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/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | tauto | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs xs : List α
a2_left_left : r.is_nullable
a2_left_right : xs = []
ys : List α
a3_left_left : s.is_nullable
a3_left_right : ys = []
a3_right : [] = cs
⊢ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs xs : List α
a2_left_left : r.is_nullable
a2_left_right : xs = []
ys : List α
a3_left_left ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | intro a1 | case h.mpr
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
⊢ (r.is_nullable ∧ s.is_nullable) ∧ cs = [] →
∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r_1 ++ s_... | case h.mpr
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1 : (r.is_nullable ∧ s.is_nullable) ∧ cs = []
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r_1 ++ s_1... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
⊢ (r.is_nullable ∧ s.is_nullable) ∧ cs = [] →
∃ r_1, (r.is_nullabl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | cases a1 | case h.mpr
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1 : (r.is_nullable ∧ s.is_nullable) ∧ cs = []
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r_1 ++ s_1... | case h.mpr.intro
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
left✝ : r.is_nullable ∧ s.is_nullable
right✝ : cs = []
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.mpr
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1 : (r.is_nullable ∧ s.is_nullable) ∧ cs = []
⊢ ∃ r_1, (r.is_nullable... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | case _ a1_left a2_right =>
cases a1_left
case _ a1_left_left a1_left_right =>
simp only [a1_left_left]
simp only [a1_left_right]
simp
simp only [a2_right] | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1_left : r.is_nullable ∧ s.is_nullable
a2_right : cs = []
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r_1 ++ s_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1_left : r.is_nullable ∧ s.is_nullable
a2_right : cs = []
⊢ ∃ r_1, (r.is_nullabl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | cases a1_left | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1_left : r.is_nullable ∧ s.is_nullable
a2_right : cs = []
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r_1 ++ s_... | case intro
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
left✝ : r.is_nullable
right✝ : s.is_nullable
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 =... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a1_left : r.is_nullable ∧ s.is_nullable
a2_right : cs = []
⊢ ∃ r_1, (r.is_nullabl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | case _ a1_left_left a1_left_right =>
simp only [a1_left_left]
simp only [a1_left_right]
simp
simp only [a2_right] | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp only [a1_left_left] | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃ r_1, (r.is_nullable ∧ r_1 = []) ∧ ∃ s_1, (s.is_nullable ∧ s_... | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃ r, (True ∧ r = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r +... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp only [a1_left_right] | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃ r, (True ∧ r = []) ∧ ∃ s_1, (s.is_nullable ∧ s_1 = []) ∧ r +... | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃ r, (True ∧ r = []) ∧ ∃ s, (True ∧ s = []) ∧ r ++ s = cs | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃ r, (True ∧ r = []) ∧ ∃ s, (True ∧ s = []) ∧ r ++ s = cs | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ [] = cs | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ ∃... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp only [a2_right] | α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ [] = cs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
r s : RegExp α
r_ih : RegExp.languageOf α r.delta = if r.is_nullable then {[]} else ∅
s_ih : RegExp.languageOf α s.delta = if s.is_nullable then {[]} else ∅
cs : List α
a2_right : cs = []
a1_left_left : r.is_nullable
a1_left_right : s.is_nullable
⊢ [... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp only [RegExp.languageOf] | α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ RegExp.languageOf α e.closure.delta =
if e.closure.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero | α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ {[]} = if e.closure.is_nullable then {[]} else ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ RegExp.languageOf α e.closure.delta =
if e.closure.is_nullable then RegExp.languageOf α RegEx... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp only [RegExp.is_nullable] | α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ {[]} = if e.closure.is_nullable then {[]} else ∅ | α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ {[]} = if True then {[]} else ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ {[]} = if e.closure.is_nullable then {[]} else ∅
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | language_of_delta | [121, 1] | [197, 11] | simp | α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ {[]} = if True then {[]} else ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
e : RegExp α
a_ih✝ :
RegExp.languageOf α e.delta =
if e.is_nullable then RegExp.languageOf α RegExp.epsilon else RegExp.languageOf α RegExp.zero
⊢ {[]} = if True then {[]} else ∅
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | induction e generalizing w | α : Type
inst✝ : DecidableEq α
a : α
w : List α
e : RegExp α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e | case char
α : Type
inst✝ : DecidableEq α
a a✝ : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (RegExp.char a✝)) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char a✝)
case epsilon
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.epsilon) ↔ a :: w ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
e : RegExp α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case char b =>
simp only [RegExp.derivative]
split_ifs
case pos c1 =>
simp only [c1]
simp only [RegExp.languageOf]
simp
case neg c1 =>
simp only [RegExp.languageOf]
simp
intro a1
contradiction | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (RegExp.char b)) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (RegExp.char b)) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case epsilon =>
simp only [RegExp.derivative]
simp only [RegExp.languageOf]
simp | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.epsilon) ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.epsilon) ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case zero =>
simp only [RegExp.derivative]
simp only [RegExp.languageOf]
simp | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α RegExp.zero | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α RegExp.zero
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case union r s r_ih s_ih =>
simp only [RegExp.derivative]
simp only [RegExp.languageOf]
specialize r_ih w
specialize s_ih w
simp
tauto | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (r... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (RegExp.char b)) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (if a = b then RegExp.epsilon else RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (RegExp.char b)) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | split_ifs | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (if a = b then RegExp.epsilon else RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | case pos
