Why does the precipitation on the cold front always exist behind the front, while the precipitation on the warm front only exists before the front?

In fact, the textbook is idealistic. Theoretically, it may be like this: the front crossing may not always bring precipitation, and whether it will rain depends on the water vapor content of the heating mass. There may be rain and snow when the cold front crosses the border in winter; When the air in the north is dry in spring, there will be dusty weather. As mentioned earlier, precipitation depends on the water vapor content of the heating mass. In other words, precipitation depends on the heating mass. Cold front, the cold air mass is strong, it moves to the warm air mass actively, and the warm air mass rises passively, forming rainfall, which occurs behind the front, mainly after the front; Warm front, the warm air mass is strong, it actively moves to the cold air mass, the warm air mass actively rises, the rising air mass forms rain when it is cold, and the precipitation is in front of the front. In short, precipitation is mostly on the side of the cold air mass.