theorem
  between4 a,b,c,d & between a,p,b implies between5 a,p,b,c,d
  proof
    assume
A1: between4 a,b,c,d & between a,p,b;
    then between a,p,b & between a,p,c & between a,p,d & between p,b,c &
    between p,b,d by Satz3p6p1,Satz3p6p2;
    hence thesis by A1,Satz3p5p2;
  end;
