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Proof step 77 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 ⊦ abs(pebs, 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 78:
⊦ abs(pebs, apebs) ↔ # pebs = # apebs ∧ (∀ n. n < # pebs → abs-peb(pebs[n], apebs[n]))
Proof step 79:
# 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 ⊦ # pebs = # copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)] ∧ (∀ n0. n0 < # pebs → abs-peb(pebs[n0], copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)][n0]))

Rule argument

spec: ubi-io-abs name: abs seq: ⊦ abs(pebs, apebs) ↔ # pebs = # apebs ∧ (∀ n. n < # pebs → abs-peb(pebs[n], apebs[n])) subst: [apebs, pebs] → [copy(apebs, 0, mkapebs(m0 + 1), 0, m0) [m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false) ], pebs] 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) ], pebs