reserve n for Nat;

theorem
  for C be compact non vertical non horizontal non empty Subset of
  TOP-REAL 2 for n be Nat holds L~Cage(C,n) = L~Upper_Seq(C,n) \/ L~
  Lower_Seq(C,n)
proof
  let C be compact non vertical non horizontal non empty Subset of TOP-REAL 2;
  let n be Nat;
  E-max L~Cage(C,n) in rng Cage(C,n) by SPRECT_2:46;
  then E-max L~Cage(C,n) in rng Rotate(Cage(C,n),W-min L~Cage(C,n)) by
FINSEQ_6:90,SPRECT_2:43;
  then
  L~Rotate(Cage(C,n),W-min L~Cage(C,n)) = L~Upper_Seq(C,n) \/ L~Lower_Seq(
  C,n) by SPPOL_2:24;
  hence thesis by REVROT_1:33;
end;
