Then one can easily construct a Vector Space Isomorphism, since all points have a unique vector associated to their translation from (since there is a Regular Group Action), and since all vectors have an associated point in which comes from , since the Group Action’s domain is defined over the entirety of the additive group and is, per hypothesis, Free and Transitive ─ which ensures that there are no “lazy” vectors: all vectors “induce movement” upon the set .
