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We prove that the double shuffle Lie algebra ds, dual to the space of new formal multiple zeta values, injects into the Kashiwara-Vergne Lie algebra krv 2 defined and studied by Alekseev-Torossian. The proof is based on a reformulation of the definition of krv 2 , and uses a theorem of Ecalle on a property of elements of ds. §1. Definitions and main results Let Q x, y denote the ring of polynomials in non-commutative variables x and y, and Lie[x, y] the Lie algebra of Lie polynomials inside it. For each n ≥ 1, let Q n x, y (resp. Lie n [x, y]) denote the subspace of homogeneous polynomials (resp. Lie polynomials) of degree n. For k ≥ 1, let Q n≥k x, y (resp. Lie n≥k [x, y]) denote the space of polynomials (resp. Lie polynomials) all of whose monomials are of degree ≥ k, i.e. the direct sum of the Q n x, y (resp. Lie n [x, y]) for n ≥ k. The main theorem of this paper gives an injective map between two Lie algebras studied in the literature concerning formal multiple zeta values: the double shuffle Lie algebra ds, investigated in papers by Racinet and Ecalle amongst others (the associated graded of ds is also studied in papers by Zagier, Kaneko and others), and the Kashiwara-Vergne Lie algebra introduced in work of Alekseev and Torossian (cf. [AT]). We begin by recalling the definitions of these two Lie algebras. As vector spaces, both are subspaces of the free Lie algebra Lie[x, y]. For any non-trivial monomial w and polynomial f ∈ Q x, y , we use the notation (f |w) for the coefficient of the monomial w in the polynomial f , and extend it by linearity to polynomials w without constant term. Set y i = x i−1 y for all i ≥ 1; then all words ending in y can be written as words in the variables y i. The stuffle product st(u, v) ∈ Q x, y of two such words u and v is defined recursively by st(1, u) = st(u, 1) = u and st(y i u, y j v) = y i st(u, y j v) + y j st(y i u, v) + y i+j st(u, v). Definition 1.1. The double shuffle Lie algebra ds * is the vector space of elements f ∈ Lie n≥3 [x, y] such that f st(u, v) = 0 for all words u, v ∈ Q x, y ending in y but not both simultaneously powers of y. * The equivalence of the present definition with the usual definition introduced in [R] is proven in [CS], Theorem 2, which proves that if a polynomial f ∈ Lie n [x, y] has the property of the present definition, then f + (−1) n−1 n (f |x n−1 y)y n satisfies the stuffle relations for all pairs of words u, v ending in y. Since the words ending in x are not involved in this condition, this is equivalent to the assertion that π y (f) + (−1) n−1 n (f |x n−1 y)y n satisfies stuffle, where π y (f) denotes the projection of f onto just its words ending in y. This is the standard form of the defining property of elements of ds.