 reserve n for Nat;

theorem ThConv8:
  for a,b,c being POINT of TarskiEuclid2Space holds
    between a,b,c iff dist(a,c) = dist(a,b) + dist(b,c)
  proof
    let a,b,c be POINT of TarskiEuclid2Space;
    hereby assume between a,b,c;
      then b is_Between a,c by GTARSKI1:def 15;
      hence dist(a,c) = dist(a,b) + dist(b,c);
    end;
    assume dist(a,c) = dist(a,b) + dist(b,c);
    then b is_Between a,c;
    hence thesis by GTARSKI1:def 15;
  end;
