% Mizar ND problem: t3_tdgroup,tdgroup,45,15 fof(dh_c2_2__tdgroup,definition, ( ( m1_subset_1(c2_2__tdgroup,u1_struct_0(k1_vectsp_1)) => ( k4_rlvect_1(k1_vectsp_1,c2_2__tdgroup,c2_2__tdgroup) = k1_rlvect_1(k1_vectsp_1) => c2_2__tdgroup = k1_rlvect_1(k1_vectsp_1) ) ) => ! [A] : ( m1_subset_1(A,u1_struct_0(k1_vectsp_1)) => ( k4_rlvect_1(k1_vectsp_1,A,A) = k1_rlvect_1(k1_vectsp_1) => A = k1_rlvect_1(k1_vectsp_1) ) ) ), introduced(definition,[new_symbol(c2_2__tdgroup),file(tdgroup,c2_2__tdgroup)]), [interesting(0.8),axiom,file(tdgroup,c2_2__tdgroup)]). fof(e2_2__tdgroup,assumption,( k4_rlvect_1(k1_vectsp_1,c2_2__tdgroup,c2_2__tdgroup) = k1_rlvect_1(k1_vectsp_1) ), introduced(assumption,[file(tdgroup,e2_2__tdgroup)]), [interesting(0.8),axiom,file(tdgroup,e2_2__tdgroup)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), [interesting(0.9),axiom,file(struct_0,l1_struct_0)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(dt_u1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( v1_funct_1(u1_rlvect_1(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,u1_rlvect_1)]). fof(dt_u2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ), file(struct_0,u2_struct_0), [interesting(0.9),axiom,file(struct_0,u2_struct_0)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc1_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(cc9_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(fc1_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]). fof(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc3_struct_0,theorem,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]). fof(rc5_struct_0,theorem,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(free_g1_rlvect_1,definition,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) ) => ! [D,E,F] : ( g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(rlvect_1,g1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,g1_rlvect_1)]). fof(abstractness_v1_rlvect_1,theorem,( ! [A] : ( l1_rlvect_1(A) => ( v1_rlvect_1(A) => A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)) ) ) ), file(rlvect_1,v1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,v1_rlvect_1)]). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(redefinition_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_g1_rlvect_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) ) => ( v1_rlvect_1(g1_rlvect_1(A,B,C)) & l1_rlvect_1(g1_rlvect_1(A,B,C)) ) ) ), file(rlvect_1,g1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,g1_rlvect_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k33_binop_2,axiom, ( v1_funct_1(k33_binop_2) & v1_funct_2(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(k33_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ), file(binop_2,k33_binop_2), [interesting(0.9),axiom,file(binop_2,k33_binop_2)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,l1_rlvect_1)]). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), [interesting(0.9),axiom,file(struct_0,l2_struct_0)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), [interesting(0.9),axiom,file(struct_0,u1_struct_0)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(fc2_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). fof(rc1_vectsp_1,theorem,( ? [A] : ( l1_rlvect_1(A) & ~ v3_struct_0(A) & v1_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) ) ), file(vectsp_1,rc1_vectsp_1), [interesting(0.9),axiom,file(vectsp_1,rc1_vectsp_1)]). fof(rc4_struct_0,theorem,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), [interesting(0.9),axiom,file(struct_0,rc4_struct_0)]). fof(spc2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) ), file(arithm,spc2_arithm), [interesting(0.9),axiom,file(arithm,spc2_arithm)]). fof(spc4_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ), file(arithm,spc4_arithm), [interesting(0.9),axiom,file(arithm,spc4_arithm)]). fof(spc7_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc9_arithm,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) ), file(arithm,spc9_arithm), [interesting(0.9),axiom,file(arithm,spc9_arithm)]). fof(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(t2_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), [interesting(0.9),axiom,file(arithm,t2_arithm)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t3_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), [interesting