reserve v,x for object;
reserve D,V,A for set;
reserve n for Nat;
reserve p,q for PartialPredicate of D;
reserve f,g for BinominativeFunction of D;
reserve D for non empty set;
reserve d for Element of D;
reserve f,g for BinominativeFunction of D;
reserve p,q,r,s for PartialPredicate of D;
reserve p,q for SCPartialNominativePredicate of V,A;
reserve f,g for SCBinominativeFunction of V,A;
reserve E for (V,A)-FPrg-yielding FinSequence;
reserve e for Element of product E;
reserve d for TypeSCNominativeData of V,A;

theorem
  <*SC_Psuperpos(p,f,v),SC_assignment(f,v),p*> is SFHT of ND(V,A)
  proof
    set P = SC_Psuperpos(p,f,v);
    set F = SC_assignment(f,v);
    for d holds d in dom P & P.d = TRUE & d in dom F & F.d in dom p implies
     p.(F.d) = TRUE
    proof
      let d such that
A1:   d in dom P & P.d = TRUE and
A2:   d in dom F and
      F.d in dom p;
      F.d = local_overlapping(V,A,d,f.d,v) by A2,NOMIN_2:def 7;
      hence p.(F.d) = TRUE by A1,NOMIN_2:35;
    end;
    hence thesis by Th27;
  end;
