isolate instances about Permutation and PermutationA which may slow rewrite

 After discovering a rewrite in Ergo that takes a loooong time due
 to a bad interaction with the instances of Permutation and PermutationA :

 - PermutationA is now in a separate file SetoidPermutation
 - File Permutation.v isn't Require'd by SetoidList anymore
   nor MergeSort.v, just the definitions in Sorted.v
 - Attempt to put a priority on these instances.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15584 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 1 insertions, 113 deletions

diff --git a/theories/Lists/SetoidList.v b/theories/Lists/SetoidList.v
index f6eab8649..7d3c383c1 100644
--- a/theories/Lists/SetoidList.v
+++ b/theories/Lists/SetoidList.v
@@ -7,7 +7,7 @@
 (***********************************************************************)
 
 Require Export List.
-Require Export Sorting.
+Require Export Sorted.
 Require Export Setoid Basics Morphisms.
 Set Implicit Arguments.
 Unset Strict Implicit.
@@ -908,118 +908,6 @@ Qed.
 
 End Find.
 
-(** Permutations of list modulo a setoid equality. *)
-(** Section contributed by Robbert Krebbers (Nijmegen University). *)
-
-Section Permutation.
-Context {A : Type} (eqA : relation A) (e : Equivalence eqA).
-
-Inductive PermutationA : list A -> list A -> Prop :=
-  | permA_nil: PermutationA nil nil
-  | permA_skip x₁ x₂ l₁ l₂ :
-     eqA x₁ x₂ -> PermutationA l₁ l₂ -> PermutationA (x₁ :: l₁) (x₂ :: l₂)
-  | permA_swap x y l : PermutationA (y :: x :: l) (x :: y :: l)
-  | permA_trans l₁ l₂ l₃ :
-     PermutationA l₁ l₂ -> PermutationA l₂ l₃ -> PermutationA l₁ l₃.
-Local Hint Constructors PermutationA.
-
-Global Instance: Equivalence PermutationA.
-Proof.
- constructor.
- - intro l. induction l; intuition.
- - intros l₁ l₂. induction 1; eauto. apply permA_skip; intuition.
- - exact permA_trans.
-Qed.
-
-Global Instance PermutationA_cons :
-  Proper (eqA ==> PermutationA ==> PermutationA) (@cons A).
-Proof.
- repeat intro. now apply permA_skip.
-Qed.
-
-Lemma PermutationA_app_head l₁ l₂ l :
-  PermutationA l₁ l₂ -> PermutationA (l ++ l₁) (l ++ l₂).
-Proof.
- induction l; trivial; intros. apply permA_skip; intuition.
-Qed.
-
-Global Instance PermutationA_app :
-  Proper (PermutationA ==> PermutationA ==> PermutationA) (@app A).
-Proof.
- intros l₁ l₂ Pl k₁ k₂ Pk.
- induction Pl.
- - easy.
- - now apply permA_skip.
- - etransitivity.
-   * rewrite <-!app_comm_cons. now apply permA_swap.
-   * rewrite !app_comm_cons. now apply PermutationA_app_head.
- - do 2 (etransitivity; try eassumption).
-   apply PermutationA_app_head. now symmetry.
-Qed.
-
-Lemma PermutationA_app_tail l₁ l₂ l :
-  PermutationA l₁ l₂ -> PermutationA (l₁ ++ l) (l₂ ++ l).
-Proof.
- intros E. now rewrite E.
-Qed.
-
-Lemma PermutationA_cons_append l x :
-  PermutationA (x :: l) (l ++ x :: nil).
-Proof.
- induction l.
- - easy.
- - simpl. rewrite <-IHl. intuition.
-Qed.
-
-Lemma PermutationA_app_comm l₁ l₂ :
-  PermutationA (l₁ ++ l₂) (l₂ ++ l₁).
-Proof.
- induction l₁.
- - now rewrite app_nil_r.
- - rewrite <-app_comm_cons, IHl₁, app_comm_cons.
-   now rewrite PermutationA_cons_append, <-app_assoc.
-Qed.
-
-Lemma PermutationA_cons_app l l₁ l₂ x :
-  PermutationA l (l₁ ++ l₂) -> PermutationA (x :: l) (l₁ ++ x :: l₂).
-Proof.
- intros E. rewrite E.
- now rewrite app_comm_cons, PermutationA_cons_append, <-app_assoc.
-Qed.
-
-Lemma PermutationA_middle l₁ l₂ x :
-  PermutationA (x :: l₁ ++ l₂) (l₁ ++ x :: l₂).
-Proof.
- now apply PermutationA_cons_app.
-Qed.
-
-Lemma PermutationA_equivlistA l₁ l₂ :
-  PermutationA l₁ l₂ -> equivlistA eqA l₁ l₂.
-Proof.
- induction 1.
- - reflexivity.
- - now apply equivlistA_cons_proper.
- - now apply equivlistA_permute_heads.
- - etransitivity; eassumption.
-Qed.
-
-Lemma NoDupA_equivlistA_PermutationA l₁ l₂ :
-  NoDupA eqA l₁ -> NoDupA eqA l₂ ->
-   equivlistA eqA l₁ l₂ -> PermutationA l₁ l₂.
-Proof.
-  intros Pl₁. revert l₂. induction Pl₁ as [|x l₁ E1].
-  - intros l₂ _ H₂. symmetry in H₂. now rewrite (equivlistA_nil_eq eqA).
-  - intros l₂ Pl₂ E2.
-    destruct (@InA_split _ eqA l₂ x) as [l₂h [y [l₂t [E3 ?]]]].
-    { rewrite <-E2. intuition. }
-    subst. transitivity (y :: l₁); [intuition |].
-    apply PermutationA_cons_app, IHPl₁.
-    now apply NoDupA_split with y.
-    apply equivlistA_NoDupA_split with x y; intuition.
-Qed.
-
-End Permutation.
-
 (** Compatibility aliases. [Proper] is rather to be used directly now.*)
 
 Definition compat_bool {A} (eqA:A->A->Prop)(f:A->bool) :=