reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th52:
  len p <= k implies p*(idseq k) = p
proof
  assume
A1: len p <= k;
  reconsider k as Element of NAT by ORDINAL1:def 12;
  dom p = Seg len p by FINSEQ_1:def 3;
  then dom p c= Seg k by A1,FINSEQ_1:5;
  hence thesis by RELAT_1:51;
end;
