[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 317 from proof refine-link (previous step)

dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), entries0[str] = entries[str], dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), root[q0].dir?, root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs0, files0), ispath(q0, ROOT_INO, ino2, dirs0, files0), of-cons(of, dirs0, files0), of-cons(of, dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), pw(user, md), px(user, md), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files0), px-parent(user, q0, ROOT_INO, dirs0, files0), ino2 ∈ dirs0, str ∈ entries, ino3 ∈ dirs0, ino1 ∈ dirs0, entries[str] ∈ files0, str ∈ entries0, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], ¬ root[q + str '].dir?, ¬ str0 ∈ entries1, ¬ entries[str] ∈ dirs0, psynced → asynced0, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_link#(q + str ', q0 + str0 ', user, abs-files(files0), abs-of(of); err2, root; psynced)⟩ ( abs-files(files0) = abs-files (files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)] [entries0[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0) ]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err2)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 318:
dirs0[ino2] = mkdir(# entries1, md, # links(ino2, dirs0), m3, entries1), files0[entries[str]] = mkfile(m0, md2, # links(entries[str], dirs0), content0), dirs0[ino1] = mkdir(# entries0, md0, # links(ino1, dirs0), m2, entries0), entries0[str] = entries[str], dirs0[ino3] = mkdir(# entries, md1, # links(ino3, dirs0), m4, entries), err0 = err2, fs = abs-files(files0), ofh = abs-of(of), path = q + str ', path' = q0 + str0 ', root.dir?, root[q].dir?, root[q0].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs0), afs-cons(dirs0, files0), afs-cons(dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(q0, ROOT_INO, ino2, dirs0, files0), ispath(q, ROOT_INO, ino1, dirs0, files0), of-cons(of, dirs, files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)]), of-cons(of, dirs0, files0), pw(user, md), px(user, md0), px(user, md), px-parent(user, q0, ROOT_INO, dirs0, files0), px-parent(user, q, ROOT_INO, dirs0, files0), str ∈ entries0, entries[str] ∈ files0, ino1 ∈ dirs0, ino3 ∈ dirs0, str ∈ entries, ino2 ∈ dirs0, dirs ≡ dirs0[ino2, mkdir(# entries1 + 1, md, # links(ino2, dirs0), m3, entries1[str0, entries[str]])], psynced → asynced0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟨choose err with pre-link(path, path', err, user, root, fs, ofh) in err0 := err; if err0 = ESUCCESS then let fid = root[path].fid in root[path'] := fnode(fid); psynced := ?⟩ ( abs-files(files0) = abs-files (files0[entries[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0)] [entries0[str], mkfile(m0, md2, # links(entries[str], dirs0) + 1, content0) ]) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), root[q + str '].dir?, str0 ∈ entries1, entries[str] ∈ dirs0

Rule argument

pos: right 1

Additional information

Used simplifier rules: posix_link#(PATH, PATH', USER, FS, OFH; ERR, ROOT; PSYNCED) {choose E with pre-link(PATH, PATH', E, USER, ROOT, FS, OFH) in ERR := E; if ERR = ESUCCESS then let FID = ROOT[PATH].fid in ROOT[PATH'] := fnode(FID); PSYNCED := ? };