7.01655644585 'hl/thm/Library/analysis/REAL_LE_LDIV_'#@#variant 'mat/le_times_to_le_div2'#@#variant
6.09617022101 'hl/thm/Library/analysis/LESS_OR_' 'mat/Zlt_to_Zle'
6.09617022101 'hl/thm/Library/floor/FLOOR_DOUBLE_/0'#@#variant 'mat/times_SSO_pred'#@#variant
5.09007087279 'hl/thm/Multivariate/vectors/MONOIDAL_VECTOR_ADD_'#@#variant 'mat/associative_append'
4.83110059916 'hl/thm/Multivariate/transcendentals/REAL_EXP_LE_X_'#@#variant 'mat/le_B_A'
4.30218188765 'hl/thm/Library/poly/POLY_MUL_'#@#variant 'mat/eq_times_f_times1'
4.1612835555 'hl/thm/real/REAL_LET_ADD2_' 'mat/le_to_lt_to_plus_lt'
4.03378572969 'hl/thm/Multivariate/transcendentals/RPOW_POS_LT_'#@#variant 'mat/lt_O_exp'#@#variant
3.47451390814 'hl/thm/realarith/REAL_LTE_TRANS_' 'mat/lt_to_le_to_lt'
3.47451390814 'hl/thm/realarith/REAL_LET_TRANS_' 'mat/le_to_lt_to_lt'
3.44174551012 'hl/thm/Multivariate/transcendentals/ATN_BOUNDS_/0'#@#variant 'mat/lt_O_S'
3.22073373277 'hl/thm/real/REAL_LT_RCANCEL_IMP_'#@#variant 'mat/lt_times_n_to_lt'#@#variant
3.12096266663 'hl/thm/Library/analysis/REAL_DOUBLE_'#@#variant 'mat/times_SSO_n'#@#variant
3.12096266663 'hl/thm/real/REAL_MUL_2_'#@#variant 'mat/times_SSO_n'#@#variant
2.90861238483 'hl/thm/real/REAL_LT_RMUL_'#@#variant 'mat/lt_times_l1'#@#variant
2.90861238483 'hl/thm/real/REAL_LT_LCANCEL_IMP_'#@#variant 'mat/lt_times_n_to_lt_r'#@#variant
2.90861238483 'hl/thm/real/REAL_LT_LCANCEL_IMP_'#@#variant 'mat/lt_times_to_lt'#@#variant
2.87372693634 'hl/thm/realarith/REAL_LT_IMP_LE_' 'mat/lt_to_le'
2.79300251124 'hl/thm/Multivariate/complexes/REAL_CX_'#@#variant 'mat/sieve_sorted'#@#variant
2.68919048646 'hl/thm/realarith/REAL_LT_REFL_' 'mat/Not_lt_n_n'
2.41555029958 'hl/thm/real/REAL_LT_IMP_NE_' 'mat/lt_to_not_eq'
2.41555029958 'hl/thm/real/REAL_LT_IMP_NE_' 'mat/eq_to_not_lt'
2.11894389269 'hl/thm/Library/floor/FLOOR_/1' 'mat/le_pred_n'
2.11894389269 'hl/thm/realarith/REAL_LTE_TOTAL_' 'mat/not_lt_to_le'
2.11894389269 'hl/thm/realarith/REAL_LET_TOTAL_' 'mat/not_le_to_lt'
2.11894389269 'hl/thm/real/REAL_LET_ANTISYM_' 'mat/le_to_not_lt'
2.11894389269 'hl/thm/realarith/REAL_LTE_ANTISYM_' 'mat/lt_to_not_le'
2.05559517358 'hl/thm/Library/analysis/REAL_LT_LMUL_IMP_'#@#variant 'mat/lt_times_r1'#@#variant
2.05559517358 'hl/thm/Library/floor/INT_OF_REAL_OF_INT_' 'mat/factorize_defactorize'
2.05559517358 'hl/thm/real/REAL_LT_LMUL_'#@#variant 'mat/lt_times_r1'#@#variant
2.05559517358 'hl/thm/int/int_abstr_' 'mat/factorize_defactorize'
1.97373573112 'hl/thm/real/REAL_ABS_LE_' 'mat/le_n_fact_n'
1.88373329496 'hl/thm/Library/transc/LN_POS_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
1.87966348598 'hl/thm/real/REAL_MIN_ACI_3' 'mat/gcd_n_n'
1.8091030762 'hl/thm/arith/ADD_CLAUSES_2' 'mat/Zplus_Zsucc'
1.78345550205 'hl/thm/arith/MULT_0_'#@#variant 'mat/Ztimes_z_OZ'
1.78345550205 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RZERO_'#@#variant 'mat/Qtimes_q_OQ'
1.71634398974 'hl/thm/realax/REAL_LE_LADD_IMP_' 'mat/le_plus_r'
1.71634398974 'hl/thm/real/REAL_LT_LADD_IMP_' 'mat/lt_plus_r'
1.71634398974 'hl/thm/arith/PRE_1' 'mat/Zpred_Zsucc'
1.53728713644 'hl/thm/real/REAL_ADD_RDISTRIB_' 'mat/times_plus_l'
1.53728713644 'hl/thm/arith/LEFT_ADD_DISTRIB_' 'mat/distr_Ztimes_Zplus'
1.53728713644 'hl/thm/arith/MULT_CLAUSES_2'#@#variant 'mat/Ztimes_Zone_l'
1.53728713644 'hl/thm/real/REAL_SUB_LDISTRIB_' 'mat/distr_times_minus'
1.53728713644 'hl/thm/real/REAL_SUB_RDISTRIB_' 'mat/times_minus_l'
1.53728713644 'hl/thm/Multivariate/transcendentals/RPOW_MUL_' 'mat/times_exp'
1.53728713644 'hl/thm/realax/REAL_ADD_LDISTRIB_' 'mat/distr_times_plus'
1.53728713644 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LID_'#@#variant 'mat/Qtimes_Qone_q'
1.51332021235 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/rtimes_Zplus'
1.51332021235 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/times_Qtimes'
1.51332021235 'hl/thm/int/int_mul_th_' 'mat/eq_times_fa_times'
1.38919896711 'hl/thm/calc_num/ARITH_16' 'mat/Zopp_Zplus'
1.38919896711 'hl/thm/Complex/complexnumbers/CNJ_MUL_' 'mat/Qinv_Qtimes\''
1.38311736374 'hl/thm/Multivariate/transcendentals/ATN_MONO_LT_' 'mat/ltS'
1.38311736374 'hl/thm/Library/floor/FLOOR_MONO_' 'mat/le_to_le_pred'
1.38311736374 'hl/thm/Multivariate/transcendentals/ATN_MONO_LT_' 'mat/lt_to_lt_S_S'
1.38311736374 'hl/thm/Library/floor/FLOOR_MONO_' 'mat/le_pred'
1.28735379879 'hl/thm/real/REAL_LT_ADD2_' 'mat/lt_plus'
1.28735379879 'hl/thm/real/REAL_LE_ADD2_' 'mat/le_plus'
1.18966870955 'hl/thm/nums/BIT0_DEF_0'#@#variant 'mat/eq_OZ_Zopp_OZ'
1.15251020848 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_Zplus'
1.15251020848 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_times'
1.15251020848 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_plus'
1.15251020848 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_Ztimes'
1.13491505986 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/prime_nth_prime'
1.13491505986 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
1.12413485674 'hl/thm/realarith/REAL_LT_TRANS_' 'mat/trans_lt'
1.12413485674 'hl/thm/realax/REAL_LE_TRANS_' 'mat/trans_le'
1.10877316137 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/Ztimes_Zone_r'
1.10877316137 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/Qtimes_q_Qone'
1.10877316137 'hl/thm/arith/ADD_0_'#@#variant 'mat/Zplus_z_OZ'
1.06591451017 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/Qinv_Qinv'
0.831683236191 'hl/thm/realax/REAL_MUL_ASSOC_' 'mat/assoc_times'
0.831683236191 'hl/thm/realax/REAL_ADD_ASSOC_' 'mat/assoc_plus'
0.831683236191 'hl/thm/calc_int/REAL_ADD_AC_1' 'mat/assoc_plus'
0.831683236191 'hl/thm/arith/ADD_ASSOC_' 'mat/assoc_Zplus'
0.831683236191 'hl/thm/real/REAL_MUL_AC_1' 'mat/assoc_times'
0.831683236191 'hl/thm/arith/MULT_ASSOC_' 'mat/assoc_Ztimes'
0.831683236191 'hl/thm/arith/MULT_AC_1' 'mat/assoc_Ztimes'
0.831683236191 'hl/thm/arith/ADD_AC_1' 'mat/assoc_Zplus'
0.749510172094 'hl/thm/arith/MULT_SYM_' 'mat/sym_Ztimes'
0.749510172094 'hl/thm/arith/ADD_AC_0' 'mat/sym_Zplus'
0.749510172094 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/sym_rtimes'
0.749510172094 'hl/thm/arith/ADD_SYM_' 'mat/sym_Zplus'
0.749510172094 'hl/thm/realax/REAL_MUL_SYM_' 'mat/sym_times'
0.749510172094 'hl/thm/real/REAL_MIN_ACI_0' 'mat/sym_gcd'
0.749510172094 'hl/thm/realax/REAL_ADD_SYM_' 'mat/sym_plus'
0.749510172094 'hl/thm/real/REAL_MUL_AC_0' 'mat/sym_times'
0.749510172094 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/sym_plus'
0.749510172094 'hl/thm/real/REAL_MIN_SYM_' 'mat/sym_gcd'
0.749510172094 'hl/thm/arith/MULT_AC_0' 'mat/sym_Ztimes'
0.749510172094 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/Library/analysis/LESS_MONO_ADD_' 'mat/le_plus_l'
0. 'hl/thm/Library/prime/DIVIDES_MUL2_' 'mat/le_plus'
0. 'hl/thm/int/int_sub_th_' 'mat/rtimes_Zplus'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/sym_times'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Library/analysis/LESS_MONO_ADD_' 'mat/le_times_l'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/sym_plus'
0. 'hl/thm/Library/transc/TAN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/arith/SUB_0_/0' 'mat/exp_SO_n'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Library/prime/DIVIDES_MUL_R_' 'mat/le_plus_l'
0. 'hl/thm/Library/transc/REAL_EXP_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/int/INT_MUL_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/realax/REAL_ADD_LINV_'#@#variant 'mat/minus_Sn_n'#@#variant
0. 'hl/thm/Library/pratt/PHI_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_1_STRONG_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_Qtimes'
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/times_fa_Qtimes'
0. 'hl/thm/int/int_of_num_' 'mat/numerator_nat_fact_to_fraction'
0. 'hl/thm/int/INT_MAX_ASSOC_' 'mat/andbA'
0. 'hl/thm/int/INT_MIN_MIN_/1' 'mat/divides_gcd_m'
0. 'hl/thm/int/INT_ADD_RINV_'#@#variant 'mat/Zplus_Zopp'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/andb_sym'
0. 'hl/thm/realax/REAL_MUL_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/realax/REAL_ADD_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/realax/HREAL_ADD_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/arith/BIT0_' 'mat/times_SSO_n'#@#variant
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/sym_times'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symm_orb'
0. 'hl/thm/Multivariate/transcendentals/COS_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/transc/COS_PI_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/SIN_PI2_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/rtimes_Zplus'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/int/INT_SUB_LDISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/Library/pratt/PHI_LIMIT_' 'mat/le_smallest_factor_n'
0. 'hl/thm/arith/MULT_0' 'mat/exp_SO_n'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/Library/transc/SQRT_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/int/INT_MIN_ACI_1' 'mat/assoc_Ztimes'
0. 'hl/thm/Library/poly/POLY_ADD_ASSOC_'#@#variant 'mat/andbA'
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/eq_times_fa_times'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/sym_Ztimes'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/andbC'
0. 'hl/thm/arith/MULT_CLAUSES_2'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/real/REAL_LE_LCANCEL_IMP_'#@#variant 'mat/lt_times_n_to_lt_r'#@#variant
0. 'hl/thm/arith/RIGHT_SUB_DISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/realax/HREAL_MUL_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/arith/MULT_AC_1' 'mat/assoc_plus'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetric_rtimes'
0. 'hl/thm/real/REAL_MIN_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_times'
0. 'hl/thm/realax/TREAL_MUL_WELLDEF_'#@#variant 'mat/lt_plus'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/sym_plus'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/andbC'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_TAU_' 'mat/monotonic_A'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/andbC'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/andbC'
0. 'hl/thm/Library/prime/DIVIDES_0_'#@#variant 'mat/divides_n_O'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetric_Qtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/andb_sym'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/sym_Ztimes'
0. 'hl/thm/realax/TREAL_LE_LADD_IMP_'#@#variant 'mat/le_plus_r'
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/int/int_min_th_' 'mat/eq_times_fa_times'
0. 'hl/thm/Multivariate/transcendentals/ASN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/arith/LE_1_4'#@#variant 'mat/bertrand_n'#@#variant
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/times_Qtimes'
0. 'hl/thm/realax/HREAL_ADD_AC_1' 'mat/andb_assoc'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_MONO_IMP_' 'mat/le_S_S'
0. 'hl/thm/arith/ADD_AC_1' 'mat/andbA'
0. 'hl/thm/arith/ONE_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/times_fa_Qtimes'
0. 'hl/thm/Multivariate/complexes/CNJ_MUL_'#@#variant 'mat/Zopp_Zplus'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/orb_sym'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetric_Ztimes'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/andbC'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_MONO_IMP_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/sym_gcd'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/realax/HREAL_LE_ADD_' 'mat/le_plus_n_r'
0. 'hl/thm/real/REAL_LT_LCANCEL_IMP_'#@#variant 'mat/lt_exp_to_lt'#@#variant
0. 'hl/thm/arith/SUB_0_/0'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/int/INT_ADD_LINV_'#@#variant 'mat/minus_Sn_n'#@#variant
0. 'hl/thm/int/INT_SGN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Library/analysis/LESS_SUC_REFL_' 'mat/le_n_Sn'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/lt_O_teta'#@#variant
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Library/calc_real/REAL_MONO_POW2_'#@#variant 'mat/lt_to_Zlt_pos_pos'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symm_andb'
0. 'hl/thm/int/INT_SUB_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/real/REAL_LT_LCANCEL_IMP_'#@#variant 'mat/le_exp_to_le'#@#variant
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symm_andb'
0. 'hl/thm/Library/transc/REAL_EXP_ADD_' 'mat/demorgan2'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/arith/DIV_LT_'#@#variant 'mat/eq_minus_n_m_O'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/andb_sym'
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/orb_sym'
0. 'hl/thm/real/REAL_MIN_ACI_1' 'mat/assoc_plus'
0. 'hl/thm/Multivariate/transcendentals/LOG_LT_X_'#@#variant 'mat/divides_smallest_factor_n'#@#variant
0. 'hl/thm/int/NUM_OF_INT_OF_NUM_' 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/orbC'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/lt_O_fact'#@#variant
0. 'hl/thm/arith/PRE_0' 'mat/A_SO'
0. 'hl/thm/Library/prime/DIVIDES_FACT_'#@#variant 'mat/divides_fact'#@#variant
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/sym_gcd'
0. 'hl/thm/Library/prime/PRIME_0_'#@#variant 'mat/not_prime_SO'#@#variant
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Library/prime/DIVIDES_MUL_L_' 'mat/lt_plus_r'
0. 'hl/thm/arith/EXP_MONO_LE_IMP_' 'mat/lt_plus_l'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/int/INT_MIN_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/eq_times_times_fa'
0. 'hl/thm/int/int_add_th_' 'mat/bool_to_nat_andb'
0. 'hl/thm/Complex/complex_transc/CEXP_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/realax/TREAL_LE_TRANS_'#@#variant 'mat/trans_lt'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/arith/FACT_MONO_' 'mat/ltS'
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/sym_gcd'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/orbC'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/real/REAL_INV_INV_' 'mat/Zopp_Zopp'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_1_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/int/int_max_th_' 'mat/eq_times_times_fa'
0. 'hl/thm/arith/LE_MULT2_' 'mat/divides_times'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/finv_finv'
0. 'hl/thm/real/REAL_LE_LMUL_'#@#variant 'mat/lt_exp'#@#variant
0. 'hl/thm/Library/transc/ATN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/transcendentals/REAL_TAN_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/andbC'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/bool_to_nat_andb'
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/eq_times_fa_times'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetricZPlus'
0. 'hl/thm/int/INT_ABS_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/bool_to_nat_andb'
0. 'hl/thm/arith/MULT_SYM_' 'mat/andb_sym'
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/eq_times_fa_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_1' 'mat/assoc_plus'
0. 'hl/thm/Library/pocklington/PHI_2_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/realax/NADD_ADD_WELLDEF_' 'mat/lt_times'
0. 'hl/thm/Library/transc/LN_POS_LT_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/Library/transc/LN_EXP_' 'mat/pred_Sn'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symm_andb'
0. 'hl/thm/realax/TREAL_NEG_WELLDEF_'#@#variant 'mat/le_to_le_pred'
0. 'hl/thm/realax/REAL_ADD_ASSOC_' 'mat/andbA'
0. 'hl/thm/real/REAL_ABS_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_ASSOC_'#@#variant 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/transcendentals/ASN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/opposite_direction_idempotent'
0. 'hl/thm/Multivariate/transcendentals/RPOW_DIV_' 'mat/times_minus_l'
0. 'hl/thm/arith/LEFT_SUB_DISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/arith/EXP_0'#@#variant 'mat/bc_n_O'#@#variant
0. 'hl/thm/Complex/complex_transc/CEXP_ADD_' 'mat/demorgan1'
0. 'hl/thm/Multivariate/transcendentals/COS_PI2_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Library/transc/EXP_LN_'#@#variant 'mat/S_pred'#@#variant
0. 'hl/thm/int/INT_MIN_ACI_1' 'mat/assoc_times'
0. 'hl/thm/int/INT_MIN_ACI_1' 'mat/andbA'
0. 'hl/thm/arith/LTE_CASES_' 'mat/not_le_to_lt'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/finv_finv'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/lt_O_S'#@#variant
