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Proof step 15 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), 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ subarray(buf, n0, n1) = mkempbuf(n1) ∧ n0 + n1 ≤ # buf → datasize(buf, n0 + n1) = datasize(buf, n0)
Proof step 17:
# 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(buf, m + n);(m + n) + datasize(buf0)) ∧ checksum(buf, m4) = checksum(subarray(buf, 0, m + n) + buf0, m4), subarray(buf, m, n) = mkempbuf(n) ∧ m + n ≤ # buf
Proof step 25:
# 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), m ≤ LEB_SIZE, m4 ≤ LEB_SIZE, m4 ≤ datasize(buf), m + n ≤ # 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)

Rule argument

spec: datasize name: datasize-add-empty-h seq: ⊦ subarray(buf, n0, n1) = mkempbuf(n1) ∧ n0 + n1 ≤ # buf → datasize(buf, n0 + n1) = datasize(buf, n0) subst: [n1, n0, buf] → [n, m, buf] flags: <all paths>

Additional information

Used terms: n, m, buf