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Proof step 110 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, 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 ⊦ n0 = m0, abs-peb(pebs[n0], apebs[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 111:
⊦ abs(pebs, apebs) ↔ # pebs = # apebs ∧ (∀ n. n < # pebs → abs-peb(pebs[n], apebs[n]))
Proof step 112:
# subarray(pebs, 0, m0) = # apebs, # buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, 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, ∀ n. n < # subarray(pebs, 0, m0) → abs-peb(subarray(pebs, 0, m0)[n], apebs[n]) ⊦ n0 = m0, abs-peb(pebs[n0], apebs[n0])

Rule argument

spec: ubi-io-abs name: abs seq: ⊦ abs(pebs, apebs) ↔ # pebs = # apebs ∧ (∀ n. n < # pebs → abs-peb(pebs[n], apebs[n])) subst: [apebs, pebs] → [apebs, subarray(pebs, 0, m0)] flags: <all paths>

Additional information

Used terms: apebs, subarray(pebs, 0, m0)