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
h✝ : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
case neg
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
h✝ : ¬a = b
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
⊢ w ∈ RegExp.languageOf α (if a = b then RegExp.epsilon else RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case pos c1 =>
simp only [c1]
simp only [RegExp.languageOf]
simp | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case neg c1 =>
simp only [RegExp.languageOf]
simp
intro a1
contradiction | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [c1] | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ b :: w ∈ RegExp.languageOf α (RegExp.char b) | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ b :: w ∈ RegExp.languageOf α (RegExp.char b) | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ {[]} ↔ b :: w ∈ {[b]} | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ RegExp.languageOf α RegExp.epsilon ↔ b :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ {[]} ↔ b :: w ∈ {[b]} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : a = b
⊢ w ∈ {[]} ↔ b :: w ∈ {[b]}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b) | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ ∅ ↔ a :: w ∈ {[b]} | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α (RegExp.char b)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ ∅ ↔ a :: w ∈ {[b]} | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ a = b → ¬w = [] | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ w ∈ ∅ ↔ a :: w ∈ {[b]}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ a = b → ¬w = [] | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
a1 : a = b
⊢ ¬w = [] | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
⊢ a = b → ¬w = []
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | contradiction | α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
a1 : a = b
⊢ ¬w = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a b : α
w : List α
c1 : ¬a = b
a1 : a = b
⊢ ¬w = []
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.epsilon) ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.epsilon) ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ ∅ ↔ a :: w ∈ {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α RegExp.epsilon
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ ∅ ↔ a :: w ∈ {[]} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ ∅ ↔ a :: w ∈ {[]}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α RegExp.zero | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α RegExp.zero | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a RegExp.zero) ↔ a :: w ∈ RegExp.languageOf α RegExp.zero
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α RegExp.zero | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ ∅ ↔ a :: w ∈ ∅ | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ RegExp.languageOf α RegExp.zero ↔ a :: w ∈ RegExp.languageOf α RegExp.zero
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ ∅ ↔ a :: w ∈ ∅ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
w : List α
⊢ w ∈ ∅ ↔ a :: w ∈ ∅
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (r... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a r... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a r... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r)... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | specialize r_ih w | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r)... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r) ∪ RegExp.langua... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | specialize s_ih w | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r) ∪ RegExp.langua... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r) ∪ RegExp.languageOf α (RegExp.d... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
⊢ w ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r) ∪ RegExp.languageOf α (RegExp.d... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r) ∨ w ∈ RegExp.languageOf α (RegE... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
⊢ w ∈ RegExp.languag... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | tauto | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a r) ∨ w ∈ RegExp.languageOf α (RegE... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
w : List α
r_ih : w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
⊢ w ∈ RegExp.languag... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a (r... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈
RegExp.languageOf α
(if r.is_... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | split_ifs | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
⊢ w ∈
RegExp.languageOf α
(if r.is_... | case pos
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
h✝ : r.is_nullable
⊢ w ∈ RegExp.language... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ w ∈ RegExp.languageOf α ((Re... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.lang... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.lang... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf α... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf α... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lang... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lang... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.la... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.la... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.la... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro xs a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.la... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.la... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.la... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2 : xs ∈ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2 : xs ∈ ... | case mp.intro
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
left... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a2_right | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro ys a3 | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a2_right | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a3 | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | case intro
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.intro (a :: xs) | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [← r_ih] | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left ... | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left ... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lang... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | exact a2_left | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lang... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.intro ys | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left... | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left... | case right.left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | exact a3_left | case right.left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegEx... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [← a3_right] | case right.right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a... | case right.right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | case right.right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegE... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lan... | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a1 | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro xs a2 | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a1 | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2 : xs ∈... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a2 | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2 : xs ∈... | case mpr.intro
