proposition: Lemma CRmorph_appart_zero : forall {R1 R2 : ConstructiveReals} (f : @ConstructiveRealsMorphism R1 R2) (x : CRcarrier R1) (app : x ≶ 0), CRmorph f x ≶ 0.
proof: Proof. intros. destruct app. - left. apply (CRlt_le_trans _ (CRmorph f 0)). + apply CRmorph_increasing. exact c. + exact (proj2 (CRmorph_zero f)). - right. apply (CRle_lt_trans _ (CRmorph f 0)). + exact (proj1 (CRmorph_zero f)). + apply CRmorph_increasing. exact c. Defined.
imports: QArith Qabs ConstructiveReals ConstructiveLimits ConstructiveAbs