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_Zpower :
forall e1 e2,
(Zpower r (e1 - 1) < Zpower r e2)%Z ->
(e1 <= e2)%Z.