I agree Our site saves small pieces of text information (cookies) on your device in order to deliver better content and for statistical purposes. You can disable the usage of cookies by changing the settings of your browser. By browsing our website without changing the browser settings you grant us permission to store that information on your device.

Download Files
### Definitions File

### Template File

### Check File

theory Defs imports Main begin consts find_pfx :: "nat list \<Rightarrow> nat \<Rightarrow> nat list" end

theory Submission imports Defs begin fun find_pfx :: "nat list \<Rightarrow> nat \<Rightarrow> nat list" where "find_pfx _ = undefined" value "find_pfx [1::nat,2,3] 2 = [1,2]" value "find_pfx [] (1::nat) = []" lemma find_pfx_append: "(find_pfx (xs1 @ [x] @ xs2) x) = (find_pfx (xs1 @ [x]) x)" sorry lemma last_find_pfx_val: "last (find_pfx (xs @ [x]) x) = x" sorry lemma pfx_append_same: "x \<in> set xs \<Longrightarrow> find_pfx (xs @ xs) x = find_pfx xs x" sorry end

theory Check imports Submission begin lemma find_pfx_append: "(find_pfx (xs1 @ [x] @ xs2) x) = (find_pfx (xs1 @ [x]) x)" by (rule Submission.find_pfx_append) lemma last_find_pfx_val: "last (find_pfx (xs @ [x]) x) = x" by (rule Submission.last_find_pfx_val) lemma pfx_append_same: "x \<in> set xs \<Longrightarrow> find_pfx (xs @ xs) x = find_pfx xs x" by (rule Submission.pfx_append_same) end

Terms and Conditions