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Proof step 96 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), n3 ≠ 0, m8 < # lpt, n3 < n, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n4 + # buf0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n3, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m7, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n0 + n ≤ # buf, n0 + n3 ≤ # buf, n4 + # buf0 + n ≤ LEB_SIZE, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨avol := subarray(avol0, m6, # lpt) [m8, mapped ( subarray(avol0, m6, # lpt)[m8].data + mkempbuf(n4 + # avol0[m6 + m8].data - # subarray(avol0, m6, # lpt)[m8].data) + subarray(buf, n0, n3)) ]⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 97:
# avol0 = # lpt + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m8] = mapped(buf0), n3 < n, m8 < # lpt, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(n3, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n4 + # buf0, EB_PAGE_SIZE), is-encoded(mksb(adr, m7, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n4 + # buf0 + n ≤ LEB_SIZE, n0 + n3 ≤ # buf, n0 + n ≤ # buf, ⌊err1⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨avol := subarray(avol0, m6, # lpt) [m8, mapped ( subarray(avol0, m6, # lpt)[m8].data + mkempbuf(n4 + # avol0[m6 + m8].data - # subarray(avol0, m6, # lpt)[m8].data) + subarray(buf, n0, n3)) ]⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n0, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data)), m2 = m6 + m8, n3 = 0

Rule argument

fma: m2 = m6 + m8

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ n1 ⊦ ¬ disk-layout(mksb(adr, n0, n1, n2, m, n3, n), mainareasize); (s) Used formulas: m2 = m6 + m8