Surprisingly, история J-10 originates in Israel. At the end of the 80-ies there was created a fighter "Lavi", which was designed to replace the entire fleet of American cars. Over time, the United States forced the Israelis to close this project and acquire F-16. To compensate for their investment in creating their own aircraft, the company IAI has sold its proven technology to China.
Having received the plans of the future fighter's glider, the Chinese faced the question of creating an engine. But at the beginning of the 90-s, the Celestial Empire did not possess such technologies, which led it to turn to Russia. As a result, the Russian AL-10F became the "heart" of J-31.