reserve n for Nat;

theorem Th33:
  for C be compact connected non vertical non horizontal Subset of
  TOP-REAL 2 holds W-bound L~Cage(C,n) + E-bound L~Cage(C,n) = W-bound C +
  E-bound C
proof
  let C be compact connected non vertical non horizontal Subset of TOP-REAL 2;
  thus W-bound L~Cage(C,n)+E-bound L~Cage(C,n) = W-bound L~Cage(C,n)+ (E-bound
  C + (E-bound C - W-bound C)/(2|^n)) by JORDAN1A:64
    .= (W-bound C - (E-bound C - W-bound C)/(2|^n))+ (E-bound C + (E-bound C
  - W-bound C)/(2|^n)) by JORDAN1A:62
    .= W-bound C + E-bound C;
end;
