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Proof step 123 from proof refine-link (previous step)

entries0[str] ∈ dirs ↔ root[q + str '].dir?, dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), c_inode = inode, err = ESUCCESS, err1 = EISDIR, err2 = ESUCCESS, ino = mkdentry(str, entries0[str]).ino, inode = getinode(ino, dirs, files), inode0 = mkinode(ino1, md0, true, # links(ino1, dirs), m2, # entries0), mkdentry(str, entries0[str]).dentry?, root[q].dir?, root.dir?, inode.directory, 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), pre-iget(ino, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries0, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [if err1 = ESUCCESS then let ino = ROOT_INO, dent = negdentry(path'.last), path = parent(path') in {vfs_walk#(path, user, dirs, files, asynced; ino, err1); if err1 = ESUCCESS then vfs_may_create#(ino, dent, user, dirs, files, asynced; inode, err1); new_inode := inode, new_dent := dent}; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then 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 ', path', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)), path' = ε

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 124:
entries0[str] ∈ dirs ↔ root[q + str '].dir?, dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), c_inode = inode, err = ESUCCESS, err1 = EISDIR, err2 = ESUCCESS, ino = mkdentry(str, entries0[str]).ino, inode = getinode(ino, dirs, files), inode0 = mkinode(ino1, md0, true, # links(ino1, dirs), m2, # entries0), mkdentry(str, entries0[str]).dentry?, root.dir?, root[q].dir?, inode.directory, 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), pre-iget(ino, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [skip; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then 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 ', path', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)), path' = ε

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ESUCCESS ≠ EISDIR; (s)