reserve k,m,n for Nat;
reserve R for commutative Ring,
        p,q for Polynomial of R,
        z0,z1 for Element of R;

theorem Th6:
  for L being Abelian add-associative right_zeroed right_complementable
    well-unital commutative distributive non empty doubleLoopStr
  holds <%0.L,0.L,1.L%> = <%0.L,1.L%>`^2
  proof
    let L be Abelian add-associative right_zeroed right_complementable
             well-unital commutative distributive non empty doubleLoopStr;
    thus <%0.L,0.L,1.L%> = <%0.L*0.L,0.L*1.L+1.L*0.L,1.L*1.L%>
    .= <%0.L,1.L%>*'<%0.L,1.L%> by Th5
    .= <%0.L,1.L%>`^2 by POLYNOM5:17;
  end;
