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Proof step 35 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + logoff0, LEB_SIZE = n0 + # buf0, avol[m5] = mapped(buf0), copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, # buf0 < n1 + logoff0 + EB_PAGE_SIZE, logoff0 < LEB_SIZE, m5 < # avol, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(log0, buf0), logoff0 ≤ # buf0, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, # buf0 ≤ LEB_SIZE ⊦ log0 = log, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-copy, inst: buffer name: subarray-elim seq: # buf = n ⊦ subarray(buf, 0, n) = buf subst: [n, buf] → [logoff0, buf0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ # mkempbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ is-encoded(nx0, buf) → (is-encoded(nx1, buf) ↔ nx0 = nx1); (s)%# buf ≤ n, n + m1 ≤ # buf + # buf0 ⊦ copy(buf + buf0, n, buf1, m0, m1) = copy(buf0, n - # buf, buf1, m0, m1); (s)% ⊦ m - m = 0; (s)%# buf = m, # buf0 = m ⊦ copy(buf, 0, buf0, 0, m) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: logoff0, buf0