[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,

Theorem recovery

dirs = dirs0 \ orphans(dirs0, files), files0 = files \ orphans(dirs0, files), ofh0 = abs-of(of), fs0 = abs-files(files), abs(tree0, ROOT_INO)(dirs0), isdir0 → isdir1, isdir1, tree0.dir?, fids-cons(tree0, fs0, ofh0), of-cons(of, dirs0, files), dom of < ino, afs-cons(dirs0, files) ⊦ ⟪vfs_recover#(isdir2; dirs, files0, asynced; of0, ino0, err)⟫ ( ( err = ESUCCESS → (∃ root, fs, ofh, psynced. posix-crash(tree0, fs0, ofh0, root, fs, ofh) ∧ ⟨posix_recover#(isdir2; root, fs, ofh; psynced, err0)⟩ ((ofh = abs-of(of0) ∧ fs = abs-files(files0) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced)) ∧ err = err0))) ∧ ( err ≠ ESUCCESS → (∀ tree, fs, ofh, isdir. ⟨posix_recover#(isdir2; root0, fs1, ofh1; psynced0, err0)⟩ (tree = root0 ∧ fs = fs1 ∧ ofh = ofh1 ∧ (isdir ↔ psynced0) ∧ err = err0))))

View the proof

Infos about the proof