File Main_ZFC.ML (Isabelle2005: October 2005)

# File Main_ZFC.ML

    structure Main_ZFC =
    struct
      val thy = the_context ();
    end;

    (* legacy ML bindings *)

    (* from AC *)
    val AC_Pi = thm "AC_Pi";
    val AC_ball_Pi = thm "AC_ball_Pi";
    val AC_Pi_Pow = thm "AC_Pi_Pow";
    val AC_func = thm "AC_func";
    val non_empty_family = thm "non_empty_family";
    val AC_func0 = thm "AC_func0";
    val AC_func_Pow = thm "AC_func_Pow";
    val AC_Pi0 = thm "AC_Pi0";
    val choice_Diff = thm "choice_Diff";

    (* from Zorn *)
    val Union_lemma0 = thm "Union_lemma0";
    val Inter_lemma0 = thm "Inter_lemma0";
    val increasingD1 = thm "increasingD1";
    val increasingD2 = thm "increasingD2";
    val TFin_UnionI = thm "TFin_UnionI";
    val TFin_is_subset = thm "TFin_is_subset";
    val TFin_induct = thm "TFin_induct";
    val increasing_trans = thm "increasing_trans";
    val TFin_linear_lemma1 = thm "TFin_linear_lemma1";
    val TFin_linear_lemma2 = thm "TFin_linear_lemma2";
    val TFin_subsetD = thm "TFin_subsetD";
    val TFin_subset_linear = thm "TFin_subset_linear";
    val equal_next_upper = thm "equal_next_upper";
    val equal_next_Union = thm "equal_next_Union";
    val chain_subset_Pow = thm "chain_subset_Pow";
    val super_subset_chain = thm "super_subset_chain";
    val maxchain_subset_chain = thm "maxchain_subset_chain";
    val choice_super = thm "choice_super";
    val choice_not_equals = thm "choice_not_equals";
    val Hausdorff_next_exists = thm "Hausdorff_next_exists";
    val TFin_chain_lemma4 = thm "TFin_chain_lemma4";
    val Hausdorff = thm "Hausdorff";
    val chain_extend = thm "chain_extend";
    val Zorn = thm "Zorn";
    val TFin_well_lemma5 = thm "TFin_well_lemma5";
    val well_ord_TFin_lemma = thm "well_ord_TFin_lemma";
    val well_ord_TFin = thm "well_ord_TFin";
    val Zermelo_next_exists = thm "Zermelo_next_exists";
    val choice_imp_injection = thm "choice_imp_injection";
    val AC_well_ord = thm "AC_well_ord";

    (* from Cardinal_AC *)
    val cardinal_eqpoll = thm "cardinal_eqpoll";
    val cardinal_idem = thm "cardinal_idem";
    val cardinal_eqE = thm "cardinal_eqE";
    val cardinal_eqpoll_iff = thm "cardinal_eqpoll_iff";
    val cardinal_disjoint_Un = thm "cardinal_disjoint_Un";
    val lepoll_imp_Card_le = thm "lepoll_imp_Card_le";
    val cadd_assoc = thm "cadd_assoc";
    val cmult_assoc = thm "cmult_assoc";
    val cadd_cmult_distrib = thm "cadd_cmult_distrib";
    val InfCard_square_eq = thm "InfCard_square_eq";
    val Card_le_imp_lepoll = thm "Card_le_imp_lepoll";
    val le_Card_iff = thm "le_Card_iff";
    val surj_implies_inj = thm "surj_implies_inj";
    val surj_implies_cardinal_le = thm "surj_implies_cardinal_le";
    val cardinal_UN_le = thm "cardinal_UN_le";
    val cardinal_UN_lt_csucc = thm "cardinal_UN_lt_csucc";
    val cardinal_UN_Ord_lt_csucc = thm "cardinal_UN_Ord_lt_csucc";
    val inj_UN_subset = thm "inj_UN_subset";
    val le_UN_Ord_lt_csucc = thm "le_UN_Ord_lt_csucc";

    (* from InfDatatype *)
    val fun_Limit_VfromE = thm "fun_Limit_VfromE";
    val fun_Vcsucc_lemma = thm "fun_Vcsucc_lemma";
    val subset_Vcsucc = thm "subset_Vcsucc";
    val fun_Vcsucc = thm "fun_Vcsucc";
    val fun_in_Vcsucc = thm "fun_in_Vcsucc";
    val fun_in_Vcsucc' = thm "fun_in_Vcsucc'";
    val Card_fun_Vcsucc = thm "Card_fun_Vcsucc";
    val Card_fun_in_Vcsucc = thm "Card_fun_in_Vcsucc";
    val Limit_csucc = thm "Limit_csucc";
    val Pair_in_Vcsucc = thm "Pair_in_Vcsucc";
    val Inl_in_Vcsucc = thm "Inl_in_Vcsucc";
    val Inr_in_Vcsucc = thm "Inr_in_Vcsucc";
    val zero_in_Vcsucc = thm "zero_in_Vcsucc";
    val nat_into_Vcsucc = thm "nat_into_Vcsucc";
    val InfCard_nat_Un_cardinal = thm "InfCard_nat_Un_cardinal";
    val le_nat_Un_cardinal = thm "le_nat_Un_cardinal";
    val UN_upper_cardinal = thm "UN_upper_cardinal";

    val inf_datatype_intrs = thms "inf_datatype_intros";