(* Definition of the hoare relation and rules *)
Definition hoare (t:terminationMeasure) (n':nat) (G R P:pred world) (c:instruction) (Q:pred world) :=
forall t', termMeasure_incr t t' ->
forall p n k stk,
(forall s, G (p,(s,t'))) ->
(forall r', guards n R stk       (p,(r',t'))) ->
(forall r', guards n Q (k::stk)  (p,(r',t'))) ->
(forall r,  guards (n'+n) P ((c ;; k)::stk) (p,(r,t'))).

Lemma hoare_ex_pre : forall t x G R T P i Q,
(forall z:T, hoare t x G R (P z) i Q) ->
hoare t x G R (exp P) i Q.