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Proof step 116 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(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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 117:
# 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, n0 ≤ m0 ⊦ 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

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ # mkapebs(n) = n; (s)% ⊦ # copy(apebs, m, apebs0, m0, n) = # apebs0; (s)% ⊦ # apebs[n, apeb] = # apebs; (s)