reserve D for non empty set;
reserve f1,f2,f3,f4 for BinominativeFunction of D;
reserve p,q,r,t,w for PartialPredicate of D;

theorem Th2:
  <*p,f1,q*> is SFHT of D & <*q,f2,r*> is SFHT of D &
  <*r,f3,w*> is SFHT of D & <*w,f4,t*> is SFHT of D &
  <*PP_inversion(q),f2,r*> is SFHT of D &
  <*PP_inversion(r),f3,w*> is SFHT of D &
  <*PP_inversion(w),f4,t*> is SFHT of D
  implies <*p,PP_composition(f1,f2,f3,f4),t*> is SFHT of D
  proof
    assume that
A1: <*p,f1,q*> is SFHT of D and
A2: <*q,f2,r*> is SFHT of D and
A3: <*r,f3,w*> is SFHT of D and
A4: <*w,f4,t*> is SFHT of D and
A5: <*PP_inversion(q),f2,r*> is SFHT of D and
A6: <*PP_inversion(r),f3,w*> is SFHT of D and
A7: <*PP_inversion(w),f4,t*> is SFHT of D;
    <*p,PP_composition(f1,f2),r*> is SFHT of D by A1,A2,A5,NOMIN_3:25;
    then <*p,PP_composition(PP_composition(f1,f2),f3),w*> is SFHT of D
    by A3,A6,NOMIN_3:25;
    hence thesis by A4,A7,NOMIN_3:25;
  end;
