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Proof step 86 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), logoff0 = # buf0 ∧ EB_PAGE_SIZE ≤ n0

User applied rule apply lemma

And obtained the following new goals

Proof step 87:
m ≠ 0 ⊦ is-aligned(m0, m) ∧ m0 < m1 ∧ m1 < m0 + m → ¬ is-aligned(m1, m)
Proof step 88:
# 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, is-aligned(logoff0, EB_PAGE_SIZE) ∧ logoff0 < # buf0 ∧ # buf0 < logoff0 + EB_PAGE_SIZE → ¬ is-aligned(# buf0, EB_PAGE_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), logoff0 = # buf0 ∧ EB_PAGE_SIZE ≤ n0

Rule argument

spec: align name: between-is-aligned seq: m ≠ 0 ⊦ is-aligned(m0, m) ∧ m0 < m1 ∧ m1 < m0 + m → ¬ is-aligned(m1, m) subst: [m, m0, m1] → [EB_PAGE_SIZE, logoff0, # buf0]

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s) Used terms: EB_PAGE_SIZE, logoff0, # buf0