(0.9),axiom,file(arithm,t3_arithm)]). fof(t4_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), [interesting(0.9),axiom,file(arithm,t4_arithm)]). fof(t5_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), [interesting(0.9),axiom,file(arithm,t5_arithm)]). fof(t6_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) ), file(arithm,t6_arithm), [interesting(0.9),axiom,file(arithm,t6_arithm)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(commutativity_k11_binop_2,theorem,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k11_binop_2(A,B) = k11_binop_2(B,A) ) ), file(binop_2,k11_binop_2), [interesting(0.9),axiom,file(binop_2,k11_binop_2)]). fof(commutativity_k3_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(involutiveness_k4_xcmplx_0,theorem,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(redefinition_k11_binop_2,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k11_binop_2(A,B) = k3_xcmplx_0(A,B) ) ), file(binop_2,k11_binop_2), [interesting(0.9),axiom,file(binop_2,k11_binop_2)]). fof(dt_k11_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k11_binop_2(A,B),k1_numbers) ) ), file(binop_2,k11_binop_2), [interesting(0.9),axiom,file(binop_2,k11_binop_2)]). fof(dt_k1_rlvect_1,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ), file(rlvect_1,k1_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k1_rlvect_1)]). fof(dt_k1_vectsp_1,axiom, ( v1_rlvect_1(k1_vectsp_1) & l1_rlvect_1(k1_vectsp_1) ), file(vectsp_1,k1_vectsp_1), [interesting(0.9),axiom,file(vectsp_1,k1_vectsp_1)]). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k4_xcmplx_0)]). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k6_xcmplx_0)]). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k7_xcmplx_0)]). fof(dt_c2_2__tdgroup,assumption,( m1_subset_1(c2_2__tdgroup,u1_struct_0(k1_vectsp_1)) ), introduced(assumption,[file(tdgroup,c2_2__tdgroup)]), [interesting(0.8),axiom,file(tdgroup,c2_2__tdgroup)]). fof(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(spc0_numerals,theorem, ( v2_xreal_0(0) & m2_subset_1(0,k1_numbers,k5_numbers) & m1_subset_1(0,k5_numbers) & m1_subset_1(0,k1_numbers) ), file(numerals,spc0_numerals), [interesting(0.9),axiom,file(numerals,spc0_numerals)]). fof(fc1_vectsp_1,theorem, ( ~ v3_struct_0(k1_vectsp_1) & v1_rlvect_1(k1_vectsp_1) ), file(vectsp_1,fc1_vectsp_1), [interesting(0.9),axiom,file(vectsp_1,fc1_vectsp_1)]). fof(fc2_vectsp_1,theorem, ( ~ v3_struct_0(k1_vectsp_1) & v1_rlvect_1(k1_vectsp_1) & v3_rlvect_1(k1_vectsp_1) & v4_rlvect_1(k1_vectsp_1) & v5_rlvect_1(k1_vectsp_1) & v6_rlvect_1(k1_vectsp_1) ), file(vectsp_1,fc2_vectsp_1), [interesting(0.9),axiom,file(vectsp_1,fc2_vectsp_1)]). fof(d6_vectsp_1,definition,( k1_vectsp_1 = g1_rlvect_1(k1_numbers,k33_binop_2,0) ), file(vectsp_1,d6_vectsp_1), [interesting(0.9),axiom,file(vectsp_1,d6_vectsp_1)]). fof(de_c3_2__tdgroup,definition,( c3_2__tdgroup = c2_2__tdgroup ), introduced(definition,[new_symbol(c3_2__tdgroup),file(tdgroup,c3_2__tdgroup)]), [interesting(0.8),axiom,file(tdgroup,c3_2__tdgroup)]). fof(e3_2__tdgroup,plain,( m1_subset_1(c2_2__tdgroup,k1_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__tdgroup])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k5_ordinal2,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc20_membered,cc6_membered,cc9_membered,fc5_membered,rc5_struct_0,t3_subset,t4_subset,t5_subset,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_rlvect_1,dt_u2_struct_0,rc4_struct_0,t1_numerals,free_g1_rlvect_1,antisymmetry_r2_hidden,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_l1_struct_0,dt_g1_rlvect_1,dt_k1_xboole_0,dt_k33_binop_2,dt_l1_rlvect_1,dt_l1_struct_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc1_struct_0,fc6_membered,rc1_membered,rc1_vectsp_1,rc3_struct_0,spc0_boole,t1_subset,t8_boole,spc0_numerals,spc0_boole,dt_k1_vectsp_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_vectsp_1,fc2_vectsp_1,t2_subset,t6_boole,t7_boole,d6_vectsp_1,existence_m1_subset_1,dt_k1_numbers,dt_m1_subset_1,dt_c2_2__tdgroup,fc2_membered]), [interesting(0.8),file(tdgroup,e3_2__tdgroup),[file(tdgroup,e3_2__tdgroup)]]). fof(dt_c3_2__tdgroup,plain,( m1_subset_1(c3_2__tdgroup,k1_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__tdgroup])],[reflexivity_r1_tarski,dt_k1_zfmisc_1,dt_k5_ordinal2,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