update proof of power: missing coq file

examples/programs/power/power_WP_M_WP_parameter_fast_exp_imperative_3.v

+(* This file is generated by Why3's Coq driver *)
+(* Beware! Only edit allowed sections below    *)
+Require Import ZArith.
+Require Import Rbase.
+Require Import ZOdiv.
+Definition unit  := unit.
+
+Parameter mark : Type.
+
+Parameter at1: forall (a:Type), a -> mark -> a.
+
+Implicit Arguments at1.
+
+Parameter old: forall (a:Type), a -> a.
+
+Implicit Arguments old.
+
+Axiom Abs_le : forall (x:Z) (y:Z), ((Zabs x) <= y)%Z <-> (((-y)%Z <= x)%Z /\
+  (x <= y)%Z).
+
+Parameter power: Z -> Z -> Z.
+
+
+Axiom Power_0 : forall (x:Z), ((power x 0%Z) = 1%Z).
+
+Axiom Power_s : forall (x:Z) (n:Z), (0%Z <  n)%Z -> ((power x
+  n) = (x * (power x (n - 1%Z)%Z))%Z).
+
+Axiom Power_1 : forall (x:Z), ((power x 1%Z) = x).
+
+Axiom Power_sum : forall (x:Z) (n:Z) (m:Z), (0%Z <= n)%Z -> ((0%Z <= m)%Z ->
+  ((power x (n + m)%Z) = ((power x n) * (power x m))%Z)).
+
+Axiom Power_mult : forall (x:Z) (n:Z) (m:Z), (0%Z <= n)%Z -> ((0%Z <= m)%Z ->
+  ((power x (n * m)%Z) = (power (power x n) m))).
+
+Axiom Power_mult2 : forall (x:Z) (y:Z) (n:Z), (0%Z <= n)%Z ->
+  ((power (x * y)%Z n) = ((power x n) * (power y n))%Z).
+
+Inductive ref (a:Type) :=
+  | mk_ref : a -> ref a.
+Implicit Arguments mk_ref.
+
+Definition contents (a:Type)(u:(ref a)): a :=
+  match u with
+  | mk_ref contents1 => contents1
+  end.
+Implicit Arguments contents.
+
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+(* DO NOT EDIT BELOW *)
+
+Theorem WP_parameter_fast_exp_imperative : forall (x:Z), forall (n:Z),
+  (0%Z <= n)%Z -> forall (e:Z), forall (p:Z), forall (r:Z), ((0%Z <= e)%Z /\
+  ((r * (power p e))%Z = (power x n))) -> ((0%Z <  e)%Z ->
+  ((~ ((ZOmod e 2%Z) = 1%Z)) -> forall (p1:Z), (p1 = (p * p)%Z) ->
+  forall (e1:Z), (e1 = (ZOdiv e 2%Z)) -> ((r * (power p1 e1))%Z = (power x
+  n)))).
+(* YOU MAY EDIT THE PROOF BELOW *)
+intros x n Hn e0 p0 r0 (He0,Hind).
+intros He0' Hmod p1 Hp e1 He.
+rewrite <- Hind.
+apply f_equal.
+subst.
+assert (h: (e0 = e0/2 + e0/2)%Z).
+assert (e0 mod 2 = 0).
+generalize (ZOmod_lt_pos e0 2).
+unfold Zabs; omega.
+rewrite (ZO_div_mod_eq e0 2) at 1; omega.
+rewrite Power_mult2; auto with zarith.
+rewrite h at 3.
+rewrite Power_sum; omega.
+Qed.
+(* DO NOT EDIT BELOW *)
+
+