abs absurd acc.cases_on add add_comm_group add_comm_semigroup add_group add_monoid and and.elim_left and.elim_right and.intro bit0 bit1 bool bool.ff bool.tt bv caching_user_attribute cast cast_eq cast_heq char char.of_nat classical classical.prop_decidable classical.type_decidable_eq coe coe_fn coe_sort coe_to_lift combinator.K comm_ring comm_semiring congr congr_arg congr_fun cyclic_numerals cyclic_numerals.bound decidable decidable.by_contradiction discrete_field distinct distrib dite div id empty empty.rec emptyc Exists eq eq.drec eq.elim_inv_inv eq.intro eq.mp eq.mpr eq.nrec eq.rec eq_rec_eq eq.refl eq.subst eq.symm eq.trans eq_of_heq eq_rec_heq exists.elim functor functorIO false false_of_true_iff_false false.rec field fin fin.mk forall_congr forall_congr_eq funext ge get_line gt has_add has_div has_mul has_le has_lt has_neg has_one has_one.one has_sizeof has_sizeof.mk has_sizeof.sizeof has_sub has_to_string has_zero has_zero.zero has_coe_t heq heq.refl heq.symm heq.trans heq_of_eq if_neg if_pos iff iff.elim_left iff.elim_right iff_false_intro iff.intro iff.mp iff.mpr iff.refl iff.symm iff.trans iff_true_intro imp_congr imp_congr_eq imp_congr_ctx imp_congr_ctx_eq implies implies_of_if_neg implies_of_if_pos implies.resolve insert int int.of_nat int.has_zero int.has_one int.has_add int.has_mul int.has_sub int.has_div int.has_le int.has_lt int.has_neg int.has_mod int_decidable_linear_ordered_comm_group IO is_associative is_associative.op_assoc is_int is_trunc.is_prop is_trunc.is_prop.elim is_trunc.is_set ite left_distrib le le.refl lift lift.down lift.up linear_ordered_comm_ring linear_ordered_ring linear_ordered_semiring list list.nil list.cons lt map map.insert map.lookup map.select map.store mod monad monad.map monad.bind monad.ret monad.and_then monadIO monoid mul mul_one mul_zero mul_zero_class name name.anonymous name.mk_string nat nat.of_num nat.succ nat.zero nat.has_zero nat.has_one nat.has_add nat.has_mul nat.has_div nat.has_sub nat.has_neg nat.has_lt nat.has_le nat.add nat.no_confusion nat.cases_on ne neg norm_num.add1 norm_num.add1_bit0 norm_num.add1_bit1_helper norm_num.add1_one norm_num.add1_zero norm_num.add_div_helper norm_num.bin_add_zero norm_num.bin_zero_add norm_num.bit0_add_bit0_helper norm_num.bit0_add_bit1_helper norm_num.bit0_add_one norm_num.bit1_add_bit0_helper norm_num.bit1_add_bit1_helper norm_num.bit1_add_one_helper norm_num.div_add_helper norm_num.div_eq_div_helper norm_num.div_helper norm_num.div_mul_helper norm_num.mk_cong norm_num.mul_bit0_helper norm_num.mul_bit1_helper norm_num.mul_div_helper norm_num.neg_add_neg_helper norm_num.neg_add_pos_helper1 norm_num.neg_add_pos_helper2 norm_num.neg_mul_neg_helper norm_num.neg_mul_pos_helper norm_num.neg_neg_helper norm_num.neg_zero_helper norm_num.nonneg_bit0_helper norm_num.nonneg_bit1_helper norm_num.nonzero_of_div_helper norm_num.nonzero_of_neg_helper norm_num.nonzero_of_pos_helper norm_num.one_add_bit0 norm_num.one_add_bit1_helper norm_num.one_add_one norm_num.pos_add_neg_helper norm_num.pos_add_pos_helper norm_num.pos_bit0_helper norm_num.pos_bit1_helper norm_num.pos_mul_neg_helper norm_num.sub_eq_add_neg_helper norm_num.subst_into_div norm_num.subst_into_prod norm_num.subst_into_subtr norm_num.subst_into_sum not not_of_iff_false not_of_not_not_not num num.pos num.zero of_iff_true one one_mul option option.none option.some or or.elim or.intro_left or.intro_right or.neg_resolve_left or.neg_resolve_right or.rec or.resolve_left or.resolve_right poly_unit poly_unit.star pos_num pos_num.bit0 pos_num.bit1 pos_num.one prod prod.mk prod.fst prod.snd propext pexpr pexpr.subst put_str put_nat to_pexpr quot.mk quot.lift rat.divide rat.of_num rat.of_int real real.has_zero real.has_one real.has_add real.has_mul real.has_sub real.has_div real.has_le real.has_lt real.has_neg real.is_int real.of_rat real.of_int real.to_int rfl right_distrib ring set_of sep select semiring sigma sigma.cases_on sigma.mk sigma.fst sigma.snd simp simplifier.assoc_subst simplifier.congr_bin_op simplifier.congr_bin_arg1 simplifier.congr_bin_arg2 simplifier.congr_bin_args singleton sizeof smt.array smt.select smt.store smt.prove sorry store string string.empty string.str sub subsingleton subsingleton.elim subsingleton.helim subtype subtype.tag subtype.elt_of subtype.rec sum sum.cases_on sum.inl sum.inr tactic tactic.eval_expr tactic.constructor tactic.step tactic.to_expr tactic.skip tactic.try tactic.interactive tactic.interactive.types.ident tactic.interactive.types.opt_ident tactic.interactive.types.using_ident tactic.interactive.types.ident_list tactic.interactive.types.raw_ident_list tactic.interactive.types.with_ident_list tactic.interactive.types.without_ident_list tactic.interactive.types.location tactic.interactive.types.qexpr tactic.interactive.types.qexpr0 tactic.interactive.types.qexpr_list tactic.interactive.types.opt_qexpr_list tactic.interactive.types.qexpr_list_or_qexpr0 tactic.interactive.types.itactic tactic.interactive.types.colon_tk tactic.interactive.types.assign_tk tactic.interactive.types.comma_tk to_string to_int to_real trans_rel_left trans_rel_right true true.intro unification_hint unification_hint.mk unification_constraint unification_constraint.mk unit unit.cases_on unit.star user_attribute weak_order well_founded xor zero zero_le_one zero_lt_one zero_mul