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 Th27:
  (for d being TypeSCNominativeData of V,A holds
   d in dom p & p.d = TRUE & d in dom f & f.d in dom q implies q.(f.d) = TRUE)
  implies
  <*p,f,q*> is SFHT of ND(V,A)
  proof
    assume
A1: for d being TypeSCNominativeData of V,A holds
    d in dom p & p.d = TRUE & d in dom f & f.d in dom q implies q.(f.d) = TRUE;
    for d being Element of ND(V,A)
    holds d in dom p & p.d = TRUE & d in dom f & f.d in dom q
    implies q.(f.d) = TRUE
    proof
      let d be Element of ND(V,A);
      d is TypeSCNominativeData of V,A by NOMIN_1:39;
      hence thesis by A1;
    end;
    then <*p,f,q*> in SFHTs(ND(V,A));
    hence thesis;
  end;
