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Proof step 14 from proof inv-write-data-wl (previous step)

LEB_SIZE = n0 + n1, apebs[n2] = mkpeb(aehdr, avhdr, buf1, 0, false), n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE), avhdr.valid?, aehdr.valid?, n2 < # apebs, ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, 0, false)), n1 ≤ LEB_SIZE, n1 ≤ # buf ⊦ datasize(buf, n1) = 0, ubi-io-peb-inv(mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ 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 16:
LEB_SIZE = n0 + n1, apebs[n2] = mkpeb(aehdr, avhdr, buf1, 0, false), n1 = align↑(datasize(buf, n1), EB_PAGE_SIZE), aehdr.valid?, avhdr.valid?, n2 < # apebs, ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, 0, false)), n1 ≤ # buf, n1 ≤ LEB_SIZE ⊦ datasize(buf, n1) = 0, # mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).data = LEB_SIZE ∧ ( ¬ mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).bad → ( mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).echdr = empty → mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).vidhdr = empty) ∧ ( mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).echdr ≠ garbage ∧ mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).vidhdr = empty → mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).fill = 0) ∧ mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).fill ≤ LEB_SIZE ∧ is-aligned(mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).fill, EB_PAGE_SIZE) ∧ subarray (mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).data, mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).fill, LEB_SIZE - mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, false).fill) = mkempbuf(LEB_SIZE - mkpeb(aehdr, avhdr, subarray(buf, 0, n1) + mkempbuf(n0), n1, 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(buf, 0, n1) + mkempbuf(n0), n1, false)] flags: <all paths>

Additional information

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