theorem Th16:
  S IsNDRankSeq V,A & n in dom S implies S|n IsNDRankSeq V,A
  proof
    assume
A1: S IsNDRankSeq V,A;
    assume
A2: n in dom S;
    then n <= len S by FINSEQ_3:25;
    then len(S|n) = n by FINSEQ_1:17;
    then S|n <> {} by A2,FINSEQ_3:24;
    hence thesis by A1,RELAT_1:59,Th15;
  end;
