environ
vocabularies HIDDEN, NUMBERS, SUBSET_1, RELAT_1, WELLORD1, RELAT_2, ZFMISC_1, TARSKI, XBOOLE_0, FUNCT_1, FINSEQ_1, PRE_TOPC, METRIC_1, SETFAM_1, CARD_5, RCOMP_1, STRUCT_0, PCOMPS_1, CARD_1, ARYTM_3, XXREAL_0, ORDINAL4, PARTFUN1, NEWTON, NAT_1, REAL_1, FINSET_1, ARYTM_1, PCOMPS_2;
notations HIDDEN, TARSKI, XBOOLE_0, ZFMISC_1, SUBSET_1, ORDINAL1, NUMBERS, XCMPLX_0, REAL_1, XREAL_0, WELLORD1, RELAT_1, FINSET_1, RELAT_2, NAT_1, SETFAM_1, XXREAL_0, FUNCT_1, PARTFUN1, FUNCT_2, NEWTON, FINSEQ_1, FINSEQ_2, STRUCT_0, METRIC_1, PRE_TOPC, TOPS_2, PCOMPS_1;
definitions TARSKI, WELLORD1, RELAT_2, SETFAM_1;
theorems PCOMPS_1, COMPTS_1, SETFAM_1, TOPS_1, TOPS_2, PRE_TOPC, SUBSET_1, TARSKI, WELLORD2, ZFMISC_1, NAT_1, PREPOWER, WELLORD1, RELAT_1, FUNCT_1, METRIC_1, FINSEQ_1, CARD_1, FINSEQ_2, FINSEQ_4, TBSP_1, NEWTON, XBOOLE_0, XBOOLE_1, XCMPLX_1, XREAL_1, XXREAL_0, ORDINAL1, PARTFUN1;
schemes NAT_1, FUNCT_2, SUBSET_1, RECDEF_1, TREES_2, FRAENKEL, XBOOLE_0, XFAMILY;
registrations SUBSET_1, ORDINAL1, RELSET_1, FINSET_1, NAT_1, FINSEQ_1, STRUCT_0, PRE_TOPC, METRIC_1, TOPS_1, XREAL_0, NEWTON;
constructors HIDDEN, SETFAM_1, RELAT_2, WELLORD1, WELLORD2, REAL_1, NAT_1, MEMBERED, NEWTON, TOPS_2, PCOMPS_1, FINSEQ_2;
requirements HIDDEN, REAL, NUMERALS, BOOLE, SUBSET, ARITHM;
equalities WELLORD1, XBOOLE_0, STRUCT_0;
expansions TARSKI, WELLORD1, RELAT_2, SETFAM_1, XBOOLE_0;
reconsider jd = 1 / 2 as Real ;