reserve D for non empty set;
reserve f1,f2,f3,f4,f5,f6,f7,f8,f9,f10 for BinominativeFunction of D;
reserve p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11 for PartialPredicate of D;
reserve q1,q2,q3,q4,q5,q6,q7,q8,q9,q10 for total PartialPredicate of D;
reserve n,m,N for Nat;
reserve fD for PFuncs(D,D)-valued FinSequence;
reserve fB for PFuncs(D,BOOLEAN)-valued FinSequence;
reserve V,A for set;
reserve val for Function;
reserve loc for V-valued Function;
reserve d1 for NonatomicND of V,A;
reserve p for SCPartialNominativePredicate of V,A;
reserve d,v for object;
reserve size for non zero Nat;
reserve inp,pos for FinSequence;
reserve prg for non empty FPrg(ND(V,A))-valued FinSequence;

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;
