Swap.v

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Require Import ZArith.
Require Import Lists.List.
Require Import Sorting.Sorted.
Require Import ZArith.
Require Import String.
Require Import Ascii.
Require Import Setoid.
Require Import SetoidClass.
Require Import Morphisms.
Require Import Basics. 
Require Import SLMech.SequentialProof.
Require Import SLMech.Assertions.
Require Import SLMech.ProgramData.
Require Import SLMech.ProgramSemantics.
Require Import SLMech.Automation.

Theorem Swap :
  forall (x y z : var) (vx vy : val) (s : store_f) (h : heap_f) (l : locals) (d : domain) (st2 : state),
    (((fun st => (store_bits (x::y::nil) (lc st))) ☆
     (x ≐ Some vx) ☆
     (y ≐ Some vy)) {|srf := s ; lc := l; hpf := h; dm := d|}) ->
    (completes {|srf := s ; lc := l; hpf := h; dm := d|} st2
     (local z skip;;
       (z ≔ x);;
       (x ≔ y);;
       (y ≔ z);; ret ;; skip)) ->
    (((x ≐ Some vy) ☆ (y ≐ Some vx)) st2).
Proof.
  intros.
  nova_star H.
  program_paths H0.
  apply intro_ssep_conj with (d' := d).
  unfold Dom.Subset.
  intros.
  auto.
  simpl.
  auto.
  simpl.
  auto.
Qed.