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Proof step 27 from proof valid-peb-write-valid-peb (previous step)

# buf = LEB_SIZE, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(buf, m3)), buf, m, false), subarray(buf, m, n0) = mkempbuf(n0), aehdr.valid?, n < # apebs, is-aligned(m, EB_PAGE_SIZE), m3 ≤ LEB_SIZE, m3 ≤ datasize(buf), m ≤ m0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ aehdr = empty, m3 = 0, m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

User applied rule cut formula

And obtained the following new goals

Proof step 28:
# buf = LEB_SIZE, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(buf, m3)), buf, m, false), buf = subarray(buf, 0, m0) + mkempbuf(LEB_SIZE - m0), subarray(buf, m, n0) = mkempbuf(n0), aehdr.valid?, n < # apebs, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0, m3 ≤ datasize(buf), m3 ≤ LEB_SIZE ⊦ aehdr = empty, m3 = 0, m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)
Proof step 45:
# buf = LEB_SIZE, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(buf, m3)), buf, m, false), subarray(buf, m, n0) = mkempbuf(n0), aehdr.valid?, n < # apebs, is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0, m3 ≤ datasize(buf), m3 ≤ LEB_SIZE ⊦ aehdr = empty, buf = subarray(buf, 0, m0) + mkempbuf(LEB_SIZE - m0), m3 = 0, m3 ≤ datasize(subarray(buf, 0, m0) + buf1) ∧ checksum(buf, m3) = checksum(subarray(buf, 0, m0) + buf1, m3)

Rule argument

fma: buf = subarray(buf, 0, m0) + mkempbuf(LEB_SIZE - m0)

Additional information

Used formulas: buf = subarray(buf, 0, m0) + mkempbuf(LEB_SIZE - m0)