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/Text.lean | Languages.thm_3_b | [246, 1] | [252, 9] | simp | Ξ± : Type
L : Language Ξ±
β’ {x | β s β β
, β t β L, s ++ t = x} = β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ {x | β s β β
, β t β L, s ++ t = x} = β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_c | [255, 1] | [262, 9] | simp only [concat] | Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ concat L1 (concat L2 L3) = concat (concat L1 L2) L3 | Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ {x | β s β L1, β t β {x | β s β L2, β t β L3, s ++ t = x}, s ++ t = x} =
{x | β s β {x | β s β L1, β t β L2, s ++ t = x}, β t β L3, s ++ t = x} | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ concat L1 (concat L2 L3) = concat (concat L1 L2) L3
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_c | [255, 1] | [262, 9] | simp | Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ {x | β s β L1, β t β {x | β s β L2, β t β L3, s ++ t = x}, s ++ t = x} =
{x | β s β {x | β s β L1, β t β L2, s ++ t = x}, β t β L3, s ++ t = x} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ {x | β s β L1, β t β {x | β s β L2, β t β L3, s ++ t = x}, s ++ t = x} =
{x | β s β {x | β s β L1, β t β L2, s ++ t = x}, β t β L3, s ++ t = x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_d | [265, 1] | [272, 10] | simp only [concat] | Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ concat L1 (L2 βͺ L3) = concat L1 L2 βͺ concat L1 L3 | Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ {x | β s β L1, β t β L2 βͺ L3, s ++ t = x} =
{x | β s β L1, β t β L2, s ++ t = x} βͺ {x | β s β L1, β t β L3, s ++ t = x} | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ concat L1 (L2 βͺ L3) = concat L1 L2 βͺ concat L1 L3
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_3_d | [265, 1] | [272, 10] | aesop | Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ {x | β s β L1, β t β L2 βͺ L3, s ++ t = x} =
{x | β s β L1, β t β L2, s ++ t = x} βͺ {x | β s β L1, β t β L3, s ++ t = x} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L1 L2 L3 : Language Ξ±
β’ {x | β s β L1, β t β L2 βͺ L3, s ++ t = x} =
{x | β s β L1, β t β L2, s ++ t = x} βͺ {x | β s β L1, β t β L3, s ++ t = x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp only [Set.subset_def] | Ξ± : Type
L : Language Ξ±
n : β
β’ exp L n β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
β’ β x β exp L n, x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
β’ exp L n β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | intro s a1 | Ξ± : Type
L : Language Ξ±
n : β
β’ β x β exp L n, x β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
s : Str Ξ±
a1 : s β exp L n
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
β’ β x β exp L n, x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | induction n generalizing s | Ξ± : Type
L : Language Ξ±
n : β
s : Str Ξ±
a1 : s β exp L n
β’ s β kleene_closure Ξ± L | case zero
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β exp L 0
β’ s β kleene_closure Ξ± L
case succ
Ξ± : Type
L : Language Ξ±
nβ : β
aβ : β s β exp L nβ, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β exp L (nβ + 1)
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
s : Str Ξ±
a1 : s β exp L n
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | case zero =>
simp only [exp] at a1
simp at a1
simp only [a1]
exact kleene_closure.eps L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β exp L 0
β’ s β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β exp L 0
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | case succ n ih =>
simp only [exp] at a1
simp only [concat] at a1
simp at a1
apply Exists.elim a1
intro xs a2
clear a1
cases a2
case _ a2_left a2_right =>
apply Exists.elim a2_right
intro ys a3
clear a2_right
cases a3
case _ a3_left a3_right =>
simp only [β a3_right]
apply kleene_closure.succ L
apply ih xs a2_left
exact a3_left | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β exp L (n + 1)
β’ s β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β exp L (n + 1)
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp only [exp] at a1 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β exp L 0
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β {[]}
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β exp L 0
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp at a1 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β {[]}
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s = []
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β {[]}
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp only [a1] | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s = []
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s = []
β’ [] β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s = []
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | exact kleene_closure.eps L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s = []
β’ [] β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s = []
β’ [] β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp only [exp] at a1 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β exp L (n + 1)
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β concat (exp L n) L
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β exp L (n + 1)
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp only [concat] at a1 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β concat (exp L n) L
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β {x | β s β exp L n, β t β L, s ++ t = x}
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β concat (exp L n) L
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp at a1 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β {x | β s β exp L n, β t β L, s ++ t = x}
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : s β {x | β s β exp L n, β t β L, s ++ t = x}
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | apply Exists.elim a1 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
