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Proof step 15 from proof refine-unmap (previous step)

# avol0 = # lpt + m5, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol1 = subarray(avol0, m5, # lpt), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt)), is-encoded(log, buf1), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟨apersistence_io_unmap#(m6, adr, m0, log, lpt, orphans; avol1)⟩ ( avol1 = subarray(avol0[m5 + m6, unmapped], m5, # avol0 - m5) ∧ is-encoded(log, avol0[m5 + m6, unmapped][m1].data) ∧ is-encoded(lpt, lebs(avol0[m5 + m6, unmapped], m4, lptlebs(# avol0 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol0[m2].data))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
# avol0 = # lpt + m5, # avol0 = n0 + m5, avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), avol1 = subarray(avol0, m5, # lpt), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(subarray(avol0, m5, # lpt)), ebm-vol-inv(avol0), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟨apersistence_io_unmap#(m6, adr, m0, log, lpt, orphans; avol1)⟩ ( avol1 = subarray(avol0[m5 + m6, unmapped], m5, n0) ∧ is-encoded(log, avol0[m5 + m6, unmapped][m1].data) ∧ is-encoded(lpt, lebs(avol0[m5 + m6, unmapped], m4, lptlebs(n0, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol0[m2].data))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [# avol0, m5, n]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol0, m5, n