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Proof step 137 from proof refine-link (previous step)

entries = ∅ ↔ sdt = ∅, dirs[entries0[str]] = mkdir(# entries, md, # links(entries0[str], dirs), m1, entries), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), root[q + str '] = dnode(md1, sdt), path' ≠ ε, root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_link#(q + str ', path', user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EISDIR = err0)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 138:
entries = ∅ ↔ sdt = ∅, root[q + str '] = dnode(md1, sdt), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), dirs[entries0[str]] = mkdir(# entries, md, # links(entries0[str], dirs), m1, entries), fs = abs-files(files), ofh = abs-of(of), path = q + str ', root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries0, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = 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(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ EISDIR = err0), path' = ε

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 := ? };