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Proof step 95 from proof prepost-read-log (previous step)

# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), n < EB_PAGE_SIZE, # 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 ⊦ mkempbuf(n1)[n] = empty, n1 = 0, ∃ 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 96:
⊦ m < n → mkempbuf(n)[m] = empty
Proof step 97:
# buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf0, avol[m5] = mapped(buf0), m5 < # avol, LEB_SIZE < n1 + # buf0 + EB_PAGE_SIZE, # buf0 < LEB_SIZE, n < EB_PAGE_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 ⊦ mkempbuf(n1)[n] = empty, n1 = 0, n < n1, ∃ buf, buf1. subarray(buf0, 0, # buf0 + EB_PAGE_SIZE) = buf + buf1 ∧ is-encoded(log, buf) ∧ is-encoded(rnode(m), buf1)

Rule argument

spec: array-splice, inst: buffer name: emparray-at seq: ⊦ m < n → mkempbuf(n)[m] = empty subst: [m, n] → [n, n1] flags: <all paths>

Additional information

Used terms: n, n1