reserve a,b,c,v,v1,x,y for object;
reserve V,A for set;
reserve d for TypeSCNominativeData of V,A;
reserve p,q,r for SCPartialNominativePredicate of V,A;
reserve n for Nat;
reserve X for Function;
reserve f,g,h for SCBinominativeFunction of V,A;

theorem
  for g being (V,A)-FPrg-yielding FinSequence
  for X being one-to-one V-valued FinSequence st
   dom g = dom X & d in_doms g
  holds NDentry(g,X,d) is NonatomicND of V,A
  proof
    let g be (V,A)-FPrg-yielding FinSequence;
    let X be one-to-one V-valued FinSequence;
    assume
A1: dom g = dom X & d in_doms g;
A2: dom NDentry(g,X,d) = rng X by Th24;
A3: rng X c= V by RELAT_1:def 19;
    rng NDentry(g,X,d) c= ND(V,A) by A1,Th30;
    hence thesis by A2,A3,Th6;
  end;
