absurd 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 char char.mk classical congr congr_arg congr_fun decidable decidable.by_contradiction distrib dite div empty empty.rec 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 exists.elim false false_of_true_iff_false false.rec field funext has_add has_div has_mul has_neg has_one has_one.one has_sub has_zero has_zero.zero heq heq.refl heq.to_eq 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 implies implies_of_if_neg implies_of_if_pos implies.resolve is_trunc.is_hprop is_trunc.is_hprop.elim is_trunc.is_hset ite left_distrib le.refl lift lift.down lift.up linear_ordered_ring linear_ordered_semiring monoid mul mul_one mul_zero mul_zero_class nat nat.of_num nat.succ nat.zero 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.pr1 prod.pr2 propext rat.divide rat.of_num right_distrib ring semiring sigma sigma.mk sorry string string.empty string.str sub subsingleton subsingleton.elim tactic tactic.all_goals tactic.and_then tactic.append tactic.apply tactic.assert_hypothesis tactic.assumption tactic.at_most tactic.beta tactic.builtin tactic.cases tactic.change tactic.check_expr tactic.clear tactic.clears tactic.determ tactic.discard tactic.eapply tactic.eassumption tactic.exact tactic.expr tactic.expr.builtin tactic.expr_list tactic.expr_list.cons tactic.expr_list.nil tactic.fail tactic.fapply tactic.fixpoint tactic.focus_at tactic.generalizes tactic.generalize_tac tactic.id tactic.identifier tactic.identifier_list tactic.interleave tactic.intro tactic.intros tactic.location tactic.with_expr tactic.none_expr tactic.note_tac tactic.now tactic.opt_expr tactic.opt_expr_list tactic.opt_identifier_list tactic.or_else tactic.par tactic.refine tactic.rename tactic.repeat tactic.revert tactic.reverts tactic.rexact tactic.rotate_left tactic.rotate_right tactic.state tactic.trace tactic.try_for tactic.using_expr tactic.whnf trans_rel_left trans_rel_right true true.intro weak_order well_founded zero zero_le_one zero_lt_one zero_mul