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/arith/ADD_CLAUSES_2' 'mat/Zplus_Zpred'
0. 'hl/thm/arith/LT_MULT2_' 'mat/le_times'
0. 'hl/thm/realarith/REAL_LTE_TOTAL_' 'mat/not_le_to_lt'
0. 'hl/thm/Multivariate/transcendentals/CCOS_CACS_'#@#variant 'mat/Zpred_Zsucc'
0. 'hl/thm/int/INT_MUL_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/bool_to_nat_andb'
0. 'hl/thm/Library/analysis/LESS_SUC_' 'mat/ltW'
0. 'hl/thm/int/INT_MUL_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/int/int_add_th_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_PHI_' 'mat/monotonic_sqrt'#@#variant
0. 'hl/thm/Library/prime/INDEX_0_'#@#variant 'mat/Qtimes_q_OQ'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Multivariate/transcendentals/RPOW_INV_' 'mat/Zplus_Zsucc'
0. 'hl/thm/realax/NADD_LE_TRANS_' 'mat/trans_lt'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/eq_times_times_fa'
0. 'hl/thm/arith/EXP_0'#@#variant 'mat/exp_n_O0'#@#variant
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/eq_times_fa_times'
0. 'hl/thm/int/INT_MUL_AC_1' 'mat/andb_assoc'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_REFL_'#@#variant 'mat/bc_n_n'#@#variant
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/not_nf_elim_not/0'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_1_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/Library/pocklington/ORDER_1_'#@#variant 'mat/Qtimes_q_OQ'
0. 'hl/thm/int/INT_ABS_LE_' 'mat/lt_n_nth_prime_n'
0. 'hl/thm/Library/transc/REAL_EXP_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_POS_LE_'#@#variant 'mat/lt_O_exp'#@#variant
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/rtimes_Zplus'
0. 'hl/thm/arith/EXP_ONE_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/arith/LT_ADD2_' 'mat/le_plus'
0. 'hl/thm/Library/transc/SIN_PI_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetric_gcd'
0. 'hl/thm/Multivariate/transcendentals/LOG_POS_LT_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/Library/integer/INT_DIVIDES_1_'#@#variant 'mat/le_O_n'
0. 'hl/thm/Library/prime/DIVIDES_1_'#@#variant 'mat/divides_SO_n'#@#variant
0. 'hl/thm/real/REAL_MIN_ACI_1' 'mat/andb_assoc'
0. 'hl/thm/int/int_max_th_' 'mat/eq_times_fa_times'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetric_Qtimes'
0. 'hl/thm/int/int_min_th_' 'mat/times_Qtimes'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_times'
0. 'hl/thm/Library/floor/RATIONAL_INTEGER_' 'mat/bertrand_n'#@#variant
0. 'hl/thm/arith/TWO_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Multivariate/vectors/LIFT_DROP_0'#@#variant 'mat/factorize_defactorize'
0. 'hl/thm/int/INT_ADD_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/Zopp_Zopp'
0. 'hl/thm/Multivariate/transcendentals/RPOW_0_'#@#variant 'mat/bc_n_O'#@#variant
0. 'hl/thm/Multivariate/transcendentals/LOG_1_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetric_rtimes'
0. 'hl/thm/Library/prime/PRIME_1_'#@#variant 'mat/not_prime_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/CNJ_DIV_' 'mat/Zopp_Zplus'
0. 'hl/thm/real/REAL_MIN_ACI_3' 'mat/orb_refl'
0. 'hl/thm/Library/pocklington/ORDER_1_'#@#variant 'mat/Ztimes_z_OZ'
0. 'hl/thm/int/INT_SGN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/arith/ADD_SUC_' 'mat/plus_n_Sm'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/Zopp_Zopp'
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/arith/MOD_1_'#@#variant 'mat/exp_n_O0'#@#variant
0. 'hl/thm/int/int_abstr_' 'mat/defactorize_factorize'
0. 'hl/thm/Library/analysis/REAL_LT_LMUL_IMP_'#@#variant 'mat/le_log'#@#variant
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_2_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/real/REAL_MIN_ACI_1' 'mat/andbA'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/plus_n_O'
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/sym_rtimes'
0. 'hl/thm/Library/pocklington/PHI_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Complex/complexnumbers/complex_tybij_raw_0'#@#variant 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/arith/LEFT_ADD_DISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_1' 'mat/assoc_times'
0. 'hl/thm/arith/MULT_AC_0' 'mat/sym_plus'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/orb_sym'
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LE_'#@#variant 'mat/lt_times_r1'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/sym_gcd'
0. 'hl/thm/real/REAL_LET_ANTISYM_' 'mat/lt_to_not_le'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_MONO_IMP_' 'mat/le_pred'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_nat_gcd'
0. 'hl/thm/int/INT_MUL_LZERO_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetricZPlus'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_Ztimes'
0. 'hl/thm/arith/MULT_0_'#@#variant 'mat/times_n_O'
0. 'hl/thm/int/INT_NEG_LMUL_' 'mat/Zplus_Zpred'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/sym_plus'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/Multivariate/transcendentals/ARG_/0'#@#variant 'mat/sieve_sorted'#@#variant
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/orb_sym'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/andbC'
0. 'hl/thm/int/INT_MAX_ACI_1' 'mat/assoc_Ztimes'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_plus'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/andbC'
0. 'hl/thm/real/REAL_LT_LMUL_'#@#variant 'mat/le_exp'#@#variant
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_Ztimes'
0. 'hl/thm/Library/prime/EXP_EXP_' 'mat/eq_minus_minus_minus_plus'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/sym_plus'
0. 'hl/thm/realax/REAL_MUL_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/real/REAL_LT_ADD2_' 'mat/divides_times'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/andb_sym'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_NEG_' 'mat/eq_minus_S_pred'
0. 'hl/thm/Complex/complex_transc/CSIN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/notb_notb'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_rtimes'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/orbC'
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/times_fa_Qtimes'
0. 'hl/thm/Library/transc/SQRT_POS_LT_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/real/REAL_MAX_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/real/REAL_INV_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_1_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_0_'#@#variant 'mat/mod_SO'#@#variant
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/int/INT_MIN_ACI_1' 'mat/andb_assoc'
0. 'hl/thm/nums/NUM_REP_RULES_1' 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/times_fa_Qtimes'
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/times_Qtimes'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/arith/MULT_EXP_' 'mat/times_exp'
0. 'hl/thm/calc_int/REAL_MUL_LNEG_' 'mat/Zplus_Zsucc'
0. 'hl/thm/int/INT_ADD_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/calc_num/ARITH_98' 'mat/Zopp_Zplus'
0. 'hl/thm/Library/transc/SIN_PI2_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/realax/REAL_LE_TRANS_' 'mat/trans_lt'
0. 'hl/thm/real/REAL_MIN_MIN_/1' 'mat/divides_gcd_m'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_nat_gcd'
0. 'hl/thm/realax/TREAL_INV_WELLDEF_'#@#variant 'mat/lt_to_lt_S_S'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RDISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/sym_plus'
0. 'hl/thm/Library/floor/INT_OF_REAL_OF_INT_' 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/andbC'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetric_rtimes'
0. 'hl/thm/int/INT_MUL_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LT_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/Multivariate/transcendentals/ASN_NEG_1_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symm_orb'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Library/transc/ATN_BOUNDS_/0'#@#variant 'mat/le_SO_fact'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RZERO_'#@#variant 'mat/Ztimes_z_OZ'
0. 'hl/thm/int/INT_LE_TRANS_' 'mat/trans_lt'
0. 'hl/thm/Multivariate/misc/SQRT_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Multivariate/transcendentals/RPOW_MUL_' 'mat/times_plus_l'
0. 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/eq_times_times_fa'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/eq_times_times_fa'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/int/INT_MIN_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/eq_plus_Zplus'
0. 'hl/thm/arith/LEFT_SUB_DISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_2_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/arith/FACT_NZ_'#@#variant 'mat/not_eq_O_S'
0. 'hl/thm/Complex/complexnumbers/complex_tybij_1'#@#variant 'mat/defactorize_factorize'
0. 'hl/thm/realax/NADD_INV_WELLDEF_' 'mat/le_S_S'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/andbC'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetric_rtimes'
0. 'hl/thm/real/REAL_ABS_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/arith/LE_0_' 'mat/divides_SO_n'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/sym_times'
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/eq_times_times_fa'
0. 'hl/thm/Library/transc/ATN_MONO_LT_' 'mat/le_to_le_pred'
0. 'hl/thm/real/REAL_SUB_REFL_'#@#variant 'mat/minus_n_n'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetric_Ztimes'
0. 'hl/thm/Multivariate/transcendentals/REAL_INV_RPOW_' 'mat/Zplus_Zpred'
0. 'hl/thm/real/REAL_LE_LCANCEL_IMP_'#@#variant 'mat/lt_times_to_lt'#@#variant
0. 'hl/thm/calc_int/REAL_MUL_LNEG_' 'mat/Zplus_Zpred'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_TAU_' 'mat/injective_nth_prime'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_ASSOC_'#@#variant 'mat/andbA'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Library/floor/RATIONAL_INV_' 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/arith/LEFT_SUB_DISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/Library/transc/COS_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/int/INT_LE_RMUL_'#@#variant 'mat/lt_times_l1'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/sym_gcd'
0. 'hl/thm/int/int_max_th_' 'mat/times_Qtimes'
0. 'hl/thm/Multivariate/transcendentals/RPOW_DIV_' 'mat/times_exp'
0. 'hl/thm/Library/transc/COS_PI_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/int/int_mul_th_' 'mat/bool_to_nat_andb'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/sym_plus'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/calc_num/ARITH_30' 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/int/int_abstr_' 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/Complex/complexnumbers/CNJ_DIV_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/realax/HREAL_MUL_RZERO_'#@#variant 'mat/Ztimes_z_OZ'
0. 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/eq_times_fa_times'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/arith/LE_1_3'#@#variant 'mat/bertrand_n'#@#variant
0. 'hl/thm/arith/LT_0_' 'mat/lt_SO_nth_prime_n'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/arith/MULT_AC_0' 'mat/orb_sym'
0. 'hl/thm/Multivariate/transcendentals/ACS_1_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/calc_num/ARITH_20' 'mat/Zopp_Zplus'
0. 'hl/thm/real/REAL_LE_RCANCEL_IMP_'#@#variant 'mat/lt_exp_to_lt1'#@#variant
0. 'hl/thm/int/INT_ADD_AC_1' 'mat/assoc_plus'
0. 'hl/thm/int/INT_ABS_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_1'#@#variant 'mat/assoc_Zplus'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL_R_' 'mat/le_times_l'
0. 'hl/thm/calc_int/REAL_NEG_ADD_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/arith/MULT_0'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/arith/ADD_CLAUSES_0'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/calc_num/ARITH_10' 'mat/Zopp_Zplus'
0. 'hl/thm/arith/MULT_AC_1' 'mat/assoc_times'
0. 'hl/thm/realax/HREAL_ADD_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/sym_gcd'
0. 'hl/thm/int/int_sub_th_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Multivariate/transcendentals/TAN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_ASSOC_'#@#variant 'mat/assoc_plus'
0. 'hl/thm/arith/RIGHT_SUB_DISTRIB_' 'mat/times_exp'
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/notb_notb'
0. 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/eq_notb_notb_b_b'
0. 'hl/thm/realax/HREAL_LE_ADD2_' 'mat/lt_plus'
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/orbC'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/sym_plus'
0. 'hl/thm/arith/DIV_LT_'#@#variant 'mat/eq_div_O'
0. 'hl/thm/int/INT_LE_ADD2_' 'mat/lt_times'
0. 'hl/thm/Complex/complexnumbers/complex_tybij_raw_0'#@#variant 'mat/factorize_defactorize'
0. 'hl/thm/int/int_min_th_' 'mat/rtimes_Zplus'
0. 'hl/thm/arith/EXP_ONE_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_1' 'mat/assoc_plus'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_NZ_'#@#variant 'mat/not_eq_O_S'
0. 'hl/thm/Library/prime/DIVIDES_EXP_' 'mat/le_times_l'
0. 'hl/thm/Library/transc/ATN_TAN_' 'mat/Zsucc_Zpred'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Library/transc/SIN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/analysis/LESS_SUC_REFL_' 'mat/le_n_fact_n'
0. 'hl/thm/real/REAL_MAX_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/andbC'
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/plus_n_O'
0. 'hl/thm/real/REAL_ABS_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/int/INT_LE_ADD2_' 'mat/le_times'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_Zplus'
0. 'hl/thm/Library/floor/FLOOR_/1' 'mat/le_prim_n'
0. 'hl/thm/arith/LTE_TRANS_' 'mat/lt_to_le_to_lt'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/arith/LET_ANTISYM_' 'mat/lt_to_not_le'
0. 'hl/thm/arith/ADD_AC_1' 'mat/andb_assoc'
0. 'hl/thm/arith/ADD_AC_0' 'mat/orb_sym'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/sym_plus'
0. 'hl/thm/int/INT_ADD_RDISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/int/INT_LE_LADD_IMP_' 'mat/lt_plus_r'
0. 'hl/thm/int/INT_LTE_TOTAL_' 'mat/not_le_to_lt'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_MUL2_' 'mat/minus_S_S'
0. 'hl/thm/Multivariate/transcendentals/ATN_TAN_' 'mat/Zpred_Zsucc'
0. 'hl/thm/arith/MULT_CLAUSES_2'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/realax/TREAL_ADD_WELLDEFR_'#@#variant 'mat/le_plus_l'
0. 'hl/thm/realax/HREAL_ADD_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/Library/transc/REAL_EXP_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/real/REAL_ABS_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/int/INT_SUB_RDISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/arith/LEFT_ADD_DISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/Library/transc/COS_PI2_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/prime_nth_prime'
0. 'hl/thm/int/INT_ADD_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/sym_plus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/arith/LET_TRANS_' 'mat/le_to_lt_to_lt'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetric_rtimes'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_times'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/Qinv_Qinv'
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/int/INT_LET_TOTAL_' 'mat/not_lt_to_le'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LE_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_rtimes'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/arith/RIGHT_SUB_DISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/real/REAL_MIN_ASSOC_' 'mat/andbA'
0. 'hl/thm/arith/ADD_AC_1' 'mat/assoc_times'
0. 'hl/thm/realax/NADD_LE_TRANS_' 'mat/trans_divides'
0. 'hl/thm/Library/integer/INT_DIVIDES_TRANS_' 'mat/trans_le'
0. 'hl/thm/int/INT_ADD_AC_1' 'mat/andb_assoc'
0. 'hl/thm/realax/HREAL_ADD_LID_'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/int/INT_SUB_REFL_'#@#variant 'mat/bc_n_n'#@#variant
0. 'hl/thm/real/REAL_LE_INV_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/andb_sym'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Library/integer/INT_PRIME_1_'#@#variant 'mat/not_prime_O'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/arith/MULT_SYM_' 'mat/sym_plus'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_ASSOC_'#@#variant 'mat/assoc_Ztimes'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_TAU_' 'mat/injective_S'#@#variant
0. 'hl/thm/arith/SUB_0_/1' 'mat/times_n_SO'
