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Proof step 153 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), err = ESUCCESS, ino = ROOT_INO, path' ≠ ε, 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), ino1 ∈ dirs, str ∈ entries0, entries0[str] ∈ files, ¬ root[q + str '].dir?, ¬ entries0[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [vfs_walk#(parent(path'), user, dirs, files, asynced; ino, err); inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); dent := negdentry(path'.last); if err = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err); new_inode := inode, new_dent := dent; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); fs := abs-files(files); if err = ESUCCESS then {c_inode := getinode(mkdentry(str, entries0[str]).ino, dirs, files); afs_link#(mkdentry(str, entries0[str]); new_inode, c_inode, new_dent, err, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_link#(q + str ', path', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0))

User applied rule insert program lemma

And obtained the following new goals

Rule argument

spec: vfs-asm name: walk-prepost-parent seq: ino = ROOT_INO, afs-cons(dirs, files), p ≠ ε ⊦ ⟪vfs_walk#(parent(p), user, dirs, files, asynced; ino, err)⟫ ∃ q, str. p = q + str ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files))) subst: [asynced, files, dirs, user, p, err, ino] → [asynced, files, dirs, user, path', err, ino] flags: <all paths>

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