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Proof step 14 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m4 ≤ LEB_SIZE, m4 ≤ datasize(buf) ⊦ aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(subarray(buf, 0, m + n));# subarray(buf, 0, m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m4 ≤ datasize(buf), m4 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(buf, m + n);(m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4)

Rule argument

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)%m ≤ # buf ⊦ datasize(subarray(buf, 0, m)) = datasize(buf, m); (s)% ⊦ ¬ m + n < m; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (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% ⊦ m ≤ n ↔ ¬ n < m; (ss)