reserve V,W for Z_Module;
reserve T for linear-transformation of V,W;
reserve T for linear-transformation of V,W;
reserve l for Linear_Combination of V;
reserve V,W for Z_Module;
reserve l for Linear_Combination of V;
reserve T for linear-transformation of V,W;

theorem ThTF3C0:
  for V,W be non empty set,
  f be FinSequence,
  l be Function of V,W
  st rng f c= V
  holds l*f is W-valued FinSequence-like
  proof
    let V,W be non empty set,
    f be FinSequence,
    l be Function of V,W;
    assume rng f c= V; then
    rng f c= dom l by FUNCT_2:def 1;
    hence thesis by FINSEQ_1:16;
  end;
