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Proof step 79 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf0, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf0), # buf0 < n1 + logoff0 + EB_PAGE_SIZE, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, logoff0 < LEB_SIZE, m5 < # avol, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(rnode(m), subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(log0, buf0), # buf0 ≤ LEB_SIZE, logoff0 ≤ # buf0, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 + EB_PAGE_SIZE ≤ # buf0 → buf0 = buf + buf1 + buf3 ∧ # buf = logoff0 ∧ # buf1 = EB_PAGE_SIZE ⊦ copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, n1 = 0, logoff0 + EB_PAGE_SIZE ≤ # buf0, ∃ buf, buf1. subarray(buf0, 0, logoff0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 80:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, LEB_SIZE = n0 + # buf0, avol[m5] = mapped(buf0), m5 < # avol, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < logoff0 + EB_PAGE_SIZE, logoff0 < LEB_SIZE, # buf0 + 1 < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < LEB_SIZE, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log0, buf0), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(rnode(m), subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0 ⊦ copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, n0 = 0, n1 = 0, ∃ buf, buf1. subarray(buf0, 0, logoff0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic% ⊦ m < n → m ≤ n; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)