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Proof step 5 from proof valid-peb0-write-append (previous step)

m0 + # buf0 = LEB_SIZE, aehdr.valid?, ubi-io-peb-inv(mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false)), m4 ≤ datasize(buf), m ≤ m0, m4 ≤ LEB_SIZE ⊦ m4 = 0, m4 ≤ datasize(subarray(buf, 0, m0) + buf0) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m0) + buf0, m4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ubi-io-peb-inv(apeb) ↔ # apeb.data = LEB_SIZE ∧ ( ¬ apeb.bad → (apeb.echdr = empty → apeb.vidhdr = empty) ∧ (apeb.echdr ≠ garbage ∧ apeb.vidhdr = empty → apeb.fill = 0) ∧ apeb.fill ≤ LEB_SIZE ∧ is-aligned(apeb.fill, EB_PAGE_SIZE) ∧ subarray(apeb.data, apeb.fill, LEB_SIZE - apeb.fill) = mkempbuf(LEB_SIZE - apeb.fill))
Proof step 7:
# mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).data = LEB_SIZE, m0 + # buf0 = LEB_SIZE, aehdr.valid?, m4 ≤ LEB_SIZE, m ≤ m0, m4 ≤ datasize(buf), ¬ mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).bad → ( mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).echdr = empty → mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).vidhdr = empty) ∧ ( mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).echdr ≠ garbage ∧ mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).vidhdr = empty → mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).fill = 0) ∧ mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).fill ≤ LEB_SIZE ∧ is-aligned(mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).fill, EB_PAGE_SIZE) ∧ subarray (mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).data, mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).fill, LEB_SIZE - mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).fill) = mkempbuf(LEB_SIZE - mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false).fill) ⊦ m4 = 0, m4 ≤ datasize(subarray(buf, 0, m0) + buf0) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m0) + buf0, m4)

Rule argument

spec: ubi-io-inv name: peb-inv seq: ⊦ ubi-io-peb-inv(apeb) ↔ # apeb.data = LEB_SIZE ∧ ( ¬ apeb.bad → (apeb.echdr = empty → apeb.vidhdr = empty) ∧ ( apeb.echdr ≠ garbage ∧ apeb.vidhdr = empty → apeb.fill = 0) ∧ apeb.fill ≤ LEB_SIZE ∧ is-aligned(apeb.fill, EB_PAGE_SIZE) ∧ subarray(apeb.data, apeb.fill, LEB_SIZE - apeb.fill) = mkempbuf(LEB_SIZE - apeb.fill)) subst: [apeb] → [mkpeb (aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avidhdr(v, m2, m3, m4, checksum(buf, m4)), buf, m, false)