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";