x y : 0 ≤ x -> 0 ≤ y -> int_abs Z N (x + y) = int_abs Z N x + int_abs Z N y. Proof. intros. apply (injective f). rewrite (preserves_plus (f:=f)), !int_abs_nonneg;auto. apply nonneg_plus_compat;trivial. Qed.
Require Import