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Proof step 12 from proof valid-peb-write-valid-peb (previous step)

# buf = LEB_SIZE, apebs[n] = mkpeb(aehdr, avhdr, buf, m, false), subarray(buf, m, LEB_SIZE - m) = mkempbuf(LEB_SIZE - m), n < # apebs, is-aligned(m, EB_PAGE_SIZE), valid-peb(mkpeb(aehdr, avhdr, buf, m, false)), m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0 ⊦ aehdr = empty, avhdr = empty, valid-peb(mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# buf = LEB_SIZE, LEB_SIZE = n0 + m, apebs[n] = mkpeb(aehdr, avhdr, buf, m, false), subarray(buf, m, n0) = mkempbuf(n0), n < # apebs, is-aligned(m, EB_PAGE_SIZE), valid-peb(mkpeb(aehdr, avhdr, buf, m, false)), m ≤ m0, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ aehdr = empty, avhdr = empty, valid-peb(mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [LEB_SIZE, m, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: LEB_SIZE, m, n0