_relset_1,cc20_membered,cc6_membered,cc9_membered,fc5_membered,rc5_struct_0,t3_subset,t4_subset,t5_subset,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k2_zfmisc_1,dt_k5_numbers,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_rlvect_1,dt_u2_struct_0,rc4_struct_0,t1_numerals,free_g1_rlvect_1,antisymmetry_r2_hidden,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_l1_struct_0,dt_g1_rlvect_1,dt_k1_xboole_0,dt_k33_binop_2,dt_l1_rlvect_1,dt_l1_struct_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,fc1_struct_0,fc6_membered,rc1_membered,rc1_vectsp_1,rc3_struct_0,spc0_boole,t1_subset,spc0_numerals,spc0_boole,dt_k1_vectsp_1,dt_u1_struct_0,cc10_membered,cc11_membered,cc15_membered,cc4_membered,fc1_vectsp_1,fc2_vectsp_1,t2_subset,t6_boole,t7_boole,t8_boole,d6_vectsp_1,existence_m1_subset_1,dt_k1_numbers,dt_m1_subset_1,dt_c2_2__tdgroup,fc2_membered,de_c3_2__tdgroup,e3_2__tdgroup]), [interesting(0.8),file(tdgroup,c3_2__tdgroup),[file(tdgroup,c3_2__tdgroup)]]). fof(rqRealDiff__k6_xcmplx_0__r0_r0_r0,theorem,( k6_xcmplx_0(0,0) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r0_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r1_rm1,theorem,( k6_xcmplx_0(0,1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm1_r1,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r0_rm2_r2,theorem,( k6_xcmplx_0(0,k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,theorem,( k6_xcmplx_0(0,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r1_r0_r1,theorem,( k6_xcmplx_0(1,0) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r0_r1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r2_rm1,theorem,( k6_xcmplx_0(1,2) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2,theorem,( k6_xcmplx_0(1,k4_xcmplx_0(1)) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]). fof(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2,theorem,( k6_xcmplx_0(2,0) = 2 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r0_r2)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),0) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),0) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(2),k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),0) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]). fof(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,theorem,( k6_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),0) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(1)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,theorem,( k6_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r1_r0,theorem,( k7_xcmplx_0(0,1) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r1_r0)]). fof(rqRealDiv__k7_xcmplx_0__r0_r2_r0,theorem,( k7_xcmplx_0(0,2) = 0 ), file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r0_r2_r0)]). fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1,theorem,( k7_xcmplx_0(1,1) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r1_r1)]). fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,theorem,( k7_xcmplx_0(1,2) = k7_xcmplx_0(1,2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]). fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(1,2)) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,theorem,( k7_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2,theorem,( k7_xcmplx_0(2,1) = 2 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r1_r2)]). fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1,theorem,( k7_xcmplx_0(2,2) = 1 ), file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r2_r2_r1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),1) = k4_xcmplx_0(1) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]). fof(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,theorem,( k7_xcmplx_0(k4_xcmplx_0(1),2) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__r0_r0_r0,theorem,( k3_xcmplx_0(0,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_r1_r0,theorem,( k3_xcmplx_0(0,1) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r1_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0,theorem,( k3_xcmplx_0(0,k4_xcmplx_0(2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rm2_r0)]). fof(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,theorem,( k3_xcmplx_0(0,k7_xcmplx_0(1,2)) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_r0_r0,theorem,( k3_xcmplx_0(1,