proposition: Fact lb_pointwise_mono_left l m k : l ⪯ m -> lb_pointwise k l ⪯ lb_pointwise k m.
proof: Proof. Proof using Hf1 Hf2. intros H; revert m H k. induction l as [ | x l IHl ]; intros m H k; auto. destruct m as [ | y m ]. * apply lbpw_mono_2; auto. * destruct k as [ | u k ]. - apply lbpw_mono_f_0; auto. - do 2 rewrite lb_pointwise_cons. apply lb_mask_inv_cons in H; destruct H. apply lb_mask_leb; auto. Qed.
imports: List Lia Bool Setoid Undecidability.Shared.Libs.DLW.Utils(utils_tac)