% Mizar ND problem: t2_bintree2,bintree2,52,31 fof(dh_c1_2__bintree2,definition, ( ( ( ~ v1_xboole_0(c1_2__bintree2) & v1_trees_1(c1_2__bintree2) & v1_bintree1(c1_2__bintree2) ) => ! [A] : ( m1_trees_1(A,c1_2__bintree2) => m2_finseq_1(A,k6_margrel1) ) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v1_bintree1(B) ) => ! [C] : ( m1_trees_1(C,B) => m2_finseq_1(C,k6_margrel1) ) ) ), introduced(definition,[new_symbol(c1_2__bintree2),file(bintree2,c1_2__bintree2)]), [interesting(0.8),axiom,file(bintree2,c1_2__bintree2)]). fof(dh_c2_2__bintree2,definition, ( ( m1_trees_1(c2_2__bintree2,c1_2__bintree2) => m2_finseq_1(c2_2__bintree2,k6_margrel1) ) => ! [A] : ( m1_trees_1(A,c1_2__bintree2) => m2_finseq_1(A,k6_margrel1) ) ), introduced(definition,[new_symbol(c2_2__bintree2),file(bintree2,c2_2__bintree2)]), [interesting(0.8),axiom,file(bintree2,c2_2__bintree2)]). fof(rc3_trees_9,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & v1_trees_2(A) & v2_trees_9(A) ) ), file(trees_9,rc3_trees_9), [interesting(0.9),axiom,file(trees_9,rc3_trees_9)]). fof(cc3_trees_9,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v2_trees_9(A) ) ) ), file(trees_9,cc3_trees_9), [interesting(0.9),axiom,file(trees_9,cc3_trees_9)]). fof(cc3_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]). fof(cc6_xreal_0,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]). fof(cc8_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]). fof(rc1_margrel1,theorem,( ? [A] : v1_margrel1(A) ), file(margrel1,rc1_margrel1), [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]). fof(rc1_trees_2,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ), file(trees_2,rc1_trees_2), [interesting(0.9),axiom,file(trees_2,rc1_trees_2)]). fof(rc2_finset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]). fof(rc2_xreal_0,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc3_xreal_0,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]). fof(rc4_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_1)]). fof(rc4_xreal_0,theorem,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]). fof(rc5_trees_9,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(trees_9,rc5_trees_9), [interesting(0.9),axiom,file(trees_9,rc5_trees_9)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(rc6_trees_9,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(trees_9,rc6_trees_9), [interesting(0.9),axiom,file(trees_9,rc6_trees_9)]). 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_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(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). 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_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_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(cc1_bintree1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ) ), file(bintree1,cc1_bintree1), [interesting(0.9),axiom,file(bintree1,cc1_bintree1)]). 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(cc1_trees_9,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ) ), file(trees_9,cc1_trees_9), [interesting(0.9),axiom,file(trees_9,cc1_trees_9)]). fof(cc1_xreal_0,theorem,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]). fof(cc2_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]). fof(cc3_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]). fof(cc4_xreal_0,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]). fof(cc5_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]). fof(cc7_xreal_0,theorem,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]). fof(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). fof(fc1_margrel1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_margrel1(k1_xboole_0) ), file(margrel1,fc1_margrel1), [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]). fof(fc1_ordinal2,theorem, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), [interesting(0.9),axiom,file(ordinal2,fc1_ordinal2)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). fof(rc1_bintree1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & v1_bintree1(A) ) ), file(bintree1,rc1_bintree1), [interesting(0.9),axiom,file(bintree1,rc1_bintree1)]). fof(rc1_nat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]). fof(rc1_xreal_0,theorem,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]). fof(rc2_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). fof(rc2_margrel1,theorem,( ? [A] : v2_margrel1(A) ), file(margrel1,rc2_margrel1), [interesting(0.9),axiom,file(margrel1,rc2_margrel1)]). fof(rc2_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]). fof(rc3_nat_1,theorem,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), [interesting(0.9),axiom,file(nat_1,rc3_nat_1)]). fof(rc9_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), [interesting(0.9),axiom,file(trees_2,rc9_trees_2)]). 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(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(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(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_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_1(B,A) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_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_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(redefinition_m1_trees_1,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) <=> m1_subset_1(B,A) ) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_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_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). 