reserve n for Nat;

theorem
  for C be compact connected non vertical non horizontal Subset of
  TOP-REAL 2 holds (Cage(C,n)/.2)`2 = N-bound L~Cage(C,n)
proof
  let C be compact connected non vertical non horizontal Subset of TOP-REAL 2;
  Cage(C,n)/.1 = N-min L~Cage(C,n) by JORDAN9:32;
  then Cage(C,n)/.2 in N-most L~Cage(C,n) by SPRECT_2:30;
  then (Cage(C,n)/.2)`2 = (N-min L~Cage(C,n))`2 by PSCOMP_1:39;
  hence thesis by EUCLID:52;
end;
