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;
reserve D,D1,D2 for NonatomicND of V,A;

theorem
  for D being TypeSCNominativeData of V,A holds
  v in V implies denaming(v,naming(V,A,v,D)) = D
  proof
    let D be TypeSCNominativeData of V,A;
    assume
A1: v in V;
    naming(V,A,v,D) = v.-->D by A1,Def13;
    then v in dom naming(V,A,v,D) by TARSKI:def 1;
    hence denaming(v,naming(V,A,v,D)) = (naming(V,A,v,D)).v by Def12
    .= (v.-->D).v by A1,Def13
    .= D by FUNCOP_1:72;
  end;
