reserve p, q for Point of TOP-REAL 2,
  r for Real,
  h for non constant standard special_circular_sequence,
  g for FinSequence of TOP-REAL 2,
  f for non empty FinSequence of TOP-REAL 2,
  I, i1, i, j, k for Nat;

theorem
  for X being Subset of REAL st X = { q`1 : q`2 = N-bound L~h & q in L~h
  } holds lower_bound X = lower_bound (proj1 | N-most L~h) by Th15;
