reserve a,a1,a2,v,v1,v2,x for object;
reserve V,A for set;
reserve m,n for Nat;
reserve S,S1,S2 for FinSequence;

theorem Th20:
  S IsNDRankSeq V,A implies S = FNDSC(V,A) | dom S
  proof
    assume
A1: S IsNDRankSeq V,A;
    set F = FNDSC(V,A);
    set G = F|dom S;
    dom F = NAT by Def3;
    hence dom S = dom G by RELAT_1:62;
    let x such that
A2: x in dom S;
    thus S.x = F.x by A1,A2,Th19
    .= G.x by A2,FUNCT_1:49;
  end;
