The documents provided do not specifically mention the requirement for a double retractable system for climbing. However, they do emphasize the importance of using appropriate fall protection systems when working at heights. For instance, when working from or on a fixed ladder or climbable structure at a height of 3 meters or more, continuous protection from falling must be provided by equipping the structure with an integral fall protection system or an alternate fall protection system [1].

In general, the use of personal fall arrest systems, which may include self-retracting lifelines, is crucial for ensuring safety when climbing. These systems must be properly designed, installed, and used according to the manufacturer's specifications or certified by a professional engineer [1].

If you are considering the use of a double retractable system, it would be important to ensure that it meets the relevant safety standards and is appropriate for the specific climbing activity and environment. Additionally, thorough training in the use of personal fall arrest systems is essential to prevent accidents [2].