(* This file was originally generated by why.
   It can be modified; only the generated parts will be overwritten. *)

Require Import Why.
Require Import Omega.
Require Import Partition.
Require Import Quicksort.

Require Import partition_why.

Proof.
intros; omega.
Qed.

  Proof.
  intuition SameLength t1 t0; omega.
Qed.

Proof.
intuition.
Qed.

Proof.
intuition; SameLength t2 t1; SameLength t1 t0; omega.
Qed.

Proof.
intros; unfold Zwf; omega.
Qed.

Proof.
intros.
apply quicksort_lemma with (t1 := t1) (t2 := t2) (p := p); intuition.
 Qed.

Proof.
intros; apply quicksort_trivial; intuition.
Qed.


Proof.
intuition omega.
Qed.

Proof.
intuition eauto.
SameLength t0 t; rewrite H3; trivial.
Qed.


Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.




Proof.
(* FILL PROOF HERE *)
Save.

Proof.
(* FILL PROOF HERE *)
Save.




