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 Th9:
  z * (v - u) = z * v - z * u
proof
  thus z * (v - u) = z * v + z * (- u) by Def2
    .= z * v - z * u by Th7;
end;
