theorem B124and234then123:
  between a,b,d & between b,c,d implies between a,b,c
  proof
     assume
H1:  between a,b,d;
     assume between b,c,d; then
     consider x such that
X1:  between b,x,b & between c,x,a by H1, A7;
     b = x by X1, A6;
     hence thesis by Bsymmetry, X1;
  end;
