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Proof step 173 from proof refine-write-data-wl (previous step)

2 * EB_PAGE_SIZE = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE)), pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, emptyleb, 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE) = emptyleb, avhdr.valid?, aehdr.valid?, m1 < # apebs, m1 < # pebs, abs(pebs, apebs), abs-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr), abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n ≤ # buf, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE ≤ PEB_SIZE, ⌊err1⌋ ⊦ datasize(buf, n) = 0, emptyleb = mkempbuf(LEB_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(LEB_SIZE), emptyleb] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # emptyleb = LEB_SIZE; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%n < # emptyleb ⊦ (emptyleb)[n] = empty; (s)% ⊦ m < n → mkempbuf(n)[m] = empty; (s) Used terms: mkempbuf(LEB_SIZE), emptyleb