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_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k5_numbers) ) ) ), file(trees_1,m1_trees_1), [interesting(0.9),axiom,file(trees_1,m1_trees_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_c1_2__bintree2,assumption, ( ~ v1_xboole_0(c1_2__bintree2) & v1_trees_1(c1_2__bintree2) & v1_bintree1(c1_2__bintree2) ), introduced(assumption,[file(bintree2,c1_2__bintree2)]), [interesting(0.8),axiom,file(bintree2,c1_2__bintree2)]). fof(cc1_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(cc1_margrel1,theorem,( ! [A] : ( m1_subset_1(A,k6_margrel1) => v2_margrel1(A) ) ), file(margrel1,cc1_margrel1), [interesting(0.9),axiom,file(margrel1,cc1_margrel1)]). fof(cc1_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(cc2_nat_1,theorem,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). 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(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(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(redefinition_m2_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(dt_k6_margrel1,axiom,( $true ), file(margrel1,k6_margrel1), [interesting(0.9),axiom,file(margrel1,k6_margrel1)]). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). fof(dt_c2_2__bintree2,assumption,( m1_trees_1(c2_2__bintree2,c1_2__bintree2) ), introduced(assumption,[file(bintree2,c2_2__bintree2)]), [interesting(0.8),axiom,file(bintree2,c2_2__bintree2)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(fc3_margrel1,theorem,( ~ v1_xboole_0(k6_margrel1) ), file(margrel1,fc3_margrel1), [interesting(0.9),axiom,file(margrel1,fc3_margrel1)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). 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(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_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). 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(redefinition_m2_finseq_2,definition,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(dt_k4_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), [interesting(0.9),axiom,file(finseq_2,k4_finseq_2)]). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), [interesting(0.9),axiom,file(finseq_1,k7_finseq_1)]). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(fc12_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]). fof(fc13_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc13_finseq_1)]). fof(fc14_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc14_finseq_1)]). fof(fc3_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]). fof(fc4_finseq_1,theorem,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]). 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(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(redefinition_k12_finseq_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(redefinition_k13_binarith,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k13_binarith(A,B) = k5_finseq_1(B) ) ), file(binarith,k13_binarith), [interesting(0.9),axiom,file(binarith,k13_binarith)]). fof(redefinition_k8_finseq_1,definition,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), [interesting(0.9),axiom,file(finseq_1,k12_finseq_1)]). fof(dt_k13_binarith,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k13_binarith(A,B),A,k4_finseq_2(1,A)) ) ), file(binarith,k13_binarith), [interesting(0.9),axiom,file(binarith,k13_binarith)]). fof(dt_k6_finseq_1,axiom,( ! [A] : ( v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A) ) ), file(finseq_1,k6_finseq_1), [interesting(0.9),axiom,file(finseq_1,k6_finseq_1)]). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), [interesting(0.9),axiom,file(finseq_1,k8_finseq_1)]). fof(s2_finseq_2__e4_2__bintree2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ( ( ( m1_trees_1(k6_finseq_1(k5_numbers),A) => r1_tarski(k2_relat_1(k6_finseq_1(k5_numbers)),k6_margrel1) ) & ! [B] : ( m2_finseq_1(B,k5_numbers) => ! [C] : ( m1_subset_1(C,k5_numbers) => ( ( m1_trees_1(B,A) => r1_tarski(k2_relat_1(B),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C)),A) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,B,k12_finseq_1(k5_numbers,C))),k6_margrel1) ) ) ) ) ) => ! [B] : ( m2_finseq_1(B,k5_numbers) => ( m1_trees_1(B,A) => r1_tarski(k2_relat_1(B),k6_margrel1) ) ) ) ) ), file(bintree2,s2_finseq_2__e4_2__bintree2), [interesting(0.9),axiom,file(bintree2,s2_finseq_2__e4_2__bintree2)]). fof(t27_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( A = k1_xboole_0 <=> k2_relat_1(A) = k1_xboole_0 ) ) ), file(finseq_1,t27_finseq_1), [interesting(0.9),axiom,file(finseq_1,t27_finseq_1)]). fof(e1_2__bintree2,plain,( k2_relat_1(k6_finseq_1(k5_numbers)) = k1_xboole_0 ), inference(mizar_by,[status(thm),assumptions([])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,rc9_trees_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc3_nat_1,rc4_finseq_1,rc5_trees_9,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t7_boole,t8_boole,redefinition_k5_numbers,dt_k1_xboole_0,dt_k2_relat_1,dt_k5_numbers,dt_k6_finseq_1,cc1_finseq_1,fc1_margrel1,fc2_finseq_1,rc1_finseq_1,t6_boole,t27_finseq_1]), [interesting(0.8),file(bintree2,e1_2__bintree2),[file(bintree2,e1_2__bintree2)]]). fof(t2_xboole_1,theorem,( ! [A] : r1_tarski(k1_xboole_0,A) ), file(xboole_1,t2_xboole_1), [interesting(0.9),axiom,file(xboole_1,t2_xboole_1)]). fof(e2_2__bintree2,plain, ( m1_trees_1(k6_finseq_1(k5_numbers),c1_2__bintree2) => r1_tarski(k2_relat_1(k6_finseq_1(k5_numbers)),k6_margrel1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_trees_9,rc3_xreal_0,rc4_xreal_0,rc9_trees_2,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finset_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,rc4_finseq_1,rc5_trees_9,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_1,cc1_bintree1,cc1_finseq_1,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc1_ordinal2,fc1_subset_1,rc1_bintree1,rc1_finseq_1,rc1_finset_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc4_finset_1,rc6_finseq_1,rc6_trees_9,rc7_finseq_1,rc8_finseq_1,t2_subset,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_trees_1,redefinition_k5_numbers,redefinition_m1_trees_1,dt_k1_xboole_0,dt_k2_relat_1,dt_k5_numbers,dt_k6_finseq_1,dt_k6_margrel1,dt_m1_trees_1,dt_c1_2__bintree2,fc1_margrel1,fc2_finseq_1,fc3_margrel1,t3_subset,t6_boole,e1_2__bintree2,t2_xboole_1]), [interesting(0.8),file(bintree2,e2_2__bintree2),[file(bintree2,e2_2__bintree2)]]). fof(dh_c1_2_1__bintree2,definition, ( ( m2_finseq_1(c1_2_1__bintree2,k5_numbers) => ! [A] : ( m1_subset_1(A,k5_numbers) => ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A))),k6_margrel1) ) ) ) ) => ! [B] : ( m2_finseq_1(B,k5_numbers) => ! [C] : ( m1_subset_1(C,k5_numbers) => ( ( m1_trees_1(B,c1_2__bintree2) => r1_tarski(k2_relat_1(B),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,B,k13_binarith(k5_numbers,C)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,B,k13_binarith(k5_numbers,C))),k6_margrel1) ) ) ) ) ), introduced(definition,[new_symbol(c1_2_1__bintree2),file(bintree2,c1_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,c1_2_1__bintree2)]). fof(dh_c2_2_1__bintree2,definition, ( ( m1_subset_1(c2_2_1__bintree2,k5_numbers) => ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ) ) ) => ! [A] : ( m1_subset_1(A,k5_numbers) => ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A))),k6_margrel1) ) ) ) ), introduced(definition,[new_symbol(c2_2_1__bintree2),file(bintree2,c2_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,c2_2_1__bintree2)]). fof(e1_2_1__bintree2,assumption, ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ), introduced(assumption,[file(bintree2,e1_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,e1_2_1__bintree2)]). fof(e2_2_1__bintree2,assumption,( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),c1_2__bintree2) ), introduced(assumption,[file(bintree2,e2_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,e2_2_1__bintree2)]). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). 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(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(fc9_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]). fof(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_c1_2_1__bintree2,assumption,( m2_finseq_1(c1_2_1__bintree2,k5_numbers) ), introduced(assumption,[file(bintree2,c1_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,c1_2_1__bintree2)]). fof(dt_c2_2_1__bintree2,assumption,( m1_subset_1(c2_2_1__bintree2,k5_numbers) ), introduced(assumption,[file(bintree2,c2_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,c2_2_1__bintree2)]). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), [interesting(0.9),axiom,file(tarski,k1_tarski)]). fof(fc1_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]). fof(fc2_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]). fof(redefinition_k6_domain_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), [interesting(0.9),axiom,file(domain_1,k6_domain_1)]). fof(dt_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), [interesting(0.9),axiom,file(domain_1,k6_domain_1)]). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(fc1_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]). fof(fc5_trees_2,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(trees_2,fc5_trees_2), [interesting(0.9),axiom,file(trees_2,fc5_trees_2)]). fof(redefinition_k2_finseq_1,definition,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(redefinition_k4_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(redefinition_k9_finseq_1,definition,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]). fof(t55_finseq_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k4_finseq_1(B) = k2_finseq_1(1) & k2_relat_1(B) = k1_tarski(A) ) ) ) ), file(finseq_1,t55_finseq_1), [interesting(0.9),axiom,file(finseq_1,t55_finseq_1)]). fof(e12_2_1__bintree2,plain,( k2_relat_1(k13_binarith(k5_numbers,c2_2_1__bintree2)) = k6_domain_1(k5_numbers,c2_2_1__bintree2) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc9_trees_2,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,cc2_xreal_0,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc1_xreal_0,cc2_finset_1,cc2_nat_1,cc3_nat_1,fc11_finseq_1,fc12_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_trees_2,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k13_binarith,redefinition_k2_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k9_finseq_1,dt_k13_binarith,dt_k1_tarski,dt_k2_finseq_1,dt_k2_relat_1,dt_k4_finseq_1,dt_k5_numbers,dt_k6_domain_1,dt_k9_finseq_1,dt_c2_2_1__bintree2,cc1_finseq_1,fc1_finset_1,fc2_subset_1,rc1_finseq_1,spc1_numerals,spc1_boole,t55_finseq_1]), [interesting(0.65),file(bintree2,e12_2_1__bintree2),[file(bintree2,e12_2_1__bintree2)]]). fof(dt_c1_2_1_1__bintree2,assumption,( $true ), introduced(assumption,[file(bintree2,c1_2_1_1__bintree2)]), [interesting(0.5),axiom,file(bintree2,c1_2_1_1__bintree2)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(dh_c1_2_1_1__bintree2,definition, ( ~ ( r2_hidden(c1_2_1_1__bintree2,k6_domain_1(k5_numbers,c2_2_1__bintree2)) & ~ r2_hidden(c1_2_1_1__bintree2,k6_margrel1) ) => ! [A] : ~ ( r2_hidden(A,k6_domain_1(k5_numbers,c2_2_1__bintree2)) & ~ r2_hidden(A,k6_margrel1) ) ), introduced(definition,[new_symbol(c1_2_1_1__bintree2),file(bintree2,c1_2_1_1__bintree2)]), [interesting(0.5),axiom,file(bintree2,c1_2_1_1__bintree2)]). fof(e1_2_1_1__bintree2,assumption,( r2_hidden(c1_2_1_1__bintree2,k6_domain_1(k5_numbers,c2_2_1__bintree2)) ), introduced(assumption,[file(bintree2,e1_2_1_1__bintree2)]), [interesting(0.5),axiom,file(bintree2,e1_2_1_1__bintree2)]). fof(t1_numerals,theorem,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), [interesting(0.9),axiom,file(numerals,t1_numerals)]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(commutativity_k7_domain_1,theorem,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k7_domain_1(A,B,C) = k7_domain_1(A,C,B) ) ), file(domain_1,k7_domain_1), [interesting(0.9),axiom,file(domain_1,k7_domain_1)]). fof(redefinition_k7_domain_1,definition,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k7_domain_1(A,B,C) = k2_tarski(B,C) ) ), file(domain_1,k7_domain_1), [interesting(0.9),axiom,file(domain_1,k7_domain_1)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k7_domain_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)) ) ), file(domain_1,k7_domain_1), [interesting(0.9),axiom,file(domain_1,k7_domain_1)]). fof(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(fc3_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). 