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Proof step 19 from proof inv-sync-erase (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf, m, false), n < # apebs, ubi-io-inv(apebs), ⌊err0⌋ ⊦ ubi-io-peb-inv(mkpeb(garbage, garbage, mkempbuf(LEB_SIZE), 0, false))

User applied rule insert rewrite lemma

And obtained the following new goals

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(garbage, garbage, mkempbuf(LEB_SIZE), 0, false)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ empty ≠ garbage; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ 0 ≤ m; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ m - 0 = m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ mkempbuf(n) = mkempbuf(m) ↔ n = m; (s) Used terms: mkpeb(garbage, garbage, mkempbuf(LEB_SIZE), 0, false)