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We give a proof to the following theorem, which is well-known among experts:A connected subcomplex $W$ of a finite dimensional CAT(0) cubed complex $X$ isconvex if and only if Lk$(v, W)$ is a full subcomplex of Lk$(v, X)$ for everyvertex $v$ of $W$.

Combinatorial local convexity implies convexity in finite dimensional CAT(0) cubed complexes