proposition: Lemma Dconst : forall (D:R -> Prop) (y x0:R), D_in (fun x:R => y) (fun x:R => 0) D x0.
proof: Proof. unfold D_in; intros; unfold limit1_in; unfold limit_in; unfold Rdiv; intros; simpl; split with eps; split; auto. intros; rewrite (Rminus_diag_eq y y (eq_refl y)); rewrite Rmult_0_l; unfold Rdist; rewrite (Rminus_diag_eq 0 0 (eq_refl 0)); unfold Rabs; case (Rcase_abs 0); intro. - absurd (0 < 0); auto. red; intro; apply (Rlt_irrefl 0 H1). - unfold Rgt in H0; assumption. Qed.
imports: Rbase Rfunctions Rlimit Lra Lia