
theorem
  for L being left_unital non empty doubleLoopStr holds {1.L}
  -RightIdeal = the carrier of L
proof
  let L be left_unital non empty doubleLoopStr;
  the carrier of L c= {1.L}-RightIdeal
  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}-RightIdeal by Def16,TARSKI:def 1;
    then (1.L)*x9 in {1.L}-RightIdeal by Def3;
    hence thesis;
  end;
  hence thesis;
end;
