
theorem
  for R being Ring, V being LeftMod of R, v being Vector of V,
  u being object st u in Lin{v} holds
  ex i being Element of R st u = i*v
  proof
    let R be Ring, V be LeftMod of R, v be Vector of V,
    u be object such that
    A1: u in Lin{v};
    consider l be Linear_Combination of {v} such that
    A2: u = Sum(l) by A1,VECTSP_7:7;
    take l.v;
    thus thesis by A2,VECTSP_6:17;
  end;
