Is “Was Duke Huan of Lu killed by Duke Xiang of Qi because he discovered the affair between his wife and Duke Xiang?” true?

The Records of the Grand Historian, 'Hereditary House of Qi Tai Gong', clearly records this historical event: 'In the fourth year, Duke Huan of Lu and his wife went to Qi. Duke Xiang of Qi had previously had an illicit affair with the wife of Lu... Duke Huan of Lu learned of it and was angry with his wife, who told Duke Xiang of Qi. Duke Xiang of Qi drank with the Duke of Lu, made him drunk, and had a strong man Peng Sheng carry him onto the Duke of Lu's carriage, then pulled and killed Duke Huan of Lu.' The description in Chapter 13 of Chronicles of the Eastern Zhou Kingdoms is completely consistent with the core historical facts recorded in the Records of the Grand Historian, both confirming that Duke Huan of Lu was murdered by Duke Xiang of Qi because he exposed the scandal of the illicit affair.