
theorem Th30:
  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 additiveSAF Form of V,W, w be Vector of W holds f.(0.V,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 additiveSAF Form of V,W, v be Vector of W;
  f.(0.V,v) = f.(0.V+0.V,v) by RLVECT_1:def 4
    .= f.(0.V,v) + f.(0.V,v) by Th26;
  hence thesis by RLVECT_1:9;
end;
