 reserve n for Nat;

theorem ThConv6:
  for p,q,r being POINT of TarskiEuclid2Space holds
    between p,q,r iff Tn2TR q in LSeg(Tn2TR p, Tn2TR r)
  proof
    let p,q,r be POINT of TarskiEuclid2Space;
    hereby
      assume between p,q,r;
      then q is_Between p,r by GTARSKI1:def 15;
      hence Tn2TR q in LSeg(Tn2TR p,Tn2TR r) by ThConv5;
    end;
    assume Tn2TR q in LSeg(Tn2TR p, Tn2TR r);
    then q is_Between p,r by ThConv5;
    hence thesis by GTARSKI1:def 15;
  end;
