proposition: Lemma inj_add n m : 0<=n -> 0<=m -> Z.abs_nat (n+m) = (Z.abs_nat n + Z.abs_nat m)%nat.
proof: Proof. intros. now rewrite <- !Zabs_N_nat, Zabs2N.inj_add, N2Nat.inj_add. Qed.
imports: Arith_base BinPos BinInt BinNat Pnat Nnat