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2,theorem,( k3_xcmplx_0(1,k4_xcmplx_0(2)) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]). fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,theorem,( k3_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]). fof(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,theorem,( k3_xcmplx_0(1,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,theorem,( k3_xcmplx_0(2,k7_xcmplx_0(1,2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]). fof(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,theorem,( k3_xcmplx_0(2,k7_xcmplx_0(k4_xcmplx_0(1),2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),1) = k4_xcmplx_0(2) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]). fof(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(1,2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,theorem,( k3_xcmplx_0(k4_xcmplx_0(2),k7_xcmplx_0(k4_xcmplx_0(1),2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),1) = k7_xcmplx_0(1,2) ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),2) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]). fof(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,theorem,( k3_xcmplx_0(k7_xcmplx_0(1,2),k4_xcmplx_0(2)) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),1) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),2) = k4_xcmplx_0(1) ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)]). fof(rqRealNeg__k4_xcmplx_0__r0_r0,theorem,( k4_xcmplx_0(0) = 0 ), file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r0_r0)]). fof(rqRealNeg__k4_xcmplx_0__rm1_r1,theorem,( k4_xcmplx_0(k4_xcmplx_0(1)) = 1 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm1_r1)]). fof(rqRealNeg__k4_xcmplx_0__rm2_r2,theorem,( k4_xcmplx_0(k4_xcmplx_0(2)) = 2 ), file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rm2_r2)]). fof(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(1,2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]). fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,theorem,( k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2)) = k7_xcmplx_0(1,2) ), file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc2_numerals,theorem, ( v2_xreal_0(2) & m2_subset_1(2,k1_numbers,k5_numbers) & m1_subset_1(2,k5_numbers) & m1_subset_1(2,k1_numbers) ), file(numerals,spc2_numerals), [interesting(0.9),axiom,file(numerals,spc2_numerals)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(commutativity_k4_rlvect_1,theorem,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(redefinition_k1_domain_1,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(redefinition_k4_rlvect_1,definition,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(redefinition_k8_funct_2,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), [interesting(0.9),axiom,file(domain_1,k1_domain_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k2_rlvect_1)]). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,k4_rlvect_1)]). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), [interesting(0.9),axiom,file(tarski,k4_tarski)]). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(d2_rlvect_1,definition,( ! [A] : ( l2_struct_0(A) => k1_rlvect_1(A) = u2_struct_0(A) ) ), file(rlvect_1,d2_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d2_rlvect_1)]). fof(e1_2__tdgroup,plain,( k1_rlvect_1(k1_vectsp_1) = 0 ), inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,dt_m2_relset_1,dt_u1_rlvect_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc5_membered,fc6_membered,rc1_membered,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,free_g1_rlvect_1,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_g1_rlvect_1,dt_k1_numbers,dt_k33_binop_2,dt_k5_numbers,dt_l1_rlvect_1,dt_l1_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc1_struct_0,fc2_membered,rc1_vectsp_1,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,existence_l2_struct_0,dt_k1_rlvect_1,dt_k1_vectsp_1,dt_l2_struct_0,dt_u2_struct_0,fc1_vectsp_1,fc2_vectsp_1,d6_vectsp_1,spc0_numerals,spc0_boole,d2_rlvect_1]), [interesting(0.8),file(tdgroup,e1_2__tdgroup),[file(tdgroup,e1_2__tdgroup)]]). fof(d3_rlvect_1,definition,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ), file(rlvect_1,d3_rlvect_1), [interesting(0.9),axiom,file(rlvect_1,d3_rlvect_1)]). fof(e1_2_1__tdgroup,plain,( 0 = k1_funct_1(u1_rlvect_1(k1_vectsp_1),k4_tarski(c3_2__tdgroup,c3_2__tdgroup)) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__tdgroup,e2_2__tdgroup])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_u2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc5_membered,fc6_membered,rc1_membered,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,free_g1_rlvect_1,abstractness_v1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_g1_rlvect_1,dt_k1_numbers,dt_k33_binop_2,dt_k5_numbers,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_m2_subset_1,cc15_membered,fc1_struct_0,fc2_membered,rc1_vectsp_1,rc3_struct_0,rc4_struct_0,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,commutativity_k4_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,redefinition_k1_domain_1,redefinition_k4_rlvect_1,redefinition_k8_funct_2,dt_k1_domain_1,dt_k1_funct_1,dt_k1_rlvect_1,dt_k1_vectsp_1,dt_k2_rlvect_1,dt_k2_zfmisc_1,dt_k4_rlvect_1,dt_k4_tarski,dt_k8_funct_2,dt_l1_rlvect_1,dt_m1_subset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_c2_2__tdgroup,dt_c3_2__tdgroup,de_c3_2__tdgroup,fc1_vectsp_1,fc2_vectsp_1,d6_vectsp_1,spc0_numerals,spc0_boole,e1_2__tdgroup,e2_2__tdgroup,d3_rlvect_1]), [interesting(0.65),file(tdgroup,e1_2_1__tdgroup),[file(tdgroup,e1_2_1__tdgroup)]]). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), [interesting(0.9),axiom,file(binop_1,k1_binop_1)]). fof(d1_binop_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ), file(binop_1,d1_binop_1), [interesting(0.9),axiom,file(binop_1,d1_binop_1)]). fof(e2_2_1__tdgroup,plain,( k1_funct_1(u1_rlvect_1(k1_vectsp_1),k4_tarski(c3_2__tdgroup,c3_2__tdgroup)) = k1_binop_1(u1_rlvect_1(k1_vectsp_1),c3_2__tdgroup,c3_2__tdgroup) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__tdgroup])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc5_membered,fc6_membered,rc1_membered,t1_subset,t4_subset,t5_subset,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m2_subset_1,dt_u2_struct_0,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc4_membered,cc6_membered,cc9_membered,fc1_struct_0,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,free_g1_rlvect_1,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_g1_rlvect_1,dt_k1_numbers,dt_k2_zfmisc_1,dt_k33_binop_2,dt_l1_rlvect_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_struct_0,dt_c2_2__tdgroup,fc2_membered,rc1_vectsp_1,spc0_numerals,spc0_boole,dt_k1_binop_1,dt_k1_funct_1,dt_k1_vectsp_1,dt_k4_tarski,dt_u1_rlvect_1,dt_c3_2__tdgroup,de_c3_2__tdgroup,fc1_vectsp_1,fc2_vectsp_1,d1_binop_1,d6_vectsp_1]), [interesting(0.65),file(tdgroup,e2_2_1__tdgroup),[file(tdgroup,e2_2_1__tdgroup)]]). fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0,theorem,( k2_xcmplx_0(0,0) = 0 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r0_r0)]). fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1,theorem,( k2_xcmplx_0(0,1) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2,theorem,( k2_xcmplx_0(0,2) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r0_r2_r2)]). fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1,theorem,( k2_xcmplx_0(1,0) = 1 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r0_r1)]). fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2,theorem,( k2_xcmplx_0(2,0) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r2_r0_r2)]). fof(rqRealMult__k3_xcmplx_0__r0_r2_r0,theorem,( k3_xcmplx_0(0,2) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r0_r2_r0)]). fof(rqRealMult__k3_xcmplx_0__r2_r0_r0,theorem,( k3_xcmplx_0(2,0) = 0 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r0_r0)]). fof(spc5_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ), file(arithm,spc5_arithm), [interesting(0.9),axiom,file(arithm,spc5_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t1_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), [interesting(0.9),axiom,file(arithm,t1_arithm)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(commutativity_k9_binop_2,theorem,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k9_binop_2(B,A) ) ), file(binop_2,k9_binop_2), [interesting(0.9),axiom,file(binop_2,k9_binop_2)]). fof(redefinition_k2_binop_1,definition,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) ) => k2_binop_1(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) ), file(binop_1,k2_binop_1), [interesting(0.9),axiom,file(binop_1,k2_binop_1)]). fof(redefinition_k9_binop_2,definition,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k9_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k9_binop_2), [interesting(0.9),axiom,file(binop_2,k9_binop_2)]). fof(dt_k2_binop_1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) ) => m1_subset_1(k2_binop_1(A,B,C,D,E,F),C) ) ), file(binop_1,k2_binop_1), [interesting(0.9),axiom,file(binop_1,k2_binop_1)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k9_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k9_binop_2(A,B),k1_numbers) ) ), file(binop_2,k9_binop_2), [interesting(0.9),axiom,file(binop_2,k9_binop_2)]). fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,( k3_xcmplx_0(1,2) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]). fof(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,( k3_xcmplx_0(2,1) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]). fof(d9_binop_2,definition,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) => ( A = k33_binop_2 <=> ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k9_binop_2(B,C) ) ) ) ) ), file(binop_2,d9_binop_2), [interesting(0.9),axiom,file(binop_2,d9_binop_2)]). fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,( k3_xcmplx_0(1,1) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]). fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,( k2_xcmplx_0(1,1) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). fof(e3_2_1__tdgroup,plain,( k1_binop_1(u1_rlvect_1(k1_vectsp_1),c3_2__tdgroup,c3_2__tdgroup) = k9_binop_2(k11_binop_2(1,c3_2__tdgroup),c3_2__tdgroup) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__tdgroup])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_l2_struct_0,dt_k1_xboole_0,dt_k5_ordinal2,dt_l1_struct_0,dt_l2_struct_0,dt_u2_struct_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_membered,rc3_struct_0,rc4_struct_0,rc5_struct_0,t1_subset,t4_subset,t5_subset,free_g1_rlvect_1,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_m1_relset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_g1_rlvect_1,dt_k1_funct_1,dt_k1_zfmisc_1,dt_k4_tarski,dt_k5_numbers,dt_l1_rlvect_1,dt_m1_relset_1,dt_m2_subset_1,dt_u1_struct_0,dt_c2_2__tdgroup,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_relset_1,cc4_membered,cc6_membered,cc9_membered,rc1_vectsp_1,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_boole,spc0_numerals,spc5_arithm,spc6_arithm,spc7_arithm,t1_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t3_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc0_boole,commutativity_k11_binop_2,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k9_binop_2,existence_m1_subset_1,existence_m2_relset_1,redefinition_k11_binop_2,redefinition_k2_binop_1,redefinition_k9_binop_2,redefinition_m2_relset_1,dt_k11_binop_2,dt_k1_binop_1,dt_k1_numbers,dt_k1_vectsp_1,dt_k2_binop_1,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k33_binop_2,dt_k3_xcmplx_0,dt_k9_binop_2,dt_m1_subset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_c3_2__tdgroup,de_c3_2__tdgroup,fc1_vectsp_1,fc2_membered,fc2_vectsp_1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,d1_binop_1,d6_vectsp_1,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,d9_binop_2,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealAdd__k2_xcmplx_0__r1_r1_r2]), [interesting(0.65),file(tdgroup,e3_2_1__tdgroup),[file(tdgroup,e3_2_1__tdgroup)]]). fof(e4_2_1__tdgroup,plain,( k9_binop_2(k11_binop_2(1,c3_2__tdgroup),c3_2__tdgroup) = k11_binop_2(2,c3_2__tdgroup) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__tdgroup])],[existence_l2_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_zfmisc_1,dt_l2_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u2_struct_0,cc1_relset_1,rc4_struct_0,free_g1_rlvect_1,reflexivity_r1_tarski,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_l1_struct_0,dt_g1_rlvect_1,dt_k33_binop_2,dt_l1_rlvect_1,dt_l1_struct_0,fc1_struct_0,rc1_vectsp_1,rc3_struct_0,rc5_struct_0,rqRealAdd__k2_xcmplx_0__r0_r0_r0,rqRealAdd__k2_xcmplx_0__r0_r1_r1,rqRealAdd__k2_xcmplx_0__r0_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r0_r1,rqRealAdd__k2_xcmplx_0__r2_r0_r2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r2_r0_r0,spc0_boole,spc0_numerals,t1_arithm,t1_numerals,t2_arithm,spc0_numerals,spc0_boole,antisymmetry_r2_hidden,dt_k1_vectsp_