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;

theorem Th18:
  <*PP_False(D),f,p*> is SFHT of D
  proof
    set F = PP_False(D);
    for d being Element of D holds
     d in dom F & F.d = TRUE & d in dom f & f.d in dom p implies
      p.(f.d) = TRUE by FUNCOP_1:7;
    then <*F,f,p*> in SFHTs(D);
    hence thesis;
  end;
