Section Zpower.
(** The radix must be greater than 1 *)
Record radix := { radix_val :> Z ; radix_prop : Zle_bool 2 radix_val = true }.
Definition radix2 := Build_radix 2 (refl_equal _).
Variable r : radix.

Theorem Zpower_lt :
forall e1 e2, (0 <= e2)%Z -> (e1 < e2)%Z ->
(Zpower r e1 < Zpower r e2)%Z.