diff options
| -rw-r--r-- | theories/FSets/FMapAVL.v | 6 | ||||
| -rw-r--r-- | theories/MSets/MSetAVL.v | 6 |
2 files changed, 6 insertions, 6 deletions
diff --git a/theories/FSets/FMapAVL.v b/theories/FSets/FMapAVL.v index f9dda5125..516015ab9 100644 --- a/theories/FSets/FMapAVL.v +++ b/theories/FSets/FMapAVL.v @@ -76,9 +76,9 @@ 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 := @@ -703,7 +703,7 @@ 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 349cdedf7..253267fc8 100644 --- a/theories/MSets/MSetAVL.v +++ b/theories/MSets/MSetAVL.v @@ -80,9 +80,9 @@ 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 := @@ -790,7 +790,7 @@ 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. |