theorem
  for p1,p2,p3,p st p2-p1,p3-p1 are_lindependent2 holds p in Triangle(p1
,p2,p3) iff tricord1(p1,p2,p3,p)=0 & tricord2(p1,p2,p3,p)>=0 & tricord3(p1,p2,
p3,p)>=0 or tricord1(p1,p2,p3,p)>=0 & tricord2(p1,p2,p3,p)=0 & tricord3(p1,p2,
p3,p)>=0 or tricord1(p1,p2,p3,p)>=0 & tricord2(p1,p2,p3,p)>=0 & tricord3(p1,p2,
  p3,p)=0 by Th56;
