
theorem
  for L being non empty doubleLoopStr, A, B being non empty Subset of L
  st A c= B holds A-LeftIdeal c= B-LeftIdeal
proof
  let L be non empty doubleLoopStr, A,B be non empty Subset of L;
  assume
A1: A c= B;
  B c= B-LeftIdeal by Def15;
  then A c= B-LeftIdeal by A1;
  hence thesis by Def15;
end;
