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_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases q | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
q : β β Ο_0 β Ο_1
p_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr a... | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
valβ : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr a... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
q : β β Ο_0 β Ο_1
p_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
simp
intro xs a1
cases a1
case _ left =>
cases left
case _ x a2 =>
cases a2
case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp
case _ right =>
cases right
case _ x a2 =... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun ar... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
cases q_0
case _ q_0 =>
simp
sorry
case _ q_0 =>
simp
sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ β (x : List (β β Ο_0 β Ο_1)),
((β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = x) β¨
β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.in... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun ar... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | intro xs a1 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ β (x : List (β β Ο_0 β Ο_1)),
((β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = x) β¨
β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.in... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
a1 :
(β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs) β¨
β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.inr β Sum... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
β’ β (x : List (β β Ο_0 β Ο_1)),
((β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = x) β¨
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases a1 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
a1 :
(β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs) β¨
β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.inr β Sum... | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
hβ : β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs
β’ Sum.inl q_0 β xs
case inr
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
a1 :
(β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs) β¨
β a ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ left =>
cases left
case _ x a2 =>
cases a2
case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
left : β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
left : β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs
β’ Sum.inl q_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ right =>
cases right
case _ x a2 =>
cases a2
case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
right : β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
right : β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases left | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
left : β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs
β’ Sum.inl q_0 β xs | case intro
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
wβ : EpsilonArrow Ο_0
hβ : wβ β M_0.epsilon_arrow_list β§ wβ.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) wβ.stop_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
left : β a β M_0.epsilon_arrow_list, a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = xs
β’ Sum.inl q_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ x a2 =>
cases a2
case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2 : x β M_0.epsilon_arrow_list β§ x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2 : x β M_0.epsilon_arrow_list β§ x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases a2 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2 : x β M_0.epsilon_arrow_list β§ x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | case intro
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
leftβ : x β M_0.epsilon_arrow_list
rightβ : x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2 : x β M_0.epsilon_arrow_list β§ x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right : x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right : x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases a2_right | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right : x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | case intro
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
leftβ : x.start_state = p_0
rightβ : List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right : x.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) x.s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Su... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp only [β a2_right_right] | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β List.... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Su... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Sum.inr β Sum.inl) x.stop_state_list = xs
β’ Sum.inl q_0 β List.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_0
a2_left : x β M_0.epsilon_arrow_list
a2_right_left : x.start_state = p_0
a2_right_right : List.map (Su... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases right | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
right : β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | case intro
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
wβ : Ο_0
hβ : wβ β M_0.accepting_state_list β§ wβ = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
right : β a β M_0.accepting_state_list, a = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ x a2 =>
cases a2
case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2 : x β M_0.accepting_state_list β§ x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2 : x β M_0.accepting_state_list β§ x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases a2 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2 : x β M_0.accepting_state_list β§ x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | case intro
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
leftβ : x β M_0.accepting_state_list
rightβ : x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2 : x β M_0.accepting_state_list β§ x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ a2_left a2_right =>
cases a2_right
case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right : x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right : x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases a2_right | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right : x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | case intro
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
