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FDS Week 2 Homework

Week 2 homework.

Resources

Definitions File

```theory Defs
imports Main
begin

end

```

Template File

```theory Template
imports Defs
begin

fun contains :: "'a \<Rightarrow> 'a list \<Rightarrow> bool"
where
"contains _ _ = undefined"

fun ldistinct :: "'a list \<Rightarrow> bool"
where
"ldistinct _ = undefined"

lemma ldistinct_rev: "ldistinct (rev xs) \<longleftrightarrow> ldistinct xs"
sorry

lemma length_fold: "length_fold xs = length xs"
sorry

lemma length_foldr: "length_foldr xs = length xs"
sorry

fun slice :: "'a list \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> 'a list"
where
"slice _ _ _ = undefined"

lemma slice_append: "slice xs s l1 @ slice xs (s+l1) l2 = slice xs s (l1+l2)"
sorry

lemma ldistinct_slice: "ldistinct xs \<Longrightarrow> ldistinct (slice xs s l)"
sorry

end

```

Check File

```theory Check
imports Submission
begin

lemma ldistinct_rev: "ldistinct (rev xs) \<longleftrightarrow> ldistinct xs"
by (rule ldistinct_rev)

lemma length_fold: "length_fold xs = length xs"
by (rule length_fold)

lemma length_foldr: "length_foldr xs = length xs"
by (rule length_foldr)

lemma slice_append: "slice xs s l1 @ slice xs (s+l1) l2 = slice xs s (l1+l2)"
by (rule slice_append)

lemma ldistinct_slice: "ldistinct xs \<Longrightarrow> ldistinct (slice xs s l)"
by (rule ldistinct_slice)

end

```

Terms and Conditions