Proposition 11

Let $(C_i)_{i \in I}$ be a family of convex cones in E; the convex cone generated by the union of the $C_i$ is identical with the set of points $\sum_{i \in J} x_i$, where J is any finite subset of I and $x_i \in C_i$ for all $i \in J$.

In fact, it is obvious that C, the set of such points, is a convex cone containing the union of the $C_i$, and that it is contained in any convex cone which contains this union.