All correct of course. A longer answer.
After primary fermentation and bottling, a second alcoholic fermentation occurs in the bottle. This second fermentation is induced by adding yeast and rock sugar.
At this time the champagne bottle is capped with a crown cap. The bottle is then riddled, so that the lees settles in the neck of the bottle. Left for about 3 years and the bottles are turned (riddled) frequently. The neck is then frozen, and the cap removed. The pressure in the bottle forces out the lees, and the bottle is quickly corked to maintain the carbon dioxide in solution and hence the bubbles.