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Proof step 94 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), # buf0 < LEB_SIZE, LEB_SIZE < n1 + # buf0 + EB_PAGE_SIZE, m5 < # avol, ebm-vol-inv(avol), is-encoded(rnode(m), subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)), is-encoded(log, buf0), # buf0 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ n1 = 0, ∃ buf, buf1. subarray(buf0, 0, # buf0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1), # subarray(mkempbuf(n1), 0, EB_PAGE_SIZE) = # emptypage ∧ (∀ n. n < # subarray(mkempbuf(n1), 0, EB_PAGE_SIZE) → subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)[n] = (emptypage)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 95:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), n < EB_PAGE_SIZE, # buf0 < LEB_SIZE, LEB_SIZE < n1 + # buf0 + EB_PAGE_SIZE, m5 < # avol, ebm-vol-inv(avol), is-encoded(rnode(m), subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)), is-encoded(log, buf0), # buf0 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ mkempbuf(n1)[n] = empty, n1 = 0, ∃ buf, buf1. subarray(buf0, 0, # buf0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

Rule argument

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n < # emptypage ⊦ (emptypage)[n] = empty; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(buf, m, n)[n0] = buf[m + n0]; (s)% ⊦ # emptypage = EB_PAGE_SIZE; (s)% ⊦ # subarray(buf, m, n) = n; (s)