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(spc0_boole,theorem,( v1_xboole_0(0) ), file(boole,spc0_boole), [interesting(0.9),axiom,file(boole,spc0_boole)]). fof(fc4_trees_9,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v2_trees_9(A) & m1_subset_1(B,A) ) => v1_finset_1(k1_trees_2(A,B)) ) ), file(trees_9,fc4_trees_9), [interesting(0.9),axiom,file(trees_9,fc4_trees_9)]). fof(fc1_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) & m1_subset_1(B,A) ) => v1_finset_1(k1_trees_2(A,B)) ) ), file(trees_2,fc1_trees_2), [interesting(0.9),axiom,file(trees_2,fc1_trees_2)]). fof(fc4_trees_2,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => v1_finset_1(k1_trees_2(A,B)) ) ), file(trees_2,fc4_trees_2), [interesting(0.9),axiom,file(trees_2,fc4_trees_2)]). fof(dt_k1_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => m1_subset_1(k1_trees_2(A,B),k1_zfmisc_1(A)) ) ), file(trees_2,k1_trees_2), [interesting(0.9),axiom,file(trees_2,k1_trees_2)]). fof(de_c3_2_1__bintree2,definition,( c3_2_1__bintree2 = c1_2_1__bintree2 ), introduced(definition,[new_symbol(c3_2_1__bintree2),file(bintree2,c3_2_1__bintree2)]), [interesting(0.65),axiom,file(bintree2,c3_2_1__bintree2)]). fof(t46_trees_1,theorem,( ! [A] : ( m2_finseq_1(A,k5_numbers) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(A,C),B) => r2_hidden(A,B) ) ) ) ) ), file(trees_1,t46_trees_1), [interesting(0.9),axiom,file(trees_1,t46_trees_1)]). fof(e3_2_1__bintree2,plain,( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[rc3_trees_9,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m1_relset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m2_subset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_bintree1,cc1_nat_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc1_margrel1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_bintree1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,spc1_boole,t2_subset,t3_subset,t4_subset,t5_subset,t8_boole,spc1_numerals,spc1_boole,antisymmetry_r2_hidden,existence_m1_trees_1,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,dt_k13_binarith,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_m2_finseq_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,cc1_finseq_1,cc1_finset_1,fc13_finseq_1,fc14_finseq_1,rc1_finseq_1,t1_subset,t6_boole,t7_boole,e2_2_1__bintree2,t46_trees_1]), [interesting(0.65),file(bintree2,e3_2_1__bintree2),[file(bintree2,e3_2_1__bintree2)]]). fof(dt_c3_2_1__bintree2,plain,( m1_trees_1(c3_2_1__bintree2,c1_2__bintree2) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_finseq_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc1_finseq_1,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_trees_9,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc1_margrel1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,rc1_bintree1,rc1_finset_1,rc1_nat_1,rc1_subset_1,rc1_trees_2,rc1_xreal_0,rc2_nat_1,rc2_subset_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_1,cc1_bintree1,cc1_finset_1,cc1_nat_1,cc2_nat_1,t2_subset,t6_boole,t7_boole,t8_boole,existence_m1_trees_1,redefinition_m1_trees_1,dt_m1_trees_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,de_c3_2_1__bintree2,e3_2_1__bintree2]), [interesting(0.65),file(bintree2,c3_2_1__bintree2),[file(bintree2,c3_2_1__bintree2)]]). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), [interesting(0.9),axiom,file(finseq_1,k13_finseq_1)]). fof(fc16_finseq_1,theorem,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc16_finseq_1)]). fof(fc9_finseq_1,theorem,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc9_finseq_1)]). fof(redefinition_k3_finseq_2,definition,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(redefinition_k3_lang1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_lang1(A,B) = k5_finseq_1(B) ) ), file(lang1,k3_lang1), [interesting(0.9),axiom,file(lang1,k3_lang1)]). fof(dt_k3_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k3_lang1(A,B),A,k3_finseq_2(A)) ) ), file(lang1,k3_lang1), [interesting(0.9),axiom,file(lang1,k3_lang1)]). fof(dt_k3_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)) ) ), file(trees_1,k3_trees_1), [interesting(0.9),axiom,file(trees_1,k3_trees_1)]). fof(t2_tarski,theorem,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), [interesting(0.9),axiom,file(tarski,t2_tarski)]). fof(fraenkel_a_2_0_bintree2,definition,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v1_bintree1(B) & m2_finseq_1(C,k5_numbers) ) => ( r2_hidden(A,a_2_0_bintree2(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k8_finseq_1(k5_numbers,C,k13_binarith(k5_numbers,D)) & r2_hidden(k8_finseq_1(k5_numbers,C,k13_binarith(k5_numbers,D)),B) ) ) ) ), file(bintree2,a_2_0_bintree2), [interesting(0.9),axiom,file(bintree2,a_2_0_bintree2)]). fof(fraenkel_a_2_1_trees_2,definition,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_trees_2(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)) & r2_hidden(k8_finseq_1(k5_numbers,C,k12_finseq_1(k5_numbers,D)),B) ) ) ) ), file(trees_2,a_2_1_trees_2), [interesting(0.9),axiom,file(trees_2,a_2_1_trees_2)]). fof(e4_2_1__bintree2,plain,( r2_hidden(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),a_2_0_bintree2(c1_2__bintree2,c1_2_1__bintree2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc3_trees_9,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc2_finseq_1,rc1_bintree1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_finset_1,rc3_nat_