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Proof step 45 from proof prepost-read-log (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = (n0 + EB_PAGE_SIZE + # buf3) + # buf, avol[m5] = mapped(buf + emptypage + buf3), LEB_SIZE < 2 * EB_PAGE_SIZE + n0 + # buf3 + # buf, # buf < LEB_SIZE, m5 < # avol, EB_PAGE_SIZE < 2 * EB_PAGE_SIZE, ebm-vol-inv(avol), is-encoded(log, buf), is-encoded(log0, buf + emptypage + buf3), # buf + EB_PAGE_SIZE + # buf3 ≤ LEB_SIZE, # buf + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ 2 * EB_PAGE_SIZE + n0 + # buf3 = 0, log0 = log

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ m ≤ m + n; (s)% ⊦ 2 * m ≠ 1; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m +1 = m + 1; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * 1 = m0; (s)%m1 ≠ 0 ⊦ m < (* m1) * m + n0 ↔ (m1 - 1) * m + n0 ≠ 0; (s)% ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)% ⊦ m + m = 2 * m; (s)% ⊦ # emptypage = EB_PAGE_SIZE; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%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%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic% ⊦ is-encoded(nx, buf) → is-aligned(# buf, EB_PAGE_SIZE); (s)%n = # buf ⊦ subarray(buf + buf0, 0, n) = buf; (s)%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + n < m0 → m + n < m0 + n0; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ #(buf + buf0) = # buf + # buf0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%n + m ≤ # buf ⊦ subarray(buf + buf0, n, m) = subarray(buf, n, m); (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)