reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;
reserve J for Nat;

theorem
  for f being FinSubsequence holds f is FinSequence implies Seq f = f
proof
  let f be FinSubsequence;
  assume f is FinSequence;
  then reconsider ss9=f as FinSequence;
  consider k be Nat such that
A1: dom ss9 = Seg k by FINSEQ_1:def 2;
  k in NAT by ORDINAL1:def 12;
  then
A2: len ss9 <= k by A1,FINSEQ_1:def 3;
  Seq f = f* Sgm Seg k by A1,FINSEQ_1:def 15
    .= f* idseq k by Th46
    .= f by A2,FINSEQ_2:54;
  hence thesis;
end;
