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Proof step 100 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)), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, EB_PAGE_SIZE + LEB_SIZE + EB_PAGE_SIZE ≤ # buf, EB_PAGE_SIZE + LEB_SIZE + EB_PAGE_SIZE ≤ # emptypeb, ∀ n. n < LEB_SIZE + EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n] = (emptypeb)[EB_PAGE_SIZE + n] ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ (n1 < LEB_SIZE → buf[2 * EB_PAGE_SIZE + n1] = empty)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 101:
# 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)), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, ∀ n2. n2 < LEB_SIZE + EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n2] = empty ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ (n1 < LEB_SIZE → buf[2 * EB_PAGE_SIZE + n1] = empty)

Rule argument

Additional information

Used simplifier rules: let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%n < # emptypeb ⊦ (emptypeb)[n] = empty; (s)% ⊦ PEB_SIZE ≤ EB_PAGE_SIZE + n → ¬ n < LEB_SIZE + EB_PAGE_SIZE; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ m; (s)% ⊦ # emptypeb = PEB_SIZE; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ LEB_SIZE + 2 * EB_PAGE_SIZE = PEB_SIZE; (s)% ⊦ m + m = 2 * m; (s)