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Proof step 42 from proof refine-write-echdr (previous step)

# buf2 = EB_PAGE_SIZE, apebs[m2] = mkpeb(empty, avhdr, buf0, m1, false), pebs[m2] = mkpeb(buf1, 0, false), m2 < # pebs, m2 < # apebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 0, false), mkpeb(empty, avhdr, buf0, m1, false)), is-encoded(echdr(m3), buf2), mtd-cons(pebs), ubi-io-inv(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ abs-peb(mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false), mkpeb(aechdr(m3), avhdr, buf0, m1, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ 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 44:
# buf2 = EB_PAGE_SIZE, pebs[m2] = mkpeb(buf1, 0, false), apebs[m2] = mkpeb(empty, avhdr, buf0, m1, false), m2 < # apebs, m2 < # pebs, abs(pebs, apebs), abs-peb(mkpeb(buf1, 0, false), mkpeb(empty, avhdr, buf0, m1, false)), is-encoded(echdr(m3), buf2), mtd-cons(pebs), ubi-io-inv(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ (mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).bad ↔ mkpeb(aechdr(m3), avhdr, buf0, m1, false).bad) ∧ ( ¬ mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).bad → mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).fill = (mkpeb(aechdr(m3), avhdr, buf0, m1, false).echdr = empty ⊃ 0 ;(mkpeb(aechdr(m3), avhdr, buf0, m1, false).vidhdr = empty ⊃ EB_PAGE_SIZE ;mkpeb(aechdr(m3), avhdr, buf0, m1, false).fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).data, 0, EB_PAGE_SIZE), mkpeb(aechdr(m3), avhdr, buf0, m1, false).echdr) ∧ abs-vidhdr (subarray(mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aechdr(m3), avhdr, buf0, m1, false).vidhdr) ∧ subarray(mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aechdr(m3), avhdr, buf0, m1, 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(aechdr(m3), avhdr, buf0, m1, false), mkpeb (copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aechdr(m3), avhdr, buf0, m1, false), mkpeb(copy(buf2, 0, buf1, 0, EB_PAGE_SIZE), EB_PAGE_SIZE, false)