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Proof step 92 from proof prepost-read-log (previous step)

# 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 93:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 94:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), # buf0 < LEB_SIZE, LEB_SIZE < n1 + # buf0 + EB_PAGE_SIZE, m5 < # avol, ebm-vol-inv(avol), is-encoded(rnode(m), subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)), is-encoded(log, buf0), # buf0 + EB_PAGE_SIZE ≤ LEB_SIZE ⊦ n1 = 0, ∃ buf, buf1. subarray(buf0, 0, # buf0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1), # subarray(mkempbuf(n1), 0, EB_PAGE_SIZE) = # emptypage ∧ (∀ n. n < # subarray(mkempbuf(n1), 0, EB_PAGE_SIZE) → subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)[n] = (emptypage)[n])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [emptypage, subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)] flags: <all paths>

Additional information

Used terms: emptypage, subarray(mkempbuf(n1), 0, EB_PAGE_SIZE)