What is shoulder-in and why is it called the foundation of all lateral work?

Shoulder-in is a lateral movement in which the horse moves along the track with its forehand brought approximately thirty degrees inward off the track while its haunches remain on the track, creating a position in which the horse travels on three tracks — the inside hind and outside fore sharing one track in the middle, with the inside fore on an inner track and the outside hind on the outer track. The horse is bent uniformly through its body around the rider's inside leg in the direction away from the direction of travel, which means the horse is moving in one direction while bent in the other — a gymnastic demand that specifically engages the inside hind leg to step under the horse's center of gravity more actively than in straight work. Shoulder-in is called the foundation of all lateral work because it teaches the horse the most important concept underlying all lateral movements — moving away from the inside leg while maintaining contact with the outside rein — and because the position of shoulder-in is used as both an exercise and a preparation for every other lateral movement. The movement was developed and described by François Robichon de la Guérinière in the eighteenth century as the exercise that most efficiently develops the suppleness, engagement, and collection preparation that all subsequent lateral work requires, and his assessment has been validated by every major classical tradition since. The specific gymnastic benefits of shoulder-in include: engagement of the inside hind leg under the body, development of the horse's responsiveness to the inside leg aid while maintaining outside rein contact, and the beginning of the balance shift that collection requires. Correctly ridden shoulder-in is also the fundamental correction for horses that fall out through the outside shoulder, that overbend to the inside, or that are above the bit — its specific demands address all of these problems simultaneously.