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Proof step 101 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(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 ≤ # buf0 ⊦ copy(buf0 + mkempbuf(n0), logoff0, buf2, 0, EB_PAGE_SIZE) = emptypage, n0 = 0, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 102:
⊦ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 → copy(buf, n0, buf0, n1, m) = subarray(buf0, 0, n1) + subarray(buf, n0, m) + subarray(buf0, n1 + m, # buf0 - n1 - m)
Proof step 103:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n0 + # buf0, LEB_SIZE = n1 + logoff0, avol[m5] = mapped(buf0), # buf0 < LEB_SIZE, # buf0 + 1 < n1 + logoff0 + EB_PAGE_SIZE, logoff0 < LEB_SIZE, # buf0 < logoff0 + EB_PAGE_SIZE, # buf0 < n1 + logoff0 + EB_PAGE_SIZE, LEB_SIZE < n1 + logoff0 + EB_PAGE_SIZE, m5 < # avol, ebm-vol-inv(avol), is-aligned(logoff0, EB_PAGE_SIZE), is-encoded(rnode(m), subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE)), is-encoded(log, subarray(buf0, 0, logoff0)), is-encoded(log0, buf0), logoff0 ≤ # buf0, logoff0 + EB_PAGE_SIZE ≤ LEB_SIZE, logoff0 + EB_PAGE_SIZE ≤ #(buf0 + mkempbuf(n0)), 0 + EB_PAGE_SIZE ≤ # buf2 ⊦ subarray(buf2, 0, 0) + subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE) + subarray(buf2, 0 + EB_PAGE_SIZE, # buf2 - 0 - EB_PAGE_SIZE) = emptypage, n0 = 0, n1 = 0

Rule argument

spec: array-splice, inst: buffer name: copy2append seq: ⊦ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 → copy(buf, n0, buf0, n1, m) = subarray(buf0, 0, n1) + subarray(buf, n0, m) + subarray(buf0, n1 + m, # buf0 - n1 - m) subst: [m, n1, buf0, n0, buf] → [EB_PAGE_SIZE, 0, buf2, logoff0, buf0 + mkempbuf(n0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s) Used terms: EB_PAGE_SIZE, 0, buf2, logoff0, buf0 + mkempbuf(n0)