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Proof step 13 from proof lf-valid-wl-free-emptyvidhdr (previous step)

wlar[n] = wl-entry(m, free), apebs[n] = mkpeb(aechdr(m), empty, buf, m0, false), n < # wlar, n < # apebs, ubi-io-peb-inv(mkpeb(aechdr(m), empty, buf, m0, false)) ⊦ m0 = 0

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(aechdr(m), empty, buf, m0, false)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ empty ≠ aechdr(m); (s)% ⊦ garbage ≠ aechdr(m); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s) Used terms: mkpeb(aechdr(m), empty, buf, m0, false)