0. 'hl/thm/arith/ADD_0_' 'mat/exp_n_SO'
0. 'hl/thm/realax/TREAL_INV_WELLDEF_'#@#variant 'mat/le_S_S'
0. 'hl/thm/real/REAL_LT_LADD_IMP_' 'mat/le_times_r'
0. 'hl/thm/int/INT_MAX_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/int/INT_MIN_ACI_1' 'mat/assoc_Zplus'
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/eq_plus_Zplus'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetric_times'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetric_Ztimes'
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LE_'#@#variant 'mat/le_log'#@#variant
0. 'hl/thm/int/INT_LT_IMP_NE_' 'mat/lt_to_not_eq'
0. 'hl/thm/real/REAL_MAX_ACI_1' 'mat/andbA'
0. 'hl/thm/Library/floor/INT_OF_REAL_OF_INT_' 'mat/defactorize_factorize'
0. 'hl/thm/realax/TREAL_LE_LADD_IMP_'#@#variant 'mat/le_times_r'
0. 'hl/thm/arith/MULT_SUC_' 'mat/times_n_Sm'
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/Library/analysis/LESS_SUC_REFL_' 'mat/lt_n_nth_prime_n'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/orb_sym'
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/orbC'
0. 'hl/thm/arith/PRE_0'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/realax/REAL_LE_LADD_IMP_' 'mat/le_times_r'
0. 'hl/thm/realax/REAL_INV_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/Complex/complex_transc/COMPLEX_II_NZ_'#@#variant 'mat/not_eq_true_false'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/nums/BIT0_DEF_0' 'mat/A_SO'
0. 'hl/thm/Multivariate/vectors/SQRT_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_1'#@#variant 'mat/andb_assoc'
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetric_rtimes'
0. 'hl/thm/Multivariate/transcendentals/REAL_ABS_RPOW_' 'mat/Zplus_Zsucc'
0. 'hl/thm/Multivariate/vectors/SQRT_POS_LE_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/arith/LT_ADD2_' 'mat/lt_times'
0. 'hl/thm/calc_int/REAL_NEG_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/arith/LT_TRANS_' 'mat/trans_divides'
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/int/INT_SUB_RDISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/orb_sym'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/sym_Ztimes'
0. 'hl/thm/arith/EXP_2_'#@#variant 'mat/exp_SSO'#@#variant
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Library/floor/INTEGER_CLOSED_6' 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/Library/floor/INTEGER_CLOSED_5' 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/real/REAL_MUL_AC_1' 'mat/andbA'
0. 'hl/thm/Library/integer/INT_DIVIDES_SUB_' 'mat/divides_plus'
0. 'hl/thm/Multivariate/transcendentals/REAL_SIN_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/arith/LT_MULT2_' 'mat/lt_times'
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_MUL_LID_'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_0_'#@#variant 'mat/exp_n_O0'#@#variant
0. 'hl/thm/int/INT_ABS_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/transc/REAL_EXP_LE_X_'#@#variant 'mat/le_S_times_SSO0'#@#variant
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/orbC'
0. 'hl/thm/Library/transc/REAL_EXP_LT_1_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/calc_num/ARITH_3'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/real/REAL_LE_RCANCEL_IMP_'#@#variant 'mat/lt_times_n_to_lt'#@#variant
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/sym_Zplus'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RINV_'#@#variant 'mat/Zplus_Zopp'
0. 'hl/thm/Library/transc/LN_1_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/andbC'
0. 'hl/thm/int/INT_MAX_ACI_1' 'mat/andb_assoc'
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/orbC'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/orb_sym'
0. 'hl/thm/Library/analysis/SUB_OLD_0' 'mat/gcd_SO_n'
0. 'hl/thm/int/INT_ADD_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/andbC'
0. 'hl/thm/Library/transc/SIN_PI_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/realax/NADD_EQ_REFL_' 'mat/divides_n_n'
0. 'hl/thm/int/int_max_th_' 'mat/rtimes_Zplus'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_ASSOC_'#@#variant 'mat/assoc_Zplus'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL2_' 'mat/lt_times'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/not_nf_elim_not/1'
0. 'hl/thm/real/REAL_LT_RMUL_'#@#variant 'mat/lt_exp1'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Complex/complexnumbers/complex_tybij_1'#@#variant 'mat/factorize_defactorize'
0. 'hl/thm/realax/HREAL_ADD_AC_1' 'mat/assoc_plus'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/int/INT_ABS_LE_' 'mat/le_n_Sn'
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Library/integer/INT_DIVIDES_ADD_' 'mat/divides_minus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_AC_1' 'mat/andbA'
0. 'hl/thm/arith/MULT_0'#@#variant 'mat/mod_O_n'
0. 'hl/thm/Multivariate/transcendentals/SIN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/Multivariate/transcendentals/ATN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/vectors/SQRT_POS_LE_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/Library/pocklington/PHI_LIMIT_' 'mat/le_sqrt_n_n'
0. 'hl/thm/realax/HREAL_INV_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/real/REAL_SUB_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/int/INT_MUL_LNEG_' 'mat/Zplus_Zpred'
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_ADD_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/int/INT_NEGNEG_' 'mat/finv_finv'
0. 'hl/thm/Multivariate/transcendentals/ASN_NEG_1_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Library/transc/SQRT_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_andb'
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/andb_sym'
0. 'hl/thm/Multivariate/transcendentals/LOG_MONO_LE_IMP_'#@#variant 'mat/lt_pred'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ACS_NEG_1_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/sym_gcd'
0. 'hl/thm/arith/SUB_0' 'mat/exp_n_SO'
0. 'hl/thm/Library/transc/COS_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/floor/FLOOR_MONO_' 'mat/ltS'
0. 'hl/thm/Multivariate/transcendentals/tan_' 'mat/eq_B1_times_B_split1_B_split2'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/arith/PRE_1' 'mat/Zsucc_Zpred'
0. 'hl/thm/realax/HREAL_MUL_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/wf/WF_num_' 'mat/antisymmetric_le'
0. 'hl/thm/Library/transc/ATN_MONO_LT_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/rtimes_Zplus'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/int/INT_MUL_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/sym_Zplus'
0. 'hl/thm/Library/analysis/REAL_INV_MUL_WEAK_'#@#variant 'mat/Qinv_Qtimes'
0. 'hl/thm/Library/analysis/DORDER_NGE_' 'mat/antisymmetric_divides'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/sym_plus'
0. 'hl/thm/Multivariate/transcendentals/ctan_'#@#variant 'mat/jj'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/Multivariate/transcendentals/TAN_PI_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/arith/LE_ADD_' 'mat/le_plus_n_r'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetric_Qtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/finv_finv'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_Zplus'
0. 'hl/thm/arith/LT_POW2_REFL_'#@#variant 'mat/le_n_Sn'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/arith/EXP_ONE_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/Library/transc/SQRT_MONO_LT_'#@#variant 'mat/lt_pred'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/eq_times_fa_times'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/sym_times'
0. 'hl/thm/int/INT_MUL_LZERO_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/arith/LT_0_' 'mat/le_SO_fact'
0. 'hl/thm/Library/prime/EXP_EXP_' 'mat/exp_exp_times'
0. 'hl/thm/realax/REAL_LE_REFL_' 'mat/divides_n_n'
0. 'hl/thm/Library/analysis/REAL_DIV_LZERO_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/Library/transc/tan_' 'mat/eq_B1_times_B_split1_B_split2'
0. 'hl/thm/Multivariate/transcendentals/LOG_POS_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/orb_sym'
0. 'hl/thm/Library/transc/SIN_PI2_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/sym_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/Multivariate/transcendentals/CSIN_CASN_'#@#variant 'mat/Zsucc_Zpred'
0. 'hl/thm/Library/analysis/REAL_INV_1OVER_'#@#variant 'mat/eq_A_A\''
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/andbC'
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/eq_times_times_fa'
0. 'hl/thm/Library/pratt/PHI_LIMIT_' 'mat/le_pred_n'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/arith/ADD_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/int/INT_LT_IMP_LE_' 'mat/lt_to_le'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetricIntPlus'
0. 'hl/thm/realax/REAL_ADD_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/Complex/complex_transc/CEXP_NONZERO_'#@#variant 'mat/not_eq_O_S'
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/sym_plus'
0. 'hl/thm/int/INT_LET_TRANS_' 'mat/le_to_lt_to_lt'
0. 'hl/thm/arith/ADD_SYM_' 'mat/orb_sym'
0. 'hl/thm/int/INT_ADD_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/Multivariate/transcendentals/SIN_PI_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/int/INT_MUL_AC_1' 'mat/assoc_times'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/int/INT_MIN_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/sym_gcd'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/Library/floor/RATIONAL_INTEGER_' 'mat/correct2'
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/times_fa_Qtimes'
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/times_Qtimes'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/sym_gcd'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/rinv_rinv'
0. 'hl/thm/Multivariate/transcendentals/SIN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LT_' 'mat/le_S_S'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_nat_gcd'
0. 'hl/thm/arith/SUB_REFL_'#@#variant 'mat/bc_n_n'#@#variant
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LT_' 'mat/le_pred'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/realarith/REAL_LET_TOTAL_' 'mat/not_lt_to_le'
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/rinv_rinv'
0. 'hl/thm/arith/ADD_AC_0' 'mat/sym_times'
0. 'hl/thm/int/INT_ADD_LINV_'#@#variant 'mat/orb_not_b_b'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/sym_plus'
0. 'hl/thm/realarith/REAL_POS_'#@#variant 'mat/sieve_sorted'#@#variant
0. 'hl/thm/realax/REAL_MUL_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/realax/TREAL_ADD_WELLDEF_'#@#variant 'mat/lt_plus'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetricIntPlus'
0. 'hl/thm/Multivariate/transcendentals/COS_PI_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/orbC'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/assoc_orb'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/orbC'
0. 'hl/thm/Library/transc/COS_PI_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/int/INT_LTE_TOTAL_' 'mat/not_lt_to_le'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_plus'
0. 'hl/thm/real/REAL_MIN_MIN_/0' 'mat/le_minus_m'
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/times_fa_Qtimes'
0. 'hl/thm/Multivariate/transcendentals/TAN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/int_sub_th_' 'mat/times_fa_Qtimes'
0. 'hl/thm/int/INT_LE_LADD_IMP_' 'mat/le_plus_r'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/andb_sym'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_nat_gcd'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/orb_sym'
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/sym_gcd'
0. 'hl/thm/real/REAL_LE_RMUL_'#@#variant 'mat/lt_times_l1'#@#variant
0. 'hl/thm/realax/REAL_ADD_LINV_'#@#variant 'mat/orb_not_b_b'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/opposite_direction_idempotent'
0. 'hl/thm/Library/pocklington/PHI_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LINV_'#@#variant 'mat/minus_Sn_n'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/andb_sym'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/andbC'
0. 'hl/thm/realax/TREAL_INV_WELLDEF_'#@#variant 'mat/le_to_le_pred'
0. 'hl/thm/arith/LE_REFL_' 'mat/divides_n_n'
0. 'hl/thm/arith/MULT_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/Library/analysis/SUB_OLD_0'#@#variant 'mat/mod_O_n'
0. 'hl/thm/Multivariate/transcendentals/EXP_LOG_'#@#variant 'mat/S_pred'#@#variant
0. 'hl/thm/int/INT_MUL_RZERO_'#@#variant 'mat/Qtimes_q_OQ'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/realax/REAL_ADD_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/int/INT_MAX_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/int/INT_LET_ANTISYM_' 'mat/lt_to_not_le'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_Qtimes'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/sym_times'
0. 'hl/thm/realax/NADD_EQ_TRANS_' 'mat/trans_le'
0. 'hl/thm/real/REAL_LE_LMUL_'#@#variant 'mat/lt_times_r1'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/sym_Ztimes'
0. 'hl/thm/arith/ADD_AC_1' 'mat/assoc_plus'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Library/transc/ATN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_MUL_'#@#variant 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/finv_finv'
0. 'hl/thm/arith/ADD_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/arith/EXP_MULT_' 'mat/exp_exp_times'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/bool_to_nat_andb'
0. 'hl/thm/Library/pocklington/PHI_2_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_MUL_'#@#variant 'mat/Qinv_Qtimes\''
0. 'hl/thm/arith/ADD_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetric_Qtimes'
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/minus_n_O'
0. 'hl/thm/calc_int/REAL_MUL_RZERO_'#@#variant 'mat/times_n_O'
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/sym_gcd'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/eq_plus_Zplus'
0. 'hl/thm/Library/prime/DIVIDES_ADD_' 'mat/divides_plus'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetric_Ztimes'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_TAU_' 'mat/monotonic_sqrt'#@#variant
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/andb_sym'
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/eq_times_times_fa'
0. 'hl/thm/Library/floor/RATIONAL_NEG_' 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/real/REAL_MIN_MIN_/1' 'mat/divides_gcd_nm/0'
0. 'hl/thm/arith/ADD_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/realarith/REAL_LE_SQUARE_'#@#variant 'mat/id_axiom'
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/sym_Ztimes'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL_R_' 'mat/le_plus_l'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/orbC'
0. 'hl/thm/realax/HREAL_MUL_ASSOC_' 'mat/andbA'
0. 'hl/thm/arith/MULT_AC_1' 'mat/andbA'
0. 'hl/thm/int/INT_NEGNEG_' 'mat/rinv_rinv'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/realax/REAL_MUL_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/Multivariate/misc/SQRT_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/real/REAL_SGN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/realax/HREAL_MUL_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/rinv_rinv'
0. 'hl/thm/Library/pocklington/PHI_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetric_Ztimes'
0. 'hl/thm/arith/LE_1_4'#@#variant 'mat/prime_to_lt_SO'#@#variant
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/orb_sym'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_Ztimes'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/sym_gcd'
0. 'hl/thm/int/INT_MIN_ACI_3' 'mat/gcd_n_n'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/andb_sym'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_plus'
0. 'hl/thm/Library/transc/COS_PI2_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/TAN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/andbC'
0. 'hl/thm/realax/REAL_ADD_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/arith/LT_ADD2_' 'mat/divides_times'
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/opposite_direction_idempotent'
0. 'hl/thm/int/INT_LT_ADD2_' 'mat/lt_plus'
0. 'hl/thm/Library/pratt/PHI_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_rtimes'
0. 'hl/thm/realax/HREAL_MUL_RZERO_'#@#variant 'mat/Qtimes_q_OQ'
0. 'hl/thm/int/INT_SUB_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetric_gcd'
