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Proof step 83 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(pebs), ubi-io-initial(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ abs-peb(mkpeb(buf, EB_PAGE_SIZE, false), mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 84:
⊦ abs-peb(peb, apeb) ↔ (peb.bad ↔ apeb.bad) ∧ ( ¬ peb.bad → peb.fill = (apeb.echdr = empty ⊃ 0;(apeb.vidhdr = empty ⊃ EB_PAGE_SIZE;apeb.fill + 2 * EB_PAGE_SIZE)) ∧ abs-echdr(subarray(peb.data, 0, EB_PAGE_SIZE), apeb.echdr) ∧ abs-vidhdr(subarray(peb.data, EB_PAGE_SIZE, EB_PAGE_SIZE), apeb.vidhdr) ∧ subarray(peb.data, 2 * EB_PAGE_SIZE, LEB_SIZE) = apeb.data)
Proof step 85:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ (mkpeb(buf, EB_PAGE_SIZE, false).bad ↔ mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).bad) ∧ ( ¬ mkpeb(buf, EB_PAGE_SIZE, false).bad → mkpeb(buf, EB_PAGE_SIZE, false).fill = (mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).echdr = empty ⊃ 0 ;(mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).vidhdr = empty ⊃ EB_PAGE_SIZE ;mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr(subarray(mkpeb(buf, EB_PAGE_SIZE, false).data, 0, EB_PAGE_SIZE), mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).echdr) ∧ abs-vidhdr (subarray(mkpeb(buf, EB_PAGE_SIZE, false).data, EB_PAGE_SIZE, EB_PAGE_SIZE), mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).vidhdr) ∧ subarray(mkpeb(buf, EB_PAGE_SIZE, false).data, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false).data)

Rule argument

spec: ubi-io-abs name: abs-peb seq: ⊦ abs-peb(peb, apeb) ↔ (peb.bad ↔ apeb.bad) ∧ ( ¬ peb.bad → peb.fill = (apeb.echdr = empty ⊃ 0 ;(apeb.vidhdr = empty ⊃ EB_PAGE_SIZE ;apeb.fill + 2 * EB_PAGE_SIZE ) ) ∧ abs-echdr (subarray(peb.data, 0, EB_PAGE_SIZE), apeb.echdr) ∧ abs-vidhdr (subarray(peb.data, EB_PAGE_SIZE, EB_PAGE_SIZE), apeb.vidhdr) ∧ subarray(peb.data, 2 * EB_PAGE_SIZE, LEB_SIZE) = apeb.data) subst: [apeb, peb] → [mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false), mkpeb(buf, EB_PAGE_SIZE, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false), mkpeb(buf, EB_PAGE_SIZE, false)