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_bintree1,cc1_finset_1,cc1_nat_1,cc2_nat_1,fc12_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_subset_1,rc2_subset_1,spc1_boole,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,spc1_numerals,spc1_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k13_binarith,dt_k5_numbers,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,t1_subset,t7_boole,t2_tarski,fraenkel_a_2_0_bintree2,e2_2_1__bintree2]), [interesting(0.65),file(bintree2,e4_2_1__bintree2),[file(bintree2,e4_2_1__bintree2)]]). fof(d5_trees_2,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => k1_trees_2(A,B) = a_2_1_trees_2(A,B) ) ) ), file(trees_2,d5_trees_2), [interesting(0.9),axiom,file(trees_2,d5_trees_2)]). fof(e5_2_1__bintree2,plain,( r2_hidden(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),k1_trees_2(c1_2__bintree2,c3_2_1__bintree2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,fc4_trees_9,rc2_finseq_1,rc3_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_trees_2,rc1_finseq_1,rc1_margrel1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k12_finseq_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k12_finseq_1,dt_k1_numbers,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_bintree1,cc1_nat_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc1_margrel1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_bintree1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,spc1_boole,t2_subset,t3_subset,t4_subset,t5_subset,spc1_numerals,spc1_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k13_binarith,dt_k1_trees_2,dt_k5_numbers,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,dt_c3_2_1__bintree2,de_c3_2_1__bintree2,cc1_finset_1,t1_subset,t6_boole,t7_boole,t8_boole,t2_tarski,fraenkel_a_2_0_bintree2,fraenkel_a_2_1_trees_2,e4_2_1__bintree2,d5_trees_2]), [interesting(0.65),file(bintree2,e5_2_1__bintree2),[file(bintree2,e5_2_1__bintree2)]]). fof(t5_bintree1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( k1_trees_2(A,B) = k1_xboole_0 <=> r2_hidden(B,k3_trees_1(A)) ) ) ) ), file(bintree1,t5_bintree1), [interesting(0.9),axiom,file(bintree1,t5_bintree1)]). fof(e6_2_1__bintree2,plain,( ~ r2_hidden(c1_2_1__bintree2,k3_trees_1(c1_2__bintree2)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,fc4_trees_9,rc2_finseq_1,rc3_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_m1_finseq_2,dt_m2_relset_1,dt_m2_subset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_trees_2,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,cc1_bintree1,cc1_finseq_1,cc1_nat_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_bintree1,rc1_finseq_1,rc1_finset_1,rc1_margrel1,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc4_finseq_1,rc4_finset_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc7_finseq_1,rc8_finseq_1,spc1_boole,t2_subset,t3_subset,t4_subset,t5_subset,spc1_numerals,spc1_boole,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k13_binarith,dt_k1_trees_2,dt_k1_xboole_0,dt_k3_trees_1,dt_k5_numbers,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,dt_c3_2_1__bintree2,de_c3_2_1__bintree2,cc1_finset_1,fc1_margrel1,fc2_finseq_1,t1_subset,t6_boole,t7_boole,t8_boole,e5_2_1__bintree2,t5_bintree1]), [interesting(0.65),file(bintree2,e6_2_1__bintree2),[file(bintree2,e6_2_1__bintree2)]]). fof(d2_bintree1,definition,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_bintree1(A) <=> ! [B] : ( m1_trees_1(B,A) => ( ~ r2_hidden(B,k3_trees_1(A)) => k1_trees_2(A,B) = k2_tarski(k7_finseq_1(B,k3_lang1(k1_numbers,0)),k7_finseq_1(B,k3_lang1(k1_numbers,1))) ) ) ) ) ), file(bintree1,d2_bintree1), [interesting(0.9),axiom,file(bintree1,d2_bintree1)]). fof(e7_2_1__bintree2,plain,( k1_trees_2(c1_2__bintree2,c3_2_1__bintree2) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k5_numbers)),k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,0)),k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_m1_relset_1,rc2_finseq_1,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc16_finseq_1,fc4_trees_9,fc9_finseq_1,rc1_margrel1,rc1_nat_1,rc1_xreal_0,rc2_finset_1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_trees_9,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_xboole_0,dt_k3_finseq_2,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finseq_1,cc1_nat_1,cc1_relset_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,cc3_trees_9,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc14_finset_1,fc1_margrel1,fc1_ordinal2,fc1_trees_2,fc2_finseq_1,fc3_finseq_1,fc4_finseq_1,fc4_trees_2,rc1_bintree1,rc1_finseq_1,rc1_finset_1,rc1_subset_1,rc1_trees_2,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,existence_m1_trees_1,redefinition_k13_binarith,redefinition_k3_lang1,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_1,dt_k13_binarith,dt_k1_numbers,dt_k1_trees_2,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_lang1,dt_k3_trees_1,dt_k5_numbers,dt_k7_domain_1,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c3_2_1__bintree2,de_c3_2_1__bintree2,cc1_bintree1,cc1_finset_1,fc1_subset_1,fc2_finset_1,fc3_subset_1,fc4_subset_1,spc0_boole,spc1_boole,t1_subset,t6_boole,t7_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e6_2_1__bintree2,d2_bintree1]), [interesting(0.65),file(bintree2,e7_2_1__bintree2),[file(bintree2,e7_2_1__bintree2)]]). fof(d2_tarski,definition,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), [interesting(0.9),axiom,file(tarski,d2_tarski)]). fof(e8_2_1__bintree2,plain, ( k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)) = k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,0)) | k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)) = k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_m1_relset_1,fc4_trees_9,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc3_trees_9,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc13_finseq_1,fc14_finseq_1,fc1_