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 Th18:
  1 <= n implies FNDSC(V,A) | Seg(n) IsNDRankSeq V,A
  proof
    set F = FNDSC(V,A);
    set S = F|Seg(n);
    dom F = NAT by Def3;
    then
A1: dom S = Seg(n) by RELAT_1:62;
    assume 1 <= n;
    then 1 in Seg(n);
    hence S.1 = F.1 by FUNCT_1:49
    .= NDSS(V,A) by Th9;
    let n be Nat such that
A2: n in dom S;
    assume n+1 in dom S;
    hence S.(n+1) = F.(n+1) by A1,FUNCT_1:49
    .= NDSS(V,A\/F.n) by Def3
    .= NDSS(V,A\/S.n) by A1,A2,FUNCT_1:49;
  end;
