[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 25 from proof recovery (previous step)

err0 = ESUCCESS, ks = fo0, ri = fi0, ro = fo0, fo0.inodes?, orphans(fs0, ri1).inodes?, afs-cons(abs-dirs(fs0, ri1), abs-files(fs0, ri1)), file-node-cons(fs0, ri1), log-cons(log0, fs0), orphans-cons(fs0, ri1, orphans(fs0, ri1)), replay-cons-strong(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(fi0), ri-inj(ri1), ubifs-cons(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0) ⊦ [aubifs_replayorphans#(fi0, fo0, fs0, log0, true; ks, err0, ri, ro); log := log0; fs := fs0; fo := fo0; fi := fi0; boolvar := true; if err0 = ESUCCESS then aubifs_replaylog#(log0, fi, ro, fo, fs, log, boolvar; err0, ri); if err0 = ESUCCESS then aubifs_core_journal_sync#(ri, fi, ro, fo, fs, log; ; boolvar, err0)] ( ( err0 = ESUCCESS → boolvar ∧ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ ri-inj(fi) ∧ log-cons(log, fs) ∧ ro.inodes? ∧ fo.inodes?) → (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ri = replay-log(log0, fs0, fi0 ⊖ fo0) ∧ ro = ∅ ∧ fs = fs0 ∧ fi = fi0 ∧ fo = fo0 ∧ log = log0 ∧ boolvar) → ( err0 = ESUCCESS → ⟨dirs := abs-dirs(fs0, ri1) \ abs-keys(orphans(fs0, ri1)), files := abs-files(fs0, ri1) \ abs-keys(orphans(fs0, ri1)); afs_recovery#(boolvar2; dirs, files; asynced, err1)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ ESUCCESS = err1)) ∧ ( err0 ≠ ESUCCESS → (∀ dirs, files, boolvar. ⟨afs_recovery#(boolvar2; dirs1, files1; asynced0, err1)⟩ (dirs = dirs1 ∧ files = files1 ∧ (boolvar ↔ asynced0) ∧ err0 = err1))))

User applied rule insert program lemma

And obtained the following new goals

Proof step 26:
ri = ri0, ro0 = ro, ks = ro, err = ESUCCESS, ks.inodes? ⊦ ⟪aubifs_replayorphans#(fi, fo, fs, log, boolvar; ks, err, ri, ro)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ks = ro ∧ ro = ∅ ∧ ri = ri0 ⊖ ro0))
Proof step 27:
boolvar0 ↔ true, err0 = ESUCCESS, fi1 = fi0, fo1 = fo0, fs1 = fs0, ks = fo0, ks = ro, log1 = log0, ri = fi0, ri = ri, ri2 = ri, ro = fo0, ro = ro, ro1 = ro, orphans(fs0, ri1).inodes?, fo0.inodes?, ks.inodes?, afs-cons(abs-dirs(fs0, ri1), abs-files(fs0, ri1)), file-node-cons(fs0, ri1), log-cons(log0, fs0), orphans-cons(fs0, ri1, orphans(fs0, ri1)), replay-cons-strong(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0), replay-safe(log0, fs0, fi0 ⊖ fo0), ri-inj(ri1), ri-inj(fi0), ubifs-cons(fs0, ri1, orphans(fs0, ri1), fi0, fo0, log0) ⊦ [aubifs_replayorphans#(fi0, fo0, fs0, log0, true; ks, err0, ri, ro)] ( (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ks = ro ∧ ro = ∅ ∧ ri = ri2 ⊖ ro1) → [log := log0; fs := fs0; fo := fo0; fi := fi0; boolvar := true; if err0 = ESUCCESS then aubifs_replaylog#(log0, fi, ro, fo, fs, log, boolvar; err0, ri); if err0 = ESUCCESS then aubifs_core_journal_sync#(ri, fi, ro, fo, fs, log; ; boolvar, err0)] ( ( err0 = ESUCCESS → boolvar ∧ ubifs-cons(fs, ri, ro, fi, fo, log) ∧ replay-cons-strong(fs, ri, ro, fi, fo, log) ∧ file-node-cons(fs, ri) ∧ orphans-cons(fs, ri, ro) ∧ ri-inj(ri) ∧ ri-inj(fi) ∧ log-cons(log, fs) ∧ ro.inodes? ∧ fo.inodes?) → (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → ri = replay-log(log0, fs0, fi0 ⊖ fo0) ∧ ro = ∅ ∧ fs = fs0 ∧ fi = fi0 ∧ fo = fo0 ∧ log = log0 ∧ boolvar) → ( err0 = ESUCCESS → ⟨dirs := abs-dirs(fs0, ri1) \ abs-keys(orphans(fs0, ri1)), files := abs-files(fs0, ri1) \ abs-keys(orphans(fs0, ri1)); afs_recovery#(boolvar2; dirs, files; asynced, err1)⟩ ( dirs = abs-dirs(fs, ri) ∧ files = abs-files(fs, ri) ∧ orphans(abs-dirs(fs, ri), abs-files(fs, ri)) = abs-keys(ro) ∧ (asynced → boolvar) ∧ ESUCCESS = err1)) ∧ ( err0 ≠ ESUCCESS → (∀ dirs, files, boolvar. ⟨afs_recovery#(boolvar2; dirs1, files1; asynced0, err1)⟩ (dirs = dirs1 ∧ files = files1 ∧ (boolvar ↔ asynced0) ∧ err0 = err1)))))

Rule argument

spec: aubifs-asm name: replayorphans-prepost seq: ri = ri0, ro0 = ro, ks = ro, err = ESUCCESS, ks.inodes? ⊦ ⟪aubifs_replayorphans# (fi, fo, fs, log, boolvar; ks, err, ri, ro)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → ks = ro ∧ ro = ∅ ∧ ri = ri0 ⊖ ro0)) subst: [boolvar, log, fs, fo, fi, ro, ri, err, ks, ri0, ro0] → [true, log0, fs0, fo0, fi0, ro, ri, err0, ks, ri, ro] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ubifs-cons(fs, ri, ro, fi, fo, log) → fo.inodes?; (ss)