
theorem
  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.1 holds p in L~R_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.1;
  then R_Cut (f,p) is being_S-Seq by A1,A2,JORDAN3:35;
  then
A3: len R_Cut (f,p) >= 2 by TOPREAL1:def 8;
  R_Cut (f,p).len R_Cut (f,p) = p by A1,JORDAN3:24;
  hence thesis by A3,JORDAN3:1;
end;
