proposition: Lemma empty_correct : forall x, contains (convert empty) x -> False.
proof: Proof. intros [|x]. { now simpl; case (_ && _). } simpl. unfold c1. rewrite F.fromZ_correct, F.zero_correct by easy. case (_ && _); simpl; lra. Qed.
imports: Coq(Bool Reals Psatz) Flocq(Raux) Stdlib Xreal Basic Sig Interval