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Proof step 2 from proof prepost-add-log-leb (previous step)

avol0 = avol, ebm-vol-inv(avol), persistence-io-inv(sb, logoff, avol, lpt, log, orphans) ⊦ ⟪persistence_io_add_log_leb#(m, sb, EB_PAGE_SIZE, LEB_SIZE; logoff, avol; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ebm-vol-inv(avol) ∧ subarray(avol, sb.main, # lpt) = subarray(avol0, sb.main, # lpt) ∧ (err = ESUCCESS → persistence-io-inv(sb, logoff, avol, lpt, log + m, orphans)) ∧ (err ≠ ESUCCESS → persistence-io-inv(sb, logoff, avol, lpt, log, orphans)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
sb.main + # lpt = # avol, avol[sb.log] = mapped(buf1), avol[sb.orph] = mapped(buf0), avol[0] = mapped(buf), avol0 = avol, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(sb, buf), is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans, sb.orphsize, buf0), mapped-full?(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_add_log_leb#(m, sb, EB_PAGE_SIZE, LEB_SIZE; logoff, avol; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ebm-vol-inv(avol) ∧ subarray(avol, sb.main, # lpt) = subarray(avol0, sb.main, # lpt) ∧ ( err = ESUCCESS → sb.main + # lpt = # 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 + m ', avol[sb.log].data) ∧ mapped-full?(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)))) ∧ ( err ≠ ESUCCESS → sb.main + # lpt = # 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(# lpt, LEB_SIZE)) ∧ is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)))))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)%m = n ⊦ disk-layout(sb, m) → disk-layout(sb, n); (s)% ⊦ nx + n = nx + n '; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)%⊦ 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)