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Proof step 114 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(pebs), ubi-io-initial(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ ubi-io-initial(copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 115:
⊦ ubi-io-initial(apebs) ↔ (∀ n. n < # apebs → ubi-io-peb-initial(apebs[n]))
Proof step 116:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ ∀ n0. n0 < # copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)] → ubi-io-peb-initial(copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)][n0])

Rule argument

spec: ubi-io-inv name: initial seq: ⊦ ubi-io-initial(apebs) ↔ (∀ n. n < # apebs → ubi-io-peb-initial(apebs[n])) subst: [apebs] → [copy(apebs, 0, mkapebs(m0 + 1), 0, m0) [m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false) ]] flags: <all paths>

Additional information

Used terms: copy(apebs, 0, mkapebs(m0 + 1), 0, m0) [m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false) ]