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
  Gauge(C,1)*(Center Gauge(C,1),1) = |[(W-bound C + E-bound C)/2,S-bound
  L~Cage(C,1)]|
proof
  set G = Gauge(C,1);
  1 <= len G by GOBRD11:34;
  then
A1: G*(Center G,1)`1 = (W-bound C + E-bound C) / 2 by JORDAN1A:38;
  Center G <= len G by Th13;
  then G*(Center G,1)`2 = S-bound L~Cage(C,1) by Th11,JORDAN1A:72;
  hence thesis by A1,EUCLID:53;
end;
