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Fixed and_null_emptystr_is theorems #128

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Jan 9, 2025
Merged

Fixed and_null_emptystr_is theorems #128

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29 changes: 13 additions & 16 deletions Katydid/Regex/Language.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -638,28 +638,25 @@ theorem simp_and_universal_r_is_l (r: Lang α):
unfold and
simp

theorem simp_and_null_l_emptystr_is_l
theorem simp_and_null_l_emptystr_is_emptystr
(r: Lang α)
(nullr: null r):
and r emptystr = r := by
and r emptystr = emptystr := by
funext xs
simp only [and, emptystr, eq_iff_iff]
apply Iff.intro
case mp =>
intro h
match h with
| And.intro hr hxs =>
exact hr
case mpr =>
-- TODO
sorry
simp at *
intro hxs
rw [hxs]
exact nullr

theorem simp_and_emptystr_null_r_is_r
theorem simp_and_emptystr_null_r_is_emptystr
(r: Lang α)
(nullr: null r):
and emptystr r = r := by
-- TODO
sorry
and emptystr r = emptystr := by
funext xs
simp at *
intro hxs
rw [hxs]
exact nullr

theorem simp_and_not_null_l_emptystr_is_emptyset
(r: Lang α)
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