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Proof step 91 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, LEB_SIZE = n0 + # buf0, avol[m5] = mapped(buf0), 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(mkempbuf(n0), logoff0 - # buf0, EB_PAGE_SIZE)), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0, # buf0 ≤ logoff0, logoff0 + EB_PAGE_SIZE ≤ # buf0 + # mkempbuf(n0) ⊦ n0 = 0, n1 = 0, subarray(mkempbuf(n0), logoff0 - # buf0, EB_PAGE_SIZE) = emptypage, ∃ buf, buf1. subarray(buf0, 0, logoff0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 92:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), m5 < # avol, LEB_SIZE < n1 + # buf0 + EB_PAGE_SIZE, # buf0 < LEB_SIZE, ebm-vol-inv(avol), is-encoded(log, buf0), is-encoded(rnode(m), subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)), # buf0 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ n1 = 0, subarray(mkempbuf(n1), 0, EB_PAGE_SIZE) = emptypage, ∃ buf, buf1. subarray(buf0, 0, # buf0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

Rule argument

Additional information

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