reserve r for Real;

theorem
  for S being symmetric triangle Reflexive non empty MetrStruct,
      p, q, r being Element of S holds
    q is_between p,r implies q is_between r,p
proof
  let S be symmetric triangle Reflexive non empty MetrStruct,
      p,q,r be Element of S;
  assume
A1: q is_between p,r;
  hence r <> q & r <> p & q <> p;
  dist(p,r) = dist(p,q) + dist(q,r) by A1;
  hence thesis;
end;
