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Proof step 39 from proof valid-peb0-write-append (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: checksum name: checksum-append-left seq: ⊦ n ≤ # buf0 → checksum(buf0 + buf1, n) = checksum(buf0, n) subst: [n, buf1, buf0] → [m4, buf0, subarray(buf, 0, m + n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → m ≤ n; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ LEB_SIZE ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ ¬ n < datasize(buf, n); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m + m0 < n → ¬ n + n0 < m; (s)%n ≠ 0, m ≤ # buf ⊦ ¬ m + n < datasize(buf, m); (s) Used terms: m4, buf0, subarray(buf, 0, m + n)