environ
vocabularies HIDDEN, NUMBERS, SUBSET_1, FINSEQ_1, EUCLID, SPRECT_2, RELAT_1, FINSEQ_5, FINSEQ_4, XXREAL_0, PARTFUN1, CARD_1, ARYTM_3, ARYTM_1, PRE_TOPC, TOPREAL1, JORDAN3, XBOOLE_0, FUNCT_1, GROUP_2, ORDINAL4, NAT_1, RLTOPSP1, TARSKI, RCOMP_1, SPPOL_1, FINSEQ_6, JORDAN9, PSCOMP_1, GRAPH_2, TOPREAL2, RELAT_2, MCART_1, GOBOARD1, JORDAN8, TREES_1, MATRIX_1, JORDAN1E;
notations HIDDEN, TARSKI, XBOOLE_0, ENUMSET1, SUBSET_1, CARD_1, ORDINAL1, NUMBERS, XCMPLX_0, XXREAL_0, NAT_1, NAT_D, FUNCT_1, PARTFUN1, FINSEQ_1, FINSEQ_4, FINSEQ_5, MATRIX_0, MATRIX_1, FINSEQ_6, STRUCT_0, GRAPH_2, PRE_TOPC, TOPREAL2, CONNSP_1, COMPTS_1, RLTOPSP1, EUCLID, PSCOMP_1, SPRECT_2, GOBOARD1, TOPREAL1, SPPOL_1, JORDAN3, JORDAN8, JORDAN9;
definitions TARSKI, TOPREAL1, SPRECT_2, XBOOLE_0;
theorems JORDAN8, PSCOMP_1, JORDAN1A, NAT_1, GOBOARD5, FINSEQ_1, FINSEQ_2, SPRECT_2, FINSEQ_4, FINSEQ_5, FINSEQ_6, GOBOARD7, SPPOL_2, REVROT_1, TOPREAL1, SPRECT_3, JORDAN5B, JORDAN3, JORDAN9, GOBOARD1, TARSKI, FINSEQ_3, FUNCT_1, TOPREAL5, JORDAN10, GRAPH_2, CARD_1, CARD_2, ENUMSET1, JORDAN1B, SPRECT_5, XBOOLE_0, XREAL_1, XXREAL_0, EUCLID, PARTFUN1, XREAL_0, MATRIX_0;
schemes ;
registrations RELSET_1, XXREAL_0, XREAL_0, FINSEQ_1, FINSEQ_6, STRUCT_0, TOPREAL2, SPPOL_2, SPRECT_2, REVROT_1, TOPREAL6, JORDAN8, JORDAN1A, CARD_1, FUNCT_1, EUCLID, NAT_1, ORDINAL1;
constructors HIDDEN, FINSEQ_4, NEWTON, FINSEQ_5, CONNSP_1, REALSET2, TOPREAL2, PSCOMP_1, GRAPH_2, JORDAN3, JORDAN8, GOBRD13, JORDAN9, NAT_D, RELSET_1, REAL_1, MATRIX_1;
requirements HIDDEN, NUMERALS, BOOLE, SUBSET, REAL, ARITHM;
equalities XBOOLE_0, PSCOMP_1, CARD_1, ORDINAL1;
expansions TARSKI, TOPREAL1, SPRECT_2, XBOOLE_0;
theorem Th6:
for
i,
j,
m,
n being
Nat st
i + j = m + n &
i <= m &
j <= n holds
i = m