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