reserve n for Nat;

theorem Th4:
  for C be compact connected non vertical non horizontal Subset of
  TOP-REAL 2 holds Upper_Seq(C,n) is_sequence_on Gauge(C,n)
proof
  let C be compact connected non vertical non horizontal Subset of TOP-REAL 2;
  Cage(C,n) is_sequence_on Gauge(C,n) by JORDAN9:def 1;
  then Rotate(Cage(C,n),W-min L~Cage(C,n)) is_sequence_on Gauge(C,n) by
REVROT_1:34;
  then Rotate(Cage(C,n),W-min L~Cage(C,n))-:E-max L~Cage(C,n) is_sequence_on
  Gauge(C,n) by Th2;
  hence thesis by JORDAN1E:def 1;
end;