β’ β (a : Str Ξ±), (a β exp L n β§ β t β L, a ++ t = s) β s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | intro xs a2 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
β’ β (a : Str Ξ±), (a β exp L n β§ β t β L, a ++ t = s) β s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
xs : Str Ξ±
a2 : xs β exp L n β§ β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
β’ β (a : Str Ξ±), (a β exp L n β§ β t β L, a ++ t = s) β s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | clear a1 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
xs : Str Ξ±
a2 : xs β exp L n β§ β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2 : xs β exp L n β§ β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s : Str Ξ±
a1 : β s_1 β exp L n, β t β L, s_1 ++ t = s
xs : Str Ξ±
a2 : xs β exp L n β§ β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | cases a2 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2 : xs β exp L n β§ β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | case intro
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
leftβ : xs β exp L n
rightβ : β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2 : xs β exp L n β§ β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | case _ a2_left a2_right =>
apply Exists.elim a2_right
intro ys a3
clear a2_right
cases a3
case _ a3_left a3_right =>
simp only [β a3_right]
apply kleene_closure.succ L
apply ih xs a2_left
exact a3_left | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | apply Exists.elim a2_right | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ β (a : Str Ξ±), a β L β§ xs ++ a = s β s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | intro ys a3 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ β (a : Str Ξ±), a β L β§ xs ++ a = s β s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
ys : Str Ξ±
a3 : ys β L β§ xs ++ ys = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
β’ β (a : Str Ξ±), a β L β§ xs ++ a = s β s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | clear a2_right | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
ys : Str Ξ±
a3 : ys β L β§ xs ++ ys = s
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3 : ys β L β§ xs ++ ys = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
a2_right : β t β L, xs ++ t = s
ys : Str Ξ±
a3 : ys β L β§ xs ++ ys = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | cases a3 | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3 : ys β L β§ xs ++ ys = s
β’ s β kleene_closure Ξ± L | case intro
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
leftβ : ys β L
rightβ : xs ++ ys = s
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3 : ys β L β§ xs ++ ys = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | case _ a3_left a3_right =>
simp only [β a3_right]
apply kleene_closure.succ L
apply ih xs a2_left
exact a3_left | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ s β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | simp only [β a3_right] | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ xs ++ ys β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | apply kleene_closure.succ L | Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ xs ++ ys β kleene_closure Ξ± L | case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ xs β kleene_closure Ξ± L
case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ ys β L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ xs ++ ys β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | apply ih xs a2_left | case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ xs β kleene_closure Ξ± L
case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ ys β L | case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ ys β L | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ xs β kleene_closure Ξ± L
case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ ys β L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_4 | [325, 1] | [361, 24] | exact a3_left | case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ ys β L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
n : β
ih : β s β exp L n, s β kleene_closure Ξ± L
s xs : Str Ξ±
a2_left : xs β exp L n
ys : Str Ξ±
a3_left : ys β L
a3_right : xs ++ ys = s
β’ ys β L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_left | [364, 1] | [374, 50] | simp only [Set.subset_def] | Ξ± : Type
L : Language Ξ±
β’ β n, exp L n β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
β’ β x β β n, exp L n, x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ β n, exp L n β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_left | [364, 1] | [374, 50] | intro s a1 | Ξ± : Type
L : Language Ξ±
β’ β x β β n, exp L n, x β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β β n, exp L n
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ β x β β n, exp L n, x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_left | [364, 1] | [374, 50] | simp at a1 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β β n, exp L n
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β β n, exp L n
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_left | [364, 1] | [374, 50] | apply Exists.elim a1 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ β (a : β), s β exp L a β s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_left | [364, 1] | [374, 50] | intro n a2 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ β (a : β), s β exp L a β s β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
n : β
a2 : s β exp L n
β’ s β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ β (a : β), s β exp L a β s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_left | [364, 1] | [374, 50] | exact Set.mem_of_subset_of_mem (thm_4 L n) a2 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
n : β
a2 : s β exp L n
β’ s β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
n : β
a2 : s β exp L n
β’ s β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp only [Set.subset_def] | Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β β n, exp L n | Ξ± : Type
L : Language Ξ±
