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Proved a few emptystr simplification rules #127

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Jan 9, 2025
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Proved a few emptystr simplification rules #127

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28 changes: 20 additions & 8 deletions Katydid/Regex/Language.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -665,15 +665,21 @@ theorem simp_and_not_null_l_emptystr_is_emptyset
(r: Lang α)
(notnullr: Not (null r)):
and r emptystr = emptyset := by
-- TODO
sorry
funext xs
simp at *
intro hr hxs
rw [hxs] at hr
contradiction

theorem simp_and_emptystr_not_null_r_is_emptyset
(r: Lang α)
(notnullr: Not (null r)):
and emptystr r = emptyset := by
-- TODO
sorry
funext xs
simp at *
intro hxs
rw [hxs]
exact notnullr

theorem simp_and_idemp (r: Lang α):
and r r = r := by
Expand Down Expand Up @@ -759,15 +765,21 @@ theorem simp_and_not_emptystr_l_not_null_r_is_r
(r: Lang α)
(notnullr: Not (null r)):
and (not emptystr) r = r := by
-- TODO
sorry
funext xs
simp [not, emptystr] at *
intro hr hxs
rw [hxs] at hr
contradiction

theorem simp_and_not_null_l_not_emptystr_r_is_l
(r: Lang α)
(notnullr: Not (null r)):
and r (not emptystr) = r := by
-- TODO
sorry
funext xs
simp [not, emptystr] at *
intro hr hxs
rw [hxs] at hr
contradiction

theorem simp_one_r_implies_star_r (r: Lang α) (xs: List α):
r xs -> star r xs := by
Expand Down
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