reserve n for Nat;

theorem Th42:
  for f be non empty FinSequence of TOP-REAL 2 for p be Point of
TOP-REAL 2 st f is almost-one-to-one special unfolded s.n.c. & p in L~f & p <>
  f.len f & p <> f.1 holds L_Cut(f,p) is being_S-Seq
proof
  let f be non empty FinSequence of TOP-REAL 2;
  let p be Point of TOP-REAL 2;
  assume that
A1: f is almost-one-to-one special unfolded s.n.c. and
A2: p in L~f and
A3: p <> f.len f and
A4: p <> f.1;
  L_Cut(f,p) is_S-Seq_joining p,f/.len f by A1,A2,A3,A4,Th40;
  hence thesis by JORDAN3:def 2;
end;
