Is “Did Duke Ding of Jin, during his reign, respond to the request of the Duke of Cai to attack Chu, listen to Zigong's advice to prepare for war against Wu, and contend with Wu for the position of leader at Huangchi?” true?

The 'Records of the Grand Historian, Biographies of Confucius' Disciples' records Zigong's northern mission to Jin, Duke Ding's preparations, and the Wu-Jin contest at Huangchi. Zigong told the ruler of Jin: 'Now Qi and Wu are about to fight. If Wu loses, Yue will surely rise against it; if Wu defeats Qi, it will certainly turn its troops upon Jin.' The text goes on: 'As expected, [Wu] brought its troops against Jin and met the men of Jin at Huangchi. Wu and Jin contended for supremacy. The men of Jin struck them and routed the Wu army.' The novel 'Chronicles of the Eastern Zhou Kingdoms' follows the historical record here rather than inventing it.