theorem Th8:
  <*p1,f1,q1*> is SFHT of D & <*q1,f2,q2*> is SFHT of D &
  <*q2,f3,q3*> is SFHT of D & <*q3,f4,q4*> is SFHT of D &
  <*q4,f5,p2*> is SFHT of D implies
  <*p1,PP_composition(f1,f2,f3,f4,f5),p2*> is SFHT of D
  proof
    assume that
A1: <*p1,f1,q1*> is SFHT of D & <*q1,f2,q2*> is SFHT of D &
    <*q2,f3,q3*> is SFHT of D & <*q3,f4,q4*> is SFHT of D and
A2: <*q4,f5,p2*> is SFHT of D;
A3: <*PP_inversion(q4),f5,p2*> is SFHT of D by NOMIN_3:19;
    <*p1,PP_composition(f1,f2,f3,f4),q4*> is SFHT of D by A1,Th7;
    hence thesis by A2,A3,NOMIN_3:25;
  end;
