environ
vocabularies HIDDEN, NUMBERS, REAL_1, SUBSET_1, XBOOLE_0, PRE_TOPC, EUCLID, NAT_1, FINSEQ_1, PARTFUN1, RELAT_1, FUNCT_1, TOPMETR, STRUCT_0, SUPINF_2, CARD_1, FINSEQ_2, ARYTM_1, ARYTM_3, XXREAL_0, RFINSEQ, CARD_3, FUNCT_4, ORDINAL4, COMPLEX1, SQUARE_1, RVSUM_1, RCOMP_1, PCOMPS_1, METRIC_1, TARSKI, ORDINAL2, TOPS_2, VALUED_1, MCART_1, FUNCT_2;
notations HIDDEN, TARSKI, XBOOLE_0, SUBSET_1, RELAT_1, ORDINAL1, NUMBERS, XCMPLX_0, XREAL_0, COMPLEX1, REAL_1, NAT_1, RVSUM_1, FUNCT_1, PARTFUN1, RELSET_1, FINSEQ_1, FUNCT_2, BINOP_1, RFINSEQ, FINSEQ_2, NAT_D, VALUED_0, STRUCT_0, TOPS_2, SQUARE_1, FUNCT_7, TOPMETR, PRE_TOPC, METRIC_1, RLVECT_1, EUCLID, PSCOMP_1, PCOMPS_1, FINSEQOP, XXREAL_0;
definitions TARSKI, RELAT_1;
theorems TARSKI, EUCLID, TOPMETR, TOPS_1, METRIC_1, FUNCT_1, RFINSEQ, FUNCT_2, RELAT_1, TBSP_1, NAT_1, FINSEQ_3, FINSEQ_1, ABSVALUE, SQUARE_1, FINSEQ_2, TOPS_2, RVSUM_1, TOPREAL3, FUNCOP_1, FINSEQ_4, FUNCT_7, SEQ_2, PSCOMP_1, XREAL_0, XBOOLE_0, COMPLEX1, XREAL_1, XXREAL_0, FINSOP_1, PARTFUN1, NAT_D, VALUED_1, PRE_TOPC, CARD_1;
schemes FUNCT_2;
registrations XBOOLE_0, NUMBERS, XXREAL_0, XREAL_0, MEMBERED, STRUCT_0, METRIC_1, PCOMPS_1, EUCLID, TOPMETR, VALUED_0, FINSEQ_1, MONOID_0, RELSET_1, FUNCT_2, SQUARE_1, RVSUM_1, PRE_POLY, FUNCT_7, ORDINAL1;
constructors HIDDEN, REAL_1, SQUARE_1, FINSEQOP, FINSEQ_4, FINSOP_1, RFINSEQ, NAT_D, FUNCT_7, TOPS_2, TOPMETR, PSCOMP_1, BINOP_2, FUNCSDOM, MONOID_0, PCOMPS_1, PRE_POLY;
requirements HIDDEN, NUMERALS, REAL, BOOLE, SUBSET, ARITHM;
equalities EUCLID, FINSEQ_2, RVSUM_1, SQUARE_1, STRUCT_0, VALUED_1;
expansions TARSKI;
Lm1:
for n, i being Nat
for p being Element of (TOP-REAL n) ex q being Real ex g being FinSequence of REAL st
( g = p & q = g /. i )