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Proof step 13 from proof valid-peb-write-valid-peb (previous step)

# 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))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ valid-peb(apeb) ↔ (∃ v, m. valid-peb(v, m, apeb))
Proof step 15:
# 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 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ m0 ⊦ aehdr = empty, avhdr = empty, ∃ v, m. valid-peb(v, m, mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false))

Rule argument

spec: valid-peb name: valid-peb0 seq: ⊦ valid-peb(apeb) ↔ (∃ v, m. valid-peb(v, m, apeb)) subst: [apeb] → [mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false)] flags: <all paths>

Additional information

Used terms: mkpeb(aehdr, avhdr, subarray(buf, 0, m0) + buf1, m1, false)