margrel1,fc1_trees_2,fc2_finseq_1,rc1_finseq_1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,rc7_finseq_1,rc8_finseq_1,existence_m1_finseq_1,existence_m1_subset_1,existence_m1_trees_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_bintree1,cc1_finset_1,cc1_nat_1,cc1_relset_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc14_finset_1,fc1_ordinal2,fc3_finseq_1,fc4_finseq_1,fc4_subset_1,fc4_trees_2,rc1_bintree1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k7_domain_1,redefinition_k8_finseq_1,dt_k13_binarith,dt_k1_trees_2,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k5_numbers,dt_k7_domain_1,dt_k8_finseq_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,dt_c3_2_1__bintree2,de_c3_2_1__bintree2,fc1_subset_1,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e7_2_1__bintree2,e5_2_1__bintree2,d2_tarski]), [interesting(0.65),file(bintree2,e8_2_1__bintree2),[file(bintree2,e8_2_1__bintree2)]]). fof(t20_finseq_2,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) => ( C = D & A = B ) ) ) ) ), file(finseq_2,t20_finseq_2), [interesting(0.9),axiom,file(finseq_2,t20_finseq_2)]). fof(e9_2_1__bintree2,plain, ( c2_2_1__bintree2 = 0 | c2_2_1__bintree2 = 1 ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc9_trees_2,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_k9_finseq_1,dt_k13_binarith,dt_k5_numbers,dt_k7_finseq_1,dt_k8_finseq_1,dt_k9_finseq_1,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,cc1_finseq_1,rc1_finseq_1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e8_2_1__bintree2,t20_finseq_2]), [interesting(0.65),file(bintree2,e9_2_1__bintree2),[file(bintree2,e9_2_1__bintree2)]]). fof(e10_2_1__bintree2,plain,( r2_hidden(c2_2_1__bintree2,k7_domain_1(k5_numbers,0,1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k7_domain_1,dt_k2_tarski,dt_k5_numbers,dt_k7_domain_1,dt_c2_2_1__bintree2,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e9_2_1__bintree2,d2_tarski]), [interesting(0.65),file(bintree2,e10_2_1__bintree2),[file(bintree2,e10_2_1__bintree2)]]). fof(d12_margrel1,definition,( k6_margrel1 = k2_tarski(0,1) ), file(margrel1,d12_margrel1), [interesting(0.9),axiom,file(margrel1,d12_margrel1)]). fof(d1_tarski,definition,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), [interesting(0.9),axiom,file(tarski,d1_tarski)]). fof(e2_2_1_1__bintree2,plain,( r2_hidden(c1_2_1_1__bintree2,k6_margrel1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2_1_1__bintree2,e1_2_1_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[cc1_finseq_1,rc1_finseq_1,rc1_margrel1,rc2_finset_1,rc3_finseq_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,dt_k1_xboole_0,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_margrel1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,existence_m1_subset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_subset_1,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,commutativity_k7_domain_1,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k7_domain_1,dt_k1_tarski,dt_k2_tarski,dt_k5_numbers,dt_k6_domain_1,dt_k6_margrel1,dt_k7_domain_1,dt_c1_2_1_1__bintree2,dt_c2_2_1__bintree2,fc1_finset_1,fc2_finset_1,fc2_subset_1,fc3_margrel1,fc3_subset_1,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_2_1_1__bintree2,e10_2_1__bintree2,d12_margrel1,d1_tarski]), [interesting(0.5),file(bintree2,e2_2_1_1__bintree2),[file(bintree2,e2_2_1_1__bintree2)]]). fof(i3_2_1_1__bintree2,theorem,( $true ), introduced(tautology,[file(bintree2,i3_2_1_1__bintree2)]), [interesting(0.5),trivial,file(bintree2,i3_2_1_1__bintree2)]). fof(i2_2_1_1__bintree2,plain,( r2_hidden(c1_2_1_1__bintree2,k6_margrel1) ), inference(conclusion,[status(thm),assumptions([dt_c1_2_1_1__bintree2,e1_2_1_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[e2_2_1_1__bintree2,i3_2_1_1__bintree2]), [interesting(0.5),file(bintree2,i2_2_1_1__bintree2),[file(bintree2,i2_2_1_1__bintree2)]]). fof(i1_2_1_1__bintree2,plain,( ~ ( r2_hidden(c1_2_1_1__bintree2,k6_domain_1(k5_numbers,c2_2_1__bintree2)) & ~ r2_hidden(c1_2_1_1__bintree2,k6_margrel1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2_1_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2]),discharge_asm(discharge,[e1_2_1_1__bintree2])],[e1_2_1_1__bintree2,i2_2_1_1__bintree2]), [interesting(0.5),file(bintree2,i1_2_1_1__bintree2),[file(bintree2,i1_2_1_1__bintree2)]]). fof(i1_2_1_1_tmp__bintree2,plain,( ~ ( r2_hidden(c1_2_1_1__bintree2,k6_domain_1(k5_numbers,c2_2_1__bintree2)) & ~ r2_hidden(c1_2_1_1__bintree2,k6_margrel1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2]),discharge_asm(discharge,[dt_c1_2_1_1__bintree2])],[dt_c1_2_1_1__bintree2,i1_2_1_1__bintree2]), [interesting(0.65),e11_2_1__bintree2]). fof(e11_2_1__bintree2,plain,( r1_tarski(k6_domain_1(k5_numbers,c2_2_1__bintree2),k6_margrel1) ), inference(let,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[i1_2_1_1_tmp__bintree2,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,rc1_finset_1,rc1_nat_1,rc1_xreal_0,rc2_margrel1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc2_nat_1,fc1_finset_1,fc1_ordinal2,fc1_subset_1,fc2_subset_1,rc1_subset_1,rc2_subset_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,redefinition_k5_numbers,redefinition_k6_domain_1,dt_k5_numbers,dt_k6_domain_1,dt_k6_margrel1,dt_c2_2_1__bintree2,fc3_margrel1,d3_tarski,dh_c1_2_1_1__bintree2]), [interesting(0.65),file(bintree2,e11_2_1__bintree2),[file(bintree2,e11_2_1__bintree2)]]). fof(t8_xboole_1,theorem,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(C,B) ) => r1_tarski(k2_xboole_0(A,C),B) ) ), file(xboole_1,t8_xboole_1), [interesting(0.9),axiom,file(xboole_1,t8_xboole_1)]). fof(e13_2_1__bintree2,plain,( r1_tarski(k2_xboole_0(k2_relat_1(c1_2_1__bintree2),k2_relat_1(k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ), inference(mizar_by,[status(thm),assumptions([e1_2_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