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Proof step 3 from proof refine-write (previous step)

# lpt = # avol0 - sb.main, sb.main + # lpt0 = # avol0, subarray(avol0, sb.main, # lpt)[m] = mapped(buf0), avol0[0] = mapped(buf1), avol0[sb.orph] = mapped(buf2), avol0[sb.log] = mapped(buf3), avol = subarray(avol0, sb.main, # lpt), m < # lpt0, disk-layout(sb, # lpt0), ebm-vol-inv(subarray(avol0, sb.main, # lpt)), ebm-vol-inv(avol0), is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf1), is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded-pad(orphans, sb.orphsize, buf2), mapped-full?(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE)), # buf0 ≤ m0, m0 + n ≤ LEB_SIZE, n0 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_write#(m, m0, n0, n, buf, sb; avol0; err)⟫ ⟨apersistence_io_write#(m, m0, n0, n, buf, sb.indexaddr, sb.maxino, log, lpt, orphans; avol; err0)⟩ ( # avol0 = sb.main + (# avol0 - sb.main) ∧ avol = subarray(avol0, sb.main, # avol0 - sb.main) ∧ is-encoded(log, avol0[sb.log].data) ∧ is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(orphans, sb.orphsize, avol0[sb.orph].data) ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# lpt = # avol0 - m6, m6 + # lpt0 = # avol0, avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), subarray(avol0, m6, # lpt)[m] = mapped(buf0), avol = subarray(avol0, m6, # lpt), sb = mksb(adr, m1, m2, m3, m4, m5, m6), m < # lpt0, disk-layout(sb, # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n, EB_PAGE_SIZE), is-aligned(m0, EB_PAGE_SIZE), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(sb, 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(# lpt0, LEB_SIZE)), n0 + n ≤ # buf, m0 + n ≤ LEB_SIZE, # buf0 ≤ m0, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_write#(m, m0, n0, n, buf, sb; avol0; err)⟫ ⟨apersistence_io_write#(m, m0, n0, n, buf, adr, m1, log, lpt, orphans; avol; err0)⟩ ( # avol0 = m6 + (# avol0 - m6) ∧ avol = subarray(avol0, m6, # avol0 - m6) ∧ is-encoded(log, avol0[m2].data) ∧ is-encoded(lpt, lebs(avol0, m5, lptlebs(# avol0 - m6, LEB_SIZE))) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err = err0)

Rule argument

spec: superblock name: elim seq: ⊦ ( ( ( ( (adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4) subst: [sb, adr, m, m0, m1, m2, m3, m4] → [sb, adr, m1, m2, m3, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( ((adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4); (elim) Used terms: sb, adr, m1, m2, m3, m4, m5, m6