theorem Satz3p11p4pb:
  between4 a,b,c,d & between b,p,c implies between5 a,b,p,c,d
  proof
    assume
A1: between4 a,b,c,d & between b,p,c;
    then between a,b,p & between p,c,d & between b,p,c & between b,p,d &
    between a,p,c by Satz3p5p1,Satz3p5p2,Satz3p6p1,Satz3p6p2;
    hence thesis by A1,Satz3p5p2;
  end;
