 reserve n for Nat;

theorem
  for p,q,r,s being Point of TarskiEuclid2Space st
    q <> r & between p,q,r & between q,r,s holds between p,r,s
  proof
    let p,q,r,s be Point of TarskiEuclid2Space;
    assume that
A1: q <> r and
A2: between p,q,r and
A3: between q,r,s;
A4: Tn2TR q in LSeg(Tn2TR p,Tn2TR r) by A2,ThConv6;
A6: Tn2TR r in LSeg(Tn2TR q,Tn2TR s) by A3,ThConv6;
    Tn2TR r in LSeg(Tn2TR p, Tn2TR s) by A1,A4,A6,THORANGE2;
    hence thesis by ThConv6;
  end;
