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Proof step 83 from proof prepost-read-log (previous step)

# 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 ⊦ n0 = 0, n1 = 0, subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE) = emptypage, ∃ buf, buf1. subarray(buf0, 0, logoff0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 84:
# buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m)
Proof step 85:
# 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 ⊦ n0 = 0, n1 = 0, subarray(buf0 + mkempbuf(n0), logoff0, EB_PAGE_SIZE) = emptypage, ∃ buf, buf1. subarray(buf0, 0, logoff0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1), # buf0 ≤ logoff0 ∧ logoff0 + EB_PAGE_SIZE ≤ # buf0 + # mkempbuf(n0)
Proof step 91:
# 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)

Rule argument

spec: array-splice, inst: buffer name: subarray-append-elim-left seq: # buf ≤ n0, n0 + m ≤ # buf + # buf0 ⊦ subarray(buf + buf0, n0, m) = subarray(buf0, n0 - # buf, m) subst: [m, n0, buf0, buf] → [EB_PAGE_SIZE, logoff0, mkempbuf(n0), buf0] flags: <all paths>

Additional information

Used terms: EB_PAGE_SIZE, logoff0, mkempbuf(n0), buf0