proposition: Lemma CRealLt_above_same : forall (x y : CReal) (n : Z), (2 * 2 ^ n < seq y n - seq x n)%Q -> forall p:Z, (p <= n)%Z -> Qlt (seq x p) (seq y p).
proof: Proof. intros x y n inf p H. simpl in inf |- *. pose proof ((cauchy x) n p n ltac:(lia) ltac:(lia)). pose proof ((cauchy y) n p n ltac:(lia) ltac:(lia)). rewrite Qabs_Qlt_condition in *. lra. Qed.
imports: QArith Qpower Qabs Qround Logic.ConstructiveEpsilon Lia Lqa QExtra ConstructiveExtra