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
lef... | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a2_right | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro ys a3 | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a2_right | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a3 | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | case intro
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [is_nullable_def] at c1 | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : r.is_nullable
xs : List α
a2_left : xs ∈ Reg... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r
ys : List... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.intro (a :: w) | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r
ys : List... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r
ys : List... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r
ys : List... | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [← a3_right] | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r... | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lang... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α r... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lang... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.intro [] | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α ... | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w xs : List α
a2_left : xs ∈ RegExp.languageOf α ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ RegExp.languageOf α (r.... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ w ∈ {x | ∃ r_1 ∈ RegExp.lan... | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.languageOf ... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.lan... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro xs a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
a1 : ∃ r_1 ∈ RegExp.l... | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
xs : List α
a2 : xs ∈... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
xs : List α
a2 : xs ∈... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.languageOf α s
w : List α
c1 : ¬r.is_nullable
⊢ (∃ r_1 ∈ RegExp.la... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
r s : RegExp α
r_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a r) ↔ a :: w ∈ RegExp.languageOf α r
s_ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a s) ↔ a :: w ∈ RegExp.langu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.derivative] | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closure | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a e).concat e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closure | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α (RegExp.derivative a e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp only [RegExp.languageOf] | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a e).concat e.closure) ↔ a :: w ∈ RegExp.languageOf α e.closure | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈
{x |
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e),
∃ s ∈ {l | ∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = l}, ... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈ RegExp.languageOf α ((RegExp.derivative a e).concat e.closure) ↔ a :: w ∈ RegExp.languageO... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | simp | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈
{x |
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e),
∃ s ∈ {l | ∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = l}, ... | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) ↔
∃ rs, (∀ r ∈ rs, r ∈ RegExp.language... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ w ∈
{x |
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e),
∃ s ∈ {l |... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | constructor | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) ↔
∃ rs, (∀ r ∈ rs, r ∈ RegExp.language... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) →
∃ rs, (∀ r ∈ rs, r ∈ RegExp.... | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | sorry | case mpr
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = a :: w) →
∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegEx... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case mpr
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ rs, (∀ r ∈ rs, r ∈ RegExp.languageOf α e) ∧ rs.join = a :: w) →
∃ r ∈ RegExp.l... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w) →
∃ rs, (∀ r ∈ rs, r ∈ RegExp.... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp.lan... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
⊢ (∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.language... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | apply Exists.elim a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp.lan... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∀ (a_1 : List α),
(a_1 ∈ Re... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | intro xs a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
⊢ ∀ (a_1 : List α),
(a_1 ∈ Re... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
xs : List α
a2 : xs ∈ RegExp.lang... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | clear a1 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ r ++ a.join = w
xs : List α
a2 : xs ∈ RegExp.lang... | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2 : xs ∈ RegExp.languageOf α (RegExp.derivative a e) ∧ ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w : List α
a1 : ∃ r ∈ RegExp.languageOf α (RegExp.derivative a e), ∃ a, (∀ r ∈ a, r ∈ RegExp.langua... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | cases a2 | case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2 : xs ∈ RegExp.languageOf α (RegExp.derivative a e) ∧ ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ RegExp... | case mp.intro
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
left✝ : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
right✝ : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ... | Please generate a tactic in lean4 to solve the state.
STATE:
case mp
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2 : xs ∈ RegExp.languageOf α (RegExp.derivative a e) ∧ ∃ a, (∀ r ∈ a, r ∈ RegExp.lan... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Brzozowski.lean | derivative_def | [295, 1] | [407, 12] | case _ a2_left a2_right =>
apply Exists.elim a2_right
intro ys a3
clear a2_right
cases a3
case _ a3_left a3_right =>
apply Exists.intro [(a :: w)]
simp
simp only [← ih]
sorry | α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegExp.languageOf α e) ∧ xs ++ a.join = w
⊢ ∃ rs, (∀ r ∈ rs, r ∈ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α : Type
inst✝ : DecidableEq α
a : α
e : RegExp α
ih : ∀ (w : List α), w ∈ RegExp.languageOf α (RegExp.derivative a e) ↔ a :: w ∈ RegExp.languageOf α e
w xs : List α
a2_left : xs ∈ RegExp.languageOf α (RegExp.derivative a e)
a2_right : ∃ a, (∀ r ∈ a, r ∈ RegE... |
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