leftβ : x = p_0
rightβ : List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right : x = p_0 β§ List.map (Sum.inr β Sum.inr) M_1.starting_state_list = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ a2_right_left a2_right_right =>
simp only [β a2_right_right]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp only [β a2_right_right] | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β xs | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β List.map (Sum.inr β Su... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.starting_state_list = xs
β’ Sum.inl q_0 β List.map (Sum.inr β Su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : Ο_0
a2_left : x β M_0.accepting_state_list
a2_right_left : x = p_0
a2_right_right : List.map (Sum.inr β Sum.inr) M_1.st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases q_0 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arr... | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 valβ : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
simp
sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start_sta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
simp
sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.sta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start_sta... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
((β a β M_0.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = stop_state_list) β¨
β a β M_0.accepting_state_list,
... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
((β a β M_0.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = stop_state_list) β¨
β a β M_0.accepting_state_list,
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_0
β’ (β stop_state_list,
((β a β M_0.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = stop_state... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.sta... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
((β a β M_0.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = stop_state_list) β¨
β a β M_0.accepting_state_list,
... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inl p_0), stop_state_list := stop_state_list } β
List.map
(fun ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
((β a β M_0.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = stop_state_list) β¨
β a β M_0.accepting_state_list,
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
q_0 : Ο_1
β’ (β stop_state_list,
((β a β M_0.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inl) a.stop_state_list = stop... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases q | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
q : β β Ο_0 β Ο_1
p_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr a... | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
valβ : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr a... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
q : β β Ο_0 β Ο_1
p_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
simp
intro xs x a1 a2 a3
simp only [β a3]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun ar... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
cases q_0
case _ q_0 =>
simp
intro xs x a1 a2 a3
simp only [β a3]
simp
case _ q_0 =>
simp
sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ β (x : List (β β Ο_0 β Ο_1)),
β x_1 β M_1.epsilon_arrow_list,
x_1.start_state = p_0 β List.map (Sum.inr β Sum.inr) x_1.stop_state_list = x β Sum.inl q_0 β x | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun ar... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | intro xs x a1 a2 a3 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ β (x : List (β β Ο_0 β Ο_1)),
β x_1 β M_1.epsilon_arrow_list,
x_1.start_state = p_0 β List.map (Sum.inr β Sum.inr) x_1.stop_state_list = x β Sum.inl q_0 β x | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
β’ β (x : List (β β Ο_0 β Ο_1)),
β x_1 β M_1.epsilon_arrow_list,
x_1.start_state = p_0 β List.map (Sum.inr β Sum.inr) x_1.stop_state_list = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp only [β a3] | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inl q_0 β xs | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inl q_0 β List.map (Sum.inr β Sum.inr) x.st... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_stat... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inl q_0 β List.map (Sum.inr β Sum.inr) x.st... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : β
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_stat... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases q_0 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arr... | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
valβ : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0 β Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
simp
intro xs x a1 a2 a3
simp only [β a3]
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.sta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ q_0 =>
simp
sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start_sta... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.sta... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ β (x : List (β β Ο_0 β Ο_1)),
β x_1 β M_1.epsilon_arrow_list,
x_1.start_state = p_0 β List.map (Sum.inr β Sum.inr) x_1.stop_state_list = x β Sum.inr (Sum.inl q_0) β x | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | intro xs x a1 a2 a3 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ β (x : List (β β Ο_0 β Ο_1)),
β x_1 β M_1.epsilon_arrow_list,
x_1.start_state = p_0 β List.map (Sum.inr β Sum.inr) x_1.stop_state_list = x β Sum.inr (Sum.inl q_0) β x | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inr (Sum.inl q_0) β xs | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
β’ β (x : List (β β Ο_0 β Ο_1)),
β x_1 β M_1.epsilon_arrow_list,
x_1.start_state = p_0 β List.map (Sum.inr β Sum.inr) x_1.stop_state_list ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp only [β a3] | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inr (Sum.inl q_0) β xs | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inr (Sum.inl q_0) β List.map (Sum.inr β S... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_state_list = xs
β’ Sum.inr (Sum.inl q_0) β List.map (Sum.inr β S... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
q_0 : Ο_0
xs : List (β β Ο_0 β Ο_1)
x : EpsilonArrow Ο_1
a1 : x β M_1.epsilon_arrow_list
a2 : x.start_state = p_0
a3 : List.map (Sum.inr β Sum.inr) x.stop_st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow =>
{ start_state := Sum.inr arrow.start_sta... | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
