reserve V,W for Z_Module;

theorem
  for V being finite-rank free Z_Module, n being Nat holds
  n <= rank V implies n Submodules_of V is non empty
  proof
    let V be finite-rank free Z_Module, n be Nat;
    assume n <= rank V;
    then ex W being strict free Submodule of V st rank W = n by RL5Lm2;
    hence thesis by RL5Def4;
  end;
