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Theorem inv-recover

avol ⊆ avol0, ∃ lpt, log, orphans. persistence-io-inv(sb, m, avol, lpt, log, orphans), m0 = EB_PAGE_SIZE, m1 = LEB_SIZE, ebm-vol-inv(avol) ⊦ ⟪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]))

Type: A proof obligation
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state: persistence-io-refine,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 21
Proof steps: 148
Used lemmas: prepost-decode-lpt, prepost-read-lebs, prepost-read-orphans, prepost-read-log, prepost-read-superblock, avol-down-size-le, avol-down-mapped-eq, avol-down-size, recover,
Used spec theorems:
Used simplifier rules: