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;

theorem
  MemberFunc (X \/ Y, A).x >= max (MemberFunc (X, A).x, MemberFunc (Y, A ).x)
proof
  MemberFunc (X \/ Y, A).x >= MemberFunc (X, A).x & MemberFunc (X \/ Y, A)
  .x >= MemberFunc (Y, A).x by Th47,XBOOLE_1:7;
  hence thesis by XXREAL_0:28;
end;
