proposition: Fact bt_pow_iter_trans t n : bt_transitive t -> bt_transitive (iter bt_pow t n) /\ t ⊆ iter bt_pow t n.
proof: Proof. revert t; induction n as [ | n IHn ]; simpl; intros t Ht; auto; split. + apply IHn, bt_pow_transitive; auto. + destruct (IHn _ (bt_pow_transitive Ht)) as [ _ H ]. apply bti_trans with (2 := H), bt_pow_trans_incl; auto. Qed.
imports: List Arith Lia Max Wellfounded Setoid Eqdep_dec Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list utils_decidable finite seteq) Undecidability.Shared.Libs.DLW.Vec(pos) Undecidability.Shared.Libs.DLW.Wf(wf_finite wf_chains) Undecidability.FOL.TRAKHTENBROT(notations fol_ops)