
theorem Th29:
  for K be add-associative right_zeroed right_complementable non
empty doubleLoopStr for V,W be right_zeroed non empty ModuleStr over K for f
  be additiveFAF Form of V,W, v be Vector of V holds f.(v,0.W) = 0.K
proof
  let F be add-associative right_zeroed right_complementable non empty
  doubleLoopStr;
  let V,W be right_zeroed non empty ModuleStr over F;
  let f be additiveFAF Form of V,W, v be Vector of V;
  f.(v,0.W) = f.(v,0.W+0.W) by RLVECT_1:def 4
    .= f.(v,0.W) + f.(v,0.W) by Th27;
  hence thesis by RLVECT_1:9;
end;
