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Prove list_drop_app #84

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merged 2 commits into from
Aug 16, 2024
Merged

Prove list_drop_app #84

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d2e7e33
Prove list_drop_app
keeganperry7 Aug 15, 2024
f21baee
Simplify proof
keeganperry7 Aug 15, 2024
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10 changes: 8 additions & 2 deletions Katydid/Std/Lists.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -816,8 +816,14 @@ theorem list_drop_app_length (xs ys: List α):

theorem list_drop_app (n: Nat) (xs ys: List α):
drop n (xs ++ ys) = (drop n xs) ++ (drop (n - length xs) ys) := by
-- TODO
sorry
induction xs generalizing n with
| nil => simp
| cons x xs ih =>
cases n with
| zero => simp
| succ n =>
simp
exact ih n

theorem list_take_length_prefix_is_prefix (xs ys: List α):
take (length xs) (xs ++ ys) = xs := by
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