environ
vocabularies HIDDEN, NUMBERS, SUBSET_1, EUCLID, PRE_TOPC, TOPREAL2, RELAT_1, STRUCT_0, ARYTM_1, SQUARE_1, XBOOLE_0, FUNCT_1, TOPS_2, RCOMP_1, ORDINAL2, TOPREAL1, XXREAL_2, MCART_1, XXREAL_0, CARD_1, ARYTM_3, PCOMPS_1, METRIC_1, TARSKI, COMPLEX1, JORDAN2C, RLTOPSP1, SPPOL_1, ZFMISC_1, JORDAN6, JORDAN3, JORDAN18, SEQ_4, REAL_1;
notations HIDDEN, TARSKI, XBOOLE_0, ZFMISC_1, SUBSET_1, FUNCT_1, RELSET_1, ORDINAL1, NUMBERS, XCMPLX_0, XXREAL_0, XREAL_0, SQUARE_1, XXREAL_2, SEQ_4, STRUCT_0, PCOMPS_1, COMPLEX1, PRE_TOPC, TOPS_2, RCOMP_1, COMPTS_1, METRIC_1, SPPOL_1, RLTOPSP1, EUCLID, TOPREAL1, PSCOMP_1, TOPREAL2, JORDAN5C, JORDAN2C, TOPREAL6, JORDAN6;
definitions TARSKI, XBOOLE_0, ZFMISC_1, XXREAL_2;
theorems JORDAN5B, TARSKI, TOPREAL1, XBOOLE_0, EUCLID, JORDAN6, TOPS_2, XBOOLE_1, SEQ_4, RELAT_1, PSCOMP_1, FUNCT_2, TOPREAL3, JORDAN1A, COMPTS_1, ZFMISC_1, JORDAN5C, TOPREAL2, JORDAN2C, SQUARE_1, RCOMP_1, TOPMETR, METRIC_1, JORDAN16, SPPOL_1, COMPLEX1, XREAL_1, TOPREAL6, XXREAL_0, JCT_MISC, PRE_TOPC, RLTOPSP1;
schemes ;
registrations RELSET_1, NUMBERS, XXREAL_0, XREAL_0, SQUARE_1, MEMBERED, COMPTS_1, EUCLID, TOPREAL1, STRUCT_0, TOPS_1, JORDAN2C, ORDINAL1;
constructors HIDDEN, REAL_1, SQUARE_1, COMPLEX1, RCOMP_1, TOPS_2, COMPTS_1, TOPREAL1, SPPOL_1, PSCOMP_1, JORDAN5C, JORDAN6, JORDAN2C, TOPREAL6, SEQ_4, RELSET_1, FUNCSDOM, BINOP_2, PCOMPS_1;
requirements HIDDEN, NUMERALS, REAL, BOOLE, SUBSET, ARITHM;
equalities XBOOLE_0, SQUARE_1, SUBSET_1;
expansions TARSKI, XBOOLE_0, XXREAL_2;
Lm1:
dom proj1 = the carrier of (TOP-REAL 2)
by FUNCT_2:def 1;
Lm2:
dom proj2 = the carrier of (TOP-REAL 2)
by FUNCT_2:def 1;
Lm3:
TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) = TopSpaceMetr (Euclid 2)
by EUCLID:def 8;