Is it correct that the Song Dynasty listed the Doctrine of the Mean and Mencius as the Four Books?

In the Song Dynasty, "The Great Learning", "The Analects of Confucius", "The Doctrine of the Mean" and "Mencius" were listed as four books.

"The Great Learning", "The Doctrine of the Mean", "The Analects of Confucius" and "Mencius" are collectively called the Four Books, which are the basic teaching materials for Confucian preaching and teaching. For hundreds of years, the "Four Books" have been widely circulated in our country, and many of their sentences have become popular aphorisms. The "Four Books" refer to the four books "The Analects", "Mencius", "The Doctrine of the Mean" and "The Great Learning". Among them, "The Analects" and "Mencius" are collections of remarks by Confucius, Mencius and their students respectively, while "The Great Learning" and "The Doctrine of the Mean" are two articles from the "Book of Rites". It was Zhu Xi, a famous scholar in the Southern Song Dynasty, who compiled them together for the first time. However, before Zhu Xi, the brothers Cheng Hao and Cheng Yi had already vigorously promoted these books. They believe that "The Great Learning" is an important book taught by Confucius on "the door to virtue for beginners" and compiled into a text by Zengzi; "The Doctrine of the Mean" is the book "Confucius taught the mind" and is the "son of the pen" written by Confucius' grandson Zisi. To teach Mencius". These two books, together with The Analects of Confucius and Mencius, express the basic ideological system of Confucianism and are the most important documents for the study of Confucianism. It is based on this point of view that Zhu Xi compiled the four books "The Analects", "Mencius", "The Great Learning" and "The Doctrine of the Mean" together. Because they come from the four representative figures of early Confucianism, Confucius, Zeng Shen, Zisi, and Mencius, they are called "Four Books", or simply "Four Books". Zhu Xi made annotations for these four books respectively. Among them, the annotations of "The Great Learning" and "The Doctrine of the Mean" are called "Zhangju", and the annotations of "The Analects" and "Mencius" are called "Collected Annotations" because they quote many other people's sayings. . It is worth noting that the order of the "Four Books" compiled by Zhu Xi was originally "Great Learning", "The Analects of Confucius", "Mencius" and "The Doctrine of the Mean", which were arranged in the order of learning from the shallower to the deeper. Because "The Great Learning" and "The Doctrine of the Mean" are short in length, later generations put "The Doctrine of the Mean" before "The Analects" for the convenience of writing and publishing. "Mencius" sequence. Because the "Four Books" annotated by Zhu Xi not only integrated the theories of the predecessors, but also had his own unique insights, which are relevant to the world; and because of the increasing status of "Cheng-Zhu Neo-Confucianism" represented by Cheng Hao, Cheng Yi brothers and Zhu Xi Therefore, after Zhu Xi's death, the imperial court approved the "Four Books" compiled and annotated by him as an official book. Within Zhu's "Four Books", the Ming and Qing Dynasties followed and derived the "eight-legged essay" examination system, and the questions are all in Zhu's "Four Books". Due to these factors, the "Four Books" not only became an important classic of Confucianism, but also became a must-read for every scholar, and became the standard primary school textbook that was unified nationwide until modern times. Therefore, some people compare the "Four Books" with the Western "Bible" and think that it is the "Bible" of the East. In fact, this comparison is not an exaggeration at all, no matter in terms of its widespread circulation or its profound impact on the personality and psychology of the Chinese people.