  In this note, we work out a simple inductive proof showing that every
polyhedral cone K is the conic hull of a finite set X of vectors. The base
cases of the induction are linear subspaces and linear halfspaces of linear
subspaces. The proof also shows that the components of the vectors in X can be
chosen (up to their sign) to be quotients of subdeterminants of the coefficient
matrix of any inequality system defining K.
