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Proof step 22 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), avol1 = subarray(avol0, m6, # lpt), n ≠ 0, m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n ≤ # buf, # buf0 ≤ m7, m7 + n ≤ LEB_SIZE, m6 ≤ # avol0, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray (avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n))], m6, # avol0 - m6) ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n))][m2].data) ∧ is-encoded (lpt, lebs (avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n))], m5, lptlebs(# avol0 - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ ESUCCESS = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# avol0 = # lpt + m6, # avol0 = n0 + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m8] = mapped(buf0), avol1 = subarray(avol0, m6, # lpt), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, 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)), m6 ≤ # avol0, m7 + n ≤ LEB_SIZE, # buf0 ≤ m7, n2 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨apersistence_io_write#(m8, m7, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray(avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n))], m6, n0) ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n))][m2].data) ∧ is-encoded (lpt, lebs (avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(m7 - # avol0[m6 + m8].data) + subarray(buf, n2, n))], m5, lptlebs(n0, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ ESUCCESS = err1), n = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m6, # avol0, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m6, # avol0, n0