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Proof step 113 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, LEB_SIZE = n0 + # buf0, avol[m5] = mapped(buf0), n < n1 + EB_PAGE_SIZE, n < n1, n + 1 < n1 + EB_PAGE_SIZE, n < EB_PAGE_SIZE, m5 < # avol, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < logoff0 + EB_PAGE_SIZE, logoff0 < LEB_SIZE, # buf0 + 1 < n1 + logoff0 + EB_PAGE_SIZE, # buf0 < LEB_SIZE, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log0, buf0), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(rnode(m), subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0 ⊦ (logoff0 + n < # buf0 ⊃ buf0[logoff0 + n];mkempbuf(n0)[logoff0 + n - # buf0]) = empty, n0 = 0

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: align name: between-is-aligned seq: m ≠ 0 ⊦ is-aligned(m0, m) ∧ m0 < m1 ∧ m1 < m0 + m → ¬ is-aligned(m1, m) subst: [m, m0, m1] → [EB_PAGE_SIZE, logoff0, # buf0]

Additional information

Used simplifier rules: ⊦ is-encoded(nx, buf) → is-aligned(# buf, EB_PAGE_SIZE); (s)% ⊦ ¬ m < n → ¬ m + m0 < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ n ≠ n0 → (n < n0 ↔ ¬ n0 < n); (ss)% ⊦ m < n → ¬ n < m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ m - m = 0; (s)% ⊦ n + 0 = n; (s)% ⊦ m ≤ m; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ EB_PAGE_SIZE + n = 0 ↔ false; (s)% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)% ⊦ m < n → n ≠ 0; (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%is-encoded-size: ⊦ is-encoded(rnd, buf) → # buf = EB_PAGE_SIZE; (forward) from specification encoding-page-size-nonempty[encoding-ref-node]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ # mkempbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → mkempbuf(n)[m] = empty; (s)%# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: EB_PAGE_SIZE, logoff0, # buf0