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

m = EB_PAGE_SIZE, m0 = LEB_SIZE, ebm-vol-inv(avol), ∃ lpt, log, orphans. persistence-io-inv(sb, logoff, avol, lpt, log, orphans) ⊦ ⟪persistence_io_add_log_leb#(m1, sb, m, m0; logoff, avol; err)⟫ ((∃ lpt, log, orphans. persistence-io-inv(sb, logoff, avol, lpt, log, orphans)) ∧ ebm-vol-inv(avol))

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), 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#(m1, sb, EB_PAGE_SIZE, LEB_SIZE; logoff, avol; err)⟫ ( (∃ lpt0, log, orphans. disk-layout(sb, # lpt0) ∧ sb.main + # lpt0 = # 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(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (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)