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author | 2012-01-12 16:02:20 +0100 | |
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committer | 2012-01-12 16:02:20 +0100 | |
commit | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (patch) | |
tree | 97ec6b7d831cc5fb66328b0c63a11db1cbb2f158 /theories/Lists/SetoidList.v | |
parent | 300293c119981054c95182a90c829058530a6b6f (diff) |
Imported Upstream version 8.4~betaupstream/8.4_beta
Diffstat (limited to 'theories/Lists/SetoidList.v')
-rw-r--r-- | theories/Lists/SetoidList.v | 11 |
1 files changed, 6 insertions, 5 deletions
diff --git a/theories/Lists/SetoidList.v b/theories/Lists/SetoidList.v index ec31f37d..97915055 100644 --- a/theories/Lists/SetoidList.v +++ b/theories/Lists/SetoidList.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (***********************************************************************) -(* $Id: SetoidList.v 12919 2010-04-10 16:30:44Z herbelin $ *) - Require Export List. Require Export Sorting. Require Export Setoid Basics Morphisms. @@ -82,6 +80,10 @@ Qed. Definition inclA l l' := forall x, InA x l -> InA x l'. Definition equivlistA l l' := forall x, InA x l <-> InA x l'. +Lemma incl_nil l : inclA nil l. +Proof. intro. intros. inversion H. Qed. +Hint Resolve incl_nil : list. + (** lists with same elements modulo [eqA] at the same place *) Inductive eqlistA : list A -> list A -> Prop := @@ -159,8 +161,7 @@ Qed. Hint Resolve In_InA. Lemma InA_split : forall l x, InA x l -> - exists l1, exists y, exists l2, - eqA x y /\ l = l1++y::l2. + exists l1 y l2, eqA x y /\ l = l1++y::l2. Proof. induction l; intros; inv. exists (@nil A); exists a; exists l; auto. @@ -747,7 +748,7 @@ rewrite filter_In in H; destruct H. eapply SortA_InfA_InA; eauto. Qed. -Implicit Arguments eq [ [A] ]. +Arguments eq {A} x _. Lemma filter_InA : forall f, Proper (eqA==>eq) f -> forall l x, InA x (List.filter f l) <-> InA x l /\ f x = true. |