On the Moving Lemma for Rational Equivalence

The construction of the rational equivalence ring C(U) for a non-singular quasi-projective variety U depends on a fundamental moving lemma (cf. Chow [2], Lemma 2, p. 456; Chevalley [1], Lemma 2, p. 3-08; and also Hodge and Pedoe [3], Lemmas I-VI, pp. 165-170).