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Proof step 35 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, m + n + # buf0 = LEB_SIZE, subarray(buf, m, n) = mkempbuf(n), subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m4 ≤ LEB_SIZE, m4 ≤ datasize(buf, m), m + n ≤ LEB_SIZE, m + n + # buf0 ≤ # buf ⊦ aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(buf, m);(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 36:
# buf = LEB_SIZE, m + n + # buf0 = LEB_SIZE, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m4 ≤ LEB_SIZE, m4 ≤ datasize(buf, m), m + n ≤ LEB_SIZE ⊦ aehdr = empty, m4 = 0, m4 ≤ (datasize(buf0) = 0 ⊃ datasize(buf, m);(m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4)

Rule argument

Additional information

Used simplifier rules: subarray-add-eq-mkempbuf: ⊦ subarray(buf, m, n0 + n1) = mkempbuf(n) ∧ m + n0 + n1 ≤ # buf → subarray(buf, m, n0) = mkempbuf(n0);% ⊦ m ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ mkempbuf(n) = mkempbuf(m) ↔ n = m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic