theory int.Power : one more lemma

lib/coq/int/Power.v

@@ -79,6 +79,13 @@ rewrite 3!power_is_exponentiation ; auto with zarith.
 apply Power_mult2 ; auto with zarith.
 Qed.
 
+(* Why3 goal *)
+Lemma Power_non_neg : forall (x:Z) (y:Z), ((0%Z <= x)%Z /\ (0%Z <= y)%Z) ->
+  (0%Z <= (power x y))%Z.
+intros x y (h1,h2).
+now apply Z.pow_nonneg.
+Qed.
+
 Open Scope Z_scope.
 
 (* Why3 goal *)

theories/int.why

@@ -235,6 +235,9 @@ theory Power
     goal CommutativeMonoid.Unit_def_l, goal CommutativeMonoid.Unit_def_r,
     goal CommutativeMonoid.Comm.Comm
 
+  lemma Power_non_neg:
+     forall x y. x >= 0 /\ y >= 0 -> power x y >= 0
+
   lemma Power_monotonic:
     forall x n m:int. 0 < x /\ 0 <= n <= m -> power x n <= power x m