Module Type NBitsProp
(Import A : NAxiomsSig')
(Import B : NSubProp A)
(Import C : NParityProp A B)
(Import D : NPowProp A B C)
(Import E : NDivProp A B)
(Import F : NLog2Prop A B C D).
Include BoolEqualityFacts A.
Ltac order_nz := try apply pow_nonzero; order'.
Hint Rewrite div_0_l mod_0_l div_1_r mod_1_r : nz.
(** Some properties of power and division *)

Lemma pow_sub_r : forall a b c, a~=0 -> c<=b -> a^(b-c) == a^b / a^c.