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

# lpt0 = # lpt, sb.main + # lpt = # avol, avol[0] = mapped(buf), avol[sb.orph] = mapped(buf0), avol[sb.log] = mapped(buf1), avol0 = avol, ns = orphans, sb0 = sb, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf), is-encoded-pad(orphans0, sb.orphsize, buf0), mapped-full?(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_commit#(lpt, adr, m1, EB_PAGE_SIZE, LEB_SIZE; orphans, sb, avol, logoff; err)⟫ ( (∃ lpt1, log, orphans. disk-layout(sb, # lpt1) ∧ sb.main + # lpt1 = # 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(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, sb.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb.indexaddr = adr ∧ sb.maxino = m1 ∧ avol[sb.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb.orphsize, avol[sb.orph].data)) ∧ ( err ≠ ESUCCESS → sb = sb0 ∧ avol[sb0.log] = avol0[sb0.log] ∧ avol[sb0.orph] = avol0[sb0.orph] ∧ lebs(avol, sb0.lpt, lptlebs(# avol - sb0.main, LEB_SIZE)) = lebs(avol0, sb0.lpt, lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ sb.main = sb0.main ∧ # avol = # avol0 ∧ subarray(avol, sb.main, # avol - sb.main) = subarray(avol0, sb.main, # avol - sb.main))

Heuristic weak unfold applied rule call right

And obtained the following new goals

Proof step 4:
# lpt0 = # lpt, sb.main + # lpt = # avol, avol[sb.log] = mapped(buf1), avol[sb.orph] = mapped(buf0), avol[0] = mapped(buf), avol0 = avol, m0 = LEB_SIZE, m1 = EB_PAGE_SIZE, m2 = m, ns = orphans, sb0 = sb, sb1 = sb, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(sb, buf), is-encoded(lpt0, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, sb.orphsize, buf0), mapped-full?(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪if # lpt + sb0.main = # avol then let m = ? in {ebm_avol_get_volume_size#(avol; ; m); m := m - sb0.main; let sb = sb0 in {sb.indexaddr := adr; sb.maxino := m2; sb.orphsize := # orphans; if sb.log = SB_LOG then {sb.log := SB_LOG + 1; sb.orph := SB_ORPH + 1; sb.lpt := SB_LPT + lptlebs(m, m0)} else {sb.log := SB_LOG; sb.orph := SB_ORPH; sb.lpt := SB_LPT}; ebm_avol_remap#(sb.log; avol; err); if err = ESUCCESS then persistence_io_write_orphans#(sb.orph, m1, m0; orphans, avol; err); if err = ESUCCESS then let buf = ? in {persistence_io_encode_lpt#(lpt, m0; ; buf, err); if err = ESUCCESS then persistence_io_write_lebs#(sb.lpt, lptlebs(m, m0), buf, m0; avol; err)}; if err = ESUCCESS then ebm_avol_sync_device#(avol; ; err); if err = ESUCCESS then persistence_io_write_superblock#(sb, m1, m0; avol; err); if err = ESUCCESS then {sb0 := sb; logoff := 0}}} else abort⟫ ( (∃ lpt1, log, orphans. disk-layout(sb0, # lpt1) ∧ sb0.main + # lpt1 = # avol ∧ avol[0].mapped? ∧ is-encoded(sb0, avol[0].data) ∧ avol[sb0.orph].mapped? ∧ is-encoded-pad(orphans, sb0.orphsize, avol[sb0.orph].data) ∧ avol[sb0.log].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[sb0.log].data = logoff) ∧ is-encoded(log, avol[sb0.log].data) ∧ mapped-full?(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)) ∧ is-encoded(lpt1, lebs(avol, sb0.lpt, lptlebs(# lpt1, LEB_SIZE)))) ∧ ebm-vol-inv(avol) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → sb0.indexaddr = adr ∧ sb0.maxino = m ∧ avol[sb0.log].data = mkbuf(0) ∧ is-encoded(lpt, lebs(avol, sb0.lpt, lptlebs(# avol - sb0.main, LEB_SIZE))) ∧ is-encoded-pad(ns, sb0.orphsize, avol[sb0.orph].data)) ∧ ( err ≠ ESUCCESS → sb0 = sb1 ∧ avol[sb1.log] = avol0[sb1.log] ∧ avol[sb1.orph] = avol0[sb1.orph] ∧ lebs(avol, sb1.lpt, lptlebs(# avol - sb1.main, LEB_SIZE)) = lebs(avol0, sb1.lpt, lptlebs(# avol - sb1.main, LEB_SIZE))) ∧ sb0.main = sb1.main ∧ # avol = # avol0 ∧ subarray(avol, sb0.main, # avol - sb0.main) = subarray(avol0, sb0.main, # avol - sb0.main))

Rule argument

pos: right 1

Additional information

Used simplifier rules: commit: ⊦ ;