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Proof step 19 from proof refine-rmdir (previous step)

err = err0, fs = abs-files(files), root.dir?, dom of < ino, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced ⊦ [let ino = ROOT_INO, dent = negdentry(path.last), path = parent(path), isdir = true, inode = ?, p_inode = ? in {vfs_walk#(path, user, dirs, files, asynced; ino, err); if err = ESUCCESS then vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err); if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then {afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(path, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0)), path = ε

Heuristic symbolic execution applied rule let right

And obtained the following new goals

Rule argument

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