[rc3_trees_9,existence_m1_finseq_2,existence_m1_relset_1,existence_m2_subset_1,redefinition_m2_subset_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m2_subset_1,cc1_relset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_margrel1,rc2_nat_1,rc2_xreal_0,rc3_finseq_1,rc3_nat_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,rc9_trees_2,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_bintree1,cc1_margrel1,cc1_nat_1,cc1_trees_9,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc12_finseq_1,fc1_finset_1,fc1_margrel1,fc1_ordinal2,fc1_subset_1,fc2_finseq_1,fc2_subset_1,fc3_finseq_1,fc4_finseq_1,fc9_finset_1,rc1_bintree1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,spc1_boole,t1_boole,t2_subset,t4_subset,t5_subset,spc1_numerals,spc1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_trees_1,existence_m2_finseq_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,dt_k13_binarith,dt_k2_relat_1,dt_k2_xboole_0,dt_k5_numbers,dt_k6_domain_1,dt_k6_margrel1,dt_k7_finseq_1,dt_k8_finseq_1,dt_m1_trees_1,dt_m2_finseq_1,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,cc1_finseq_1,cc1_finset_1,fc13_finseq_1,fc14_finseq_1,fc3_margrel1,rc1_finseq_1,t1_subset,t3_subset,t6_boole,t7_boole,t8_boole,e12_2_1__bintree2,e1_2_1__bintree2,e2_2_1__bintree2,e11_2_1__bintree2,t46_trees_1,t8_xboole_1]), [interesting(0.65),file(bintree2,e13_2_1__bintree2),[file(bintree2,e13_2_1__bintree2)]]). fof(t44_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ), file(finseq_1,t44_finseq_1), [interesting(0.9),axiom,file(finseq_1,t44_finseq_1)]). fof(e14_2_1__bintree2,plain,( r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ), inference(mizar_by,[status(thm),assumptions([e1_2_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_finset_1,fc4_subset_1,rc1_margrel1,rc2_finseq_1,rc2_finset_1,rc3_finseq_1,rc4_finseq_1,rc5_trees_9,rc6_finseq_1,rc9_trees_2,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_relset_1,existence_m2_subset_1,redefinition_m2_relset_1,redefinition_m2_subset_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_relset_1,dt_m2_subset_1,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,fc1_margrel1,fc2_finseq_1,rc1_nat_1,rc1_xreal_0,rc2_margrel1,rc2_nat_1,rc2_xreal_0,rc3_nat_1,rc3_xreal_0,rc4_xreal_0,t1_boole,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc9_finset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,spc1_boole,t2_subset,t6_boole,t7_boole,t8_boole,spc1_numerals,spc1_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,dt_k13_binarith,dt_k2_relat_1,dt_k2_xboole_0,dt_k5_numbers,dt_k6_margrel1,dt_k7_finseq_1,dt_k8_finseq_1,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,cc1_finseq_1,fc3_margrel1,rc1_finseq_1,t3_subset,e13_2_1__bintree2,t44_finseq_1]), [interesting(0.65),file(bintree2,e14_2_1__bintree2),[file(bintree2,e14_2_1__bintree2)]]). fof(i5_2_1__bintree2,theorem,( $true ), introduced(tautology,[file(bintree2,i5_2_1__bintree2)]), [interesting(0.65),trivial,file(bintree2,i5_2_1__bintree2)]). fof(i4_2_1__bintree2,plain,( r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ), inference(conclusion,[status(thm),assumptions([e1_2_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2,e2_2_1__bintree2])],[e14_2_1__bintree2,i5_2_1__bintree2]), [interesting(0.65),file(bintree2,i4_2_1__bintree2),[file(bintree2,i4_2_1__bintree2)]]). fof(i3_2_1__bintree2,plain, ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ), inference(discharge_asm,[status(thm),assumptions([e1_2_1__bintree2,dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2]),discharge_asm(discharge,[e2_2_1__bintree2])],[e2_2_1__bintree2,i4_2_1__bintree2]), [interesting(0.65),file(bintree2,i3_2_1__bintree2),[file(bintree2,i3_2_1__bintree2)]]). fof(i2_2_1__bintree2,plain, ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2,dt_c2_2_1__bintree2]),discharge_asm(discharge,[e1_2_1__bintree2])],[e1_2_1__bintree2,i3_2_1__bintree2]), [interesting(0.65),file(bintree2,i2_2_1__bintree2),[file(bintree2,i2_2_1__bintree2)]]). fof(i2_2_1_tmp__bintree2,plain, ( m1_subset_1(c2_2_1__bintree2,k5_numbers) => ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,c2_2_1__bintree2))),k6_margrel1) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2]),discharge_asm(discharge,[dt_c2_2_1__bintree2])],[dt_c2_2_1__bintree2,i2_2_1__bintree2]), [interesting(0.65),i1_2_1__bintree2]). fof(i1_2_1__bintree2,plain,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A))),k6_margrel1) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_2__bintree2,dt_c1_2_1__bintree2])],[i2_2_1_tmp__bintree2,dh_c2_2_1__bintree2]), [interesting(0.65),file(bintree2,i1_2_1__bintree2),[file(bintree2,i1_2_1__bintree2)]]). fof(i1_2_1_tmp__bintree2,plain, ( m2_finseq_1(c1_2_1__bintree2,k5_numbers) => ! [A] : ( m1_subset_1(A,k5_numbers) => ( ( m1_trees_1(c1_2_1__bintree2,c1_2__bintree2) => r1_tarski(k2_relat_1(c1_2_1__bintree2),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,c1_2_1__bintree2,k13_binarith(k5_numbers,A))),k6_margrel1) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bintree2]),discharge_asm(discharge,[dt_c1_2_1__bintree2])],[dt_c1_2_1__bintree2,i1_2_1__bintree2]), [interesting(0.8),e3_2__bintree2]). fof(e3_2__bintree2,plain,( ! [A] : ( m2_finseq_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k5_numbers) => ( ( m1_trees_1(A,c1_2__bintree2) => r1_tarski(k2_relat_1(A),k6_margrel1) ) => ( m1_trees_1(k8_finseq_1(k5_numbers,A,k13_binarith(k5_numbers,B)),c1_2__bintree2) => r1_tarski(k2_relat_1(k8_finseq_1(k5_numbers,A,k13_binarith(k5_numbers,B))),k6_margrel1) ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_2__bintree2])],[i1_2_1_tmp__bintree2,dh_c1_2_1__bintree2]), [interesting(0.8),file(bintree2,e3_2__bintree2),[file(bintree2,e3_2__bintree2)]]). fof(e4_2__bintree2,plain,( ! [A] : ( m2_finseq_1(A,k5_numbers) => ( m1_trees_1(A,c1_2__bintree2) => r1_tarski(k2_relat_1(A),k6_margrel1) ) ) ), inference(mizar_from,[status(thm),assumptions([dt_c1_2__bintree2])],[redefinition_m2_subset_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m2_subset_1,cc1_relset_1,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_trees_9,rc3_xreal_0,rc4_xreal_0,rc9_trees_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_finseq_1,dt_k5_ordinal2,dt_k7_finseq_1,dt_m1_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_finseq_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc11_finseq_1,fc12_finseq_1,fc13_finseq_1,fc14_finseq_1,fc1_ordinal2,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,rc1_bintree1,rc1_finseq_1,rc1_finset_1,rc1_nat_1,rc1_subset_1,rc1_trees_2,rc1_xreal_0,rc2_margrel1,rc2_nat_1,rc2_subset_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,spc1_numerals,spc1_boole,reflexivity_r1_tarski,redefinition_k12_finseq_1,redefinition_k13_binarith,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m1_trees_1,redefinition_m2_finseq_1,dt_k12_finseq_1,dt_k13_binarith,dt_k2_relat_1,dt_k5_numbers,dt_k6_finseq_1,dt_k6_margrel1,dt_k8_finseq_1,dt_m1_subset_1,dt_m1_trees_1,dt_m2_finseq_1,dt_c1_2__bintree2,cc1_bintree1,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc2_nat_1,fc3_margrel1,s2_finseq_2__e4_2__bintree2,e2_2__bintree2,e3_2__bintree2]), [interesting(0.8),file(bintree2,e4_2__bintree2),[file(bintree2,e4_2__bintree2)]]). fof(e5_2__bintree2,plain,( r1_tarski(k2_relat_1(c2_2__bintree2),k6_margrel1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bintree2,dt_c1_2__bintree2])],[cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_margrel1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_trees_9,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_finset_1,cc2_xreal_0,cc3_nat_1,cc3_trees_9,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc11_finseq_1,fc14_finset_1,fc1_margrel1,fc2_finseq_1,fc4_subset_1,rc1_bintree1,rc1_finset_1,rc1_nat_1,rc1_trees_2,rc1_xreal_0,rc2_finseq_1,rc2_margrel1,rc2_nat_1,rc3_finset_1,rc3_nat_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,rc9_trees_2,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc1_bintree1,cc1_finseq_1,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc2_nat_1,fc1_ordinal2,fc1_subset_1,rc1_finseq_1,rc1_subset_1,rc2_subset_1,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_m1_trees_1,existence_m2_finseq_1,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_finseq_1,dt_k2_relat_1,dt_k5_numbers,dt_k6_margrel1,dt_m1_trees_1,dt_m2_finseq_1,dt_c1_2__bintree2,dt_c2_2__bintree2,fc3_margrel1,t3_subset,e4_2__bintree2]), [interesting(0.8),file(bintree2,e5_2__bintree2),[file(bintree2,e5_2__bintree2)]]). fof(d4_finseq_1,definition,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_1), [interesting(0.9),axiom,file(finseq_1,d4_finseq_1)]). fof(e6_2__bintree2,plain,( m2_finseq_1(c2_2__bintree2,k6_margrel1) ), inference(mizar_by,[status(thm),assumptions([dt_c2_2__bintree2,dt_c1_2__bintree2])],[rc3_trees_9,cc3_trees_9,cc3_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_margrel1,rc1_trees_2,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc5_trees_9,rc6_finseq_1,rc6_trees_9,antisymmetry_r2_hidden,existence_m1_relset_1,dt_k1_numbers,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc1_bintree1,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc2_xreal_0,cc3_nat_1,cc4_xreal_0,cc5_xreal_0,cc7_xreal_0,fc14_finset_1,fc1_margrel1,fc1_ordinal2,fc2_finseq_1,fc4_subset_1,rc1_bintree1,rc1_nat_1,rc1_xreal_0,rc2_finseq_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,rc9_trees_2,t1_subset,t4_subset,t5_subset,t8_boole,existence_m1_subset_1,existence_m1_trees_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m1_trees_1,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m1_trees_1,dt_m2_relset_1,dt_c1_2__bintree2,cc1_finset_1,cc1_margrel1,cc1_nat_1,cc2_finset_1,cc2_nat_1,fc11_finseq_1,fc1_subset_1,rc1_finset_1,rc1_subset_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t7_boole,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k2_relat_1,dt_k6_margrel1,dt_m1_finseq_1,dt_m2_finseq_1,dt_c2_2__bintree2,cc1_finseq_1,fc3_margrel1,rc1_finseq_1,t3_subset,e5_2__bintree2,d4_finseq_1]), [interesting(0.8),file(bintree2,e6_2__bintree2),[file(bintree2,e6_2__bintree2)]]). fof(i3_2__bintree2,theorem,( $true ), introduced(tautology,[file(bintree2,i3_2__bintree2)]), [interesting(0.8),trivial,file(bintree2,i3_2__bintree2)]). fof(i2_2__bintree2,plain,( m2_finseq_1(c2_2__bintree2,k6_margrel1) ), inference(conclusion,[status(thm),assumptions([dt_c2_2__bintree2,dt_c1_2__bintree2])],[e6_2__bintree2,i3_2__bintree2]), [interesting(0.8),file(bintree2,i2_2__bintree2),[file(bintree2,i2_2__bintree2)]]). fof(i2_2_tmp__bintree2,plain, ( m1_trees_1(c2_2__bintree2,c1_2__bintree2) => m2_finseq_1(c2_2__bintree2,k6_margrel1) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__bintree2]),discharge_asm(discharge,[dt_c2_2__bintree2])],[dt_c2_2__bintree2,i2_2__bintree2]), [interesting(0.8),i1_2__bintree2]). fof(i1_2__bintree2,plain,( ! [A] : ( m1_trees_1(A,c1_2__bintree2) => m2_finseq_1(A,k6_margrel1) ) ), inference(let,[status(thm),assumptions([dt_c1_2__bintree2])],[i2_2_tmp__bintree2,dh_c2_2__bintree2]), [interesting(0.8),file(bintree2,i1_2__bintree2),[file(bintree2,i1_2__bintree2)]]). fof(i1_2_tmp__bintree2,plain, ( ( ~ v1_xboole_0(c1_2__bintree2) & v1_trees_1(c1_2__bintree2) & v1_bintree1(c1_2__bintree2) ) => ! [A] : ( m1_trees_1(A,c1_2__bintree2) => m2_finseq_1(A,k6_margrel1) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__bintree2])],[dt_c1_2__bintree2,i1_2__bintree2]), [interesting(1),t2_bintree2]). fof(t2_bintree2,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k6_margrel1) ) ) ), inference(let,[status(thm),assumptions([])],[i1_2_tmp__bintree2,dh_c1_2__bintree2]), [interesting(1),file(bintree2,t2_bintree2),[file(bintree2,t2_bintree2)]]).