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 Th32:
  for R being Ring
  for V being LeftMod of R
  for l, m being Linear_Combination of V
  st (Carrier l) misses (Carrier m) holds
  Carrier (l - m) = (Carrier l) \/ (Carrier m)
  proof
    let R be Ring;
    let V be LeftMod of R;
    let l, m be Linear_Combination of V such that
    A1: (Carrier l) misses (Carrier m);
    Carrier(-m) = Carrier m by VECTSP_6:38;
    hence thesis by A1,Th31;
  end;
