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Proof step 97 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 ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ # subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) = # mkempbuf(LEB_SIZE) ∧ (∀ n. n < # subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE) → subarray(buf, 2 * EB_PAGE_SIZE, LEB_SIZE)[n] = mkempbuf(LEB_SIZE)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 98:
# 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) ∧ (n1 < LEB_SIZE → buf[2 * EB_PAGE_SIZE + n1] = empty)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → mkempbuf(n)[m] = empty; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)