
theorem Th19:
  for f being FinSequence of TOP-REAL 2, p being Point of TOP-REAL 2 st
  p in L~f & f is being_S-Seq & p <> f.len f holds p in L~L_Cut (f,p)
proof
  let f be FinSequence of TOP-REAL 2, p be Point of TOP-REAL 2;
  assume that
A1: p in L~f and
A2: f is being_S-Seq;
  assume p <> f.len f;
  then L_Cut (f,p) is being_S-Seq by A1,A2,JORDAN3:34;
  then
A3: len L_Cut (f,p) >= 2 by TOPREAL1:def 8;
  L_Cut (f,p).1 = p by A1,JORDAN3:23;
  hence thesis by A3,JORDAN3:1;
end;
