
theorem Th46:
  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 RKer f = RKer (LQForm 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 (RKer f) = rightker f by Def19
    .= rightker (LQForm f) by Th44
    .= the carrier of (RKer (LQForm f)) by Def19;
  hence thesis by VECTSP_4:29;
end;
