
theorem
  for f being FinSequence of TOP-REAL 2, p, q being Point of TOP-REAL 2 st
  p <> f.len f & p in L~f & q in L~f & f is being_S-Seq holds
  p in L~L_Cut(f,q) or q in L~L_Cut(f,p)
proof
  let f be FinSequence of TOP-REAL 2, p, q be Point of TOP-REAL 2;
  assume
A1: p <> f.len f;
  assume that
A2: p in L~f and
A3: q in L~f and
A4: f is being_S-Seq;
  per cases by A1;
  suppose p <> f.len f & q = f.len f;
    hence thesis by A2,A3,A4,Th22;
  end;
  suppose p = f.len f & q <> f.len f;
    hence thesis by A2,A3,A4,Th22;
  end;
  suppose p <> f.len f & q <> f.len f;
    hence thesis by A2,A3,A4,Lm2;
  end;
end;
