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Proof step 43 from proof valid-peb-write-valid-peb (previous step)

LEB_SIZE = n0 + m, LEB_SIZE = n1 + m0, apebs[n] = mkpeb(aehdr, avidhdr(v, m2, m4, m3, checksum(subarray(buf, 0, m0), m3)), subarray(buf, 0, m0) + mkempbuf(n1), m, false), subarray(subarray(buf, 0, m0) + mkempbuf(n1), m, n0) = mkempbuf(n0), aehdr.valid?, n < # apebs, is-aligned(m, EB_PAGE_SIZE), m3 ≤ LEB_SIZE, m3 ≤ m0, m ≤ m0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, m3 ≤ datasize(subarray(buf, 0, m0)) ⊦ aehdr = empty, checksum(subarray(buf, 0, m0) + mkempbuf(n1), m3) = checksum(subarray(buf, 0, m0) + buf1, m3), m3 = 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] → [m3, mkempbuf(n1), subarray(buf, 0, m0)] flags: <all paths>

Additional information

Used simplifier rules: ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;%ls-array-append-length0: # buf0 = 0 ⊦ buf + buf0 = buf;% ⊦ n ≤ # buf0 → checksum(buf0 + buf1, n) = checksum(buf0, n); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: m3, mkempbuf(n1), subarray(buf, 0, m0)