Gysbrehght
The CFM document on smart cockpit gives clearer explanation according to that:
Due to lower ambient air temperature and higher air density in the actual take off conditions, actual TAS is lower and actual thrust is higher and
• If performance is limited by the one engine inoperative minimum climb gradient requirements, the higher actual thrust will result in a higher climb gradient
• If performance is limited by obstacle clearance, the higher climb gradient combined with the shorter takeoff distance will result in extra clearance margin