proposition: Lemma Zabs_nat_inj : forall a b, 0 <= a -> 0 <= b -> Z.abs_nat a = Z.abs_nat b -> a = b.
proof: Proof. intros a b Pa Pb E. rewrite <- (Z.abs_eq a), <- (Z.abs_eq b); eauto. do 2 rewrite <- inj_Zabs_nat. auto. Qed.
imports: ZArith Lia Znumtheory