overlay window property not respected

[martin rudalics]

The Emacs Lisp manual specifies the window property of an overlay as:

`window'
     If the `window' property is non-`nil', then the overlay applies
     only on that window.

Executing

(defun foobar ()
  (interactive)
  (insert "foo")
  (let ((overlay (make-overlay (- (point) 3) (point))))
    (overlay-put overlay 'window (selected-window))
    (overlay-put overlay 'display "bar")
    (split-window)))

has "bar" appear in _both_ windows.  According to the manual "bar"
should replace "foo" in the initially selected window only.

(I posted this on emacs-devel before but didn't get a response.)