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;
