proposition: Fact nat2bt_strict n m : nat2bt n ∈ nat2bt m <-> n < m.
proof: Proof. split. + intros H. destruct (le_lt_dec m n) as [ H1 | ]; auto. generalize (nat2bt_mono H1 H); intros H2. apply btm_depth in H2; lia. + intros H; apply (nat2bt_mono H). simpl; btm simpl. 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)