In this preprint we consider a regular local ring, a quadratic space over the ring and a unit. Assuming that the ring contains the rational number field we prove the following result. If the space represents the unit over the quotient field of the ring then the space represents the unit over the ring too. The proof is based on a variant of the Springer theorem and on a moving lemma. The variant of the Springer theorem is proved in a joint work with U. Rehmann. The moving lemma is inspired by a moving lemma for algebraic cobordism proved by M. Levine and F. Morel.