reserve i,j,k,m,n for Nat,
  f for FinSequence of the carrier of TOP-REAL 2,
  G for Go-board;

theorem Th7:
  for C being compact non vertical non horizontal Subset of
TOP-REAL 2 for n being Nat holds Upper_Seq(C,n)/. len Upper_Seq(C,n)
  = E-max(L~Cage(C,n))
proof
  let C be compact non vertical non horizontal Subset of TOP-REAL 2;
  let n be Nat;
A1: Upper_Seq(C,n) = Rotate(Cage(C,n),W-min L~Cage(C,n))-:E-max L~Cage(C,n)
  & rng Rotate(Cage(C,n),W-min L~Cage(C,n)) = rng Cage(C,n) by FINSEQ_6:90
,JORDAN1E:def 1,SPRECT_2:43;
  then
  len Upper_Seq(C,n) = (E-max L~Cage(C,n))..Rotate(Cage(C,n),W-min L~Cage(
  C,n)) by FINSEQ_5:42,SPRECT_2:46;
  hence thesis by A1,FINSEQ_5:45,SPRECT_2:46;
end;
