reserve i,j,l for Nat;

theorem
  for f being non empty FinSequence of TOP-REAL 2, p being Point of
  TOP-REAL 2 st f is being_S-Seq & p = f/.len f holds L~L_Cut (f,p) = {}
proof
  let f be non empty 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 len f >= 1 by XXREAL_0:2;
  then len f in dom f by FINSEQ_3:25;
  then p = f.len f by A2,PARTFUN1:def 6;
  then L_Cut (f,p) = <*p*> by A1,JORDAN5B:17;
  then len L_Cut (f,p) = 1 by FINSEQ_1:39;
  hence thesis by TOPREAL1:22;
end;
