reserve n,n1,m,m1,k for Nat;
reserve x,X,X1 for set;
reserve g,g1,g2,t,x0,x1,x2 for Complex;
reserve s1,s2,q1,seq,seq1,seq2,seq3 for Complex_Sequence;
reserve Y for Subset of COMPLEX;
reserve f,f1,f2,h,h1,h2 for PartFunc of COMPLEX,COMPLEX;
reserve p,r,s for Real;
reserve Ns,Nseq for increasing sequence of NAT;

theorem
  h is total implies (g(#)h)/*seq = g(#)(h/*seq)
proof
  assume h is total;
  then dom h = COMPLEX by PARTFUN1:def 2;
  then rng seq c= dom h;
  hence thesis by Th8;
end;
