[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 170 from proof refine-write-data-wl (previous step)

apebs[m1] = mkpeb(aehdr, avhdr, buf2, 0, false), pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), n = align↑(datasize(buf, n), EB_PAGE_SIZE), subarray(buf0, 2 * EB_PAGE_SIZE, LEB_SIZE) = emptyleb, aehdr.valid?, avhdr.valid?, m1 < # pebs, m1 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf0, 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, n ≤ # buf, ⌊err1⌋ ⊦ datasize(buf, n) = 0, 2 * EB_PAGE_SIZE = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE)) ∧ abs-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr) ∧ abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr) ∧ emptyleb = mkempbuf(LEB_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 171:
⊦ 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 172:
mkpeb(buf0, 2 * EB_PAGE_SIZE, false).bad ↔ mkpeb(aehdr, avhdr, buf2, 0, false).bad, pebs[m1] = mkpeb(buf0, 2 * EB_PAGE_SIZE, false), apebs[m1] = mkpeb(aehdr, avhdr, buf2, 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), 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⌋ , ¬ mkpeb(buf0, 2 * EB_PAGE_SIZE, false).bad → mkpeb(buf0, 2 * EB_PAGE_SIZE, false).fill = (mkpeb(aehdr, avhdr, buf2, 0, false).echdr = empty ⊃ 0 ;(mkpeb(aehdr, avhdr, buf2, 0, false).vidhdr = empty ⊃ EB_PAGE_SIZE;mkpeb(aehdr, avhdr, buf2, 0, false).fill + 2 * EB_PAGE_SIZE) ) ∧ abs-echdr(subarray(mkpeb(buf0, 2 * EB_PAGE_SIZE, false).data, 0, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, buf2, 0, false).echdr) ∧ abs-vidhdr(subarray(mkpeb(buf0, 2 * EB_PAGE_SIZE, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aehdr, avhdr, buf2, 0, false).vidhdr) ∧ subarray(mkpeb(buf0, 2 * EB_PAGE_SIZE, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aehdr, avhdr, buf2, 0, false).data ⊦ datasize(buf, n) = 0, 2 * EB_PAGE_SIZE = (aehdr = empty ⊃ 0;(avhdr = empty ⊃ EB_PAGE_SIZE;2 * EB_PAGE_SIZE)) ∧ abs-echdr(subarray(buf0, 0, EB_PAGE_SIZE), aehdr) ∧ abs-vidhdr(subarray(buf0, EB_PAGE_SIZE, EB_PAGE_SIZE), avhdr) ∧ emptyleb = mkempbuf(LEB_SIZE)

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, buf2, 0, false), mkpeb(buf0, 2 * EB_PAGE_SIZE, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, buf2, 0, false), mkpeb(buf0, 2 * EB_PAGE_SIZE, false)