(β a β M_1.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inr) a.stop_state_list = stop_state_list) β§
Sum.inr (Sum.inr q_0) β stop_state_list) β
... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
{ start_state := Sum.inr (Sum.inr p_0), stop_state_list := stop_state_list } β
List.map
(fun arrow ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | sorry | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
(β a β M_1.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inr) a.stop_state_list = stop_state_list) β§
Sum.inr (Sum.inr q_0) β stop_state_list) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 q_0 : Ο_1
β’ (β stop_state_list,
(β a β M_1.epsilon_arrow_list,
a.start_state = p_0 β§ List.map (Sum.inr β Sum.inr) a.stop_state_list = stop_state_li... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | constructor | case right.right
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ ((fun state => state β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False) β§
(fun sta... | case right.right.left
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ (fun state => state β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False
case right.right... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ ((fun state => state β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inl p') => p'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | funext p | case right.right.left
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ (fun state => state β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | case right.right.left.h
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p : β β Ο_0 β Ο_1
β’ (p β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match p with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.left
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ (fun state => state β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inl p') => p'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases p | case right.right.left.h
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p : β β Ο_0 β Ο_1
β’ (p β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match p with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | case right.right.left.h.inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
valβ : β
β’ (Sum.inl valβ β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inl valβ with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False
case ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.left.h
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p : β β Ο_0 β Ο_1
β’ (p β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match p with
| Sum.inr (Sum.inl p') => p' β M_0... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.starting_stat... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
cases p_0
case _ p_0 =>
simp
case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.start... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.starting_stat... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases p_0 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
valβ : Ο_0
β’ (Sum.inr (Sum.inl valβ) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inl valβ) with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False
ca... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inl p') => p' β M_0.start... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inl p') => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inl p') => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inl p') => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inl p') => p' β M_0.starting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inl M_0.starting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inl p') => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | funext p | case right.right.right
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ (fun state => state β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | case right.right.right.h
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p : β β Ο_0 β Ο_1
β’ (p β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match p with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.right
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
β’ (fun state => state β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) = fun p =>
match p with
| Sum.inr (Sum.inr p') => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases p | case right.right.right.h
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p : β β Ο_0 β Ο_1
β’ (p β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match p with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | case right.right.right.h.inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
valβ : β
β’ (Sum.inl valβ β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inl valβ with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False
ca... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right.right.h
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p : β β Ο_0 β Ο_1
β’ (p β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match p with
| Sum.inr (Sum.inr p') => p' β M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
cases p_0
case _ p_0 =>
simp
case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.acce... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : β
β’ (Sum.inl p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inl p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_st... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | cases p_0 | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | case inl
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
valβ : Ο_0
β’ (Sum.inr (Sum.inl valβ) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inl valβ) with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False
... | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0 β Ο_1
β’ (Sum.inr p_0 β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr p_0 with
| Sum.inr (Sum.inr p') => p' β M_1.acce... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inr p') =>... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | case _ p_0 =>
simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inr p') =>... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_0
β’ (Sum.inr (Sum.inl p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inl p_0) with
| Sum.inr (Sum.inr p') =>... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/RegExpToEpsilonNFA.lean | match_concat_EpsilonNFA_toAbstract | [557, 1] | [690, 19] | simp | Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inr p') => p' β M_1.accepting_state_list
