reserve S for non empty satisfying_Tarski-model
              TarskiGeometryStruct,
        a,b,c,d,c9,x,y,z,p,q,q9 for POINT of S;

theorem Prelim08:
  for S being TarskiGeometryStruct
  for a,b,c being POINT of S st
  (Middle a,b,c or between a,b,c) holds Collinear a,b,c
  proof
    let S be TarskiGeometryStruct;
    let a,b,c be POINT of S;
    assume Middle a,b,c or between a,b,c;
    then between a,b,c by GTARSKI3:def 12;
    hence thesis by GTARSKI1:def 17;
  end;
