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Proof step 94 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(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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 95:
# 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 ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = mkempbuf(LEB_SIZE)

Rule argument

Additional information

Used simplifier rules: n < # emptypage ⊦ (emptypage)[n] = empty; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # emptypage = EB_PAGE_SIZE; (s)% ⊦ # subarray(buf, m, n) = n; (s)