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Proof step 80 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), n0 ≤ m0, EB_PAGE_SIZE ≤ PEB_SIZE ⊦ abs-peb(pebs[n0], copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)][n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 81:
⊦ m ≠ n → apebs[n, apeb][m] = apebs[m]
Proof step 82:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 = m0, 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 ≤ m0 ⊦ abs-peb(pebs[n0], copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[m0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false)][n0])
Proof step 106:
# 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 ≤ m0 ⊦ n0 = m0, abs-peb(pebs[n0], copy(apebs, 0, mkapebs(m0 + 1), 0, m0)[n0])

Rule argument

spec: array, inst: apebs name: Put-other seq: ⊦ m ≠ n → apebs[n, apeb][m] = apebs[m] subst: [m, apeb, n, apebs] → [n0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false), m0, copy(apebs, 0, mkapebs(m0 + 1), 0, m0)] flags: <all paths>

Additional information

Used terms: n0, mkpeb(aechdr(n), empty, mkempbuf(LEB_SIZE), 0, false), m0, copy(apebs, 0, mkapebs(m0 + 1), 0, m0)