0. 'hl/thm/real/REAL_ABS_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/orb_sym'
0. 'hl/thm/nums/BIT0_DEF_1' 'mat/times_SSO'#@#variant
0. 'hl/thm/Library/transc/REAL_EXP_SUB_' 'mat/demorgan1'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_rtimes'
0. 'hl/thm/arith/LE_TRANS_' 'mat/trans_le'
0. 'hl/thm/Multivariate/transcendentals/RPOW_INV_' 'mat/Zplus_Zpred'
0. 'hl/thm/arith/LT_IMP_LE_' 'mat/lt_to_le'
0. 'hl/thm/Multivariate/transcendentals/LOG_POS_LT_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/realax/TREAL_EQ_IMP_LE_'#@#variant 'mat/lt_to_le'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ACS_1_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ASN_1_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Complex/cpoly/POLY_DIVIDES_ADD_'#@#variant 'mat/divides_minus'
0. 'hl/thm/Multivariate/transcendentals/LOG_POS_LT_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/real/REAL_LE_LMUL_'#@#variant 'mat/le_exp'#@#variant
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LE_' 'mat/le_S_S'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LE_' 'mat/le_pred'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/Library/poly/POLY_ADD_ASSOC_'#@#variant 'mat/assoc_Ztimes'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_SIGMA_' 'mat/injective_nth_prime'#@#variant
0. 'hl/thm/realax/HREAL_ADD_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/realax/TREAL_LE_LADD_IMP_'#@#variant 'mat/lt_plus_r'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/andb_sym'
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/real/REAL_INV_INV_' 'mat/rinv_rinv'
0. 'hl/thm/arith/LET_CASES_' 'mat/not_lt_to_le'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL_L_' 'mat/le_times_r'
0. 'hl/thm/Multivariate/complexes/RE_CX_'#@#variant 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/Multivariate/complexes/CNJ_DIV_'#@#variant 'mat/Zopp_Zplus'
0. 'hl/thm/Library/prime/DIVIDES_TRANS_' 'mat/trans_le'
0. 'hl/thm/int/INT_POS_'#@#variant 'mat/sieve_sorted'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/sym_Zplus'
0. 'hl/thm/Library/transc/REAL_EXP_MONO_IMP_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetric_Qtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/Library/prime/INDEX_TRIVIAL_BOUND_' 'mat/divides_gcd_nm/0'
0. 'hl/thm/real/REAL_MAX_ASSOC_' 'mat/andbA'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/pocklington/PHI_LIMIT_' 'mat/le_smallest_factor_n'
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/sym_times'
0. 'hl/thm/Multivariate/transcendentals/REAL_ABS_PI_' 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/COS_PI_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_ASSOC_'#@#variant 'mat/andb_assoc'
0. 'hl/thm/calc_int/REAL_ADD_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/int/INT_MIN_MIN_/0' 'mat/divides_gcd_nm/1'
0. 'hl/thm/realax/TREAL_ADD_WELLDEF_'#@#variant 'mat/le_plus'
0. 'hl/thm/Library/prime/DIVIDES_MUL_R_' 'mat/le_times_l'
0. 'hl/thm/Library/prime/DIVIDES_MUL2_' 'mat/lt_times'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_LT_1_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/andb_sym'
0. 'hl/thm/Library/prime/DIVIDES_ADD_' 'mat/divides_minus'
0. 'hl/thm/realax/HREAL_ADD_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/arith/LT_MULT2_' 'mat/lt_plus'
0. 'hl/thm/Library/transc/SIN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/orb_sym'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Multivariate/transcendentals/SIN_PI_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/Library/prime/PRIME_DIVEXP_' 'mat/divides_exp_to_divides'
0. 'hl/thm/real/REAL_LT_LADD_IMP_' 'mat/le_plus_r'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Library/floor/FLOOR_/1' 'mat/le_sqrt_n_n'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/eq_plus_Zplus'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_rtimes'
0. 'hl/thm/arith/PRE_0'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Multivariate/transcendentals/RPOW_ONE_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/Library/prime/PRIME_0_' 'mat/not_prime_SO'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ATN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/int_add_th_' 'mat/eq_times_fa_times'
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/rtimes_Zplus'
0. 'hl/thm/Multivariate/transcendentals/ACS_NEG_1_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/sym_gcd'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/Library/pocklington/PHI_LIMIT_' 'mat/le_prim_n'
0. 'hl/thm/Multivariate/transcendentals/ACS_1_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ASN_1_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/rtimes_Zplus'
0. 'hl/thm/Multivariate/transcendentals/ATN_BOUNDS_/0'#@#variant 'mat/lt_O_fact'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_Ztimes'
0. 'hl/thm/Library/prime/DIVIDES_TRANS_' 'mat/trans_divides'
0. 'hl/thm/int/INT_ADD_LID_'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/Multivariate/transcendentals/REAL_COS_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/calc_num/ARITH_7' 'mat/A_SO'#@#variant
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/calc_num/ARITH_1' 'mat/A_SO'#@#variant
0. 'hl/thm/arith/FACT_MONO_' 'mat/le_S_S'
0. 'hl/thm/Library/prime/DIVIDES_MUL2_' 'mat/le_times'
0. 'hl/thm/int/INT_ADD_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/arith/ADD_SYM_' 'mat/sym_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/sym_plus'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetric_times'
0. 'hl/thm/Library/integer/INT_DIVIDES_TRANS_' 'mat/trans_divides'
0. 'hl/thm/arith/EXP_MULT_' 'mat/eq_minus_minus_minus_plus'
0. 'hl/thm/Multivariate/transcendentals/tan_' 'mat/jj'
0. 'hl/thm/arith/MULT_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RDISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/sym_times'
0. 'hl/thm/realax/NADD_LE_RMUL_' 'mat/lt_plus_l'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/andb_sym'
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/eq_times_fa_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/orb_sym'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/orb_sym'
0. 'hl/thm/Library/pratt/PHI_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetric_rtimes'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetric_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/int/INT_MUL_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/realax/HREAL_INV_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/transc/SIN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Library/transc/SQRT_POS_LE_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/int/INT_ADD_AC_1' 'mat/assoc_times'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/int/INT_LE_LMUL_'#@#variant 'mat/lt_exp'#@#variant
0. 'hl/thm/Library/pocklington/PHI_2_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/arith/LTE_ANTISYM_' 'mat/le_to_not_lt'
0. 'hl/thm/Library/transc/SQRT_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/notb_notb'
0. 'hl/thm/Library/transc/SQRT_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/realax/NADD_ADD_LCANCEL_' 'mat/le_plus_to_le'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/int/INT_NEG_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetricZPlus'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/rtimes_Zplus'
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/eq_times_times_fa'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/sym_gcd'
0. 'hl/thm/Multivariate/complexes/CNJ_MUL_'#@#variant 'mat/Qinv_Qtimes\''
0. 'hl/thm/int/INT_NEGNEG_' 'mat/eq_notb_notb_b_b'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ATN_BOUNDS_/0'#@#variant 'mat/lt_O_nth_prime_n'
0. 'hl/thm/realax/NADD_EQ_IMP_LE_' 'mat/lt_to_le'
0. 'hl/thm/int/INT_MIN_ACI_1' 'mat/assoc_plus'
0. 'hl/thm/real/REAL_SGN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/analysis/LESS_EQ_SUC_REFL_' 'mat/le_n_Sn'
0. 'hl/thm/arith/MULT_0' 'mat/gcd_SO_n'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/sym_gcd'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/andb_sym'
0. 'hl/thm/realax/HREAL_ADD_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_times'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/orb_sym'
0. 'hl/thm/Library/prime/LESS_MONO_ADD_' 'mat/le_plus_l'
0. 'hl/thm/arith/SUB_1' 'mat/eq_minus_S_pred'
0. 'hl/thm/arith/ADD_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/vectors/LIFT_DROP_1'#@#variant 'mat/defactorize_factorize'
0. 'hl/thm/Multivariate/transcendentals/ATN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/int/INT_LE_TRANS_' 'mat/trans_le'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL_R_' 'mat/lt_plus_l'
0. 'hl/thm/Multivariate/transcendentals/CSIN_CASN_'#@#variant 'mat/pred_Sn'
0. 'hl/thm/real/REAL_MAX_ACI_3' 'mat/gcd_n_n'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetric_times'
0. 'hl/thm/Library/transc/LN_POS_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetricZPlus'
0. 'hl/thm/arith/LE_TRANS_' 'mat/trans_lt'
0. 'hl/thm/realax/NADD_INV_WELLDEF_' 'mat/le_pred'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/arith/LE_MULT2_' 'mat/le_plus'
0. 'hl/thm/real/REAL_LE_RCANCEL_IMP_'#@#variant 'mat/le_exp_to_le1'#@#variant
0. 'hl/thm/Library/analysis/LESS_EQ_SUC_REFL_' 'mat/lt_n_nth_prime_n'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_SIGMA_' 'mat/monotonic_A'#@#variant
0. 'hl/thm/real/REAL_SGN_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Complex/cpoly/POLY_DIVIDES_REFL_'#@#variant 'mat/divides_n_n'
0. 'hl/thm/lists/APPEND_1' 'mat/cons_append_commute'
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/sym_gcd'
0. 'hl/thm/Complex/cpoly/POLY_DIVIDES_TRANS_'#@#variant 'mat/trans_divides'
0. 'hl/thm/arith/ADD1_'#@#variant 'mat/plus_n_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/andb_sym'
0. 'hl/thm/arith/LE_MULT2_' 'mat/le_times'
0. 'hl/thm/Library/floor/RATIONAL_ABS_' 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Multivariate/complexes/RE_CX_'#@#variant 'mat/factorize_defactorize'
0. 'hl/thm/int/int_min_th_' 'mat/eq_times_times_fa'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_andb'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LE_'#@#variant 'mat/le_exp'#@#variant
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/times_Qtimes'
0. 'hl/thm/arith/FACT_0'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/CNJ_ADD_' 'mat/Zopp_Zplus'
0. 'hl/thm/Library/prime/DIVIDES_1_'#@#variant 'mat/le_O_n'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_ASSOC_'#@#variant 'mat/assoc_times'
0. 'hl/thm/arith/MULT_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/transcendentals/SIN_PI2_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/real/REAL_SGN_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/SIN_PI_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/sym_Zplus'
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/int/int_add_th_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_MAX_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/int/INT_SUB_ADD_' 'mat/minus_plus_m_m'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Library/transc/REAL_EXP_SUB_' 'mat/demorgan2'
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_2_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/Multivariate/transcendentals/COS_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/realax/REAL_ADD_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/int/INT_NEG_ADD_' 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RINV_'#@#variant 'mat/rtimes_rinv'
0. 'hl/thm/real/REAL_LT_LMUL_'#@#variant 'mat/lt_exp'#@#variant
0. 'hl/thm/int/INT_LT_ADD2_' 'mat/lt_times'
0. 'hl/thm/realax/NADD_LE_ADD_' 'mat/le_plus_n_r'
0. 'hl/thm/calc_num/ARITH_3'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/int/int_mul_th_' 'mat/eq_times_times_fa'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/times_fa_Qtimes'
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/rtimes_Zplus'
0. 'hl/thm/int/INT_ADD_LDISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/real/REAL_MAX_ACI_1' 'mat/assoc_Zplus'
0. 'hl/thm/real/REAL_LE_ADD2_' 'mat/lt_plus'
0. 'hl/thm/Multivariate/vectors/SQRT_DIV_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/orbC'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/andb_sym'
0. 'hl/thm/Complex/complex_transc/CCOS_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/arith/LTE_CASES_' 'mat/not_lt_to_le'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/real/REAL_ABS_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_TAN_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Library/prime/DIVIDES_MUL2_' 'mat/lt_plus'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/andb_sym'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LT_'#@#variant 'mat/lt_times_r1'#@#variant
0. 'hl/thm/Multivariate/complexes/REAL_INV_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/andbC'
0. 'hl/thm/arith/LE_1_3'#@#variant 'mat/prime_to_lt_SO'#@#variant
0. 'hl/thm/Library/analysis/SUB_OLD_0'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/arith/SUB_REFL_' 'mat/bc_n_n'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/arith/EVEN_OR_ODD_' 'mat/not_not_bertrand_to_bertrand'
0. 'hl/thm/realax/TREAL_ADD_WELLDEF_'#@#variant 'mat/le_times'
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/eq_times_fa_times'
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/rtimes_Zplus'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/assoc_orb'
0. 'hl/thm/realax/HREAL_MUL_LZERO_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/real/REAL_INV_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/arith/LE_ADDR_' 'mat/le_plus_n'
0. 'hl/thm/Library/floor/FLOOR_MONO_' 'mat/le_S_S'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/times_fa_Qtimes'
0. 'hl/thm/int/INT_LE_LMUL_'#@#variant 'mat/le_exp'#@#variant
0. 'hl/thm/Library/transc/SQRT_POS_LE_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/real/REAL_ADD_RDISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/Library/pocklington/EVEN_PHI_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/arith/LE_0_'#@#variant 'mat/divides_SO_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/times_Qtimes'
0. 'hl/thm/Multivariate/misc/SQRT_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/real/REAL_MAX_MAX_/1' 'mat/le_plus_n'
0. 'hl/thm/int/INT_ADD_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/int/int_min_th_' 'mat/times_fa_Qtimes'
0. 'hl/thm/int/INT_MIN_ACI_3' 'mat/orb_refl'
0. 'hl/thm/int/INT_NEG_RMUL_' 'mat/plus_n_Sm'
0. 'hl/thm/Library/prime/PRIME_GE_2_'#@#variant 'mat/prime_to_lt_SO'#@#variant
0. 'hl/thm/Complex/complex_transc/CEXP_SUB_' 'mat/demorgan1'
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/arith/LT_ADD2_' 'mat/lt_plus'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/real/REAL_INV_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/eq_times_times_fa'
0. 'hl/thm/realax/REAL_ADD_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/real/REAL_LE_ADD2_' 'mat/le_times'
0. 'hl/thm/arith/MULT_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/orbC'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/andb_sym'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LDISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/times_Qtimes'
0. 'hl/thm/Library/poly/POLY_DIVIDES_ADD_'#@#variant 'mat/divides_minus'
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/orb_sym'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/sym_times'
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/andb_sym'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/assoc_orb'
0. 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/bool_to_nat_andb'
0. 'hl/thm/real/REAL_ABS_LE_' 'mat/lt_n_nth_prime_n'
0. 'hl/thm/Library/transc/REAL_EXP_MONO_IMP_' 'mat/ltS'
0. 'hl/thm/int/INT_MUL_AC_1' 'mat/assoc_plus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_LDISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/real/REAL_LE_POW2_'#@#variant 'mat/sieve_sorted'#@#variant
0. 'hl/thm/arith/ADD_ASSOC_' 'mat/andbA'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetric_Qtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/realax/HREAL_LE_ADD2_' 'mat/lt_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_LMUL_' 'mat/Zplus_Zsucc'
