diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/FSets/FMapAVL.v | 8 | ||||
| -rw-r--r-- | theories/MSets/MSetAVL.v | 6 |
2 files changed, 7 insertions, 7 deletions
diff --git a/theories/FSets/FMapAVL.v b/theories/FSets/FMapAVL.v index cf0449f8..49f595d7 100644 --- a/theories/FSets/FMapAVL.v +++ b/theories/FSets/FMapAVL.v @@ -8,7 +8,7 @@ (* Finite map library. *) -(* $Id: FMapAVL.v 13427 2010-09-17 17:37:52Z letouzey $ *) +(* $Id: FMapAVL.v 13768 2011-01-06 13:55:35Z glondu $ *) (** * FMapAVL *) @@ -78,9 +78,9 @@ Definition empty := Leaf. Definition is_empty m := match m with Leaf => true | _ => false end. -(** * Appartness *) +(** * Membership *) -(** The [mem] function is deciding appartness. It exploits the [bst] property +(** The [mem] function is deciding membership. It exploits the [bst] property to achieve logarithmic complexity. *) Fixpoint mem x m : bool := @@ -705,7 +705,7 @@ Proof. destruct m; simpl; intros; try discriminate; red; intuition_in. Qed. -(** * Appartness *) +(** * Membership *) Lemma mem_1 : forall m x, bst m -> In x m -> mem x m = true. Proof. diff --git a/theories/MSets/MSetAVL.v b/theories/MSets/MSetAVL.v index c41df7c2..96580749 100644 --- a/theories/MSets/MSetAVL.v +++ b/theories/MSets/MSetAVL.v @@ -82,9 +82,9 @@ Definition empty := Leaf. Definition is_empty s := match s with Leaf => true | _ => false end. -(** ** Appartness *) +(** ** Membership *) -(** The [mem] function is deciding appartness. It exploits the +(** The [mem] function is deciding membership. It exploits the binary search tree invariant to achieve logarithmic complexity. *) Fixpoint mem x s := @@ -792,7 +792,7 @@ Proof. split; auto. try discriminate. intro H; elim (H x); auto. Qed. -(** * Appartness *) +(** * Membership *) Lemma mem_spec : forall s x `{Ok s}, mem x s = true <-> InT x s. Proof. |