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Proof step 130 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), n0 < m0, # apebs < 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(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, # apebs ≤ n0 ⊦ n0 = m0, ubi-io-peb-initial(apebs[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

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] → [apebs, subarray(pebs, 0, m0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # subarray(pebs, m, n) = n; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ n < n; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%is-encoded-size: ⊦ is-encoded(ehdr, buf) → # buf = EB_PAGE_SIZE; (forward) from specification encoding-page-size-nonempty[encoding-echeader]% ⊦ m ≤ n → (n < m ↔ false); (s)%# pebs = n ⊦ subarray(pebs, 0, n) = pebs; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: apebs, subarray(pebs, 0, m0)