theorem
  p,q out s,r implies s <> p & s <> q & r <> p & r <> q & p <> q
  proof
    assume
A1: p,q out s,r;
    then p <> q & Line(p,q) out s,r;
    then ex x be POINT of S st between s,Line(p,q),x & between r,Line(p,q),x;
    hence thesis by A1,GTARSKI3:83;
  end;
