Proof step 168 from proof refine-link (previous step)

Heuristic conditional right split applied rule if right

And obtained the following new goals

• Proof step 169:

  root[q0].dir? ↔ ino2 ∈ dirs, files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), dent = negdentry((q0 + str0 ').last), err = err1, err1 = ESUCCESS, ino = ino2, inode = mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m), 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(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [{inode := getinode(ino, dirs, files); err := ESUCCESS} or fail#(; ; err); if err = ESUCCESS then if ¬ inode.directory then err := ENOTDIR else if ¬ px(user, inode.meta) ∨ ¬ pw(user, inode.meta) then err := EACCESS else {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS}; new_inode := inode, new_dent := negdentry((q0 + str0 ').last); err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)), q0 + str0 ' = ε, root[q + str '].dir?, entries0[str] ∈ dirs

• Proof step 495:

  root[q0].dir? ↔ ino2 ∈ dirs, files[entries0[str]] = mkfile(m, md, # links(entries0[str], dirs), content), dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), dent = negdentry((q0 + str0 ').last), err = err1, err1 = ESUCCESS, ino = ino2, inode = mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m), 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(q0, ROOT_INO, ino2, dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q0, ROOT_INO, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [abort; if err = ESUCCESS then if ¬ inode.directory then err := ENOTDIR else if ¬ px(user, inode.meta) ∨ ¬ pw(user, inode.meta) then err := EACCESS else {afs_lookup#(ino, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS}; new_inode := inode, new_dent := negdentry((q0 + str0 ').last); err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', q0 + str0 ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)), q0 + str0 ' = ε, root[q + str '].dir?, pre-iget(ino, dirs, files), entries0[str] ∈ dirs

Rule argument

Additional information