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Proof step 9 from proof valid-peb-write-valid-peb (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), n < # apebs, ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m, boolvar)), valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0 ⊦ valid-peb(mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ 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 11:
# mkpeb(aehdr, avhdr, buf, m, boolvar).data = LEB_SIZE, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), n < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf, m, boolvar)), m ≤ m0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, ¬ mkpeb(aehdr, avhdr, buf, m, boolvar).bad → (mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = empty → mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = empty) ∧ ( mkpeb(aehdr, avhdr, buf, m, boolvar).echdr ≠ garbage ∧ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = empty → mkpeb(aehdr, avhdr, buf, m, boolvar).fill = 0) ∧ mkpeb(aehdr, avhdr, buf, m, boolvar).fill ≤ LEB_SIZE ∧ is-aligned(mkpeb(aehdr, avhdr, buf, m, boolvar).fill, EB_PAGE_SIZE) ∧ subarray (mkpeb(aehdr, avhdr, buf, m, boolvar).data, mkpeb(aehdr, avhdr, buf, m, boolvar).fill, LEB_SIZE - mkpeb(aehdr, avhdr, buf, m, boolvar).fill) = mkempbuf(LEB_SIZE - mkpeb(aehdr, avhdr, buf, m, boolvar).fill) ⊦ valid-peb(mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false))

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, buf, m, boolvar)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, buf, m, boolvar)