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_u1_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_vectsp_1,fc2_vectsp_1,fc5_membered,fc6_membered,rc1_membered,t1_subset,t3_subset,t4_subset,t5_subset,d6_vectsp_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c2_2__tdgroup,cc15_membered,fc2_membered,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t6_boole,t7_boole,t8_boole,commutativity_k11_binop_2,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k9_binop_2,redefinition_k11_binop_2,redefinition_k9_binop_2,dt_k11_binop_2,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k9_binop_2,dt_c3_2__tdgroup,de_c3_2__tdgroup,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.65),file(tdgroup,e4_2_1__tdgroup),[file(tdgroup,e4_2_1__tdgroup)]]). fof(e4_2__tdgroup,plain,( 0 = k11_binop_2(2,c3_2__tdgroup) ), inference(iterative_eq,[status(thm),assumptions([e2_2__tdgroup,dt_c2_2__tdgroup])],[e1_2_1__tdgroup,e2_2_1__tdgroup,e3_2_1__tdgroup,e4_2_1__tdgroup]), [interesting(0.8),file(tdgroup,e4_2__tdgroup),[file(tdgroup,e4_2__tdgroup)]]). fof(rqRealNeg__k4_xcmplx_0__r2_rm2,theorem,( k4_xcmplx_0(2) = k4_xcmplx_0(2) ), file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r2_rm2)]). fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,theorem,( k7_xcmplx_0(1,k4_xcmplx_0(2)) = k7_xcmplx_0(k4_xcmplx_0(1),2) ), file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2), [interesting(0.9),axiom,file(arithm,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]). fof(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,theorem,( k3_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(1),2),k4_xcmplx_0(2)) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)]). fof(rqRealNeg__k4_xcmplx_0__r1_rm1,theorem,( k4_xcmplx_0(1) = k4_xcmplx_0(1) ), file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1), [interesting(0.9),axiom,file(arithm,rqRealNeg__k4_xcmplx_0__r1_rm1)]). fof(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,theorem,( k6_xcmplx_0(k4_xcmplx_0(1),k4_xcmplx_0(1)) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]). fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2,theorem,( k6_xcmplx_0(0,2) = k4_xcmplx_0(2) ), file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]). fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1,theorem,( k6_xcmplx_0(2,1) = 1 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r1_r1)]). fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0,theorem,( k6_xcmplx_0(1,1) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r1_r1_r0)]). fof(rqRealDiff__k6_xcmplx_0__r2_r2_r0,theorem,( k6_xcmplx_0(2,2) = 0 ), file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0), [interesting(0.9),axiom,file(arithm,rqRealDiff__k6_xcmplx_0__r2_r2_r0)]). fof(e5_2__tdgroup,plain,( c2_2__tdgroup = k1_rlvect_1(k1_vectsp_1) ), inference(mizar_by,[status(thm),assumptions([e2_2__tdgroup,dt_c2_2__tdgroup])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_l1_struct_0,existence_m1_relset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_l1_struct_0,dt_m1_relset_1,dt_m2_relset_1,dt_u1_rlvect_1,dt_u2_struct_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_struct_0,fc5_membered,fc6_membered,rc1_membered,rc3_struct_0,rc5_struct_0,t1_subset,t3_subset,t4_subset,t5_subset,free_g1_rlvect_1,abstractness_v1_rlvect_1,existence_l1_rlvect_1,existence_l2_struct_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_g1_rlvect_1,dt_k1_numbers,dt_k33_binop_2,dt_k5_numbers,dt_l1_rlvect_1,dt_l2_struct_0,dt_m1_subset_1,dt_m2_subset_1,dt_u1_struct_0,cc15_membered,fc2_membered,rc1_vectsp_1,rc4_struct_0,spc2_arithm,spc4_arithm,spc7_arithm,spc9_arithm,t1_numerals,t2_arithm,t2_subset,t3_arithm,t4_arithm,t5_arithm,t6_arithm,t6_boole,t7_boole,t8_boole,commutativity_k11_binop_2,commutativity_k3_xcmplx_0,involutiveness_k4_xcmplx_0,redefinition_k11_binop_2,dt_k11_binop_2,dt_k1_rlvect_1,dt_k1_vectsp_1,dt_k3_xcmplx_0,dt_k4_xcmplx_0,dt_k6_xcmplx_0,dt_k7_xcmplx_0,dt_c2_2__tdgroup,dt_c3_2__tdgroup,de_c3_2__tdgroup,fc1_vectsp_1,fc2_vectsp_1,rqRealDiff__k6_xcmplx_0__r0_r0_r0,rqRealDiff__k6_xcmplx_0__r0_r1_rm1,rqRealDiff__k6_xcmplx_0__r0_rm1_r1,rqRealDiff__k6_xcmplx_0__r0_rm2_r2,rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r1_r0_r1,rqRealDiff__k6_xcmplx_0__r1_r2_rm1,rqRealDiff__k6_xcmplx_0__r1_rm1_r2,rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