theorem Prelim05:
  for S being satisfying_CongruenceIdentity satisfying_SegmentConstruction
  satisfying_BetweennessIdentity satisfying_Pasch TarskiGeometryStruct
  for a,b being POINT of S holds Collinear a,b,b & Collinear b,b,a &
  Collinear b,a,b
  proof
    let S be satisfying_CongruenceIdentity
    satisfying_SegmentConstruction satisfying_BetweennessIdentity
    satisfying_Pasch TarskiGeometryStruct;
    let a,b be POINT of S;
    between a,b,b & between b,b,a by GTARSKI3:13,15;
    hence thesis by GTARSKI1:def 17;
  end;
