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;

theorem Th38:
  0 <= MemberFunc (X, A).x & MemberFunc (X, A).x <= 1
proof
  card (X /\ Class (the InternalRel of A, x)) / (card Class (the
  InternalRel of A, x)) >= 0;
  hence 0 <= MemberFunc (X, A).x by Def9;
  card (X /\ Class (the InternalRel of A, x)) <= (card Class (the
  InternalRel of A, x)) by NAT_1:43,XBOOLE_1:17;
  then card (X /\ Class (the InternalRel of A, x)) / (card Class (the
  InternalRel of A, x)) <= 1 by XREAL_1:185;
  hence thesis by Def9;
end;