0. 'hl/thm/real/REAL_MAX_ACI_1' 'mat/assoc_times'
0. 'hl/thm/Library/pocklington/ORDER_1_'#@#variant 'mat/times_n_O'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/rinv_rinv'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_Qtimes'
0. 'hl/thm/Library/pocklington/PHI_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetricIntPlus'
0. 'hl/thm/realax/REAL_MUL_LID_'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/Complex/complexnumbers/CNJ_ADD_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/sym_Ztimes'
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/rtimes_Zplus'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL2_' 'mat/le_plus'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_' 'mat/le_times'
0. 'hl/thm/Multivariate/transcendentals/COS_PI2_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/prime/DIVIDES_EXP_' 'mat/lt_plus_l'
0. 'hl/thm/realax/NADD_LE_RMUL_' 'mat/le_plus_l'
0. 'hl/thm/Multivariate/transcendentals/RPOW_ONE_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL2_' 'mat/le_times'
0. 'hl/thm/real/REAL_MIN_ACI_1' 'mat/assoc_Ztimes'
0. 'hl/thm/int/INT_LE_REFL_' 'mat/divides_n_n'
0. 'hl/thm/Library/integer/INT_PRIME_1_'#@#variant 'mat/not_prime_SO'#@#variant
0. 'hl/thm/Multivariate/complexes/REAL_IMP_CNJ_'#@#variant 'mat/prime_to_smallest_factor'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/notb_notb'
0. 'hl/thm/realax/HREAL_MUL_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/arith/LE_1_4'#@#variant 'mat/correct2'
0. 'hl/thm/Complex/cpoly/POLY_MUL_'#@#variant 'mat/eq_times_f_times1'
0. 'hl/thm/Library/prime/INDEX_1_'#@#variant 'mat/exp_n_O0'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ATN_MONO_LT_' 'mat/le_S_S'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/realax/NADD_LE_LMUL_' 'mat/lt_plus_r'
0. 'hl/thm/calc_int/REAL_MUL_RZERO_'#@#variant 'mat/Ztimes_z_OZ'
0. 'hl/thm/int/INT_LT_TRANS_' 'mat/trans_le'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/orb_sym'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/sym_times'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/eq_notb_notb_b_b'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/int/INT_ADD_ASSOC_' 'mat/andbA'
0. 'hl/thm/Library/transc/LN_EXP_' 'mat/Zsucc_Zpred'
0. 'hl/thm/arith/ADD_0_' 'mat/times_n_SO'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL_L_' 'mat/le_plus_r'
0. 'hl/thm/arith/ADD_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/arith/LT_TRANS_' 'mat/trans_lt'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/sym_gcd'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/int/INT_NEG_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/arith/LT_MULT2_' 'mat/le_plus'
0. 'hl/thm/nums/BIT0_DEF_0'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/int/INT_MUL_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetric_gcd'
0. 'hl/thm/real/REAL_LT_INV_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/arith/FACT_LT_' 'mat/lt_SO_nth_prime_n'
0. 'hl/thm/Library/prime/DIVIDES_EXP_' 'mat/le_plus_l'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/calc_int/REAL_ADD_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_ADD_' 'mat/demorgan1'
0. 'hl/thm/int/NUM_OF_INT_OF_NUM_' 'mat/defactorize_factorize'
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LZERO_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/Library/analysis/LESS_EQUAL_ANTISYM_' 'mat/le_to_le_to_eq'
0. 'hl/thm/Library/transc/TAN_PI_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/floor/FLOOR_MONO_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/times_fa_Qtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/real/REAL_MUL_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/Multivariate/transcendentals/PI_NZ_'#@#variant 'mat/not_eq_true_false'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/rtimes_Zplus'
0. 'hl/thm/arith/MULT_0'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/int/int_add_th_' 'mat/rtimes_Zplus'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_plus'
0. 'hl/thm/Library/transc/ATN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/bool_to_nat_andb'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetric_gcd'
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/andb_sym'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Multivariate/misc/SQRT_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/orb_sym'
0. 'hl/thm/realax/HREAL_ADD_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/int/int_sub_th_' 'mat/times_Qtimes'
0. 'hl/thm/arith/MULT_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/int/INT_LE_ADD2_' 'mat/divides_times'
0. 'hl/thm/arith/PRE_1' 'mat/pred_Sn'
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/eq_times_fa_times'
0. 'hl/thm/Multivariate/misc/SQRT_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/int/INT_LE_ADD2_' 'mat/le_plus'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/bool_to_nat_andb'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_PHI_' 'mat/increasing_nth_prime'
0. 'hl/thm/Multivariate/transcendentals/LOG_1_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/arith/MOD_LT_' 'mat/lt_to_eq_mod'
0. 'hl/thm/int/INT_LET_TOTAL_' 'mat/not_le_to_lt'
0. 'hl/thm/int/INT_MUL_RZERO_'#@#variant 'mat/times_n_O'
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_1_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/orb_sym'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/rinv_rinv'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/realax/TREAL_MUL_WELLDEF_'#@#variant 'mat/le_plus'
0. 'hl/thm/Library/floor/RATIONAL_INV_' 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/sym_plus'
0. 'hl/thm/arith/MULT_AC_0' 'mat/orbC'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/symmetric_Ztimes'
0. 'hl/thm/int/INT_LET_ADD2_' 'mat/le_to_lt_to_plus_lt'
0. 'hl/thm/real/REAL_ABS_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/int/int_max_th_' 'mat/times_fa_Qtimes'
0. 'hl/thm/arith/MULT_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/calc_int/REAL_ADD_RINV_'#@#variant 'mat/Zplus_Zopp'
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/times_fa_Qtimes'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/nums/NUM_REP_RULES_1' 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/realax/REAL_ADD_LDISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/Library/transc/REAL_EXP_MONO_IMP_' 'mat/le_pred'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetricIntPlus'
0. 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/finv_finv'
0. 'hl/thm/Library/pocklington/PHI_LIMIT_' 'mat/le_pred_n'
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/orb_sym'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/times_fa_Qtimes'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/andb_sym'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_REFL_'#@#variant 'mat/minus_n_n'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/int/INT_MIN_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/Library/poly/POLYDIFF_ADD_'#@#variant 'mat/Qinv_Qtimes\''
0. 'hl/thm/Library/prime/DIVIDES_MUL_R_' 'mat/lt_plus_l'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_MONO_IMP_' 'mat/le_to_le_pred'
0. 'hl/thm/Multivariate/vectors/LIFT_DROP_0'#@#variant 'mat/defactorize_factorize'
0. 'hl/thm/Complex/cpoly/POLY_ADD_'#@#variant 'mat/eq_times_f_times1'
0. 'hl/thm/arith/EXP_ADD_' 'mat/exp_plus_times'
0. 'hl/thm/Multivariate/transcendentals/LOG_POS_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/eq_times_fa_times'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/orb_sym'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_andb'
0. 'hl/thm/Multivariate/transcendentals/CSIN_CASN_'#@#variant 'mat/Zpred_Zsucc'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/orb_sym'
0. 'hl/thm/realax/NADD_LE_TRANS_' 'mat/trans_le'
0. 'hl/thm/int/INT_MUL_RZERO_'#@#variant 'mat/Ztimes_z_OZ'
0. 'hl/thm/Multivariate/transcendentals/ACS_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Complex/cpoly/POLY_DIVIDES_TRANS_'#@#variant 'mat/trans_le'
0. 'hl/thm/realax/TREAL_ADD_WELLDEFR_'#@#variant 'mat/le_times_l'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/orbC'
0. 'hl/thm/arith/LET_ADD2_' 'mat/le_to_lt_to_plus_lt'
0. 'hl/thm/Multivariate/transcendentals/REAL_ABS_PI_' 'mat/A_SO'#@#variant
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/int/int_mul_th_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/orbC'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/orbC'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_' 'mat/divides_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/real/REAL_LE_LCANCEL_IMP_'#@#variant 'mat/lt_exp_to_lt'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/sym_times'
0. 'hl/thm/arith/LEFT_SUB_DISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LE_'#@#variant 'mat/lt_exp'#@#variant
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/sym_rtimes'
0. 'hl/thm/real/REAL_MIN_MIN_/0' 'mat/divides_gcd_n'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/Qinv_Qinv'
0. 'hl/thm/Library/prime/DIVIDES_MUL_L_' 'mat/le_plus_r'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/real/REAL_LE_LCANCEL_IMP_'#@#variant 'mat/le_exp_to_le'#@#variant
0. 'hl/thm/arith/FACT_MONO_' 'mat/le_pred'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_plus'
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/orbC'
0. 'hl/thm/Library/prime/PRIME_1_'#@#variant 'mat/not_prime_O'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/arith/LE_ADD2_' 'mat/lt_times'
0. 'hl/thm/realax/TREAL_ADD_WELLDEF_'#@#variant 'mat/lt_times'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symm_orb'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/Multivariate/transcendentals/SIN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/eq_times_times_fa'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Multivariate/vectors/SQRT_POS_LT_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/calc_num/ARITH_7' 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/realax/NADD_LE_0_'#@#variant 'mat/divides_SO_n'#@#variant
0. 'hl/thm/arith/ADD_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/Multivariate/transcendentals/SIN_PI2_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/calc_num/ARITH_1' 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/lt_O_S'#@#variant
0. 'hl/thm/Multivariate/transcendentals/LOG_EXP_' 'mat/Zsucc_Zpred'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/times_Qtimes'
0. 'hl/thm/arith/LE_TRANS_' 'mat/trans_divides'
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/bool_to_nat_andb'
0. 'hl/thm/realax/NADD_ADD_LCANCEL_' 'mat/lt_plus_to_lt_r'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/arith/MULT_0_'#@#variant 'mat/Qtimes_q_OQ'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/transcendentals/LOG_MONO_LT_IMP_'#@#variant 'mat/lt_pred'#@#variant
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/eq_times_fa_times'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_LE_X_'#@#variant 'mat/le_times_SSO_n_exp_SSO_n'#@#variant
0. 'hl/thm/int/INT_NEG_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/arith/LE_MULT2_' 'mat/lt_times'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/not_nf_elim_not/0'
0. 'hl/thm/int/int_sub_th_' 'mat/bool_to_nat_andb'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_1_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_MUL_' 'mat/times_minus_l'
0. 'hl/thm/arith/TWO_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetricZPlus'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/sym_rtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/sym_times'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/orbC'
0. 'hl/thm/real/REAL_LE_INV_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/Library/poly/POLY_ADD_ASSOC_'#@#variant 'mat/andb_assoc'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Library/transc/ATN_MONO_LT_' 'mat/le_pred'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/prime_nth_prime'
0. 'hl/thm/Complex/complex_transc/CCOS_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/real/REAL_MAX_ACI_1' 'mat/assoc_plus'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/opposite_direction_idempotent'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_LMUL_' 'mat/Zplus_Zpred'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/andbC'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_ASSOC_' 'mat/andbA'
0. 'hl/thm/arith/MULT_EXP_' 'mat/times_plus_l'
0. 'hl/thm/Multivariate/transcendentals/LOG_POS_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/realax/TREAL_EQ_TRANS_'#@#variant 'mat/trans_le'
0. 'hl/thm/Library/integer/INT_PRIME_0_'#@#variant 'mat/not_prime_O'
0. 'hl/thm/real/REAL_INV_INV_' 'mat/opposite_direction_idempotent'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/andb_sym'
0. 'hl/thm/realax/HREAL_ADD_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/eq_times_times_fa'
0. 'hl/thm/arith/LT_POW2_REFL_'#@#variant 'mat/lt_n_nth_prime_n'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/sym_Zplus'
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/bool_to_nat_andb'
0. 'hl/thm/Library/transc/ATN_/2' 'mat/pred_Sn'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/int/INT_ADD_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/sym_gcd'
0. 'hl/thm/Multivariate/transcendentals/REAL_COS_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/arith/SUB_0_/0' 'mat/gcd_SO_n'
0. 'hl/thm/Library/transc/ATN_TAN_' 'mat/pred_Sn'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetricZPlus'
0. 'hl/thm/Multivariate/vectors/SQRT_POS_LT_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/real/REAL_SGN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/arith/ADD_AC_0' 'mat/sym_gcd'
0. 'hl/thm/Library/transc/COS_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Complex/complex_transc/CEXP_ADD_' 'mat/demorgan2'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_AC_1' 'mat/assoc_times'
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/sym_Ztimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/bool_to_nat_andb'
0. 'hl/thm/arith/ONE_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/realax/HREAL_LE_ADD2_' 'mat/le_times'
0. 'hl/thm/realax/HREAL_ADD_AC_1' 'mat/andbA'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Library/analysis/REAL_LE_RMUL_IMP_'#@#variant 'mat/lt_times_l1'#@#variant
0. 'hl/thm/int/INT_LT_TRANS_' 'mat/trans_divides'
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/sym_times'
0. 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/eq_plus_Zplus'
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/sym_times'
0. 'hl/thm/calc_int/REAL_NEG_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/sym_gcd'
0. 'hl/thm/Library/transc/tan_' 'mat/jj'
0. 'hl/thm/Library/analysis/SUB_OLD_0' 'mat/exp_SO_n'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_andb'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL_L_' 'mat/lt_plus_r'
0. 'hl/thm/Library/transc/ATN_MONO_LT_' 'mat/le_S_S'
0. 'hl/thm/realax/REAL_LE_LADD_IMP_' 'mat/lt_plus_r'
0. 'hl/thm/int/INT_LE_LADD_IMP_' 'mat/le_times_r'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/arith/EXP_0'#@#variant 'mat/mod_SO'#@#variant
0. 'hl/thm/calc_num/ARITH_7' 'mat/A_SSO'#@#variant
0. 'hl/thm/calc_num/ARITH_1' 'mat/A_SSO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symm_orb'
0. 'hl/thm/Complex/complexnumbers/CNJ_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/orbC'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/sym_plus'
0. 'hl/thm/arith/ADD_0_' 'mat/div_SO'
0. 'hl/thm/realax/NADD_ADD_WELLDEF_' 'mat/le_times'
0. 'hl/thm/int/INT_ADD_LDISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/bool_to_nat_andb'
0. 'hl/thm/calc_int/REAL_MUL_RZERO_'#@#variant 'mat/Qtimes_q_OQ'
0. 'hl/thm/realax/NADD_LE_LMUL_' 'mat/le_plus_r'
0. 'hl/thm/int/INT_MUL_RNEG_' 'mat/plus_n_Sm'
0. 'hl/thm/Library/transc/LN_LT_X_'#@#variant 'mat/lt_sqrt_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ATN_BOUNDS_/0'#@#variant 'mat/lt_O_teta'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/sym_rtimes'
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/orbC'
0. 'hl/thm/int/INT_MAX_ACI_1' 'mat/assoc_times'
0. 'hl/thm/int/INT_SUB_LDISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/Library/transc/LN_EXP_' 'mat/Zpred_Zsucc'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_Zplus'