β’ β x β kleene_closure Ξ± L, x β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | intro s a1 | Ξ± : Type
L : Language Ξ±
β’ β x β kleene_closure Ξ± L, x β β n, exp L n | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β kleene_closure Ξ± L
β’ s β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ β x β kleene_closure Ξ± L, x β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | induction a1 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β kleene_closure Ξ± L
β’ s β β n, exp L n | case eps
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β β n, exp L n
case succ
Ξ± : Type
L : Language Ξ±
s sβ tβ : Str Ξ±
aβΒΉ : sβ β kleene_closure Ξ± L
aβ : tβ β L
a_ihβ : sβ β β n, exp L n
β’ sβ ++ tβ β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β kleene_closure Ξ± L
β’ s β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | case eps =>
simp
apply Exists.intro 0
simp only [exp]
simp | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β β n, exp L n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β β n, exp L n | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ β i, [] β exp L i | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | apply Exists.intro 0 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ β i, [] β exp L i | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β exp L 0 | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ β i, [] β exp L i
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp only [exp] | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β exp L 0 | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β exp L 0
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β {[]} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
β’ [] β {[]}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp at ih_3 | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : xs β β n, exp L n
β’ xs ++ ys β β n, exp L n | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
β’ xs ++ ys β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : xs β β n, exp L n
β’ xs ++ ys β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | apply Exists.elim ih_3 | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
β’ xs ++ ys β β n, exp L n | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
β’ β (a : β), xs β exp L a β xs ++ ys β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
β’ xs ++ ys β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | intro n a2 | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
β’ β (a : β), xs β exp L a β xs ++ ys β β n, exp L n | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
n : β
a2 : xs β exp L n
β’ xs ++ ys β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
β’ β (a : β), xs β exp L a β xs ++ ys β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | clear ih_3 | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
n : β
a2 : xs β exp L n
β’ xs ++ ys β β n, exp L n | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β β n, exp L n | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
ih_3 : β i, xs β exp L i
n : β
a2 : xs β exp L n
β’ xs ++ ys β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β β n, exp L n | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β i, xs ++ ys β exp L i | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | apply Exists.intro (n + 1) | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β i, xs ++ ys β exp L i | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β exp L (n + 1) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β i, xs ++ ys β exp L i
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp only [exp] | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β exp L (n + 1) | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β concat (exp L n) L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β exp L (n + 1)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp only [concat] | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β concat (exp L n) L | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β {x | β s β exp L n, β t β L, s ++ t = x} | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β concat (exp L n) L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β {x | β s β exp L n, β t β L, s ++ t = x} | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β s β exp L n, β t β L, s ++ t = xs ++ ys | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs ++ ys β {x | β s β exp L n, β t β L, s ++ t = x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | apply Exists.intro xs | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β s β exp L n, β t β L, s ++ t = xs ++ ys | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs β exp L n β§ β t β L, xs ++ t = xs ++ ys | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β s β exp L n, β t β L, s ++ t = xs ++ ys
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | constructor | Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs β exp L n β§ β t β L, xs ++ t = xs ++ ys | case left
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs β exp L n
case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β t β L, xs ++ t = xs ++ ys | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs β exp L n β§ β t β L, xs ++ t = xs ++ ys
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | exact a2 | case left
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs β exp L n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ xs β exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | apply Exists.intro ys | case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β t β L, xs ++ t = xs ++ ys | case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ ys β L β§ xs ++ ys = xs ++ ys | Please generate a tactic in lean4 to solve the state.
STATE:
case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ β t β L, xs ++ t = xs ++ ys
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | simp | case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ ys β L β§ xs ++ ys = xs ++ ys | case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ ys β L | Please generate a tactic in lean4 to solve the state.
