
... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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,
... | 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,
{ star... | Please generate a tactic in lean4 to solve the state.
STATE:
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) ∧
... |
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,
{ star... | 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_li... | Please generate a tactic in lean4 to solve the state.
STATE:
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) ∧
... |
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_sta... | 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_sta... | Please generate a tactic in lean4 to solve the state.
STATE:
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_stat... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢... |
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, ... | 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,
{... | Please generate a tactic in lean4 to solve the state.
STATE:
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_st... |
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