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Proof step 6 from proof refine-unmap (previous step)

# lpt = n0, # avol0 = n0 + m5, m5 + # lpt0 = # avol0, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol = subarray(avol0, m5, # lpt), m < # lpt0, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt)), is-encoded(lpt0, lebs(avol0, m4, lptlebs(# lpt0, LEB_SIZE))), 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(# lpt0, LEB_SIZE)), m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_unmap#(m, mksb(adr, m0, m1, m2, m3, m4, m5); avol0)⟫ ⟨apersistence_io_unmap#(m, adr, m0, log, lpt, orphans; avol)⟩ ( # avol0 = m5 + (# avol0 - m5) ∧ avol = subarray(avol0, m5, # avol0 - m5) ∧ is-encoded(log, avol0[m1].data) ∧ is-encoded(lpt, lebs(avol0, m4, lptlebs(# avol0 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol0[m2].data))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# avol0 = # lpt + m5, avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), avol = subarray(avol0, m5, # lpt), m < # 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 ⊦ ⟪persistence_io_unmap#(m, mksb(adr, m0, m1, m2, m3, m4, m5); avol0)⟫ ⟨apersistence_io_unmap#(m, adr, m0, log, lpt, orphans; avol)⟩ ( # avol0 = m5 + (# avol0 - m5) ∧ avol = subarray(avol0, m5, # avol0 - m5) ∧ is-encoded(log, avol0[m1].data) ∧ is-encoded(lpt, lebs(avol0, m4, lptlebs(# avol0 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol0[m2].data))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ is-encoded(lpt0, buf) ∧ # lpt0 = # lpt1 → (is-encoded(lpt1, buf) ↔ lpt0 = lpt1); (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic