reserve E for compact non vertical non horizontal Subset of TOP-REAL 2,
  C for compact connected non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  i, j, m, n for Nat,
  p for Point of TOP-REAL 2;

theorem
  for f be FinSequence of TOP-REAL 2 for p be Point of TOP-REAL 2 st f
  is being_S-Seq & p in L~f holds L_Cut(f,p).(len L_Cut(f,p)) = f.(len f)
proof
  let f be FinSequence of TOP-REAL 2;
  let p be Point of TOP-REAL 2 such that
A1: f is being_S-Seq and
A2: p in L~f;
  Rev f is being_S-Seq by A1;
  then
A3: 2 <= len Rev f by TOPREAL1:def 8;
A4: p in L~Rev f by A2,SPPOL_2:22;
  then L_Cut(Rev Rev f,p) = Rev R_Cut(Rev f,p) by A1,JORDAN3:22;
  hence L_Cut(f,p).(len L_Cut(f,p)) = Rev R_Cut(Rev f,p).(len R_Cut(Rev f,p))
  by FINSEQ_5:def 3
    .= R_Cut(Rev f,p).1 by FINSEQ_5:62
    .= Rev f.1 by A4,A3,Th3,XXREAL_0:2
    .= f.(len f) by FINSEQ_5:62;
end;