0. 'hl/thm/int/INT_MAX_ACI_1' 'mat/andbA'
0. 'hl/thm/nums/IND_SUC_0_' 'mat/not_eq_O_S'
0. 'hl/thm/realax/HREAL_MUL_LZERO_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_ADD_' 'mat/demorgan2'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_LT_1_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/int/INT_MUL_ASSOC_' 'mat/andbA'
0. 'hl/thm/Library/floor/RATIONAL_INTEGER_' 'mat/prime_to_lt_O'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/sym_times'
0. 'hl/thm/arith/FACT_MONO_' 'mat/le_to_le_pred'
0. 'hl/thm/realax/HREAL_ADD_LDISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Multivariate/transcendentals/COS_PI2_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Library/pratt/PHI_0_' 'mat/A_SO'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/sym_plus'
0. 'hl/thm/Library/analysis/LESS_EQ_SUC_REFL_' 'mat/le_n_fact_n'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/calc_int/REAL_ADD_AC_1' 'mat/andb_assoc'
0. 'hl/thm/arith/MULT_SYM_' 'mat/orbC'
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_2_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/arith/MULT_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LNEG_' 'mat/Zplus_Zsucc'
0. 'hl/thm/int/int_mul_th_' 'mat/rtimes_Zplus'
0. 'hl/thm/arith/LE_1_3'#@#variant 'mat/correct2'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/Library/pratt/PHI_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/realax/TREAL_EQ_TRANS_'#@#variant 'mat/trans_divides'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_andb'
0. 'hl/thm/real/REAL_MAX_ACI_1' 'mat/andb_assoc'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/andb_sym'
0. 'hl/thm/arith/MULT_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/arith/MULT_AC_0' 'mat/sym_times'
0. 'hl/thm/realax/TREAL_MUL_WELLDEF_'#@#variant 'mat/le_times'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetricIntPlus'
0. 'hl/thm/arith/LT_REFL_' 'mat/Not_lt_n_n'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_LT_1_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/eq_plus_Zplus'
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/eq_times_fa_times'
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/rtimes_Zplus'
0. 'hl/thm/Library/transc/LN_1_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/realax/HREAL_MUL_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/notb_notb'
0. 'hl/thm/int/INT_LTE_TRANS_' 'mat/lt_to_le_to_lt'
0. 'hl/thm/Multivariate/transcendentals/ATN_TAN_' 'mat/Zsucc_Zpred'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/orb_sym'
0. 'hl/thm/real/REAL_MAX_ACI_3' 'mat/orb_refl'
0. 'hl/thm/real/REAL_SUB_ADD_' 'mat/minus_plus_m_m'
0. 'hl/thm/realax/TREAL_LE_TRANS_'#@#variant 'mat/trans_le'
0. 'hl/thm/Library/transc/SQRT_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/int/INT_NEGNEG_' 'mat/Qinv_Qinv'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/orbC'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/andbC'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/sym_times'
0. 'hl/thm/arith/MOD_1_'#@#variant 'mat/mod_SO'#@#variant
0. 'hl/thm/int/INT_NEGNEG_' 'mat/opposite_direction_idempotent'
0. 'hl/thm/Library/poly/POLY_DIVIDES_TRANS_'#@#variant 'mat/trans_divides'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/andbC'
0. 'hl/thm/realax/HREAL_ADD_ASSOC_' 'mat/andbA'
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/realax/REAL_ADD_LID_'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_Zplus'
0. 'hl/thm/Library/integer/INT_DIVIDES_SUB_' 'mat/divides_minus'
0. 'hl/thm/realarith/REAL_LT_TRANS_' 'mat/trans_divides'
0. 'hl/thm/realax/HREAL_ADD_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/eq_times_times_fa'
0. 'hl/thm/realax/TREAL_MUL_WELLDEFR_'#@#variant 'mat/le_times_l'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/andbC'
0. 'hl/thm/int/INT_ADD_RDISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/arith/MULT_2_'#@#variant 'mat/times_SSO_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/real/REAL_SUB_RDISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/real/REAL_NEG_LMUL_' 'mat/Zplus_Zpred'
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/times_Qtimes'
0. 'hl/thm/arith/ADD_CLAUSES_0'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_' 'mat/le_plus'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/arith/ADD_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/arith/FACT_1' 'mat/factS'
0. 'hl/thm/realax/TREAL_EQ_REFL_'#@#variant 'mat/divides_n_n'
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/eq_notb_notb_b_b'
0. 'hl/thm/Multivariate/transcendentals/COS_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/times_Qtimes'
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_plus'
0. 'hl/thm/Multivariate/transcendentals/LOG_EXP_' 'mat/pred_Sn'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/assoc_orb'
0. 'hl/thm/calc_num/ARITH_0'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/INT_OF_NUM_MIN_' 'mat/eq_times_times_fa'
0. 'hl/thm/Library/transc/TAN_PI_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Library/poly/POLY_DIVIDES_REFL_'#@#variant 'mat/divides_n_n'
0. 'hl/thm/arith/SUB_ADD_' 'mat/plus_minus_m_m'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_MONO_IMP_' 'mat/ltS'
0. 'hl/thm/Library/analysis/SUB_LESS_EQ_' 'mat/divides_gcd_nm/1'
0. 'hl/thm/realax/HREAL_MUL_LZERO_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/realax/NADD_ADD_WELLDEF_' 'mat/divides_times'
0. 'hl/thm/int/INT_LTE_ANTISYM_' 'mat/le_to_not_lt'
0. 'hl/thm/int/INT_ADD_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/times_fa_Qtimes'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_Qtimes'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/sym_times'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetricIntPlus'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_SIGMA_' 'mat/increasing_nth_prime'
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/rtimes_Zplus'
0. 'hl/thm/arith/RIGHT_ADD_DISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/times_Qtimes'
0. 'hl/thm/int/INT_MIN_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/real/REAL_INV_INV_' 'mat/Qinv_Qinv'
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Library/integer/INT_DIVIDES_0_'#@#variant 'mat/divides_n_O'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symm_andb'
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/orbC'
0. 'hl/thm/arith/LE_ADD2_' 'mat/divides_times'
0. 'hl/thm/int/INT_LE_ADD2_' 'mat/lt_plus'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/sym_Zplus'
0. 'hl/thm/int/INT_MUL_LZERO_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/arith/EXP_1' 'mat/exp_S'
0. 'hl/thm/arith/MULT_AC_1' 'mat/andb_assoc'
0. 'hl/thm/calc_num/ARITH_104' 'mat/Qinv_Qtimes\''
0. 'hl/thm/int/INT_OF_NUM_ADD_' 'mat/eq_times_times_fa'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/int/INT_MAX_MAX_/0' 'mat/le_plus_n_r'
0. 'hl/thm/Library/poly/POLYDIFF_ADD_'#@#variant 'mat/Zopp_Zplus'
0. 'hl/thm/Library/transc/LN_LE_'#@#variant 'mat/divides_max_prime_factor_n'#@#variant
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symmetric_gcd'
0. 'hl/thm/Multivariate/transcendentals/RPOW_DIV_' 'mat/times_plus_l'
0. 'hl/thm/real/REAL_ADD_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/Library/analysis/LESS_EQUAL_ANTISYM_' 'mat/antisym_le'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/eq_plus_Zplus'
0. 'hl/thm/calc_num/ARITH_104' 'mat/Zopp_Zplus'
0. 'hl/thm/realax/TREAL_LE_TRANS_'#@#variant 'mat/trans_divides'
0. 'hl/thm/arith/ADD_SYM_' 'mat/sym_gcd'
0. 'hl/thm/nums/NOT_SUC_'#@#variant 'mat/not_eq_O_S'
0. 'hl/thm/Library/analysis/REAL_LE_RDIV_'#@#variant 'mat/divides_times_to_divides_div'#@#variant
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_1'#@#variant 'mat/assoc_times'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetricZPlus'
0. 'hl/thm/realax/REAL_LE_TRANS_' 'mat/trans_divides'
0. 'hl/thm/arith/SUB_0_/1' 'mat/exp_n_SO'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symmetric_times'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/orb_sym'
0. 'hl/thm/Library/transc/REAL_EXP_LT_1_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/Library/transc/REAL_EXP_MONO_IMP_' 'mat/le_to_le_pred'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_1'#@#variant 'mat/andbA'
0. 'hl/thm/calc_int/REAL_ADD_RINV_'#@#variant 'mat/rtimes_rinv'
0. 'hl/thm/arith/MULT_SYM_' 'mat/orb_sym'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/sym_Zplus'
0. 'hl/thm/int/INT_LE_SQUARE_'#@#variant 'mat/id_axiom'
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Library/floor/RATIONAL_NEG_' 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/real/REAL_LT_RCANCEL_IMP_'#@#variant 'mat/lt_exp_to_lt1'#@#variant
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/bool_to_nat_andb'
0. 'hl/thm/realax/NADD_LE_REFL_' 'mat/divides_n_n'
0. 'hl/thm/Library/pocklington/EVEN_PHI_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/int/INT_LE_LMUL_'#@#variant 'mat/lt_times_r1'#@#variant
0. 'hl/thm/int/INT_MUL_AC_1' 'mat/andbA'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_ASSOC_' 'mat/andbA'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/orbC'
0. 'hl/thm/int/INT_SGN_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/int/INT_MAX_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/Library/prime/INDEX_TRIVIAL_BOUND_' 'mat/divides_gcd_m'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/eq_times_fa_times'
0. 'hl/thm/Library/floor/RATIONAL_NUM_' 'mat/sieve_sorted'#@#variant
0. 'hl/thm/arith/LE_ADD2_' 'mat/le_times'
0. 'hl/thm/int/INT_LET_ANTISYM_' 'mat/le_to_not_lt'
0. 'hl/thm/arith/ADD_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/assoc_orb'
0. 'hl/thm/realax/HREAL_ADD_RDISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/Library/poly/POLY_DIVIDES_TRANS_'#@#variant 'mat/trans_le'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Library/transc/LN_LT_X_'#@#variant 'mat/divides_smallest_factor_n'#@#variant
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/sym_gcd'
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/times_fa_Qtimes'
0. 'hl/thm/Library/pocklington/PHI_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/orb_sym'
0. 'hl/thm/Library/floor/FLOOR_/0' 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ATN_LE_X_'#@#variant 'mat/lt_sqrt_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/bool_to_nat_andb'
0. 'hl/thm/arith/MOD_1_'#@#variant 'mat/bc_n_O'#@#variant
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetricIntPlus'
0. 'hl/thm/int/INT_NEGNEG_' 'mat/notb_notb'
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/sym_plus'
0. 'hl/thm/arith/LE_MULT2_' 'mat/lt_plus'
0. 'hl/thm/lists/APPEND_NIL_' 'mat/append_nil'
0. 'hl/thm/real/REAL_LT_LMUL_'#@#variant 'mat/le_log'#@#variant
0. 'hl/thm/realax/HREAL_LE_MUL_RCANCEL_IMP_' 'mat/lt_plus_l'
0. 'hl/thm/real/REAL_LE_ADD2_' 'mat/lt_times'
0. 'hl/thm/Library/prime/DIVIDES_SUB_' 'mat/divides_plus'
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Library/transc/LN_POS_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/int/INT_ABS_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/eq_times_fa_times'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symmetric_gcd'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Library/prime/PRIME_GE_2_'#@#variant 'mat/prime_to_lt_O'#@#variant
0. 'hl/thm/real/REAL_ABS_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/real/REAL_ABS_DIV_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/sym_rtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_1' 'mat/andbA'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/orbC'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LNEG_' 'mat/Zplus_Zpred'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symm_orb'
0. 'hl/thm/Library/floor/REAL_FLOOR_REFL_' 'mat/prime_to_smallest_factor'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_rtimes'
0. 'hl/thm/Multivariate/transcendentals/LOG_EXP_' 'mat/Zpred_Zsucc'
0. 'hl/thm/arith/MULT_SUC_' 'mat/exp_S'
0. 'hl/thm/pair/pair_INDUCT_' 'mat/Prod_ind'
0. 'hl/thm/Complex/complex_transc/CEXP_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_andb'
0. 'hl/thm/arith/SUB_ADD_' 'mat/divides_to_div'
0. 'hl/thm/Multivariate/complexes/CNJ_DIV_'#@#variant 'mat/Qinv_Qtimes\''
0. 'hl/thm/Library/analysis/SUB_OLD_0'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ACS_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LDISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/Library/analysis/REAL_LE_RMUL_IMP_'#@#variant 'mat/lt_exp1'#@#variant
0. 'hl/thm/arith/MULT_SYM_' 'mat/sym_times'
0. 'hl/thm/real/REAL_ABS_LE_' 'mat/le_n_Sn'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/realax/TREAL_MUL_WELLDEF_'#@#variant 'mat/lt_times'
0. 'hl/thm/realax/REAL_MUL_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/Library/analysis/REAL_INV_1OVER_'#@#variant 'mat/eq_B_B1'
0. 'hl/thm/realax/TREAL_MUL_WELLDEFR_'#@#variant 'mat/le_plus_l'
0. 'hl/thm/Library/analysis/REAL_LT_LMUL_IMP_'#@#variant 'mat/lt_exp'#@#variant
0. 'hl/thm/real/REAL_ABS_DIV_' 'mat/Zopp_Zplus'
0. 'hl/thm/arith/ADD_AC_0' 'mat/sym_plus'
0. 'hl/thm/real/REAL_MIN_MIN_/0' 'mat/divides_gcd_nm/1'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_LDISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/Multivariate/transcendentals/ATN_TAN_' 'mat/pred_Sn'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/Zplus_z_OZ'
0. 'hl/thm/realax/REAL_OF_NUM_MUL_' 'mat/eq_times_times_fa'
0. 'hl/thm/int/INT_NEG_LMUL_' 'mat/Zplus_Zsucc'
0. 'hl/thm/arith/EXP_MONO_LE_IMP_' 'mat/le_times_l'
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/rtimes_Zplus'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/sym_Zplus'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/realax/REAL_INV_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/Library/transc/ATN_MONO_LT_' 'mat/ltS'
0. 'hl/thm/arith/DIV_1_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/orbC'
0. 'hl/thm/arith/ADD_SUB_' 'mat/minus_plus_m_m'
0. 'hl/thm/arith/ONE_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/int/INT_NEG_ADD_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_nat_gcd'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/calc_num/ARITH_0'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/LOG_1_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/arith/MULT_AC_0' 'mat/andbC'
0. 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/bool_to_nat_andb'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/sym_gcd'
0. 'hl/thm/real/REAL_MIN_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/real/REAL_LT_ADD2_' 'mat/le_times'
0. 'hl/thm/int/INT_MAX_ACI_1' 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/andbC'
0. 'hl/thm/int/int_min_th_' 'mat/bool_to_nat_andb'
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_2_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/arith/LT_MULT2_' 'mat/divides_times'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RDISTRIB_' 'mat/times_minus_l'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Multivariate/vectors/SQRT_DIV_' 'mat/Zopp_Zplus'
0. 'hl/thm/arith/LTE_ANTISYM_' 'mat/lt_to_not_le'
0. 'hl/thm/Complex/complexnumbers/complex_tybij_1'#@#variant 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/int/INT_ABS_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/sym_times'
0. 'hl/thm/arith/SUB_0' 'mat/div_SO'
0. 'hl/thm/realarith/REAL_LTE_ANTISYM_' 'mat/le_to_not_lt'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/Library/analysis/DORDER_NGE_' 'mat/antisymmetric_le'
0. 'hl/thm/Library/prime/DIVIDES_REFL_' 'mat/divides_n_n'
0. 'hl/thm/Multivariate/transcendentals/ACS_0_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/orb_sym'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/opposite_direction_idempotent'
0. 'hl/thm/arith/DIV_LT_'#@#variant 'mat/lt_to_div_O'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_TAU_' 'mat/increasing_nth_prime'
0. 'hl/thm/Multivariate/complexes/COMPLEX_INV_INV_'#@#variant 'mat/finv_finv'
0. 'hl/thm/Library/prime/DIVIDES_SUB_' 'mat/divides_minus'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/Qinv_Qinv'
0. 'hl/thm/int/INT_ABS_LE_' 'mat/le_n_fact_n'
0. 'hl/thm/real/REAL_MIN_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/realax/HREAL_LE_ADD2_' 'mat/divides_times'
0. 'hl/thm/arith/ADD_AC_0' 'mat/andbC'
