The subspaces of a given linear space form a lattice with the join operation \(\vee\) (sum of subspaces) and the meet operation \(\wedge\) (set- theoretic intersection of subspaces). An equality of two expressions constructed from variables with the use of these operations is called an identity if it is satisfied independently of which subspaces of which space are taken as the values of the variables. Gel’fand and Ponomarev obtained a number of important results on the structure of the lattices under consideration, and they posed the problem of studying the sets of identities of these lattices. A. L. Semenov conjectured that the problem of recognizing whether an equality is an identity is algorithmically decidable for lattices of linear subspaces. The main result in this note is a proof of this conjecture.