reserve n for Nat;

theorem Th9:
  for C be compact non vertical non horizontal Subset of TOP-REAL
2 for n be Nat holds len Lower_Seq(C,n) = len Rotate(Cage(C,n),W-min L~Cage(C,n
  ))- (E-max L~Cage(C,n))..Rotate(Cage(C,n),W-min L~Cage(C,n))+1
proof
  let C be compact non vertical non horizontal 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;
  hence thesis by FINSEQ_5:50;
end;
