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Proof step 17 from proof inv-write-data (previous step)

LEB_SIZE = (n0 + n4) + n5, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), aehdr.valid?, avhdr.valid?, n < # apebs, is-aligned(n5, EB_PAGE_SIZE), is-aligned(n4, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), m ≤ n5, n5 + n4 ≤ LEB_SIZE, n1 + n4 ≤ # buf, m ≤ LEB_SIZE, n5 ≤ LEB_SIZE, n4 + n5 ≤ LEB_SIZE ⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 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 19:
LEB_SIZE = (n0 + n4) + n5, apebs[n] = mkpeb(aehdr, avhdr, buf0, m, false), avhdr.valid?, aehdr.valid?, n < # apebs, is-aligned(n4, EB_PAGE_SIZE), is-aligned(n5, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf0, m, false)), n4 + n5 ≤ LEB_SIZE, n5 ≤ LEB_SIZE, m ≤ LEB_SIZE, n1 + n4 ≤ # buf, n5 + n4 ≤ LEB_SIZE, m ≤ n5 ⊦ # mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).data = LEB_SIZE ∧ ( ¬ mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).bad → ( mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).echdr = empty → mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).vidhdr = empty) ∧ ( mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).echdr ≠ garbage ∧ mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).vidhdr = empty → mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill = 0) ∧ mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill ≤ LEB_SIZE ∧ is-aligned(mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill, EB_PAGE_SIZE) ∧ subarray (mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).data, mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill, LEB_SIZE - mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill) = mkempbuf(LEB_SIZE - mkpeb(aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false).fill))

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, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false)] flags: <all paths>

Additional information

Used terms: mkpeb (aehdr, avhdr, subarray(buf0, 0, n5) + subarray(buf, n1, n4) + mkempbuf(n0), n5 + n4, false)