proposition: Fact df_pred_ext f ν ω : (forall x, ν x = ω x) -> ⟦f⟧ ν <-> ⟦f⟧ ω.
proof: Proof. induction f as [ | | [] | [] f Hf g Hg | f Hf ] in ν, ω |- *; intros H; simpl. 1-4: rewrite !H; tauto. 1-2: rewrite Hf, Hg; auto; tauto. split; intros (n & Hn); exists n; revert Hn; apply Hf; intros []; simpl; auto. Qed.
imports: Arith Nat ZArith Lia Undecidability.Shared.Libs.DLW.Utils(utils_tac gcd sums bounded_quantification)