STATE:
case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ ys β L β§ xs ++ ys = xs ++ ys
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5_right | [376, 1] | [406, 19] | exact ih_2 | case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ ys β L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
Ξ± : Type
L : Language Ξ±
s xs ys : Str Ξ±
aβ : xs β kleene_closure Ξ± L
ih_2 : ys β L
n : β
a2 : xs β exp L n
β’ ys β L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5 | [409, 1] | [416, 25] | apply Set.eq_of_subset_of_subset | Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L = β n, exp L n | case a
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β β n, exp L n
case a
Ξ± : Type
L : Language Ξ±
β’ β n, exp L n β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L = β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5 | [409, 1] | [416, 25] | exact thm_5_right L | case a
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β β n, exp L n | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β β n, exp L n
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_5 | [409, 1] | [416, 25] | exact thm_5_left L | case a
Ξ± : Type
L : Language Ξ±
β’ β n, exp L n β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
β’ β n, exp L n β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | induction n | Ξ± : Type
L : Language Ξ±
n : β
β’ concat (exp L n) L = concat L (exp L n) | case zero
Ξ± : Type
L : Language Ξ±
β’ concat (exp L 0) L = concat L (exp L 0)
case succ
Ξ± : Type
L : Language Ξ±
nβ : β
aβ : concat (exp L nβ) L = concat L (exp L nβ)
β’ concat (exp L (nβ + 1)) L = concat L (exp L (nβ + 1)) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
n : β
β’ concat (exp L n) L = concat L (exp L n)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | case zero =>
simp only [exp]
simp only [concat]
simp | Ξ± : Type
L : Language Ξ±
β’ concat (exp L 0) L = concat L (exp L 0) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ concat (exp L 0) L = concat L (exp L 0)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | case succ k ih =>
simp only [exp]
conv => left; simp only [ih]
simp only [thm_3_c] | Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (exp L (k + 1)) L = concat L (exp L (k + 1)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (exp L (k + 1)) L = concat L (exp L (k + 1))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | simp only [exp] | Ξ± : Type
L : Language Ξ±
β’ concat (exp L 0) L = concat L (exp L 0) | Ξ± : Type
L : Language Ξ±
β’ concat {[]} L = concat L {[]} | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ concat (exp L 0) L = concat L (exp L 0)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | simp only [concat] | Ξ± : Type
L : Language Ξ±
β’ concat {[]} L = concat L {[]} | Ξ± : Type
L : Language Ξ±
β’ {x | β s β {[]}, β t β L, s ++ t = x} = {x | β s β L, β t β {[]}, s ++ t = x} | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ concat {[]} L = concat L {[]}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | simp | Ξ± : Type
L : Language Ξ±
β’ {x | β s β {[]}, β t β L, s ++ t = x} = {x | β s β L, β t β {[]}, s ++ t = x} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ {x | β s β {[]}, β t β L, s ++ t = x} = {x | β s β L, β t β {[]}, s ++ t = x}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | simp only [exp] | Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (exp L (k + 1)) L = concat L (exp L (k + 1)) | Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (concat (exp L k) L) L = concat L (concat (exp L k) L) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (exp L (k + 1)) L = concat L (exp L (k + 1))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | conv => left; simp only [ih] | Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (concat (exp L k) L) L = concat L (concat (exp L k) L) | Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (concat L (exp L k)) L = concat L (concat (exp L k) L) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (concat (exp L k) L) L = concat L (concat (exp L k) L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.concat_exp_comm | [419, 1] | [433, 26] | simp only [thm_3_c] | Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (concat L (exp L k)) L = concat L (concat (exp L k) L) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
k : β
ih : concat (exp L k) L = concat L (exp L k)
β’ concat (concat L (exp L k)) L = concat L (concat (exp L k) L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | apply Set.eq_of_subset_of_subset | Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L = {[]} βͺ concat L (kleene_closure Ξ± L) | case a
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β {[]} βͺ concat L (kleene_closure Ξ± L)
case a
Ξ± : Type
L : Language Ξ±
β’ {[]} βͺ concat L (kleene_closure Ξ± L) β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L = {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp only [Set.subset_def] | case a
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β {[]} βͺ concat L (kleene_closure Ξ± L) | case a
Ξ± : Type
L : Language Ξ±
β’ β x β kleene_closure Ξ± L, x β {[]} βͺ concat L (kleene_closure Ξ± L) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
β’ kleene_closure Ξ± L β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | intro s a1 | case a
Ξ± : Type
L : Language Ξ±
β’ β x β kleene_closure Ξ± L, x β {[]} βͺ concat L (kleene_closure Ξ± L) | case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β kleene_closure Ξ± L
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
β’ β x β kleene_closure Ξ± L, x β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp only [thm_5 L] at a1 | case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β kleene_closure Ξ± L
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β β n, exp L n
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β kleene_closure Ξ± L
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp at a1 | case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β β n, exp L n
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : s β β n, exp L n
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | cases a1 | case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | case a.intro
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
wβ : β
