
theorem Th10:
  for L being non empty doubleLoopStr holds the carrier of L is Ideal of L
proof
  let L be non empty doubleLoopStr;
  the carrier of L c= the carrier of L;
  then reconsider cL = the carrier of L as Subset of L;
A1: cL is left-ideal;
A2: cL is right-ideal;
  cL is add-closed;
  hence thesis by A1,A2;
end;
