reserve n for Nat;

theorem Th35:
  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;
  assume that
A1: f is being_S-Seq and
A2: p in L~f;
A3: len f in dom f by A1,FINSEQ_5:6;
  L_Cut(f,p) <> {} by A2,JORDAN1E:3;
  then len L_Cut(f,p) in dom L_Cut(f,p) by FINSEQ_5:6;
  hence L_Cut(f,p)/.len L_Cut(f,p) = L_Cut(f,p).len L_Cut(f,p) by
PARTFUN1:def 6
    .= f.len f by A1,A2,JORDAN1B:4
    .= f/.len f by A3,PARTFUN1:def 6;
end;
