theorem Th23:
  S1 IsNDRankSeq V,A & S2 IsNDRankSeq V,A implies S1+*S2 = S1 or S1+*S2 = S2
  proof
    assume S1 IsNDRankSeq V,A & S2 IsNDRankSeq V,A;
    then
A1: S1+*S2 = S2+*S1 by Th21,FUNCT_4:34;
    dom S1 c= dom S2 or dom S2 c= dom S1 by Th3;
    hence thesis by A1,FUNCT_4:19;
  end;
