 reserve V for Z_Module;
 reserve W for Subspace of V;
 reserve v, u for Vector of V;
 reserve i for Element of INT.Ring;

theorem ThLin1:
  for u being object holds u in Lin{v} implies
  ex i being Element of INT.Ring st u = i*v
  proof
    let u be object;
    assume u in Lin{v};
    then consider l be Linear_Combination of {v} such that
    A1: u = Sum(l) by ZMODUL02:64;
    take l.v;
    thus thesis by A1,ZMODUL02:21;
  end;
