[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 6 from proof inv-commit (previous step)

# 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 = m3, 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 ⊦ ⟪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}}⟫ ( (∃ 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 = m3 ∧ 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# lpt0 = # lpt, sb.main + # lpt = # avol, avol[0] = mapped(buf), avol[sb.orph] = mapped(buf0), avol[sb.log] = mapped(buf1), 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 ⊦ ⟪ebm_avol_get_volume_size#(avol; ; m); m := m - sb.main; let sb1 = sb in {sb1.indexaddr := adr; sb1.maxino := m3; sb1.orphsize := # orphans; m0 := LEB_SIZE; if sb1.log = 1 then {sb1.log := 2; sb1.orph := 4; sb1.lpt := 5 + lptlebs(m, m0)} else {sb1.log := 1; sb1.orph := 3; sb1.lpt := 5}; avol1 := avol; ebm_avol_remap#(sb1.log; avol; err); ns := orphans; m1 := EB_PAGE_SIZE; if err = ESUCCESS then persistence_io_write_orphans#(sb1.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#(sb1.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#(sb1, m1, m0; avol; err); sb0 := sb; if err = ESUCCESS then {sb0 := sb1; logoff := 0}}⟫ ( (∃ 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 = m3 ∧ 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 = sb ∧ avol[sb.log] = avol1[sb.log] ∧ avol[sb.orph] = avol1[sb.orph] ∧ lebs(avol, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE)) = lebs(avol1, sb.lpt, lptlebs(# avol - sb.main, LEB_SIZE))) ∧ sb0.main = sb.main ∧ # avol = # avol1 ∧ subarray(avol, sb0.main, # avol - sb0.main) = subarray(avol1, sb0.main, # avol - sb0.main))

Rule argument

Additional information

Used simplifier rules: ⊦ SB_LPT = 5; (s)% ⊦ SB_ORPH = 3; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ SB_LOG = 1; (s)