reserve a,b for Complex;
reserve V,X,Y for ComplexLinearSpace;
reserve u,u1,u2,v,v1,v2 for VECTOR of V;
reserve z,z1,z2 for Complex;

theorem
  z * Sum<* u,v1,v2 *> = z * u + z * v1 + z * v2
proof
  thus z * Sum<* u,v1,v2 *> = z * (u + v1 + v2) by RLVECT_1:46
    .= z * (u + v1) + z * v2 by Def2
    .= z * u + z * v1 + z * v2 by Def2;
end;