hβ : s β exp L wβ
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
a1 : β i, s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | case _ i a2 =>
simp
sorry | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L) | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s = [] β¨ s β concat L (kleene_closure Ξ± L) | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s β {[]} βͺ concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | sorry | Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s = [] β¨ s β concat L (kleene_closure Ξ± L) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
s : Str Ξ±
i : β
a2 : s β exp L i
β’ s = [] β¨ s β concat L (kleene_closure Ξ± L)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp only [Set.subset_def] | case a
Ξ± : Type
L : Language Ξ±
β’ {[]} βͺ concat L (kleene_closure Ξ± L) β kleene_closure Ξ± L | case a
Ξ± : Type
L : Language Ξ±
β’ β x β {[]} βͺ concat L (kleene_closure Ξ± L), x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
β’ {[]} βͺ concat L (kleene_closure Ξ± L) β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | intro x a1 | case a
Ξ± : Type
L : Language Ξ±
β’ β x β {[]} βͺ concat L (kleene_closure Ξ± L), x β kleene_closure Ξ± L | case a
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1 : x β {[]} βͺ concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
β’ β x β {[]} βͺ concat L (kleene_closure Ξ± L), x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp at a1 | case a
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1 : x β {[]} βͺ concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | case a
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1 : x = [] β¨ x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1 : x β {[]} βͺ concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | cases a1 | case a
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1 : x = [] β¨ x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | case a.inl
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
hβ : x = []
β’ x β kleene_closure Ξ± L
case a.inr
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
hβ : x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1 : x = [] β¨ x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | case _ a1_left =>
simp only [a1_left]
exact kleene_closure.eps L | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ x β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | case _ a1_right =>
simp only [thm_5 L] at a1_right
sorry | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp only [a1_left] | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ x β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ [] β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | exact kleene_closure.eps L | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ [] β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_left : x = []
β’ [] β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | simp only [thm_5 L] at a1_right | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (β n, exp L n)
β’ x β kleene_closure Ξ± L | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (kleene_closure Ξ± L)
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/Parsing/Text.lean | Languages.thm_6 | [436, 1] | [459, 14] | sorry | Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (β n, exp L n)
β’ x β kleene_closure Ξ± L | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
Ξ± : Type
L : Language Ξ±
x : Str Ξ±
a1_right : x β concat L (β n, exp L n)
β’ x β kleene_closure Ξ± L
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | cases v | v : Var
β’ Var.lc_at 0 v β v.isFree | case free_
aβ : String
β’ Var.lc_at 0 (free_ aβ) β (free_ aβ).isFree
case bound_
aβ : β
β’ Var.lc_at 0 (bound_ aβ) β (bound_ aβ).isFree | Please generate a tactic in lean4 to solve the state.
STATE:
v : Var
β’ Var.lc_at 0 v β v.isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | case free_ x =>
simp only [Var.lc_at]
simp only [isFree] | x : String
β’ Var.lc_at 0 (free_ x) β (free_ x).isFree | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : String
β’ Var.lc_at 0 (free_ x) β (free_ x).isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | case bound_ i =>
simp only [Var.lc_at]
simp only [isFree]
simp | i : β
β’ Var.lc_at 0 (bound_ i) β (bound_ i).isFree | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : β
β’ Var.lc_at 0 (bound_ i) β (bound_ i).isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | simp only [Var.lc_at] | x : String
β’ Var.lc_at 0 (free_ x) β (free_ x).isFree | x : String
β’ True β (free_ x).isFree | Please generate a tactic in lean4 to solve the state.
STATE:
x : String
β’ Var.lc_at 0 (free_ x) β (free_ x).isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | simp only [isFree] | x : String
β’ True β (free_ x).isFree | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : String
β’ True β (free_ x).isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | simp only [Var.lc_at] | i : β
β’ Var.lc_at 0 (bound_ i) β (bound_ i).isFree | i : β
β’ i < 0 β (bound_ i).isFree | Please generate a tactic in lean4 to solve the state.
STATE:
i : β
β’ Var.lc_at 0 (bound_ i) β (bound_ i).isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | simp only [isFree] | i : β
β’ i < 0 β (bound_ i).isFree | i : β
β’ i < 0 β False | Please generate a tactic in lean4 to solve the state.
STATE:
i : β
β’ i < 0 β (bound_ i).isFree
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.lc_at_zero_iff_is_free | [171, 1] | [182, 9] | simp | i : β
β’ i < 0 β False | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
i : β
β’ i < 0 β False
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/LN/Paper.lean | LN.free_var_list_to_string_list | [186, 1] | [210, 24] | induction vs | vs : List Var
h1 : β v β vs, Var.lc_at 0 v
β’ β xs, vs = List.map free_ xs | case nil
h1 : β v β [], Var.lc_at 0 v
β’ β xs, [] = List.map free_ xs
case cons
headβ : Var
tailβ : List Var
tail_ihβ : (β v β tailβ, Var.lc_at 0 v) β β xs, tailβ = List.map free_ xs
h1 : β v β headβ :: tailβ, Var.lc_at 0 v
β’ β xs, headβ :: tailβ = List.map free_ xs | Please generate a tactic in lean4 to solve the state.
STATE:
vs : List Var
h1 : β v β vs, Var.lc_at 0 v
β’ β xs, vs = List.map free_ xs
TACTIC:
|
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