reserve n,i,k,m for Nat;
reserve r,r1,r2,s,s1,s2 for Real;
reserve p,p1,p2,q1,q2 for Point of TOP-REAL n;

theorem
  p is_extremal_in {p}
proof
  thus p in {p} by TARSKI:def 1;
  let p1,p2;
  assume that
  p in LSeg(p1,p2) and
A1: LSeg(p1,p2) c= {p};
  p2 in LSeg(p1,p2) by RLTOPSP1:68;
  hence thesis by A1,TARSKI:def 1;
end;
