proposition: Lemma CRealAbsLUB : forall x y : CReal, x <= y /\ (- x) <= y <-> (CReal_abs x) <= y.
proof: Proof. split. - intros [H H0]. apply CReal_abs_le. split. 2: exact H. apply (CReal_plus_le_reg_r (y-x)). ring_simplify. exact H0. - intros. apply CReal_abs_def2 in H. destruct H. split. + exact H. + fold (-x <= y). apply (CReal_plus_le_reg_r (x-y)). ring_simplify. exact H0. Qed.
imports: QArith_base Qabs ConstructiveReals ConstructiveCauchyRealsMult Logic.ConstructiveEpsilon ConstructiveCauchyAbs Lia Lqa Qpower QExtra PosExtra ConstructiveExtra Qminmax