
theorem
  for f being FinSequence of TOP-REAL 2,
  p being Point of TOP-REAL 2 st f is being_S-Seq & p = f.len f holds
  L_Cut (f,p) = <*p*>
proof
  let f be FinSequence of TOP-REAL 2, p be Point of TOP-REAL 2;
  assume that
A1: f is being_S-Seq and
A2: p = f.len f;
  len f >= 2 by A1,TOPREAL1:def 8;
  then p in L~f by A2,JORDAN3:1;
  then
A3: p in L~Rev f by SPPOL_2:22;
A4: L_Cut(f,p) =L_Cut(Rev Rev f,p)
    .= Rev R_Cut(Rev f,p) by A1,A3,JORDAN3:22;
  p = (Rev f).1 by A2,FINSEQ_5:62;
  then R_Cut(Rev f,p) = <*p*> by JORDAN3:def 4;
  hence thesis by A4,FINSEQ_5:60;
end;
