reserve Al for QC-alphabet;
reserve a,b,c,d for object,
  i,j,k,m,n for Nat,
  p,q,r for Element of CQC-WFF(Al),
  x,y,y0 for bound_QC-variable of Al,
  X for Subset of CQC-WFF(Al),
  A for non empty set,
  J for interpretation of Al,A,
  v,w for Element of Valuations_in(Al,A),
  Sub for CQC_Substitution of Al,
  f,f1,g,h,h1 for FinSequence of CQC-WFF(Al);
reserve fin,fin1 for FinSequence;

theorem Th8:
  f is_Subsequence_of f^g
proof
  set a = len f;
  take N = Seg a;
  reconsider f1 = (f^g)|N as FinSequence by FINSEQ_1:15;
A1: N = dom f by FINSEQ_1:def 3;
  then f c= f1 by FINSEQ_1:21;
  hence thesis by A1,Th7;
end;
