diff options
Diffstat (limited to 'theories/Sets/Uniset.v')
| -rw-r--r-- | theories/Sets/Uniset.v | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/theories/Sets/Uniset.v b/theories/Sets/Uniset.v index 7940bda1a7..0ff304ed6b 100644 --- a/theories/Sets/Uniset.v +++ b/theories/Sets/Uniset.v @@ -41,21 +41,21 @@ Definition Singleton (a:A) := end). Definition In (s:uniset) (a:A) : Prop := charac s a = true. -Hint Unfold In. +Hint Unfold In : core. (** uniset inclusion *) Definition incl (s1 s2:uniset) := forall a:A, leb (charac s1 a) (charac s2 a). -Hint Unfold incl. +Hint Unfold incl : core. (** uniset equality *) Definition seq (s1 s2:uniset) := forall a:A, charac s1 a = charac s2 a. -Hint Unfold seq. +Hint Unfold seq : core. Lemma leb_refl : forall b:bool, leb b b. Proof. destruct b; simpl; auto. Qed. -Hint Resolve leb_refl. +Hint Resolve leb_refl : core. Lemma incl_left : forall s1 s2:uniset, seq s1 s2 -> incl s1 s2. Proof. @@ -71,7 +71,7 @@ Lemma seq_refl : forall x:uniset, seq x x. Proof. destruct x; unfold seq; auto. Qed. -Hint Resolve seq_refl. +Hint Resolve seq_refl : core. Lemma seq_trans : forall x y z:uniset, seq x y -> seq y z -> seq x z. Proof. @@ -94,21 +94,21 @@ Lemma union_empty_left : forall x:uniset, seq x (union Emptyset x). Proof. unfold seq; unfold union; simpl; auto. Qed. -Hint Resolve union_empty_left. +Hint Resolve union_empty_left : core. Lemma union_empty_right : forall x:uniset, seq x (union x Emptyset). Proof. unfold seq; unfold union; simpl. intros x a; rewrite (orb_b_false (charac x a)); auto. Qed. -Hint Resolve union_empty_right. +Hint Resolve union_empty_right : core. Lemma union_comm : forall x y:uniset, seq (union x y) (union y x). Proof. unfold seq; unfold charac; unfold union. destruct x; destruct y; auto with bool. Qed. -Hint Resolve union_comm. +Hint Resolve union_comm : core. Lemma union_ass : forall x y z:uniset, seq (union (union x y) z) (union x (union y z)). @@ -116,7 +116,7 @@ Proof. unfold seq; unfold union; unfold charac. destruct x; destruct y; destruct z; auto with bool. Qed. -Hint Resolve union_ass. +Hint Resolve union_ass : core. Lemma seq_left : forall x y z:uniset, seq x y -> seq (union x z) (union y z). Proof. @@ -124,7 +124,7 @@ unfold seq; unfold union; unfold charac. destruct x; destruct y; destruct z. intros; elim H; auto. Qed. -Hint Resolve seq_left. +Hint Resolve seq_left : core. Lemma seq_right : forall x y z:uniset, seq x y -> seq (union z x) (union z y). Proof. @@ -132,7 +132,7 @@ unfold seq; unfold union; unfold charac. destruct x; destruct y; destruct z. intros; elim H; auto. Qed. -Hint Resolve seq_right. +Hint Resolve seq_right : core. (** All the proofs that follow duplicate [Multiset_of_A] *) |