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Proof step 31 from proof valid-peb0-write-append (previous step)

# buf = LEB_SIZE, LEB_SIZE = (n + # buf0) + m, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), subarray(buf, m, n) = mkempbuf(n), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m4 ≤ LEB_SIZE, m4 ≤ datasize(buf, LEB_SIZE), m + n ≤ LEB_SIZE, ∃ n0. m + n0 = 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
# buf = LEB_SIZE, m + n + # buf0 = LEB_SIZE, subarray(buf, m, n + # buf0) = mkempbuf(n + # buf0), subarray(buf, m, n) = mkempbuf(n), aehdr.valid?, is-aligned(m, EB_PAGE_SIZE), m4 ≤ LEB_SIZE, m4 ≤ datasize(buf, LEB_SIZE), 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: eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic