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Proof step 92 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 ⊦ subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE) = emptypage ∧ subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkempbuf(LEB_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 93:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 94:
# 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 ⊦ ( # subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE) = # emptypage ∧ (∀ n. n < # subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE) → subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE)[n] = (emptypage)[n])) ∧ subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkempbuf(LEB_SIZE)

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [emptypage, subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE)] flags: <all paths>

Additional information

Used terms: emptypage, subarray(buf, EB_PAGE_SIZE, EB_PAGE_SIZE)