0. 'hl/thm/realax/TREAL_NEG_WELLDEF_'#@#variant 'mat/le_pred'
0. 'hl/thm/arith/SUB_0_/1' 'mat/div_SO'
0. 'hl/thm/int/INT_ADD_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/Library/prime/LESS_MONO_ADD_' 'mat/le_times_l'
0. 'hl/thm/realax/NADD_ADD_WELLDEF_' 'mat/le_plus'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_RMUL_' 'mat/plus_n_Sm'
0. 'hl/thm/Multivariate/transcendentals/ASN_1_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Library/floor/RATIONAL_INTEGER_' 'mat/prime_to_lt_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LT_'#@#variant 'mat/le_exp'#@#variant
0. 'hl/thm/Complex/cpoly/POLY_DIVIDES_ADD_'#@#variant 'mat/divides_plus'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/0' 'mat/not_nf_elim_not/1'
0. 'hl/thm/int/int_add_th_' 'mat/eq_times_times_fa'
0. 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/times_fa_Qtimes'
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/eq_plus_Zplus'
0. 'hl/thm/realax/HREAL_MUL_RZERO_'#@#variant 'mat/times_n_O'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetric_Qtimes'
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_1_STRONG_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/times_fa_Qtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/eq_times_fa_times'
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/sym_times'
0. 'hl/thm/realax/NADD_INV_WELLDEF_' 'mat/le_to_le_pred'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symm_orb'
0. 'hl/thm/realax/HREAL_ADD_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/orb_sym'
0. 'hl/thm/Library/transc/SQRT_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/int/INT_NEG_MUL2_' 'mat/minus_S_S'
0. 'hl/thm/real/REAL_INV_INV_' 'mat/notb_notb'
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/bool_to_nat_andb'
0. 'hl/thm/int/int_min_th_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/real/REAL_MIN_ACI_0' 'mat/sym_plus'
0. 'hl/thm/realax/TREAL_INV_WELLDEF_'#@#variant 'mat/ltS'
0. 'hl/thm/Multivariate/transcendentals/LOG_LE_'#@#variant 'mat/divides_max_prime_factor_n'#@#variant
0. 'hl/thm/realax/NADD_INV_WELLDEF_' 'mat/ltS'
0. 'hl/thm/realax/REAL_INV_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/realax/REAL_MUL_ASSOC_' 'mat/andbA'
0. 'hl/thm/realax/REAL_ADD_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_Zplus'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/associative_times'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/andb_sym'
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_2_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/arith/LEFT_ADD_DISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/Multivariate/transcendentals/TAN_PI_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/arith/FACT_0'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_POLY_NEG_CLAUSES_0'#@#variant 'mat/Zpred_Zplus_neg_O'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_POLY_NEG_CLAUSES_0'#@#variant 'mat/Zsucc_Zplus_pos_O'
0. 'hl/thm/int/INT_LT_ADD2_' 'mat/divides_times'
0. 'hl/thm/Multivariate/transcendentals/LOG_LT_X_'#@#variant 'mat/lt_sqrt_n'#@#variant
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Library/transc/TAN_PI_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/int/INT_LT_ADD2_' 'mat/le_plus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LZERO_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/int/INT_MAX_MAX_/1' 'mat/le_plus_n'
0. 'hl/thm/int/int_mul_th_' 'mat/eq_plus_Zplus'
0. 'hl/thm/int/INT_MAX_SYM_' 'mat/orbC'
0. 'hl/thm/Complex/complexnumbers/complex_tybij_raw_0'#@#variant 'mat/defactorize_factorize'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_ADD_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/opposite_direction_idempotent'
0. 'hl/thm/int/INT_ADD_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/realax/NADD_LE_RMUL_' 'mat/le_times_l'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/andbC'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_ADD_' 'mat/minus_plus_m_m'
0. 'hl/thm/Library/floor/RATIONAL_ABS_' 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ASN_NEG_1_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/sym_times'
0. 'hl/thm/realax/HREAL_ADD_LDISTRIB_' 'mat/distr_times_minus'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RID_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/associative_andb'
0. 'hl/thm/Library/transc/ATN_BOUNDS_/0'#@#variant 'mat/lt_SO_nth_prime_n'
0. 'hl/thm/arith/LE_1_4'#@#variant 'mat/prime_to_lt_O'#@#variant
0. 'hl/thm/Library/prime/INDEX_0_'#@#variant 'mat/times_n_O'
0. 'hl/thm/Library/transc/SIN_PI_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/sym_times'
0. 'hl/thm/Multivariate/transcendentals/COS_PI_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/andbC'
0. 'hl/thm/int/INT_LE_RMUL_'#@#variant 'mat/lt_exp1'#@#variant
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/minus_n_O'
0. 'hl/thm/Library/transc/SQRT_POS_LT_'#@#variant 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_1'#@#variant 'mat/assoc_plus'
0. 'hl/thm/Library/prime/DIVIDES_DIV_'#@#variant 'mat/mod_O_to_divides'#@#variant
0. 'hl/thm/arith/LE_ADD2_' 'mat/lt_plus'
0. 'hl/thm/real/REAL_OF_NUM_MAX_' 'mat/eq_times_times_fa'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/eq_times_fa_times'
0. 'hl/thm/int/int_max_th_' 'mat/bool_to_nat_andb'
0. 'hl/thm/int/INT_ADD_AC_1' 'mat/andbA'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LT_' 'mat/ltS'
0. 'hl/thm/arith/LE_0_'#@#variant 'mat/le_O_n'
0. 'hl/thm/realax/HREAL_ADD_AC_1' 'mat/assoc_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/orbC'
0. 'hl/thm/arith/RIGHT_ADD_DISTRIB_' 'mat/times_exp'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/sym_plus'
0. 'hl/thm/Library/integer/INT_DIVIDES_1_'#@#variant 'mat/divides_SO_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RDISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/int/int_add_th_' 'mat/times_fa_Qtimes'
0. 'hl/thm/arith/FACT_LT_' 'mat/le_SO_fact'
0. 'hl/thm/int/INT_MUL_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_Ztimes'
0. 'hl/thm/Complex/complex_transc/CCOS_0_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Library/poly/POLY_DIVIDES_ADD_'#@#variant 'mat/divides_plus'
0. 'hl/thm/Complex/cpoly/POLY_DIVIDES_TRANS_'#@#variant 'mat/trans_lt'
0. 'hl/thm/Multivariate/vectors/LIFT_DROP_1'#@#variant 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/plus_n_O'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_DIV_' 'mat/eq_plus_Zplus'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/Qtimes_q_Qone'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/sym_gcd'
0. 'hl/thm/int/INT_LT_REFL_' 'mat/Not_lt_n_n'
0. 'hl/thm/realax/HREAL_ADD_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL2_' 'mat/divides_times'
0. 'hl/thm/realax/TREAL_ADD_WELLDEF_'#@#variant 'mat/divides_times'
0. 'hl/thm/real/REAL_SUB_LDISTRIB_' 'mat/distr_times_plus'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/sym_plus'
0. 'hl/thm/int/INT_ABS_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_1_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/real/REAL_MIN_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/arith/ADD_SYM_' 'mat/sym_plus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/andb_sym'
0. 'hl/thm/int/INT_MAX_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/int/INT_MIN_MIN_/1' 'mat/divides_gcd_nm/0'
0. 'hl/thm/Library/pocklington/PHI_0_' 'mat/A_SO'
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/sym_gcd'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_ASSOC_'#@#variant 'mat/assoc_times'
0. 'hl/thm/Library/transc/LN_1_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Complex/complexnumbers/CNJ_SUB_' 'mat/Zopp_Zplus'
0. 'hl/thm/Library/transc/TAN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/arith/MULT_CLAUSES_3'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/arith/FACT_MONO_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_PHI_' 'mat/monotonic_A'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_1' 'mat/andbA'
0. 'hl/thm/realax/HREAL_ADD_RDISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/rinv_rinv'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/arith/ADD_CLAUSES_0'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/arith/MULT_SYM_' 'mat/andbC'
0. 'hl/thm/Multivariate/complexes/RE_CX_'#@#variant 'mat/defactorize_factorize'
0. 'hl/thm/int/INT_LT_TRANS_' 'mat/trans_lt'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LT_' 'mat/le_to_le_pred'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/calc_int/REAL_NEG_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Library/prime/DIVIDES_TRANS_' 'mat/trans_lt'
0. 'hl/thm/arith/RIGHT_ADD_DISTRIB_' 'mat/times_plus_l'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_1'#@#variant 'mat/assoc_Ztimes'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symm_andb'
0. 'hl/thm/int/int_max_th_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Library/poly/POLY_ADD_SYM_'#@#variant 'mat/sym_Ztimes'
0. 'hl/thm/arith/TWO_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/sym_plus'
0. 'hl/thm/Multivariate/complexes/CX_DIV_'#@#variant 'mat/bool_to_nat_andb'
0. 'hl/thm/Complex/complex_transc/CSIN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetric_Ztimes'
0. 'hl/thm/real/REAL_INV_INV_' 'mat/eq_notb_notb_b_b'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/realax/NADD_MUL_WELLDEF_' 'mat/lt_plus'
0. 'hl/thm/arith/ADD_AC_0' 'mat/orbC'
0. 'hl/thm/int/INT_OF_NUM_MUL_' 'mat/eq_times_times_fa'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Multivariate/transcendentals/CCOS_CACS_'#@#variant 'mat/Zsucc_Zpred'
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/realarith/REAL_MUL_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/symmetric_gcd'
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/real/REAL_MAX_SYM_' 'mat/sym_plus'
0. 'hl/thm/Complex/complex_transc/CEXP_0_'#@#variant 'mat/B_SSSO'#@#variant
0. 'hl/thm/Library/analysis/LESS_MONO_ADD_' 'mat/lt_plus_l'
0. 'hl/thm/int/int_sub_th_' 'mat/eq_times_times_fa'
0. 'hl/thm/real/REAL_MUL_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/arith/ADD_SYM_' 'mat/andbC'
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/sym_Ztimes'
0. 'hl/thm/Library/pratt/PHI_LIMIT_' 'mat/le_sqrt_n_n'
0. 'hl/thm/int/int_of_num_th_' 'mat/numerator_nat_fact_to_fraction'
0. 'hl/thm/Library/analysis/REAL_DIV_LZERO_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/andbC'
0. 'hl/thm/arith/LT_0_'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Multivariate/transcendentals/TAN_PI_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/lists/NOT_CONS_NIL_' 'mat/nil_cons'
0. 'hl/thm/iterate/MONOIDAL_MUL_' 'mat/symmetric_times'
0. 'hl/thm/calc_int/REAL_MUL_RNEG_' 'mat/plus_n_Sm'
0. 'hl/thm/arith/MULT_AC_0' 'mat/sym_gcd'
0. 'hl/thm/realax/NADD_LE_0_'#@#variant 'mat/le_O_n'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/arith/LE_ADD2_' 'mat/le_plus'
0. 'hl/thm/arith/EXP_1' 'mat/times_n_Sm'
0. 'hl/thm/arith/MULT_CLAUSES_2'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/Library/integer/INT_DIVIDES_ADD_' 'mat/divides_plus'
0. 'hl/thm/real/REAL_SUB_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/Multivariate/transcendentals/COS_BOUNDS_/0'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/arith/MOD_LT_' 'mat/le_to_mod'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/int/INT_LT_IMP_NE_' 'mat/eq_to_not_lt'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LE_' 'mat/ltS'
0. 'hl/thm/Library/prime/INDEX_0_'#@#variant 'mat/Ztimes_z_OZ'
0. 'hl/thm/int/INT_MAX_ACI_3' 'mat/gcd_n_n'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_Qtimes'
0. 'hl/thm/int/INT_MUL_LNEG_' 'mat/Zplus_Zsucc'
0. 'hl/thm/arith/LET_ANTISYM_' 'mat/le_to_not_lt'
0. 'hl/thm/Multivariate/transcendentals/REAL_SIN_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/int/INT_LTE_ANTISYM_' 'mat/lt_to_not_le'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LID_'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/Library/analysis/SUB_LESS_EQ_' 'mat/le_minus_m'
0. 'hl/thm/realax/NADD_INV_WELLDEF_' 'mat/lt_to_lt_S_S'
0. 'hl/thm/Multivariate/transcendentals/REAL_INV_RPOW_' 'mat/Zplus_Zsucc'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/sym_times'
0. 'hl/thm/Complex/complexnumbers/CX_SUB_' 'mat/eq_times_times_fa'
0. 'hl/thm/real/REAL_LT_POW2_'#@#variant 'mat/sieve_sorted'#@#variant
0. 'hl/thm/arith/ADD_AC_0' 'mat/andb_sym'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_LZERO_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/associative_Qtimes'
0. 'hl/thm/real/REAL_LT_ADD2_' 'mat/le_plus'
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/Library/transc/LN_POS_LT_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_1' 'mat/andb_assoc'
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/minus_n_O'
0. 'hl/thm/Library/integer/INT_PRIME_0_'#@#variant 'mat/not_prime_SO'#@#variant
0. 'hl/thm/realax/HREAL_LE_TRANS_' 'mat/trans_divides'
0. 'hl/thm/real/REAL_SUB_REFL_'#@#variant 'mat/bc_n_n'#@#variant
0. 'hl/thm/calc_int/REAL_MUL_LZERO_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/real/REAL_OF_NUM_MIN_' 'mat/rtimes_Zplus'
0. 'hl/thm/Library/floor/FLOOR_FRAC_/1'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/nums/BIT0_DEF_0'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/realax/NADD_EQ_TRANS_' 'mat/trans_lt'
0. 'hl/thm/int/INT_ABS_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/int/INT_LT_ADD2_' 'mat/le_times'
0. 'hl/thm/real/REAL_LT_INV_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/arith/SUB_0' 'mat/times_n_SO'
0. 'hl/thm/Library/transc/REAL_EXP_LT_1_'#@#variant 'mat/le_SSO_fact'#@#variant
0. 'hl/thm/realax/REAL_MUL_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/real/REAL_MAX_MAX_/0' 'mat/le_plus_n_r'
0. 'hl/thm/Complex/complexnumbers/CNJ_SUB_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/realax/HREAL_ADD_LCANCEL_' 'mat/inj_plus_r'
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LT_'#@#variant 'mat/lt_exp'#@#variant
0. 'hl/thm/int/INT_MIN_ASSOC_' 'mat/andbA'
0. 'hl/thm/int/INT_ABS_MUL_' 'mat/Zopp_Zplus'
0. 'hl/thm/Multivariate/transcendentals/ctan_'#@#variant 'mat/eq_B1_times_B_split1_B_split2'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/real/REAL_LE_RMUL_'#@#variant 'mat/lt_exp1'#@#variant
0. 'hl/thm/arith/EXP_MONO_LE_IMP_' 'mat/le_plus_l'
0. 'hl/thm/Library/transc/ATN_TAN_' 'mat/Zpred_Zsucc'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/notb_notb'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/sym_times'
0. 'hl/thm/Multivariate/vectors/SQRT_MONO_LE_' 'mat/le_to_le_pred'
0. 'hl/thm/int/int_sub_th_' 'mat/eq_times_fa_times'
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/sym_times'
0. 'hl/thm/real/REAL_LE_ADD2_' 'mat/divides_times'
0. 'hl/thm/Multivariate/transcendentals/ATN_MONO_LT_' 'mat/le_to_le_pred'
0. 'hl/thm/real/REAL_DIV_1_'#@#variant 'mat/div_SO'#@#variant
0. 'hl/thm/realax/HREAL_LE_TRANS_' 'mat/trans_lt'
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Library/transc/REAL_EXP_POS_LT_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/realax/REAL_MUL_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/calc_num/ARITH_3'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/realax/TREAL_ADD_WELLDEFR_'#@#variant 'mat/lt_plus_l'
0. 'hl/thm/Multivariate/transcendentals/ATN_MONO_LT_' 'mat/le_pred'
0. 'hl/thm/arith/SUB_0_/0'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/arith/EXP_1_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/Library/transc/REAL_EXP_POS_LE_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/arith/SUB_SUC_' 'mat/minus_S_S'
0. 'hl/thm/real/REAL_INV_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/real/REAL_MAX_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/orbC'
0. 'hl/thm/Multivariate/complexes/CNJ_CNJ_'#@#variant 'mat/eq_notb_notb_b_b'
0. 'hl/thm/calc_int/REAL_NEG_ADD_' 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_ADD_' 'mat/Zopp_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/realax/HREAL_LE_TRANS_' 'mat/trans_le'
0. 'hl/thm/int/NUM_OF_INT_OF_NUM_' 'mat/factorize_defactorize'
0. 'hl/thm/Library/floor/INTEGER_CLOSED_6' 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/Library/floor/INTEGER_CLOSED_5' 'mat/lt_SO_smallest_factor'#@#variant
0. 'hl/thm/arith/MULT_ASSOC_' 'mat/andbA'
