 reserve S for satisfying_Tarski-model TarskiGeometryStruct;
 reserve a, b, c, d, e, f, o, p, q, r, s,
    v, w, u, x, y, z, a9, b9, c9, d9, x9, y9, z for POINT of S;

theorem B123and134Ordered:
  between a,b,c & between a,c,d implies a,b,c,d are_ordered
  proof
    assume between a,b,c & between a,c,d; then
    between d,c,a & between c,b,a by Bsymmetry; then
    d,c,b,a are_ordered by B124and234Ordered;
    hence thesis by Bsymmetry;
  end;
