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Proof step 125 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, n0 < # mkapebs(m0 + 1), 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((n0 < 0 ∨ 0 + m0 ≤ n0 ⊃ mkapebs(m0 + 1)[n0];apebs[n0 + 0 - 0]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 126:
# 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, ubi-io-peb-initial(apebs[n0])

Rule argument

Additional information

Used simplifier rules: ⊦ m - 0 = m; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ m < 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m ≠ n → (m < n + 1 ↔ m < n); (s)% ⊦ # mkapebs(n) = n; (s)