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Proof step 41 from proof refine-write-data-wl (previous step)

LEB_SIZE = n0 + n, apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE) = emptyleb, aehdr.valid?, avhdr.valid?, m1 < # pebs, m1 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), 2 * EB_PAGE_SIZE ≤ PEB_SIZE, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE + n ≤ PEB_SIZE, n ≤ # buf ⊦ datasize(buf, n) = 0, abs-peb (mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false), mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 42:
⊦ abs-peb(peb, apeb) ↔ (peb.bad ↔ apeb.bad) ∧ ( ¬ peb.bad → peb.fill = (apeb.echdr = empty ⊃ 0;(apeb.vidhdr = empty ⊃ EB_PAGE_SIZE;apeb.fill + 2 * EB_PAGE_SIZE)) ∧ abs-echdr(subarray(peb.data, 0, EB_PAGE_SIZE), apeb.echdr) ∧ abs-vidhdr(subarray(peb.data, EB_PAGE_SIZE, EB_PAGE_SIZE), apeb.vidhdr) ∧ subarray(peb.data, 2 * EB_PAGE_SIZE, LEB_SIZE) = apeb.data)
Proof step 43:
LEB_SIZE = n0 + n, pebs[m1] = mkpeb(buf1, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf1, 2 * EB_PAGE_SIZE, LEB_SIZE) = emptyleb, avhdr.valid?, aehdr.valid?, m1 < # apebs, m1 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 2 * EB_PAGE_SIZE, false), mkpeb(aehdr, avhdr, buf2, 0, false)), is-aligned(n, EB_PAGE_SIZE), mtd-cons(pebs), ubi-io-inv(apebs), n ≤ # buf, 2 * EB_PAGE_SIZE + n ≤ PEB_SIZE, n ≤ LEB_SIZE, 2 * EB_PAGE_SIZE ≤ PEB_SIZE ⊦ datasize(buf, n) = 0, ( mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false).bad ↔ mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).bad) ∧ ( ¬ mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false).bad → mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false).fill = (mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).echdr = empty ⊃ 0 ;(mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).vidhdr = empty ⊃ EB_PAGE_SIZE ;mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false).data, 0, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).echdr) ∧ abs-vidhdr (subarray(mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).vidhdr) ∧ subarray(mkpeb(copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false).data)

Rule argument

spec: ubi-io-abs name: abs-peb seq: ⊦ abs-peb(peb, apeb) ↔ (peb.bad ↔ apeb.bad) ∧ ( ¬ peb.bad → peb.fill = (apeb.echdr = empty ⊃ 0 ;(apeb.vidhdr = empty ⊃ EB_PAGE_SIZE ;apeb.fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(peb.data, 0, EB_PAGE_SIZE), apeb.echdr) ∧ abs-vidhdr (subarray(peb.data, EB_PAGE_SIZE, EB_PAGE_SIZE), apeb.vidhdr) ∧ subarray(peb.data, 2 * EB_PAGE_SIZE, LEB_SIZE) = apeb.data) subst: [apeb, peb] → [mkpeb (aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false), mkpeb (copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n0), n, false), mkpeb (copy(buf, 0, buf1, 2 * EB_PAGE_SIZE, n), 2 * EB_PAGE_SIZE + n, false)