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Proof step 5 from proof initialization (previous step)

# lpt0 = # lpt0, LEB_SIZE = LEB_SIZE, adr0 = adr1, lpt2 = lpt0, m7 = # lpt0, m8 = LEB_SIZE, m9 = m3 ⊦ [persistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; sb, m4, m5, avol0; logoff, err)] ( ( err = ESUCCESS → (∃ lpt, log, orphans. persistence-io-inv(sb, logoff, avol0, lpt, log, orphans)) ∧ m4 = EB_PAGE_SIZE ∧ m5 = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr0 ∧ sb.maxino = m9 ∧ subarray(avol0, sb.main, # avol0 - sb.main) = fill(mkavolume(m7), unmapped) ∧ is-encoded(lpt2, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded([], avol0[sb.log].data) ∧ is-encoded(∅, avol0[sb.orph].data)) → ( err = ESUCCESS → ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ ( m6 = sb.maxino ∧ adr2 = sb.indexaddr ∧ # avol0 = sb.main + (# avol0 - sb.main) ∧ avol1 = subarray(avol0, sb.main, # avol0 - sb.main) ∧ is-encoded(plog, avol0[sb.log].data) ∧ is-encoded(lpt1, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns0, sb.orphsize, avol0[sb.orph].data) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ adr, m, log, avol, lpt, ns. ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ (adr = adr2 ∧ m = m6 ∧ log = plog ∧ avol = avol1 ∧ lpt = lpt1 ∧ ns = ns0 ∧ err = err0))))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ [persistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; sb, m4, m5, avol0; logoff, err)] ( ( err = ESUCCESS → (∃ lpt, log, orphans. disk-layout(sb, # lpt) ∧ sb.main + # lpt = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(sb, avol0[0].data) ∧ avol0[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol0[sb.orph].data) ∧ avol0[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol0[sb.log].data = logoff) ∧ is-encoded(log, avol0[sb.log].data) ∧ mapped-full?(avol0, sb.lpt, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# lpt, LEB_SIZE)))) ∧ m4 = EB_PAGE_SIZE ∧ m5 = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr1 ∧ sb.maxino = m3 ∧ subarray(avol0, sb.main, # avol0 - sb.main) = fill(mkavolume(# lpt0), unmapped) ∧ is-encoded(lpt0, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ avol0[sb.log].data = mkbuf(0) ∧ avol0[sb.orph].data = mkbuf(0)) → ( err = ESUCCESS → ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ ( m6 = sb.maxino ∧ adr2 = sb.indexaddr ∧ # avol0 = sb.main + (# avol0 - sb.main) ∧ avol1 = subarray(avol0, sb.main, # avol0 - sb.main) ∧ is-encoded(plog, avol0[sb.log].data) ∧ is-encoded(lpt1, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns0, sb.orphsize, avol0[sb.orph].data) ∧ ESUCCESS = err0)) ∧ ( err ≠ ESUCCESS → (∀ adr, m, log, avol, lpt, ns. ⟨apersistence_io_format#(# lpt0, LEB_SIZE, lpt0, adr1, m3; ; adr2, m6, plog, avol1, lpt1, ns0, err0)⟩ (adr = adr2 ∧ m = m6 ∧ log = plog ∧ avol = avol1 ∧ lpt = lpt1 ∧ ns = ns0 ∧ err = err0))))

Rule argument

Additional information

Used simplifier rules: ⊦ is-encoded(∅, buf) ↔ buf = mkbuf(0); (s)% ⊦ is-encoded([], buf) ↔ buf = mkbuf(0); (s)%⊦ persistence-io-inv(sb, logoff, avol, lpt, log, orphans) ↔ (∃ mainareasize. disk-layout(sb, mainareasize) ∧ sb.main + mainareasize = # avol ∧ avol[0].mapped? ∧ is-encoded(sb, avol[0].data) ∧ avol[sb.orph].mapped? ∧ is-encoded-pad(orphans, sb.orphsize, avol[sb.orph].data) ∧ avol[sb.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb.log].data = logoff) ∧ is-encoded(log, avol[sb.log].data) ∧ mapped-full?(avol, sb.lpt, lptlebs(mainareasize, LEB_SIZE)) ∧ # lpt = mainareasize ∧ is-encoded (lpt, lebs(avol, sb.lpt, lptlebs(mainareasize, LEB_SIZE)))); (s)