Moving a Derivation Along a Derivation Preserves the Spine in Adhesive Categories

In this paper, we investigate the relationship between two elementary operations on derivations in the framework of graph transformation based on adhesive categories: moving a derivation along a derivation based on parallel and sequential independence on one hand and restriction of a derivation with respect to a monomorphism into the start object on the other hand. Intuitively, a restriction clips off parts of the start object that are never matched by a rule application throughout the derivation on the other hand. As main result, it is shown that moving a derivation preserves its spine being the minimal restriction.