reserve n for Nat;

theorem Th11:
  for C be compact connected non vertical non horizontal
  Subset of TOP-REAL 2 holds W-bound L~Cage(C,n) < W-bound C
proof
  let C be compact connected non vertical non horizontal Subset of TOP-REAL 2;
A1: 2|^n > 0 by NEWTON:83;
  E-bound C > W-bound C + 0 by SPRECT_1:31;
  then E-bound C - W-bound C > 0 by XREAL_1:20;
  then
A2: (E-bound C - W-bound C)/(2|^n) > W-bound C - W-bound C by A1,XREAL_1:139;
  W-bound L~Cage(C,n) = W-bound C - (E-bound C - W-bound C)/(2|^n)
  by JORDAN1A:62;
  hence thesis by A2,XREAL_1:11;
end;
