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Proof step 112 from proof initial-ex-abstract-initial (previous step)

# subarray(pebs, 0, m0) = # apebs, # buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, 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, ∀ n. n < # subarray(pebs, 0, m0) → abs-peb(subarray(pebs, 0, m0)[n], apebs[n]) ⊦ n0 = m0, abs-peb(pebs[n0], apebs[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 113:
# buf = PEB_SIZE, # apebs + 1 = # pebs, pebs[# apebs] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < # 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, ∀ n1. n1 < # apebs → abs-peb(pebs[n1], apebs[n1]) ⊦ n0 = # apebs, abs-peb(pebs[n0], apebs[n0])

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(pebs, m, n)[n0] = pebs[m + n0]; (s)% ⊦ # subarray(pebs, m, n) = n; (s)