theorem
  between4 a,b,c,d & between c,p,d implies between5 a,b,c,p,d
  proof
    assume
A1: between4 a,b,c,d & between c,p,d;
    then between a,p,d & between a,c,p & between b,c,p & between b,p,d &
    between c,p,d by Satz3p5p1,Satz3p5p2;
    hence thesis by A1,Satz3p5p1;
  end;
