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<* v,u *> = z * v + z * u
proof
  thus z * Sum<* v,u *> = z * (v + u) by RLVECT_1:45
    .= z * v + z * u by Def2;
end;
