set f = FuncZero (([#] V),W);
reconsider f = FuncZero (([#] V),W) as Function of V,W ;
A1: for x, y being Vector of V holds f . (x + y) = (f . x) + (f . y) by RLVECT_1:def 4;
take f ; :: thesis: ( f is additive & f is homogeneous )
for a being Element of F
for x being Element of V holds f . (a * x) = a * (f . x) by VECTSP_1:14;
hence ( f is additive & f is homogeneous ) by A1, MOD_2:def 2, VECTSP_1:def 20; :: thesis: verum