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;
