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;
