
theorem
  for L being well-unital non empty doubleLoopStr holds {1.L}-Ideal =
  the carrier of L
proof
  let L be well-unital non empty doubleLoopStr;
  the carrier of L c= {1.L}-Ideal
  proof
    let x be object;
    assume x in the carrier of L;
    then reconsider x9=x as Element of L;
    1.L in {1.L} & {1.L} c= {1.L}-Ideal by Def14,TARSKI:def 1;
    then x9*1.L in {1.L}-Ideal by Def2;
    hence thesis;
  end;
  hence thesis;
end;
