
theorem
  for V, W being add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital
  non empty ModuleStr over INT.Ring, f being homogeneousSAF FrForm of V,W,
  w being Vector of W holds f.(0.V,w) = 0.F_Real
  proof
    let V, W be add-associative right_zeroed right_complementable
    vector-distributive scalar-distributive scalar-associative scalar-unital
    non empty ModuleStr over INT.Ring;
    let f be homogeneousSAF FrForm of V,W, v be Vector of W;
    thus f.(0.V,v) = f.((0.INT.Ring)*(0.V),v) by VECTSP10:1
    .= 0.INT.Ring *f.(0.V,v) by HTh31
    .= 0.F_Real;
  end;
