proposition: Lemma CReal_abs_lt : forall x y : CReal, CReal_abs x < y -> prod (x < y) (-x < y).
proof: Proof. split. - apply (CReal_le_lt_trans _ _ _ (CReal_le_abs x)), H. - apply (CReal_le_lt_trans _ _ _ (CReal_le_abs (-x))). rewrite CReal_abs_opp. exact H. Qed.
imports: QArith Qabs Qpower ConstructiveCauchyReals ConstructiveCauchyRealsMult Lia Lqa QExtra