| x => False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
instβ : DecidableEq Ξ±
Ο_0 Ο_1 : Type
M_0 : EpsilonNFA Ξ± Ο_0
M_1 : EpsilonNFA Ξ± Ο_1
p_0 : Ο_1
β’ (Sum.inr (Sum.inr p_0) β List.map Sum.inr (List.map Sum.inr M_1.accepting_state_list)) =
match Sum.inr (Sum.inr p_0) with
| Sum.inr (Sum.inr p') =>... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | induction h1 generalizing V | D : Type
I J : Interpretation D
V : VarAssignment D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h1 : IsSub P zs H A B
h2 :
β (Q : PredName) (ds : List D),
Q = P β§ ds.length = zs.length β (Holds D I (Function.updateListITE V zs ds) E H β J.pred_var_ P ds)
h3_const : I.pred_const_ = J.pred_cons... | case pred_const_
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
Xβ : PredName
xsβ : List VarName
V : VarAssignment ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
V : VarAssignment D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h1 : IsSub P zs H A B
h2 :
β (Q : PredName) (ds : List D),
Q = P β§ ds.length = zs.length β (Holds D I (Function.updateListITE V zs ds) E... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case pred_const_ h1_X h1_ts =>
simp only [Holds]
simp only [h3_const] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case pred_occurs_in h1_X h1_ts h1_1 h1_2 =>
obtain s1 := Sub.Var.All.Rec.substitution_theorem D I V E (Function.updateListITE id zs h1_ts) H h1_2
obtain s2 := Function.updateListITE_comp id V zs h1_ts
simp only [s2] at s1
simp at s1
specialize h2 h1_X (List.map V h1_ts)
simp only [s1] at h2
simp only [Hol... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case eq_ h1_x h1_y =>
simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x h1_y : VarName
V : VarAssignment D
h2 :
β (Q : PredName) (ds ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case true_ | false_ =>
simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
V : VarAssignment D
h2 :
β (Q : PredName) (ds : List D),
Q = P... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
V : Var... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case not_ h1_phi h1_phi' _ h1_ih =>
simp only [Holds]
congr! 1
exact h1_ih V h2 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi h1_phi' : Formula
aβ : IsSub P zs H h1_phi h1_phi'
h1_ih :
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_phi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | case
forall_ h1_x h1_phi h1_phi' h1_1 _ h1_ih
| exists_ h1_x h1_phi h1_phi' h1_1 _ h1_ih =>
simp only [Holds]
first | apply forall_congr' | apply exists_congr
intro d
apply h1_ih
intro Q ds a1
specialize h2 Q ds a1
have s1 :
Holds D I (Function.updateListITE (Function.updateITE V h1_x d) zs ds) E H ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : VarName
h1_phi h1_phi' : Formula
h1_1 : Β¬isFreeIn h1_x H
aβ :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_x : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [Holds] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [h3_const] | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp at h1_1 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : Β¬(h1_X = P β§ h1_ts.lengt... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply Holds_coincide_PredVar | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact h3_const | case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro X ds a1 | case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [predVarOccursIn] at a1 | case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | cases a1 | case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 ... | case h2.intro
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | subst a1_left | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredName) (ds... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply h3_var | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredName) (ds... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredNa... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredNa... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro a2 | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredNa... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | subst a2 | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_ts : List VarName
V : VarAssignment D
h2 :
β (Q : PredNa... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp at h1_1 | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | intro contra | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | apply h1_1 | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | trans List.length ds | case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_va... | D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_var_ Q ds... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [eq_comm] | D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_var_ Q ds... | D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_var_ Q ds... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact a1_right | D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_var_ Q ds... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | exact contra | D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = X β§ ds.length = zs.length) β (I.pred_var_ Q ds... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h1_ts : List VarName
V : VarAssignment D
X : PredName
ds : List D
a1_right : ds.length = h1_ts.length
h3_var : β (Q : PredName) (ds : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | obtain s1 := Sub.Var.All.Rec.substitution_theorem D I V E (Function.updateListITE id zs h1_ts) H h1_2 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | obtain s2 := Function.updateListITE_comp id V zs h1_ts | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp only [s2] at s1 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | simp at s1 | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/One/Ind/Sub.lean | FOL.NV.Sub.Pred.One.Ind.substitution_theorem | [131, 1] | [245, 15] | specialize h2 h1_X (List.map V h1_ts) | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : PredName
h1_ts : List VarName
h1_1 : h1_X = P β§ h1_ts.length ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I J : Interpretation D
E : Env
A : Formula
P : PredName
zs : List VarName
H B : Formula
h3_const : I.pred_const_ = J.pred_const_
h3_var : β (Q : PredName) (ds : List D), Β¬(Q = P β§ ds.length = zs.length) β (I.pred_var_ Q ds β J.pred_var_ Q ds)
h1_X : ... |
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