
theorem Th47:
  for K be add-associative right_zeroed right_complementable
Abelian associative well-unital distributive non empty doubleLoopStr for V,W
  be VectSp of K, f be bilinear-Form of V,W holds LKer f = LKer (RQForm f)
proof
  let K be add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr;
  let V,W be VectSp of K, f be bilinear-Form of V,W;
  the carrier of (LKer f) = leftker f by Def18
    .= leftker (RQForm f) by Th45
    .= the carrier of (LKer (RQForm f)) by Def18;
  hence thesis by VECTSP_4:29;
end;
