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 V being non empty set
  for v1,v2 being Element of V st a is TypeSCNominativeData of V,A holds
  naming(V,A,<*v1,v2*>,a) = v1.-->(v2.-->a)
  proof
    let V be non empty set;
    let v1,v2 be Element of V such that
A1: a is TypeSCNominativeData of V,A;
    set f = <*v1,v2*>;
    set g = namingSeq(V,A,f,a);
A2: len f = 2 by FINSEQ_1:44;
A5: len g = len f by Def14;
A6: g.1 is NonatomicND of V,A by A2,Th58;
A7: g.1 = naming(V,A,f.len f,a) by Def14
    .= v2.-->a by A2,A1,Def13;
    thus naming(V,A,<*v1,v2*>,a) = naming(V,A,f.(len f-1),g.1) by A2,A5,Def14
    .= v1.-->(v2.-->a) by A2,A6,A7,Def13;
  end;
