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),len Gauge(C,1)) = |[(W-bound C + E-bound
  C)/2,N-bound L~Cage(C,1)]|
proof
  set G = Gauge(C,1);
  1 <= len G by GOBRD11:34;
  then
A1: G*(Center G,len G)`1 = (W-bound C + E-bound C) / 2 by JORDAN1A:38;
  1 <= Center G by Th11;
  then G*(Center G,len G)`2 = N-bound L~Cage(C,1) by Th13,JORDAN1A:70;
  hence thesis by A1,EUCLID:53;
end;
