theorem Th12:
  <*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,q5*> is SFHT of D & <*q5,f6,q6*> is SFHT of D &
  <*q6,f7,q7*> is SFHT of D & <*q7,f8,q8*> is SFHT of D &
  <*q8,f9,p2*> is SFHT of D implies
  <*p1,PP_composition(f1,f2,f3,f4,f5,f6,f7,f8,f9),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 &
    <*q4,f5,q5*> is SFHT of D & <*q5,f6,q6*> is SFHT of D &
    <*q6,f7,q7*> is SFHT of D & <*q7,f8,q8*> is SFHT of D and
A2: <*q8,f9,p2*> is SFHT of D;
A3: <*PP_inversion(q8),f9,p2*> is SFHT of D by NOMIN_3:19;
    <*p1,PP_composition(f1,f2,f3,f4,f5,f6,f7,f8),q8*> is SFHT of D by A1,Th11;
    hence thesis by A2,A3,NOMIN_3:25;
  end;
