proposition: Lemma inj_add n m : 0<=n -> 0<=m -> Z.abs_N (n+m) = (Z.abs_N n + Z.abs_N m)%N.
proof: Proof. intros. rewrite !abs_N_nonneg; trivial. - now apply Z2N.inj_add. - now apply Z.add_nonneg_nonneg. Qed.
imports: Arith_base BinPos BinInt BinNat Pnat Nnat