reserve i,j,k,n for Nat,
  C for being_simple_closed_curve Subset of TOP-REAL 2;

theorem Th6:
  n is_sufficiently_large_for C implies cell(Gauge(C,n),X-SpanStart
  (C,n)-'1,Y-SpanStart(C,n)) c= BDD C
proof
  assume
A1: n is_sufficiently_large_for C;
  then Y-SpanStart(C,n) <= 2|^(n-'ApproxIndex C)*(Y-InitStart C-'2)+2 by Th5;
  hence thesis by A1,Def3;
end;
