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

# lpt0 = # avol0 - sb.main, # lpt = # lpt0, sb.main + # lpt1 = # avol0, avol0[sb.log] = mapped(buf1), avol0[sb.orph] = mapped(buf0), avol0[0] = mapped(buf), adr = sb.indexaddr, avol = subarray(avol0, sb.main, # lpt0), m = sb.maxino, orphans = ns0, disk-layout(sb, # lpt1), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, sb.main, # lpt0)), is-encoded(lpt1, lebs(avol0, sb.lpt, lptlebs(# lpt1, LEB_SIZE))), is-encoded(sb, buf), is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded-pad(ns, sb.orphsize, buf0), mapped-full?(avol0, sb.lpt, lptlebs(# lpt1, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_commit#(lpt, adr1, m3, EB_PAGE_SIZE, LEB_SIZE; orphans, sb, avol0, logoff; err)⟫ ⟨apersistence_io_commit#(lpt, adr1, m3, avol; ns0, adr, m, plog, lpt0, ns; err0)⟩ ( m = sb.maxino ∧ adr = sb.indexaddr ∧ # avol0 = sb.main + (# avol0 - sb.main) ∧ avol = subarray(avol0, sb.main, # avol0 - sb.main) ∧ is-encoded(plog, avol0[sb.log].data) ∧ is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb.orphsize, avol0[sb.orph].data) ∧ orphans = ns0 ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# lpt = # lpt0, # lpt0 = # avol0 - m6, m6 + # lpt1 = # avol0, avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), adr = adr0, avol = subarray(avol0, m6, # lpt0), m = m0, orphans = ns0, sb = mksb(adr0, m0, m1, m2, m4, m5, m6), disk-layout(sb, # lpt1), ebm-vol-inv(subarray(avol0, m6, # lpt0)), ebm-vol-inv(avol0), is-encoded(plog, buf1), is-encoded(lpt0, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(sb, buf), is-encoded(lpt1, lebs(avol0, m5, lptlebs(# lpt1, LEB_SIZE))), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt1, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_commit#(lpt, adr1, m3, EB_PAGE_SIZE, LEB_SIZE; orphans, sb, avol0, logoff; err)⟫ ⟨apersistence_io_commit#(lpt, adr1, m3, avol; ns0, adr, m, plog, lpt0, ns; err0)⟩ ( m = sb.maxino ∧ adr = sb.indexaddr ∧ # avol0 = sb.main + (# avol0 - sb.main) ∧ avol = subarray(avol0, sb.main, # avol0 - sb.main) ∧ is-encoded(plog, avol0[sb.log].data) ∧ is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb.orphsize, avol0[sb.orph].data) ∧ orphans = ns0 ∧ 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] → [sb, adr1, m1, m2, m3, m4, m5]

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, adr1, m1, m2, m3, m4, m5