0. 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/rtimes_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RNEG_' 'mat/plus_n_Sm'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/real/REAL_SUB_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/symm_andb'
0. 'hl/thm/Library/prime/DIVIDES_MUL_L_' 'mat/le_times_r'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_nat_gcd'
0. 'hl/thm/int/INT_MUL_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/Library/transc/LN_POS_LT_'#@#variant 'mat/prime_smallest_factor_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_SUB_' 'mat/demorgan1'
0. 'hl/thm/Library/integer/INT_DIVIDES_MUL2_' 'mat/lt_plus'
0. 'hl/thm/Library/integer/INT_DIVIDES_TRANS_' 'mat/trans_lt'
0. 'hl/thm/real/REAL_MUL_AC_1' 'mat/assoc_plus'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_nat_gcd'
0. 'hl/thm/realax/NADD_LE_LMUL_' 'mat/le_times_r'
0. 'hl/thm/Multivariate/transcendentals/REAL_ABS_PI_' 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/Library/transc/ATN_/2' 'mat/Zsucc_Zpred'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_ASSOC_'#@#variant 'mat/assoc_plus'
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/bool_to_nat_andb'
0. 'hl/thm/arith/ADD_CLAUSES_0'#@#variant 'mat/Ztimes_Zone_l'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/int/INT_MIN_SYM_' 'mat/orb_sym'
0. 'hl/thm/realax/HREAL_INV_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/ACS_NEG_1_'#@#variant 'mat/A_SSSO'#@#variant
0. 'hl/thm/real/REAL_MAX_ASSOC_' 'mat/assoc_Zplus'
0. 'hl/thm/Library/transc/ATN_/0'#@#variant 'mat/lt_SO_nth_prime_n'
0. 'hl/thm/int/INT_MUL_SYM_' 'mat/sym_gcd'
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/lt_O_nth_prime_n'#@#variant
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/prime_nth_prime'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RZERO_'#@#variant 'mat/times_n_O'
0. 'hl/thm/realax/TREAL_LE_REFL_'#@#variant 'mat/divides_n_n'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/Zopp_Zopp'
0. 'hl/thm/int/int_mul_th_' 'mat/times_fa_Qtimes'
0. 'hl/thm/real/REAL_NEG_LMUL_' 'mat/Zplus_Zsucc'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/real/REAL_MAX_ACI_0' 'mat/andb_sym'
0. 'hl/thm/int/INT_ABS_POS_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/realax/HREAL_OF_NUM_ADD_' 'mat/eq_times_fa_times'
0. 'hl/thm/calc_num/ARITH_0'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/real/REAL_NEG_RMUL_' 'mat/plus_n_Sm'
0. 'hl/thm/int/INT_ADD_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Library/pocklington/EVEN_PHI_'#@#variant 'mat/lt_SO_n_to_lt_O_pred_n'#@#variant
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/sym_plus'
0. 'hl/thm/Library/pratt/PHI_LIMIT_' 'mat/le_prim_n'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_LEMMA_' 'mat/le_plus_r'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_LEMMA_' 'mat/le_times_r'
0. 'hl/thm/real/REAL_LE_LMUL_'#@#variant 'mat/le_log'#@#variant
0. 'hl/thm/Library/prime/PRIME_GE_2_'#@#variant 'mat/bertrand_n'#@#variant
0. 'hl/thm/Multivariate/misc/GE_REFL_' 'mat/divides_n_n'
0. 'hl/thm/int/INT_MIN_MIN_/0' 'mat/le_minus_m'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/symmetric_times'
0. 'hl/thm/int/INT_ADD_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/Library/transc/SIN_PI2_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/arith/MULT_EXP_' 'mat/times_minus_l'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/arith/LE_1_3'#@#variant 'mat/prime_to_lt_O'#@#variant
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/sym_plus'
0. 'hl/thm/Library/prime/PRIME_0_'#@#variant 'mat/not_prime_O'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/int/INT_MIN_ACI_0' 'mat/sym_Zplus'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/minus_n_O'
0. 'hl/thm/int/INT_SUB_RZERO_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/arith/EVEN_DOUBLE_'#@#variant 'mat/lt_O_fact'#@#variant
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/assoc_orb'
0. 'hl/thm/arith/ADD_SYM_' 'mat/orbC'
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/Library/floor/INTEGER_CLOSED_0' 'mat/sieve_sorted'#@#variant
0. 'hl/thm/Library/transc/REAL_EXP_NZ_'#@#variant 'mat/not_eq_O_S'
0. 'hl/thm/int/INT_MAX_ACI_1' 'mat/assoc_plus'
0. 'hl/thm/realax/HREAL_OF_NUM_MUL_' 'mat/times_fa_Qtimes'
0. 'hl/thm/int/INT_LE_TRANS_' 'mat/trans_divides'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/Library/prime/LESS_MONO_ADD_' 'mat/lt_plus_l'
0. 'hl/thm/Multivariate/transcendentals/ASN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/vectors/LIFT_DROP_0'#@#variant 'mat/numeratorQ_nat_fact_all_to_Q'
0. 'hl/thm/Complex/complexnumbers/CX_MUL_' 'mat/times_fa_Qtimes'
0. 'hl/thm/real/REAL_MIN_ACI_1' 'mat/assoc_Zplus'
0. 'hl/thm/real/REAL_LT_RCANCEL_IMP_'#@#variant 'mat/le_exp_to_le1'#@#variant
0. 'hl/thm/realax/TREAL_NEG_WELLDEF_'#@#variant 'mat/lt_to_lt_S_S'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_times'
0. 'hl/thm/Multivariate/vectors/SQRT_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/int/INT_MUL_AC_0' 'mat/sym_plus'
0. 'hl/thm/Multivariate/transcendentals/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_S'#@#variant
0. 'hl/thm/trivia/one_INDUCT_' 'mat/unit_ind'
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_SYM_' 'mat/andbC'
0. 'hl/thm/arith/LT_POW2_REFL_'#@#variant 'mat/le_n_fact_n'
0. 'hl/thm/Library/prime/DIVIDES_MUL2_' 'mat/divides_times'
0. 'hl/thm/Complex/complex_transc/CSIN_0_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/wf/WF_num_' 'mat/antisymmetric_divides'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/andbC'
0. 'hl/thm/int/INT_ADD_RID_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/arith/MULT_SYM_' 'mat/sym_gcd'
0. 'hl/thm/Library/pocklington/PHI_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/real/REAL_SUB_RZERO_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/int/INT_ADD_RINV_'#@#variant 'mat/rtimes_rinv'
0. 'hl/thm/real/REAL_NEG_MUL2_' 'mat/minus_S_S'
0. 'hl/thm/Multivariate/transcendentals/ATN_BOUNDS_/0'#@#variant 'mat/le_SO_fact'#@#variant
0. 'hl/thm/real/REAL_SGN_DIV_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/calc_int/REAL_NEG_NEG_' 'mat/Zopp_Zopp'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/Zopp_Zopp'
0. 'hl/thm/arith/MULT_ASSOC_' 'mat/andb_assoc'
0. 'hl/thm/realax/NADD_ADD_WELLDEF_' 'mat/lt_plus'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_LEMMA_' 'mat/lt_plus_r'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_PHI_' 'mat/injective_nth_prime'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_0' 'mat/sym_Zplus'
0. 'hl/thm/real/REAL_MUL_AC_0' 'mat/orbC'
0. 'hl/thm/Library/multiplicative/MOBIUS_PRIME_'#@#variant 'mat/prime_to_primeb_true'
0. 'hl/thm/Library/analysis/REAL_DIV_LZERO_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/times_Qtimes'
0. 'hl/thm/arith/ADD_SYM_' 'mat/andb_sym'
0. 'hl/thm/realax/HREAL_LE_MUL_RCANCEL_IMP_' 'mat/le_plus_l'
0. 'hl/thm/arith/LT_ADD2_' 'mat/le_times'
0. 'hl/thm/realax/HREAL_ADD_LID_'#@#variant 'mat/rtimes_one_r'
0. 'hl/thm/realax/REAL_MUL_SYM_' 'mat/andb_sym'
0. 'hl/thm/arith/FACT_0'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Library/transc/SQRT_MONO_LE_'#@#variant 'mat/lt_pred'#@#variant
0. 'hl/thm/real/REAL_SGN_DIV_' 'mat/Zopp_Zplus'
0. 'hl/thm/int/INT_MUL_RID_'#@#variant 'mat/plus_n_O'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LINV_'#@#variant 'mat/orb_not_b_b'
0. 'hl/thm/real/REAL_MIN_SYM_' 'mat/sym_times'
0. 'hl/thm/Library/prime/PRIME_DIVPROD_' 'mat/divides_times_to_divides'
0. 'hl/thm/int/INT_SGN_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/realax/HREAL_ADD_AC_1' 'mat/assoc_Ztimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_MUL_' 'mat/times_Qtimes'
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/realarith/REAL_LT_TRANS_' 'mat/trans_le'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_0' 'mat/andbC'
0. 'hl/thm/Multivariate/transcendentals/REAL_ABS_RPOW_' 'mat/Zplus_Zpred'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/Qinv_Qinv'
0. 'hl/thm/calc_int/REAL_MUL_LZERO_'#@#variant 'mat/gcd_SO_n'#@#variant
0. 'hl/thm/Library/analysis/SUB_LESS_EQ_' 'mat/divides_gcd_n'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_SYM_'#@#variant 'mat/sym_gcd'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/andb_sym'
0. 'hl/thm/realax/HREAL_ADD_AC_0' 'mat/sym_Ztimes'
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/rtimes_Zplus'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/symm_andb'
0. 'hl/thm/Library/transc/REAL_EXP_ADD_' 'mat/demorgan1'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/real/REAL_MAX_ASSOC_' 'mat/assoc_plus'
0. 'hl/thm/Multivariate/misc/SQRT_1_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/arith/FACT_LE_'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/real/REAL_LT_ADD2_' 'mat/lt_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_INV_INV_' 'mat/eq_notb_notb_b_b'
0. 'hl/thm/arith/SUB_0_/0'#@#variant 'mat/mod_O_n'
0. 'hl/thm/Library/analysis/REAL_10_'#@#variant 'mat/not_eq_true_false'
0. 'hl/thm/Library/transc/SIN_BOUNDS_/0'#@#variant 'mat/lt_O_teta'#@#variant
0. 'hl/thm/Library/analysis/REAL_LT_LMUL_IMP_'#@#variant 'mat/le_exp'#@#variant
0. 'hl/thm/Library/pratt/PHI_LOWERBOUND_1_STRONG_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/realax/TREAL_NEG_WELLDEF_'#@#variant 'mat/ltS'
0. 'hl/thm/real/REAL_INV_1_'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_MONO_LT_'#@#variant 'mat/le_log'#@#variant
0. 'hl/thm/Library/poly/MONOIDAL_POLY_ADD_'#@#variant 'mat/associative_Qtimes'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/rtimes_Zplus'
0. 'hl/thm/realax/HREAL_ADD_SYM_' 'mat/sym_times'
0. 'hl/thm/iterate/MONOIDAL_REAL_MUL_' 'mat/associative_Ztimes'
0. 'hl/thm/real/REAL_ABS_POS_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/realax/HREAL_LE_ADD2_' 'mat/le_plus'
0. 'hl/thm/Library/isum/MONOIDAL_INT_ADD_' 'mat/associative_Zplus'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_LID_'#@#variant 'mat/Qtimes_Qone_q'
0. 'hl/thm/realax/NADD_MUL_WELLDEF_' 'mat/lt_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_AC_1' 'mat/andb_assoc'
0. 'hl/thm/int/INT_SUB_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/Multivariate/transcendentals/CCOS_CACS_'#@#variant 'mat/pred_Sn'
0. 'hl/thm/real/REAL_MIN_ACI_1' 'mat/assoc_times'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Complex/complex_transc/CEXP_SUB_' 'mat/demorgan2'
0. 'hl/thm/int/INT_NEGNEG_' 'mat/Zopp_Zopp'
0. 'hl/thm/Library/pratt/PHI_1_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/realax/TREAL_MUL_WELLDEF_'#@#variant 'mat/divides_times'
0. 'hl/thm/Library/transc/COS_PI2_'#@#variant 'mat/B_SSSSO'#@#variant
0. 'hl/thm/Multivariate/transcendentals/RPOW_ONE_'#@#variant 'mat/mod_O_n'
0. 'hl/thm/realax/TREAL_INV_WELLDEF_'#@#variant 'mat/le_pred'
0. 'hl/thm/int/INT_SGN_MUL_' 'mat/Qinv_Qtimes\''
0. 'hl/thm/realax/HREAL_LE_REFL_' 'mat/divides_n_n'
0. 'hl/thm/arith/SUB_0'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/iterate/MONOIDAL_ADD_' 'mat/associative_rtimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Multivariate/transcendentals/ATN_LE_X_'#@#variant 'mat/divides_smallest_factor_n'#@#variant
0. 'hl/thm/Library/integer/INT_DIVIDES_REFL_' 'mat/divides_n_n'
0. 'hl/thm/realax/REAL_ADD_LDISTRIB_' 'mat/eq_gcd_times_times_times_gcd'
0. 'hl/thm/realax/TREAL_ADD_SYM_EQ_'#@#variant 'mat/sym_rtimes'
0. 'hl/thm/calc_int/REAL_ADD_AC_0' 'mat/sym_rtimes'
0. 'hl/thm/realax/NADD_EQ_TRANS_' 'mat/trans_divides'
0. 'hl/thm/realax/TREAL_MUL_WELLDEFR_'#@#variant 'mat/lt_plus_l'
0. 'hl/thm/Multivariate/complexes/MONOIDAL_COMPLEX_MUL_'#@#variant 'mat/assoc_orb'
0. 'hl/thm/Library/transc/ATN_/2' 'mat/Zpred_Zsucc'
0. 'hl/thm/Multivariate/complexes/REAL_INV_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_SUB_RZERO_'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/Library/prime/PRIME_GE_2_'#@#variant 'mat/correct2'
0. 'hl/thm/arith/MULT_AC_0' 'mat/andb_sym'
0. 'hl/thm/calc_num/ARITH_98' 'mat/Qinv_Qtimes\''
0. 'hl/thm/arith/FACT_LT_'#@#variant 'mat/not_nf_elim_not/0'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/times_fa_Qtimes'
0. 'hl/thm/Multivariate/complexes/CX_MUL_'#@#variant 'mat/times_Qtimes'
0. 'hl/thm/Multivariate/vectors/LIFT_DROP_1'#@#variant 'mat/factorize_defactorize'
0. 'hl/thm/calc_int/REAL_MUL_LZERO_'#@#variant 'mat/exp_SO_n'#@#variant
0. 'hl/thm/int/INT_MAX_ACI_3' 'mat/orb_refl'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_ADD_RDISTRIB_' 'mat/times_exp'
0. 'hl/thm/iterate/MONOIDAL_REAL_ADD_' 'mat/symm_orb'
0. 'hl/thm/real/REAL_INV_INV_' 'mat/finv_finv'
0. 'hl/thm/realax/REAL_ADD_SYM_' 'mat/sym_Zplus'
0. 'hl/thm/Complex/complexnumbers/CNJ_CNJ_' 'mat/Zopp_Zopp'
0. 'hl/thm/Multivariate/complexes/COMPLEX_MUL_AC_0'#@#variant 'mat/sym_rtimes'
0. 'hl/thm/Library/pratt/PHI_0_'#@#variant 'mat/A_SO'#@#variant
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_PHI_' 'mat/injective_S'#@#variant
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/Qinv_Qinv'
0. 'hl/thm/arith/SUB_REFL_'#@#variant 'mat/minus_n_n'
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/eq_plus_Zplus'
0. 'hl/thm/real/REAL_MIN_ASSOC_' 'mat/assoc_Ztimes'
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_SUB_' 'mat/demorgan2'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/Ztimes_Zone_r'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_1' 'mat/assoc_Zplus'
0. 'hl/thm/realax/TREAL_NEG_WELLDEF_'#@#variant 'mat/le_S_S'
0. 'hl/thm/arith/PRE_0'#@#variant 'mat/A_SSO'#@#variant
0. 'hl/thm/Library/integer/INT_PRIME_DIVPROD_' 'mat/divides_times_to_divides'
0. 'hl/thm/Library/analysis/SEQ_SUBLE_' 'mat/le_n_fn'
0. 'hl/thm/Library/transc/TAN_0_'#@#variant 'mat/eq_OZ_Zopp_OZ'
0. 'hl/thm/realax/HREAL_MUL_SYM_' 'mat/sym_rtimes'
0. 'hl/thm/realax/TREAL_MUL_SYM_EQ_'#@#variant 'mat/sym_gcd'
0. 'hl/thm/Library/poly/POLY_ADD_'#@#variant 'mat/eq_times_f_times1'
0. 'hl/thm/int/INT_MIN_MIN_/0' 'mat/divides_gcd_n'
0. 'hl/thm/Library/prime/INDEX_1_'#@#variant 'mat/bc_n_O'#@#variant
0. 'hl/thm/realax/REAL_ADD_ASSOC_' 'mat/assoc_times'
0. 'hl/thm/arith/LET_CASES_' 'mat/not_le_to_lt'
0. 'hl/thm/Complex/complexnumbers/CX_DIV_' 'mat/bool_to_nat_andb'
0. 'hl/thm/int/INT_MUL_LID_'#@#variant 'mat/gcd_O_n'
0. 'hl/thm/int/INT_ADD_SYM_' 'mat/sym_Ztimes'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NEG_NEG_' 'mat/eq_notb_notb_b_b'
0. 'hl/thm/Library/poly/POLY_DIVIDES_TRANS_'#@#variant 'mat/trans_lt'
0. 'hl/thm/Library/prime/INDEX_1_'#@#variant 'mat/mod_SO'#@#variant
0. 'hl/thm/Library/transc/ATN_/0'#@#variant 'mat/le_SO_fact'
0. 'hl/thm/Library/pocklington/PHI_LOWERBOUND_1_STRONG_'#@#variant 'mat/lt_O_smallest_factor'#@#variant
0. 'hl/thm/Multivariate/transcendentals/REAL_EXP_POS_LE_'#@#variant 'mat/not_nf_elim_not/1'
0. 'hl/thm/Library/floor/FLOOR_/1' 'mat/le_smallest_factor_n'
0. 'hl/thm/int/INT_OF_NUM_MAX_' 'mat/eq_plus_Zplus'
0. 'hl/thm/realax/HREAL_LE_MUL_RCANCEL_IMP_' 'mat/le_times_l'
0. 'hl/thm/realax/HREAL_ADD_LDISTRIB_' 'mat/distr_Ztimes_Zplus'
0. 'hl/thm/Complex/complexnumbers/CX_ADD_' 'mat/eq_times_fa_times'
0. 'hl/thm/int/INT_LE_LMUL_'#@#variant 'mat/le_log'#@#variant
0. 'hl/thm/arith/SUB_0_/1'#@#variant 'mat/rtimes_r_one'
0. 'hl/thm/calc_num/ARITH_30' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_SIGMA_' 'mat/injective_S'#@#variant
0. 'hl/thm/Library/transc/COS_BOUNDS_/0'#@#variant 'mat/lt_SO_nth_prime_n'#@#variant
0. 'hl/thm/arith/LT_TRANS_' 'mat/trans_le'
0. 'hl/thm/arith/ADD_0_'#@#variant 'mat/times_n_SO'#@#variant
0. 'hl/thm/int/INT_MAX_ACI_0' 'mat/sym_plus'
0. 'hl/thm/real/REAL_MAX_ACI_1' 'mat/assoc_Ztimes'
0. 'hl/thm/calc_num/ARITH_20' 'mat/Qinv_Qtimes\''
0. 'hl/thm/Complex/complexnumbers/COMPLEX_MUL_AC_1' 'mat/assoc_times'
0. 'hl/thm/realax/TREAL_EQ_TRANS_'#@#variant 'mat/trans_lt'
0. 'hl/thm/Complex/complexnumbers/COMPLEX_NORM_POS_'#@#variant 'mat/sieve_sorted'#@#variant
0. 'hl/thm/calc_int/REAL_ADD_RID_'#@#variant 'mat/exp_n_SO'#@#variant
0. 'hl/thm/Library/transc/REAL_EXP_MONO_IMP_' 'mat/le_S_S'
0. 'hl/thm/realax/REAL_OF_NUM_ADD_' 'mat/eq_plus_Zplus'
0. 'hl/thm/Library/multiplicative/MULTIPLICATIVE_SIGMA_' 'mat/monotonic_sqrt'#@#variant
0. 'hl/thm/calc_num/ARITH_16' 'mat/Qinv_Qtimes\''
0. 'hl/thm/int/INT_SUB_REFL_'#@#variant 'mat/minus_n_n'
0. 'hl/thm/real/REAL_MUL_AC_1' 'mat/andb_assoc'
0. 'hl/thm/calc_num/ARITH_10' 'mat/Qinv_Qtimes\''
