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Proof step 34 from proof refine-read-echdr (previous step)

apebs[m2] = mkpeb(aehdr1, avhdr, buf0, m1, false), pebs[m2] = mkpeb(buf1, m0, false), emptypage = subarray(buf1, 0, EB_PAGE_SIZE), m2 < # pebs, m2 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, m0, false), mkpeb(aehdr1, avhdr, buf0, m1, false)), mtd-cons(pebs), ubi-io-inv(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ empty = aehdr1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ 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 36:
mkpeb(buf1, m0, false).bad ↔ mkpeb(aehdr1, avhdr, buf0, m1, false).bad, pebs[m2] = mkpeb(buf1, m0, false), apebs[m2] = mkpeb(aehdr1, avhdr, buf0, m1, false), emptypage = subarray(buf1, 0, EB_PAGE_SIZE), m2 < # apebs, m2 < # pebs, abs(pebs, apebs), mtd-cons(pebs), ubi-io-inv(apebs), EB_PAGE_SIZE ≤ PEB_SIZE, ¬ mkpeb(buf1, m0, false).bad → mkpeb(buf1, m0, false).fill = (mkpeb(aehdr1, avhdr, buf0, m1, false).echdr = empty ⊃ 0 ;(mkpeb(aehdr1, avhdr, buf0, m1, false).vidhdr = empty ⊃ EB_PAGE_SIZE;mkpeb(aehdr1, avhdr, buf0, m1, false).fill + 2 * EB_PAGE_SIZE) ) ∧ abs-echdr(subarray(mkpeb(buf1, m0, false).data, 0, EB_PAGE_SIZE), mkpeb(aehdr1, avhdr, buf0, m1, false).echdr) ∧ abs-vidhdr(subarray(mkpeb(buf1, m0, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aehdr1, avhdr, buf0, m1, false).vidhdr) ∧ subarray(mkpeb(buf1, m0, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aehdr1, avhdr, buf0, m1, false).data ⊦ empty = aehdr1

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(aehdr1, avhdr, buf0, m1, false), mkpeb(buf1, m0, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr1, avhdr, buf0, m1, false), mkpeb(buf1, m0, false)