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;
