The kinetic energy functional Ts[ρ] in a reference system of non-interacting electrons is a key quantity in density functional theory. Approximating it as an explicit functional of the electron density ρ is the object of continuous interest since the earliest days of quantum mechanics (Thomas–Fermi electron gas theory). A simple proof of the exact inequality Ts[ρA + ρB] − Ts[ρA] − Ts[ρB] ≥ 0 valid for a special class of spin-compensated pairs of electron densities ρA and ρB (vAB-representable pairs) is provided. The derived relation is discussed to rationalize some of the results of the past attempts to approximate Ts[ρ]. It is also discussed as a tool for deriving approximations to the functional Ts[ρ] and/or the bi-functional Tnads[ρA, ρB] = Ts[ρA + ρB] − Ts[ρA] − Ts[ρB].