2,rqRealDiff__k6_xcmplx_0__r2_r0_r2,rqRealDiff__k6_xcmplx_0__rm1_r0_rm1,rqRealDiff__k6_xcmplx_0__rm1_r1_rm2,rqRealDiff__k6_xcmplx_0__rm1_rm2_r1,rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2,rqRealDiff__k6_xcmplx_0__rm2_r0_rm2,rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1,rqRealDiff__k6_xcmplx_0__rm2_rm2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2,rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2,rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0,rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1,rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2,rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1,rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0,rqRealDiv__k7_xcmplx_0__r0_r1_r0,rqRealDiv__k7_xcmplx_0__r0_r2_r0,rqRealDiv__k7_xcmplx_0__r1_r1_r1,rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2,rqRealDiv__k7_xcmplx_0__r1_rm1_rm1,rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2,rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2,rqRealDiv__k7_xcmplx_0__r2_r1_r2,rqRealDiv__k7_xcmplx_0__r2_r2_r1,rqRealDiv__k7_xcmplx_0__rm1_r1_rm1,rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2,rqRealMult__k3_xcmplx_0__r0_r0_r0,rqRealMult__k3_xcmplx_0__r0_r1_r0,rqRealMult__k3_xcmplx_0__r0_rm2_r0,rqRealMult__k3_xcmplx_0__r0_rn1d2_r0,rqRealMult__k3_xcmplx_0__r1_r0_r0,rqRealMult__k3_xcmplx_0__r1_rm2_rm2,rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2,rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2,rqRealMult__k3_xcmplx_0__r2_rn1d2_r1,rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_r0_r0,rqRealMult__k3_xcmplx_0__rm2_r1_rm2,rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1,rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1,rqRealMult__k3_xcmplx_0__rn1d2_r0_r0,rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2,rqRealMult__k3_xcmplx_0__rn1d2_r2_r1,rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1,rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1,rqRealNeg__k4_xcmplx_0__r0_r0,rqRealNeg__k4_xcmplx_0__rm1_r1,rqRealNeg__k4_xcmplx_0__rm2_r2,rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2,rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2,d6_vectsp_1,spc0_numerals,spc1_numerals,spc2_numerals,spc0_boole,spc1_boole,spc2_boole,e4_2__tdgroup,e1_2__tdgroup,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqRealNeg__k4_xcmplx_0__r2_rm2,rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2,rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1,rqRealNeg__k4_xcmplx_0__r1_rm1,rqRealDiff__k6_xcmplx_0__rm1_rm1_r0,rqRealDiff__k6_xcmplx_0__r0_r2_rm2,rqRealDiff__k6_xcmplx_0__r2_r1_r1,rqRealDiff__k6_xcmplx_0__r1_r1_r0,rqRealDiff__k6_xcmplx_0__r2_r2_r0,rqRealMult__k3_xcmplx_0__r2_r0_r0,rqRealMult__k3_xcmplx_0__r0_r2_r0]), [interesting(0.8),file(tdgroup,e5_2__tdgroup),[file(tdgroup,e5_2__tdgroup)]]). fof(i3_2__tdgroup,theorem,( $true ), introduced(tautology,[file(tdgroup,i3_2__tdgroup)]), [interesting(0.8),trivial,file(tdgroup,i3_2__tdgroup)]). fof(i2_2__tdgroup,plain,( c2_2__tdgroup = k1_rlvect_1(k1_vectsp_1) ), inference(conclusion,[status(thm),assumptions([e2_2__tdgroup,dt_c2_2__tdgroup])],[e5_2__tdgroup,i3_2__tdgroup]), [interesting(0.8),file(tdgroup,i2_2__tdgroup),[file(tdgroup,i2_2__tdgroup)]]). fof(i1_2__tdgroup,plain, ( k4_rlvect_1(k1_vectsp_1,c2_2__tdgroup,c2_2__tdgroup) = k1_rlvect_1(k1_vectsp_1) => c2_2__tdgroup = k1_rlvect_1(k1_vectsp_1) ), inference(discharge_asm,[status(thm),assumptions([dt_c2_2__tdgroup]),discharge_asm(discharge,[e2_2__tdgroup])],[e2_2__tdgroup,i2_2__tdgroup]), [interesting(0.8),file(tdgroup,i1_2__tdgroup),[file(tdgroup,i1_2__tdgroup)]]). fof(i1_2_tmp__tdgroup,plain, ( m1_subset_1(c2_2__tdgroup,u1_struct_0(k1_vectsp_1)) => ( k4_rlvect_1(k1_vectsp_1,c2_2__tdgroup,c2_2__tdgroup) = k1_rlvect_1(k1_vectsp_1) => c2_2__tdgroup = k1_rlvect_1(k1_vectsp_1) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c2_2__tdgroup])],[dt_c2_2__tdgroup,i1_2__tdgroup]), [interesting(1),t3_tdgroup]). fof(t3_tdgroup,theorem,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_vectsp_1)) => ( k4_rlvect_1(k1_vectsp_1,A,A) = k1_rlvect_1(k1_vectsp_1) => A = k1_rlvect_1(k1_vectsp_1) ) ) ), inference(let,[status(thm),assumptions([])],[i1_2_tmp__tdgroup,dh_c2_2__tdgroup]), [interesting(1),file(tdgroup,t3_tdgroup),[file(tdgroup,t3_tdgroup)]]).