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