reserve A for Tolerance_Space,
  X, Y for Subset of A;
reserve A for Approximation_Space,
  X for Subset of A;
reserve A for finite Tolerance_Space,
  X for Subset of A,
  x for Element of A;
reserve A for finite Approximation_Space,
  X, Y for Subset of A,
  x for Element of A;
reserve A for Tolerance_Space,
  X, Y, Z for Subset of A;

theorem Th59:
  X _c= Y & Y _c= Z implies X _c= Z
proof
  assume X _c= Y & Y _c= Z;
  then LAp X c= LAp Y & LAp Y c= LAp Z;
  then LAp X c= LAp Z;
  hence thesis;
end;
