
theorem
  for L being right_unital non empty doubleLoopStr holds {1.L}
  -LeftIdeal = the carrier of L
proof
  let L be right_unital non empty doubleLoopStr;
  the carrier of L c= {1.L}-LeftIdeal
  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}-LeftIdeal by Def15,TARSKI:def 1;
    then x9*1.L in {1.L}-LeftIdeal by Def2;
    hence thesis;
  end;
  hence thesis;
end;
