Is the disney movie "lady and the tramp" based on a book?

Hi- What I found on Wikipedia said that it was just some sketches (Joe Grant) and then a short story (Ward Greene) called "Happy Dan, The Whistling Dog". So thanks to those two men and their ideas we got the movie of "lady and the tramp", Greene then wrote a novelization of the film released 2 years before the film. So movie idea first then book, but book came out before movie! A little weird, but true! Hope I help :).