reserve A for Tolerance_Space,
  X, Y for Subset of A;

theorem Th24:
  X c= Y implies LAp X c= LAp Y
proof
  assume
A1: X c= Y;
  let x be object;
  assume
A2: x in LAp X;
  then Class (the InternalRel of A, x) c= X by Th8;
  then Class (the InternalRel of A, x) c= Y by A1;
  hence thesis by A2;
end;
