(* QuickChick Prelude *)
Set Warnings "-extraction-opaque-accessed,-extraction".
Set Warnings "-notation-overridden,-parsing".
Set Bullet Behavior "Strict Subproofs".
(* End prelude *)
Definition Assertion := state -> Prop.
Definition assert_implies (P Q : Assertion) : Prop :=
forall st, P st -> Q st.
Notation "P ->> Q" := (assert_implies P Q)
(at level 80) : hoare_spec_scope.
Open Scope hoare_spec_scope.
Notation "P <<->> Q" :=
(P ->> Q /\ Q ->> P) (at level 80) : hoare_spec_scope.
Definition hoare_triple
(P:Assertion) (c:com) (Q:Assertion) : Prop :=
forall st st',
c / st \\ st'  ->
P st  ->
Q st'.
Notation "{{ P }}  c  {{ Q }}" :=
(hoare_triple P c Q) (at level 90, c at next level)
: hoare_spec_scope.

Theorem hoare_post_true : forall (P Q : Assertion) c,
(forall st, Q st) ->
{{P}} c {{Q}}.