proposition: Lemma inj_pow n m : 0 <= n -> 0 <= m -> Z.to_nat (n ^ m) = (Z.to_nat n ^ Z.to_nat m)%nat.
proof: Proof. intros Hn Hm. now rewrite <- !Z_N_nat, Z2N.inj_pow, N2Nat.inj_pow. Qed.
imports: Arith_base BinPos BinInt BinNat Pnat Nnat