reserve E for compact non vertical non horizontal Subset of TOP-REAL 2,
  C for compact connected non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  i, j, m, n for Nat,
  p for Point of TOP-REAL 2;

theorem Th18:
  not cell(Gauge(E,0),2,2) c= BDD E
proof
  assume
A1: cell(Gauge(E,0),2,2) c= BDD E;
  E c= cell(Gauge(E,0),2,2) by Th17;
  then
A2: E c= BDD E by A1;
  set e = the Element of E;
A3: BDD E misses E by JORDAN1A:7;
  e in E;
  hence thesis by A2,A3,XBOOLE_0:3;
end;
