forall q r : Q, abs (q + r) <= abs q + abs r. Proof. intros. rewrite (Qabs_is_join (q + r)). apply join_le. - rewrite negate_plus_distr. apply plus_le_compat;apply Qabs_le_neg_raw. - apply plus_le_compat;apply Qabs_le_raw. Qed.
Require Import Import Quoting.Instances. Import NatPair.Instances.