 reserve n for Nat;

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