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Proof step 2 from proof inv-recover (previous step)

m0 = EB_PAGE_SIZE, m1 = LEB_SIZE, ebm-vol-inv(avol), avol ⊆ avol0, ∃ lpt, log, orphans. persistence-io-inv(sb, m, avol, lpt, log, orphans) ⊦ ⟪persistence_io_recover#(; adr, m2, orphans, log, lpt, sb0, logoff, m3, m4, avol0; err)⟫ ( ( err = ESUCCESS → (∃ lpt, log, orphans. persistence-io-inv(sb0, logoff, avol0, lpt, log, orphans)) ∧ m3 = EB_PAGE_SIZE ∧ m4 = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0 = sb ∧ # avol0 = # avol ∧ adr = sb0.indexaddr ∧ m2 = sb0.maxino ∧ # lpt = # avol0 - sb0.main ∧ is-encoded(lpt, lebs(avol0, sb0.lpt, lptlebs(# avol0 - sb0.main, LEB_SIZE))) ∧ lebs(avol0, sb0.lpt, lptlebs(# avol0 - sb0.main, LEB_SIZE)) = lebs(avol, sb0.lpt, lptlebs(# avol0 - sb0.main, LEB_SIZE)) ∧ is-encoded(log, avol0[sb0.log].data) ∧ is-encoded-pad(orphans, sb0.orphsize, avol0[sb0.orph].data) ∧ avol0[sb0.orph] = avol[sb0.orph] ∧ avol0[sb0.log] = avol[sb0.log]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
sb.main + # lpt0 = # avol, avol[sb.log] = mapped(buf1), avol[sb.orph] = mapped(buf0), avol[0] = mapped(buf), disk-layout(sb, # lpt0), ebm-vol-inv(avol), is-encoded(sb, buf), is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded-pad(orphans0, sb.orphsize, buf0), mapped-full?(avol, sb.lpt, lptlebs(# lpt0, LEB_SIZE)), avol ⊆ avol0, m ≠ LEB_SIZE → # buf1 = m ⊦ ⟪persistence_io_recover#(; adr, m2, orphans, log, lpt, sb0, logoff, m3, m4, avol0; err)⟫ ( ( err = ESUCCESS → (∃ lpt1, log1, orphans1. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol0 ∧ avol0[0].mapped? ∧ is-encoded(sb0, avol0[0].data) ∧ avol0[sb0.orph].mapped? ∧ is-encoded-pad(orphans1, sb0.orphsize, avol0[sb0.orph].data) ∧ avol0[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol0[sb0.log].data = logoff) ∧ is-encoded(log1, avol0[sb0.log].data) ∧ mapped-full?(avol0, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol0, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ m3 = EB_PAGE_SIZE ∧ m4 = LEB_SIZE ∧ ebm-vol-inv(avol0)) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0 = sb ∧ # avol0 = # avol ∧ adr = sb.indexaddr ∧ m2 = sb.maxino ∧ # lpt = # avol0 - sb.main ∧ is-encoded(lpt, lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE))) ∧ lebs(avol0, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE)) = lebs(avol, sb.lpt, lptlebs(# avol0 - sb.main, LEB_SIZE)) ∧ is-encoded(log, avol0[sb.log].data) ∧ is-encoded-pad(orphans, sb.orphsize, avol0[sb.orph].data) ∧ avol0[sb.orph] = avol[sb.orph] ∧ avol0[sb.log] = avol[sb.log]))

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)